Dissociative adsorption of molecular hydrogen on silicon surfaces

Surface Science Reports 61 (2006) 465–526 www.elsevier.com/locate/surfrep

Dissociative adsorption of molecular hydrogen on silicon surfaces M. D¨urr a,b , U. H¨ofer a a Department of Physics and Materials Science Centre, Philipps University of Marburg, Renthof 5, D-35032 Marburg, Germany b Department of Natural Sciences – Chemical Engineering, University of Applied Sciences, Kanalstr. 33, D-73728 Esslingen, Germany

Accepted 11 August 2006

Abstract The dissociative adsorption of molecular hydrogen on silicon is considered to be the prototype for an activated chemical reaction at a semiconductor surface. The covalent nature of the silicon–silicon and silicon–hydrogen bonds lead to large lattice distortion in the transition state of the reaction. As a result, the apparently simple reaction exhibits relatively complex pathways and surprisingly rich dynamics. The report reviews, among others, experiments using optical second-harmonic generation, molecular beam techniques and scanning tunnelling microscopy which, in close connection with state-of-the-art density functional theory, have led to a detailed microscopic understanding of H2 adsorption on Si(001) and Si(111) surfaces. On the dimerized Si(001) surface, dissociative adsorption as well as recombinative desorption of H2 is shown to involve the dangling bonds of two neighbouring dimers. Preadsorption of atomic hydrogen or thermal excitation is able to substantially alter the adsorption barrier. As a consequence, the reactivity strongly depends on coverage and surface temperature. In contrast to activated adsorption of hydrogen at metal surfaces, even the most basic description of the dynamics has to include phonon excitation of the silicon substrate. c 2006 Elsevier B.V. All rights reserved.

Keywords: Semiconductor surface; Hydrogen; Silicon; Dissociative adsorption; Recombinative desorption; Activated adsorption; Sticking coefficient; Reaction dynamics; Scanning tunnelling microscopy; Second-harmonic generation; Supersonic molecular beam

Contents 1.

2.

3.

Introduction............................................................................................................................................................................ 466 1.1. Small sticking coefficients — history............................................................................................................................... 467 1.2. Energy barriers and detailed balance ............................................................................................................................... 468 1.3. Phonon-assisted sticking ................................................................................................................................................ 470 1.4. Overview ..................................................................................................................................................................... 471 Measurement of sticking coefficients with SHG .......................................................................................................................... 472 2.1. Origin of SHG from silicon surfaces................................................................................................................................ 472 2.2. Sticking coefficients of thermal H2 .................................................................................................................................. 475 2.2.1. Flat Si(111) and Si(001) surfaces........................................................................................................................ 475 2.2.2. Reactivity of different surface sites ..................................................................................................................... 476 2.2.3. Coverage dependence of sticking........................................................................................................................ 477 2.2.4. Comparison of measured sticking coefficients ...................................................................................................... 478 2.3. Chemisorption energy.................................................................................................................................................... 478 Reaction pathways of H2 /Si(001) .............................................................................................................................................. 479 3.1. Structure and electronic properties of Si(001) ................................................................................................................... 480 3.2. Adsorption of atomic hydrogen....................................................................................................................................... 481 3.3. Models for dissociative adsorption .................................................................................................................................. 482 3.3.1. Single-dimer mechanism ................................................................................................................................... 482 E-mail addresses: [email protected] (M. D¨urr), [email protected] (U. H¨ofer).

c 2006 Elsevier B.V. All rights reserved. 0167-5729/$ - see front matter doi:10.1016/j.surfrep.2006.08.002

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3.3.2. Two-dimer mechanism ...................................................................................................................................... 483 3.3.3. Dihydrides — defects........................................................................................................................................ 484 3.4. Real space investigations of adsorption pathways.............................................................................................................. 485 3.4.1. Adsorption on clean Si(001) .............................................................................................................................. 485 3.4.2. Adsorption on hydrogen pre-covered Si(001) ....................................................................................................... 486 3.4.3. Adsorption at DB step sites................................................................................................................................ 488 3.5. Real space investigations of desorption pathways.............................................................................................................. 489 3.6. Results of ab initio theory .............................................................................................................................................. 491 3.6.1. Terrace adsorption ............................................................................................................................................ 491 3.6.2. Adsorption at DB steps ..................................................................................................................................... 494 3.7. Kinetics of adsorption and desorption .............................................................................................................................. 495 Reaction dynamics of H2 /Si(001).............................................................................................................................................. 499 4.1. Introduction.................................................................................................................................................................. 499 4.1.1. Combination of SHG and molecular beam techniques ........................................................................................... 499 4.2. Adsorption experiments ................................................................................................................................................. 499 4.2.1. Influence of surface temperature and beam energy ................................................................................................ 499 4.2.2. Influence of molecular vibrations........................................................................................................................ 502 4.2.3. Adsorption of D2 on Si(001) .............................................................................................................................. 503 4.2.4. Dynamics at statically distorted adsorption sites ................................................................................................... 504 4.3. Desorption experiments ................................................................................................................................................. 506 4.3.1. Translational energy distribution of desorbing molecules....................................................................................... 506 4.3.2. Vibrational and rotational energy distribution of desorbing molecules ..................................................................... 508 4.4. Comparison of adsorption and desorption — detailed balance ............................................................................................ 509 4.4.1. Translational energy.......................................................................................................................................... 510 4.4.2. Molecular excitations ........................................................................................................................................ 511 4.5. Angular distributions measured in adsorption and desorption ............................................................................................. 512 4.5.1. Angular resolved sticking probabilities on flat surfaces ......................................................................................... 512 4.5.2. Angular resolved sticking at step sites ................................................................................................................. 513 4.5.3. Angular resolved desorption from flat surfaces and comparison with adsorption....................................................... 514 4.6. Quantum dynamics calculations...................................................................................................................................... 515 4.7. Comparison of H2 /Si and H2 /Cu..................................................................................................................................... 517 4.7.1. Energy dependence of sticking and influence of vibrational excitations ................................................................... 517 4.7.2. Energy distribution in desorption ........................................................................................................................ 518 4.7.3. Influence of surface temperature on sticking probability ........................................................................................ 518 4.7.4. Influence of molecular rotations ......................................................................................................................... 519 4.7.5. Surface corrugation and angular distribution of sticking probabilities...................................................................... 520 Hydrogen on Si(111)7×7......................................................................................................................................................... 520 5.1. Dynamics of adsorption ................................................................................................................................................. 520 5.2. Dynamics of desorption ................................................................................................................................................. 521 5.3. Microscopic reaction pathways ....................................................................................................................................... 522 5.4. Comparison Si(111)–Si(001) .......................................................................................................................................... 523 Acknowledgements ................................................................................................................................................................. 524 References ............................................................................................................................................................................. 524

1. Introduction The interaction of H2 with various metals has been investigated intensively in order to understand the dynamics of molecular dissociation and recombination reactions at surfaces. Experimentally, molecular beam techniques and state specific probing, originally developed for studying chemical reactions in the gas phase, have been adopted to the ultra-high vacuum environment and were combined with the methods of surface science [1–5]. Theoretically, it has become possible to perform calculations on potential energy surfaces based on ab initio theory that include up to six degrees of freedom: distance from the surface, intermolecular spacing, surface corrugation and molecular orientation [6–8]. Together, these efforts have resulted in a rather satisfactory understanding of the effects

of translational energy, vibrational and rotational excitations and even molecular alignment in some model reactions, in particular H2 /Cu or H2 /Pd. Silicon is the natural choice of a semiconductor surface for the extension of this work. First of all, silicon is the most important material in semiconductor technology. The interaction of hydrogen with Si surfaces is of considerable importance, e.g. for the growth of epitaxial Si layers by chemical vapour deposition [9]. Secondly, the (001) and (111) surfaces of silicon are the best characterized semiconductor surfaces and it is relatively easy to prepare them with good quality. Finally, the adsorption of atomic hydrogen on these surfaces is straightforward and well understood [10–13]. At least at low coverages hydrogen atoms simply stick to the Si dangling bond and do not cause a breaking of Si–Si

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bonds. The induced structural changes of the surface, although important, can thus still be treated in terms of distortions from the equilibrium structure. In this review, we will therefore concentrate on the adsorption of H2 on such well-defined single crystal silicon surfaces as a prototype for dissociative adsorption on semiconductor surfaces. Historically, systematic investigations of the system first focussed on the reverse reaction, recombinative desorption of H2 from Si surfaces. Due to the small sticking probability of H2 /Si, quantitative adsorption experiments only started in 1994. The experiments clearly showed that the reaction dynamics of H2 /Si involves an interesting new aspect. In the case of H2 adsorption on metal surfaces, the substrate was typically considered to be static, at least in a first approximation. Due to the directionality of the covalent Si–Si and Si–H bonds this is not appropriate in the case of H2 /Si. Already a very basic understanding of energy barriers and transitions states makes it necessary to take possible rearrangements of substrate atoms into account. For some experimental parameters, the reaction dynamics is even dominated by the substrate degrees of freedom. In the introductory section of this review we will first present the main phenomenological results that highlighted this influence of the lattice degree of freedom on the reaction dynamics. Since then, decisive progress in terms of an identification of the microscopic reaction pathways for dissociative adsorption of H2 on the dimerized Si(001) surface has been made. The emphasis of this review will be on these more recent experiments, the present understanding of the dynamics of H2 interaction with this surface, and a comparison with H2 /Si(111)7×7 and H2 /Cu(111). Earlier experimental and theoretical work has been the subject of previous reviews by Kolasinski [14], H¨ofer [15] and Doren [16]. 1.1. Small sticking coefficients — history The first conclusive experiments of hydrogen adsorption on silicon were conducted by Law at the Bell Laboratories almost 50 years ago [17]. Law showed that under common experimental conditions only atomic hydrogen adsorbs quantitatively on clean Si surfaces and that the sticking coefficient of molecular hydrogen is extremely small. The main components of his glass apparatus with a base pressure of 5×10−10 mbar were a singlecrystal Si filament and an ion-gauge (Fig. 1). Clean silicon surfaces were prepared by heating the Si filament to temperatures close to 1550 K. The sample, which was kept at room temperature, was then exposed to H2 gas that was purified by passing it through a liquid-nitrogen trap. The surface coverage that resulted from various exposure times and gas pressures was determined with the flash desorption technique, i.e. the Si filament was rapidly heated to a temperature where hydrogen desorbed and the pressure was recorded with the ion gauge. Complimentary experiments with a quadrupole mass spectrometer showed that only molecular H2 and no hydrogen atoms desorbed. In an earlier experiment Law had already noted that hydrogen uptake was influenced strongly by the ion gauge due to dissociation of H2 at the hot filament [17]. The data shown

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Fig. 1. Schematic arrangement of the vacuum system used by Law for his investigation of hydrogen adsorption on silicon. Reprinted with permission from Law [17]. c 1959, American Institute of Physics, AIP.

Fig. 2. Adsorption of molecular hydrogen on the surfaces of single-crystal Si filaments as function of time at varying pressures (in Torr) after Law [17]. A pressure of 1 × 10−6 Torr corresponds to a gas flux of 1.62 × 1015 H2 molecules/s or 2 × 1017 H atoms/min; 2 N M denotes the measured H coverage. The increase by 1012 atoms cm−2 observed between 100 and 500 min for a pressure of 3 × 10−5 Torr corresponds to sticking coefficient of ∼10−9 . Reprinted with permission from Law [17]. c 1959, AIP.

in Fig. 2 were corrected for this effect by switching off the ion gauge for variable times during exposure and extrapolating to zero on-time of the gauge. The tungsten filament in the setup of Fig. 1 allowed controlled investigations of the adsorption of atomic hydrogen which forms when the filament is heated [18]. Whereas a coverage of 9 × 1014 atoms/cm2 could be reached by adsorption of atomic hydrogen, adsorption of molecular hydrogen saturated at 2 × 1013 atoms/cm2 , i.e. at only ∼2% of the maximum coverage. From the data shown in Fig. 2 one can derive that the sticking coefficient for further hydrogen adsorption is below 10−9 . Until this saturation value is reached the sticking coefficient is higher, up to 10−6 . Most likely these higher values for the initial adsorption were due to H2 dissociation at step and defect sites as will be discussed in Section 2.2.2. Probably the facets of the single

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M. D¨urr, U. H¨ofer / Surface Science Reports 61 (2006) 465–526 Table 1 Experimental values of the H2 dissociation energy E H−H , the activation energy for recombinative desorption E des and the chemisorption energy qst for hydrogen on Si(111)7×7 and Si(001)2×1. The Si–H bond energies E Si–H and the adsorption barrier E ads are given in terms of differences between these values: E Si–H = 1/2(qst + E H−H ), E ads = E des − qst

E H−H (eV) E des (eV) qst (eV) E Si–H (eV) E ads (eV)

Fig. 3. Schematic 1-dimensional energy diagram for recombinative desorption and dissociative adsorption of H2 /Si(001). Note: although the reaction involves two surface dimers as shown in Section 3, hydrogen saturates the two dangling bonds of one dimer in the energetic ground state.

crystal – mostly (111) – were relatively rough due to extended heating of the filament close to melting temperature [17]. This would explain the relative abundance of ∼2% of these more reactive sites which is much higher than on well-prepared surfaces in present-day experiments. Law’s work turned out to be the most sensitive and accurate investigation of the sticking coefficient of H2 /Si for quite some time. His lower limit for adsorption at the majority sites was confirmed by more modern TPD studies for cleaved Si(111) surfaces (s0 < 10−6 ) by Schulze and Henzler [19] and by Liehr and co-workers for the surfaces of Si(001) wafers [20]. Reports of higher sticking coefficients that occasionally appeared in the literature are likely to be caused by defects on the surface or by inappropriate experimental conditions as discussed in detail by Kolasinski in his review [14]. At the beginning of the 1990s the sticking coefficient of thermal gas was sometimes considered to be ‘unmeasurably small’ [21]. 1.2. Energy barriers and detailed balance Although molecular hydrogen does not readily dissociate on Si surfaces, the reaction is energetically favourable. The dissociation energy of H2 is considerably smaller than the Si–H bond energy. A schematic diagram that illustrates the energetic situation in adsorption and desorption is shown in Fig. 3, the relevant energies for Si(111)7×7 and Si(001)2×1 are collected in Table 1. The activation energy for desorption E des is very well known experimentally. It has been determined by performing isothermal desorption experiments at low coverages over a relatively wide range of desorption rates [24,25]. The values have been confirmed by carefully analyzed TPD studies [27–29]. Previous values derived from laser-induced thermal desorption (LITD) experiments were less precise [30–33] and in one case considerably too low [30,31]. The chemisorption energy E Si–H is not directly accessible experimentally. The energy given in the table is the sum of the isosteric heat of

Si(111)7×7

Si(001)2×1

References

4.478 2.40 ± 0.1 1.7 ± 0.2 3.1 0.7

4.478 2.48 ± 0.1 1.9 ± 0.3 3.2 0.6

[22,23] [24,25] [26]

H2 adsorption, qst , as determined by the experiment described in Section 2.3, and the dissociation energy E H−H . It does not include corrections due to lattice relaxation upon hydrogen adsorption [26]. It must be stressed that 1D-potentials, such as the one shown in Fig. 3, that go back to the work of Lennard-Jones [34], have severe limitations and must be used for illustrative purposes only. Since the potential does not include other important degrees of freedom, like the H–H distance that necessarily changes during dissociation or the orientation of molecule and its impact parameter on the surface, it cannot account for most of the interesting dynamical effects which are the subject of Section 4 of this review. Nevertheless, the 1D-potential is useful to highlight a problem that arose in the 1990s. If we consider Fig. 3 to represent a cut through the multidimensional potential energy surface along the equilibrium reaction path, i.e. with minimum energy in other degrees of freedom, then the size of the dissociation barrier estimated from E ads = E des −qst is consistent with the small sticking probability: For E ads = 0.6 eV, e.g., the Boltzmann-factor exp(−E ads /kT ) becomes ∼10−10 at room temperature, i.e. a fraction of ∼10−10 of the thermally distributed H2 has a kinetic energy that is higher than the barrier height E ads and is able to stick. This would be consistent with the adsorption experiments by Law [17], in particular if one considers that the effective sticking coefficient will of course be further reduced due to molecules hitting the surface with wrong orientation or nonideal lattice impact parameters. However, the simple picture of H2 interaction with Si surfaces described by Fig. 3, breaks down if one tries to reconcile it with the reverse reaction of dissociative adsorption, i.e. recombinative desorption. In 1994 Kolasinski and coworkers [35] performed time-of-flight measurements of the desorbing H2 molecules. Results such as those plotted in Fig. 4 showed mean translation energies in the range of 150–250 meV for molecules desorbing from the Si(001) and Si(111) surfaces. According to Fig. 3, however, H2 would have to cross a substantial adsorption barrier upon desorption and one expects a kinetic energy in the order of this barrier height. More precisely, according to the principle of detailed balance, the deviation of the energy distribution of the state-resolved flux of desorbing particles Φdes from a Boltzmann distribution is related to the sticking coefficient s [36–39]. It can be shown that

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Fig. 4. Time-of-flight spectrum for D2 thermally desorbed from the monohydride phase on Si(100)2×1 with Tmax = 920 K induced by pulsed laser heating of the surface. The dots represent the data (averaged over 256 laser shots) while the solid line represents a fit by a Maxwell–Boltzmann distribution. Reprinted with permission from Kolasinski et al. [35]. c 1994, American Physical Society, APS.

Φdes (E, θ, ν, j; Ts )dΩ dE ∝ s(E, θ, ν, j; Ts )   E + Eν + E j E cos θ dθdE × exp − kTs

(1)

applies for a reaction which follows the same pathway in adsorption and desorption. In this equation E, ν, j denote the kinetic energy and the vibrational and rotational state of the H2 molecule, Ts is the surface temperature and Φdes dΩ dE is the state-resolved flux of desorbing molecules in the energy interval dE at angle θ. The relationship (1) between the adsorption function s and the desorption flux Φdes at a constant surface temperature is illustrated by Fig. 5 for the vibrational ground state and trajectories along the surface normal. Whereas a sticking coefficient of unity would lead to a maximum of Φdes corresponding to the desorption temperature, a sharp onset of sticking around the energy E kin = E ads = E 0 would simply cut this distribution and shift the maximum to about E 0 . However, typical experimental sticking coefficients have sshaped functional forms of the kinetic energy with a finite width around a mean barrier height E 0 . The width W of these adsorption functions can be related to the distribution of barriers E ads (E 0 , W ) which arises, e.g. from molecules incident at different lattice impact parameters and with different orientations. Φdes thus depends not only on E 0 and Ts but also on this distribution of barriers. Although the results of the desorption experiment by Kolasinski et al. seem not to be in

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accordance with (1) at a first glance, it will be shown below that this is no longer the case if an appropriate distribution E ads (E 0 , W ) will be taken into account. As we will make use of the principle of detailed balance on several occasions in this review, a few general comments on its applicability might be appropriate at this point (the more as in some of the literature of H/Si there is considerable misunderstanding concerning the implications of detailed balance). In thermal equilibrium, microscopic reversibility demands that each trajectory of the reaction A → B has an exact counterpart in the reverse reaction B → A. Thus the state resolved rates, i.e. the detailed rates of forward and backward reactions must be equal k(A → B) = k(B → A). This is the principle of detailed balance and it is valid irrespectively of the nature of the interaction potential between the molecules since the Schr¨odinger equation as well as the classical equations of motion are invariant under time reversal. Of course, adsorption/desorption experiments, like most studies of chemical reactions, are usually not performed under conditions of complete thermal equilibrium. Moreover, in a complicated system the degrees of freedom are usually not under full control of the experiment. Nevertheless, the principle of detailed balance and Eq. (1) may be of considerable merit relating rate constants also in these situations. Provided there is thermal equilibrium among the uncontrolled degrees of freedom, the principle of detailed balance allows one to establish a relationship between the remaining coordinates [40]. In case of the interaction of molecular hydrogen with silicon H2 (ν, j, E) + Si(n s ) Si(n 0s ) + 2H(ad)

(2)

the clean silicon surface is characterized by certain phononic and electronic degrees of freedom n s that change to n 0s in the adsorbed state. In general we will have no detailed information about n s and n 0s . However, if there is thermal equilibrium among these surface degrees of freedom, it can be shown that the state-resolved adsorption and desorption functions are again related by Eq. (1). There are, especially for the H/Si system, many reasons why such an equilibrium of those surface degrees of freedom should not be established. Most prominent among those, different coverages in the adsorption and desorption experiments may cause the surface to be in a different configuration and thus hn 0s i 6= hn s i. Additionally, the H2 molecules are considerably lighter than the Si atoms. It is thus conceivable that the reaction

Fig. 5. Relationship between the adsorption function s0 (E kin ) and the energy distribution of desorbing particles Φdes (E kin ) along the surface normal derived from the principle of detailed balance for a surface temperature of 1000 K. The dashed lines indicate the situation for a barrierless adsorption channel. The solid line illustrates the situation for a mean adsorption barrier E 0 .

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involves so-called slow intermediates. In particular, it has been proposed that the reaction gives rise to long-lived excitations of electron–hole pairs [41], in contrast to a fast equilibration of the surface degrees of freedom. On the other hand, detailed balance and relationship (1) has been applied very successfully to adsorption/desorption in many cases [3,42,43]. This indicates that, although the prerequisites are not exactly fulfilled, the principle seems to be very robust, if applied properly. Indeed, in Section 4 we will show that the H2 /Si system perhaps has to be treated slightly more carefully than other adsorption systems but that detailed balance can be applied very successfully. The distribution of barriers on the surface, i.e. the width of the adsorption function and its dependence on surface temperature and coverage will turn out to be most crucial for the reaction dynamics. Application of detailed balance, under proper consideration of those parameters, then allows for a better understanding of the experimental results. 1.3. Phonon-assisted sticking A very simple model that both explained the lack of translational heating in desorption despite the presence of a large adsorption barrier and at the same time assured that detailed balance is fully applicable was proposed by Brenig et al. [44]. In this model, it is assumed that the dissociation barrier can be strongly reduced by the displacement of the topmost Si atoms from their equilibrium position. The initial motivation for the introduction of this model was twofold. First of all, due to the covalent nature of the Si–Si and Si–H bonds, lattice relaxation is generally expected to strongly affect reaction barriers. In the case of surface diffusion of hydrogen, e.g. calculated barriers are lowered by as much as 1 eV when the Si atoms are allowed to relax [45–49] and reach good agreement with experimental values [50–53]. Second, an obvious difference between the adsorption and desorption experiment discussed above is the substrate temperature at which they were performed. Since lattice distortion will be excited thermally, the inclusion of this degree of freedom then provides a means of distributing the barrier energy E ads differently between the Si lattice and the H2 gas for adsorption and desorption without violating detailed balance. Fig. 6 shows a pseudo-3D plot of the potential energy surface (PES) proposed by Brenig and co-workers in their 1994 paper [44]. Displayed is a view of the adsorption barrier from the gas-phase side. For the clean surface, the equilibrium distance ˚ With the of the reactive Si atom to the next layer is ∼1.2 A. lattice frozen in this configuration, the incoming H2 molecule experiences a very large barrier to adsorption. Even if the Si lattice fully relaxes the H2 molecule has to overcome the saddle point at a height of 1 eV. Therefore, H2 molecules with thermal energies that hit the lattice in its equilibrium configuration will lead to some lattice excitation and get reflected. The PES is thus consistent with the small sticking coefficient at room temperature. In desorption, the minimum energy path leads ˚ over the saddle point where the Si–Si spacing is ∼1.7 A. After crossing the barrier, the H2 molecule experiences only

Fig. 6. Model potential for the interaction of molecular hydrogen with a silicon surface as function of a characteristic Si–Si spacing and the Si–H2 distance (=path). The pseudo-3D plot of the PES shows a view from the gas phase side. The saddle point of the PES with the transition state for desorption is at path coordinate 0. For the clean surface, the equilibrium distance of the reactive ˚ Reprinted with permission from Brenig Si atom to the next layer is ∼1.2 A. et al. [44]. c 1994, Springer-Verlag.

a small potential drop upon leaving the surface. Most of the activation energy that was necessary to bring the system into the transition state is released into the lattice coordinate, i.e. leads to the excitation of Si phonons. The H2 molecules themselves leave the surface with little kinetic energy, consistent with the experiment of Kolasinski et al. The application of time reversal within the framework of this model has far-reaching consequences. Since recombinative desorption leads to the creation of Si phonons and H2 molecules desorbing with little kinetic energy, the creation of Si phonons by heating the lattice should allow H2 molecules with little kinetic energy to overcome the barrier. Thus the sticking coefficient is expected to increase strongly as function of the substrate temperature. This effect of ‘phonon-assisted sticking’ is completely analogous the well known effect of vibrational assisted sticking of molecules on metal surfaces [54]. The sticking probabilities predicted by Brenig and co-workers on the basis of this model are shown in Fig. 7. At a surface temperature of 300 K the sticking coefficient stot drops steeply for molecules that have a translational energy E kin of less than the minimum barrier height of 1 eV. With increasing surface temperature, the absolute values of stot increase and the dependence on E kin becomes smaller. The dependence on surface temperature is particularly strong for low energetic molecules and the calculations predict that at surface temperatures exceeding 600 K it should be possible to adsorb H2 from a thermal gas [44]. The first quantitative measurements of the sticking of H2 on well prepared silicon surfaces confirmed this prediction very clearly, at least in a qualitative way [55]. The experiment will be described in more detail in Section 2.2, the results obtained for Si(111)7×7 are shown in Fig. 8 in the form of an Arrhenius plot. Sticking of H2 could indeed be observed for surface temperatures in excess of '600 K. The sticking coefficient s0 increases by almost four orders of magnitude from ∼2 × 10−9

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freedom of H2 except the somehow unspecified reactionpath coordinate. For this reason the model is not expected to predict any details of the reaction dynamics and any quantitative agreement with the experiment is to some extent accidental. Clearly, one cannot quantitatively describe hydrogen dissociation without including, e.g. the H–H spacing in the potential energy surface. 1.4. Overview

Fig. 7. Sticking coefficient for the adsorption of molecular hydrogen on silicon as function of kinetic energy for various surface temperatures as predicted by the model of Brenig et al. Reprinted with permission from Brenig et al. [44]. c 1994, Springer-Verlag.

Fig. 8. Experimentally determined initial sticking coefficient of thermal H2 gas at Tgas = 300 K on the Si(111)7×7 surface as a function of the inverse surface temperature. The solid line is the best fit to an Arrhenius law [s0 = A exp(−E A /kTs )] with an apparent activation energy of E A = 0.87 ± 0.1 eV and a prefactor of A = 7 × 10−2±0.5 . Reprinted with permission from Bratu and H¨ofer [55]. c 1995, APS.

to 10−5 when the temperature is raised to 1050 K. However, the absolute values of s0 are about 1–2 orders of magnitude smaller than expected from the calculations for small translational energies (E kin ' 0 in Fig. 7) and the temperature dependence is even stronger. On Si(100)2×1 the overall sticking coefficients were found to be by a factor of 2–10 higher than on Si(111)7×7 with a slightly weaker temperature dependence [56]. The original model by Brenig et al. was of course rather rough and only meant to highlight the general importance of lattice relaxation for understanding H2 interaction with Si surfaces. It did not specify the relevant surface degree of freedom nor did the PES include any other degrees of

In the following, we will describe the microscopic mechanism of H2 interaction with Si(001) in Section 3. It will be shown that H2 adsorption involves two adjacent dimers of the reconstructed surface and that the lowering of the dissociation barrier results from a concerted movement of both of these dimers. In Section 4 we will then consider the dynamics in some more detail. We will discuss how other degrees of freedom such as internal vibrations, angle of incidence, and surface coverage influence reactivity and we will show that calculations with an appropriately extended version of Brenig’s model can quantitatively describe most of the experimental results. In Section 5 we will summarize the present understanding of H2 interaction with Si(111)7×7. Although the dynamics have not been investigated in as much detail, results similar to Si(001)2×1 have been found. The nature of the respective lattice distortion seems to be clear also for Si(111)7×7: to lower the adsorption barrier, the backbonds of the Si adatoms have to be considerably stretched in the transition state. Several of the results discussed in Sections 3–5 have been obtained by novel combinations of experimental methods. In particular, optical second-harmonic generation (SHG) has been very decisive for the reliable determination of small sticking coefficients of H2 /Si. We describe this technique in some detail in an own section, Section 2. The combination of SHG together with molecular beam techniques was used for the investigation of the dynamics of the individual reaction channels. Scanning tunnelling microscopy (STM) in combination with supersonic gas dosing and laser-induced thermal desorption (LITD) has been important for the identification of the reaction pathway in adsorption and desorption, respectively. The basic ideas behind these procedures are outlined in connection with the obtained results in Sections 3.4, 3.5 and 4.2. We restrict ourselves in this review to the formation of Si monohydride by H2 adsorption and also consider only desorption from this most simple hydrogenated silicon surface. Information about recombinative desorption from dihydrides, which are formed at high H-coverage, may be found in [11]. The interaction of H2 with surfaces of nanocrystals and porous silicon, as well as silane chemistry is discussed in [57]. We also would like to mention that there are quite a number of interesting investigations concerning the dynamics of atomic hydrogen on silicon surfaces that are not the subject of this review. Lattice relaxation is particularly important in the case of surface diffusion [45–53,58–60] and during hydrogen abstraction reactions [61–65]. Electronically induced desorption of H from Si surfaces for different systems and

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techniques were discussed in [13,66–69]. Hydrogen interaction with modified Si surfaces has been reviewed in [12]. 2. Measurement of sticking coefficients with SHG

for Si(001)2×1 and Si(111)7×7, respectively. The measured SHG intensity I (2ω) is proportional to the square of the pump ↔ intensity I (ω) and the relevant tensor elements of χ (2) s ↔

In the field of gas-surface dynamics the technique of choice for measuring sticking coefficients of the order of 0.1 and higher is the method of King and Wells [70]. Smaller sticking coefficients are usually determined by measuring the surface coverage with standard techniques like TPD after exposing the sample to a sufficiently high gas dose [1]. In the case of H2 adsorption on silicon the use of optical second-harmonic generation (SHG) has been very important. As a purely optical, but nevertheless very surface sensitive technique, it allows to monitor adsorbate coverages in real time while exposing the sample to a high gas flux. This did not only enable the determination of hydrogen coverages at high temperatures where desorption occurs simultaneously and therefore made the test of Brenig’s prediction of phonon-assisted sticking possible. Also below the desorption temperature, the technique has significant advantages in measuring small sticking probabilities. First of all, it is compatible with high gas pressures. Together with a sensitivity to hydrogen coverages of less than 0.01 ML this allows to measure very small sticking coefficients. Secondly, by directly recording coverages as function of time, it is relatively straightforward to distinguish adsorption at sites of different reactivity and to measure coverage dependent sticking coefficients. Although SHG is elegant and relatively simple to implement in existing experimental set-ups, it has not been widely used in the gas surface dynamics community so far. For this reason we will give a brief overview of the technical aspects of the determination of sticking coefficients with SHG in this section. We will first start with a short discussion of the origin of SHG from silicon surfaces. This is then followed by some selected examples of adsorption of thermal H2 gas on silicon. They both demonstrate the benefits of the technique and make familiar the fundamental characteristics of the H2 /Si system. Finally, the determination of the chemisorption energy of H/Si(111) and H/Si(001) with SHG is shown. Sticking coefficients measured by combining the capabilities of a molecular beam and SHG will be discussed in Sections 4.2 and 5.1. 2.1. Origin of SHG from silicon surfaces In a typical SHG experiment, the incident electric field E(t) = E(ω) cos(ωt) of a pulsed laser beam generates a nonlinear polarization of the medium. Within the electric dipole approximation, a second-order contribution ↔

P(2) (2ω) = χ (2) : E(ω)E(ω)

(3)

may only exist when the inversion symmetry is broken. For many materials this is only the case at their surface. Often the detected 2ω-component of the reflected radiation originates from the first few atomic layers and is very sensitive to ↔ adsorption [71–73]. The surface nonlinear susceptibility χ (2) s is a third-rank tensor which has 3 and 4 independent components

2 2 I (2ω) ∝ |e(2ω) · χ (2) s : e(ω)e(ω)| I (ω).

(4)

In this equation e are polarization vectors that include the relevant Fresnel factors for coupling the radiation in and out of a thin sheet at the surface [72]. The calculation of second-order nonlinear susceptibilities at surfaces is very demanding [74–77]. Although there has been an enormous progress in the past decade, it is not possible to make exact predictions of the quantity of interest for the present (2) application, the dependence of χs on surface coverage. For this reason, it is generally necessary to calibrate the SHG response with another surface technique before it can be used to accurately measure surface coverages. The result of this calibration, as far as most examples in this review are concerned, is very simple. For sufficiently low coverages, the nonlinear susceptibility is a linear function of the number of dangling bonds on the surface. When they are quenched by hydrogen adsorp(2) tion, χs decreases linearly with the coverage θ (2)

χs(2) (θ ) ' χs,0 (1 − αθ ),

θ  1.

(5)

The proportionality constant α is in the range of 1–3 [55,56,78, 79]. In the following we briefly discuss the microscopic origin of this simple relationship. For the details concerning the underlying results of SHG spectroscopy of Si(001) and Si(111) surfaces see Refs. [15,80–83]. An overview of other applications of SHG from semiconductor surfaces may be found in reviews by McGilp, L¨upke, and Downer [84–86]. SHG is a special case of the parametric conversion of two photons h¯ ω1 and h¯ ω2 to a sum-frequency photon h¯ Ω = h¯ ω1 + h¯ ω2 . Such processes are resonantly enhanced whenever ωi or Ω coincide with real optical transitions in the system. Spectroscopic SHG experiments of the Si(111)7×7 surface together with the band structure of Si(111)7×7 are shown in Fig. 9. The data reveal two resonant structures in the wavelength range 700–1100 nm [15,81,82,87]. The peak at λ = 740 nm is a 2ω resonance that almost coincides with the E1 -transition between the valence and conduction band of bulk silicon at 3.4 eV [88,89]. It arises because the bulk electronic structure is distorted at the surface. Under the present experimental geometry (s-polarized fundamental and SH light) the signal is likely to be dominated by the S3 –U2 transition between the bonding (S3 ) and antibonding (U2 ) states of adatom backbonds. This resonance exhibits relatively little sensitivity on adsorbed hydrogen because the 7×7 surface structure remains intact for moderate exposures [90]. The broad feature of clean Si(111)7×7, that extends in Fig. 9 from λ = 850 nm beyond the accessible wavelength range, completely disappears if hydrogen is adsorbed. Its origin is a resonant enhancement of SHG by the Si dangling bond states that are quenched upon hydrogen adsorption [91]. Between 1000 nm and 1100 nm, hydrogen adsorption reduces the nonlinear susceptibility almost

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473

Fig. 9. Left: Schematic band structure of Si(111)7×7 in an extended Brillouin zone. The shaded areas indicate the projected bulk valence and conduction bands. Occupied and unoccupied surface states are denoted by S1 , S2 , S3 and U1 , U2 , respectively. The inset at the bottom shows a side view of part of the 7×7 unit cell. The adatoms (A) have partially filled dangling bonds and give rise to the surface band U1 /S1 ; the dangling bonds of rest atoms (R) are filled and form the band (2) (2) S2 . Right: Wavelength dependence of the second-order nonlinear susceptibility χs (anisotropic component, χs,xxx ) for clean Si(111)7×7 and a Si(111) surface with all dangling bonds saturated by atomic hydrogen. The tunable excitation radiation was provided by a Titanium–Sapphire femtosecond laser. Adopted with permission from H¨ofer [15]. c 1996, Springer-Verlag.

by a factor of 10 which leads to a dramatic decrease of the (2) measured signal I 2ω ∝ |χs |2 by a factor of 100. The spectra of Fig. 9 as well as the coverage dependence of SHG at different wavelengths can be described quantitatively by a very simple empirical two-component model based on this qualitative explanation of the origin of the nonlinear response [83]: (2)

(2)

(2)

χs(2) (θ ) = χs,db (1 − θ ) + χs,bb + χNR .

(6)

(2)

The term χs,db is a broad one-photon resonance centred at 1.25 eV and describes the contribution from the dangling bonds. (2) χs,bb is the two-photon resonance due to the backbonds at (2)

3.36 eV and χNR a weak overall nonresonant background. For (2) simplicity, the coverage dependence of χs,bb , in particular the small shift of the resonance frequency ωng , is neglected and the (2) dangling-bond term χs,db is assumed to vanish completely for the passivated surface (θ = 1). The spectroscopic results suggest that excitation wavelengths around λ = 1000 nm are most appropriate for sensitive, quantitative SHG measurements of H/Si(111)7×7. The signal is then dominated by the contribution from the dangling bonds (2) χs,db and for low coverages, the relationship (6) reduces to the linear dependence in (5). All the measurements presented in this review have been taken using pulsed Nd:YAG lasers as the (2) source for SHG. The calibrated dependence χs (θ ) of Si(111)

at the fundamental wavelength λ = 1064 nm (h¯ ω = 1.165 eV) of these lasers is displayed in Fig. 10. For the measurements, the Si sample was exposed to a constant flux of atomic hydrogen that was created by dissociation of H2 at a hot filament. The SHG signal was recorded during the dosage at a surface temperature of 600 K where the monohydride is the only stable hydrogen adsorption state. The exposure was then converted to hydrogen coverage θ with the help of a series of temperature programmed desorption (TPD) experiments. (2) The data exhibit a minimum of χs (θ) around 0.8 ML due to (2) a partial cancellation of the two complex quantities χs,db (1 − θ) (2)

and χs,bb . This cancellation predicted by the two-component model (6) is confirmed by phase measurements (Fig. 10). For coverages below 0.4 ML the linear relationship is an excellent approximation of the experimental coverage dependence. Due (2) (2) to the destructive interference of χs,db (1 − θ ) and χs,bb the slope α predicted by the model is 1.18. The measured slope is slightly higher, α = 1.3, which indicates the presence of some nonlocal influence of hydrogen adsorption on the surface electronic states. Probably hydrogen adsorption leads to some charge redistribution between the remaining dangling bonds. The SH spectroscopy of the clean Si(100) surface reveals qualitatively similar features [15] (Fig. 11(a)), a relatively sharp peak close to h¯ ω = 1.7 eV (2h¯ ω = 3.4 eV) and a broad dangling-bond derived structure extending towards lower photon energies. Hydrogen adsorption almost completely

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Fig. 10. Dependence of the magnitude (full circles) and the phase (open (2) (2) squares) of the nonlinear susceptibility χs = |χs |eiφ of Si(111)7×7 on the coverage with atomic hydrogen for an excitation wavelength of 1064 nm. (2) For low hydrogen coverages (θ < 0.4 ML), |χs | depends linearly on the number of unreacted Si dangling bonds with a proportionality constant α = 1.3. Adopted with permission from H¨ofer [15]. c 1996, Springer-Verlag.

quenches the intensity below h¯ ω ' 1.5 eV as the dangling bonds of the clean surface become saturated by H-atoms. But also the intensity near 1.7 eV gets substantially reduced; a systematic series of SHG spectra in the vicinity of this resonance has been recorded by Dadap et al. [80]. In general, (2) the coverage dependence of χs is slightly more complex than in the case of Si(111). It depends more sensitively on the optical geometry and polarization of incoming ω- and detected 2ω-radiation [79,87] and the range of coverages where the simple linear relationship (5) holds is smaller [56,92].

(2)

A systematic calibration of the SHG response of H/Si(001) at the frequency of the Nd:YAG laser has been performed by Yilmaz et al. [79]. At surface temperature of 200 K (600 K) the initial slope of the SHG signal I (2ω) versus hydrogen coverage (Fig. 11(b)) is −6.0 ML−1 (−4.0 ML−1 ) which corresponds to α = 3 (α = 2) in Eq. (5). The value for 600 K is smaller (2) than α = 3.1 that we use to convert χs into coverage, but is still within the error margin of 50% [56]. The temperature dependence of the SHG-calibration of Fig. 11(b) has different origins. First of all, atomic hydrogen has a tendency to pair at one dimer of Si(001) as discussed in Section 3. For this reason, the distribution of atomic hydrogen depends on the mobility of hydrogen on the surface and thus on the temperature of the sample [79]. Another reason is the temperature dependence of the nonlinear susceptibility itself which results, e.g. in a shift (2) of the χs,bb resonance to lower energies [80]. However, the (2)

effect of the surface temperature on χs (θ ) is much weaker than its influence on the reactivity of the surface. Therefore it is (2) justified to neglect the temperature dependence of χs (θ ) for the measurement of initial sticking coefficients. Quite generally, as will become obvious in the rest of this review, the sticking coefficient of H2 /Si can change by several orders of magnitude. In many cases other uncertainties like the exact flux of the incoming molecules and their internal energy are much more crucial for the accuracy of the experiments. Many of them could in fact have been done without paying any attention to the calibration of the SHG response. Notable exceptions are, of course, coverage-dependent experiments and kinetic measurements. Although the SHG experiments discussed in this review have been performed with nanosecond Nd:YAG lasers, it should be mentioned that also femtosecond Ti:Sapphire lasers, typically operating around 800 nm (h¯ ω ' 1.5 eV), are excellent sources

Fig. 11. (a) Wavelength dependence of χs for clean and hydrogen covered Si(100) surfaces measured at a surface temperature of 80 K (45◦ angle of incidence, p-polarized fundamental and SH radiation). Reprinted with permission from H¨ofer [15]. c 1996, Springer-Verlag.

(2) (b) Normalized SHG intensity of the Si(001) surface as function of hydrogen coverage at different temperatures. Please note that the y-axis is I (2ω) and not χs . (2) 1/2 A plot of |χs (θ )| ∝ I (θ ) would show a more linear initial decrease at low coverages θ [56]. Reprinted with permission from Yilmaz et al. [79]. c 2004, APS.

475

M. D¨urr, U. H¨ofer / Surface Science Reports 61 (2006) 465–526 Table 2 Concentration of dangling bonds on Si(111)7×7 and Si(001)2×1 and conversion factor from H2 pressure p to gas exposure Φ at Tgas = 300 K Si(111)7×7 Monolayer (1 ML) Φ/ p(H2 )

Si(001)2×1

0.30 × 1015 cm−2 0.68 × 1015 cm−2 7.2 × 106 ML s−1 mbar−1 3.2 × 106 ML s−1 mbar−1

In case the gas flux Φ is constant as it was for many experiments discussed later in this review, in particular those performed with supersonic molecular beams, and under conditions of negligible desorption, the initial sticking coefficient s0 (θ → 0) is directly given by the slope of the (2) measured χs (t), (2)

for SHG experiments from silicon and other surfaces. This has been demonstrated by Downer and co-workers [93,94] by monitoring the hydrogen coverage during silane adsorption on Si(001) or in growth studies of Ge/Si(001). Possible advantages of the use of a high repetition rate Ti:Sapphire oscillator are long-term stability and perfect linearity of the photon counting system used for SHG detection. The main disadvantage is continuous-wave (cw) heating of the substrate under the laser spot which is difficult to compensate. Nd:YAG laser pulses usually cause little cw-heating but lead to a large transient temperature rise under the laser spot. However, unless it does not cause surface damage [95,96], a temperature rise of a few nanoseconds was shown to have no influence on the measured reaction rates. For both laser systems the experimental SHG signal from clean silicon surfaces may be as high as 106 photons/s.

s = Φ −1

h i 1θ (2) −1 1χs ' − Φαχs,0 . 1t 1t

(7)

In case of a significant influence of desorption on the surface coverage, s0 is determined by a simple numerical fitting procedure. It then also accounts for changing gas flux during exposure. At any given time, the H-coverage θ(t) of the surface is determined by the rates of adsorption Rads and desorption Rdes , Z t θ(t) = [Rads (θ, Ts , t 0 ) − Rdes (θ, Ts )]dt 0 . (8) 0

2.2. Sticking coefficients of thermal H2 The following examples demonstrate some of the advantages of SHG for the determination of sticking probabilities on silicon surfaces. First of all, the possibility to monitor surface coverage in real time and at high gas pressure is shown to allow for the measurement of low sticking probabilities at surface temperatures above the onset of hydrogen desorption. Furthermore, real-time monitoring of H-coverage was used to quantify sticking probabilities of different reaction channels on vicinal Si(001) and to investigate the coverage dependence of s0 on flat Si(111). As a further example, the determination of the chemisorption energy is briefly reviewed in Section 2.3. 2.2.1. Flat Si(111) and Si(001) surfaces In a typical adsorption experiment with thermal hydrogen gas, the clean surface is kept at a constant temperature and the SHG signal is recorded as a function of time. At t = 0, the UHV chamber is then backfilled for 100–1000 s with purified H2 or D2 from a liquid-nitrogen-cooled reservoir. In most experiments the gas pressure varied between 10−4 and 10−2 mbar resulting in a flux Φ of hydrogen molecules on the surface between 3 × 102 and 5 × 104 ML/s (compare Table 2). For some measurements gas pressures up to 10−1 mbar and total exposures up to 107 Langmuir ('10 mbar s) were used. Typical data from the first set of experiments [55] that determined the sticking coefficient for H2 /Si(111) are plotted in Fig. 12. For these measurements the hydrogen pressure in the chamber was regulated by hand. It was recorded with a spinning rotor gauge and the ion gauge was switched off to avoid H2 dissociation at the hot filament [55].

Fig. 12. H2 pressure in the UHV chamber and nonlinear response of Si(111) during adsorption experiments at three different substrate temperatures Ts . The (2) symbols of the upper traces indicate the measured nonlinear susceptibility χs ; the lines are the results of a numerical evaluation of Eqs. (8)–(10) using the recorded H2 pressure p shown below and a sticking probability s0 that best fits the experiment. Reprinted with permission from Bratu and H¨ofer [55]. c 1995, APS.

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The adsorption rate Rads (θ, Ts , t) = Φ(t)s0 (Ts ) f (θ )

(9)

is given by the flux Φ(t) of H2 molecules derived from the measured pressure p(t), and by the sticking coefficient of the clean surface s0 multiplied by a factor f (θ ) that describes the coverage dependence of the sticking coefficient. Since the coverage dependence of the sticking coefficient is weak for θ ≤ 0.1 ML ( f (θ ) ' 1, compare Fig. 14), the sticking coefficient s0 is then the only unknown parameter. The treatment of desorption in the numerical fit depends on the substrate temperature. For Ts < 700 K, desorption is negligible on the timescale of our experiment and θ (t) is solely determined by sticking of molecular hydrogen (Fig. 12(a)). For higher temperatures the coverage dependence of the desorption rate   −E des m 0 Rdes (θ, Ts ) = θ νdes exp (10) kTs may be directly deduced from the recovery of the SH signal, measured after the gas flux has been turned off (Fig. 12(b)). In practice, this procedure works for Rdes < 1 ML/s. For higher desorption rates the equilibrium between adsorption and desorption Rads = Rdes is established faster than the time constant for pressure changes in the present experiment (Fig. 12(c)). In these cases, which occur for Ts > Tdes ' 850 K, the sticking coefficients may no longer be determined independently from θ (t). One can extend the range of temperature somewhat into this regime by determining 0 and (fractional) reaction activation energy E des , prefactor νdes order m from fits of Eq. (10) to the data obtained for Ts < Tdes and extrapolation to higher temperature. With f (θ ) ≡ 1 (low coverage approximation) the equilibrium coverage is then given by: " #1/m Φ(t)s0 . (11) θ(t) = 0 exp(−E /kT ) νdes s des The values of the initial sticking coefficient s0 of H2 on Si(111)7×7 inferred from Fig. 12 and from similar data have already been displayed in Fig. 8 as a function of the inverse substrate temperature. The lowest still detectable sticking probability was '2 × 10−9 for Ts = 580 K. s0 increases by three orders of magnitude when the temperature is raised from 600 to 900 K. In later experiments the sensitivity could be improved to s0 = 5 × 10−11 for Ts = 520 K [97]. This is a sensitivity to sticking on an otherwise very reactive surface that has rarely been achieved before. It is mainly limited by the presence of water contamination in the dosing gas of the UHV chamber. Water is well known to have a very high sticking coefficient for dissociative adsorption on silicon surfaces [98– 100]. Since the dissociation products H and OH also quench the Si dangling bonds, relative water concentrations of 10−8 may already disturb the experiment. Fortunately, the presence of H2 O adsorption may be distinguished experimentally from H2 adsorption by the different desorption behaviour as discussed in Ref. [56].

Table 3 Sticking coefficients of thermal H2 at Tgas = 300 K on Si(111) and Si(001) surfaces at different temperatures. The values for the DB -steps correspond to a miscut angle of 5.5◦ . A and E A denote prefactor and Arrhenius energy that can be used to parameterize s0 between 550 and 1000 K by s0 = A exp(−E A /kTs ) Si(111)7×7

Si(001)2×1

Si(001)DB -steps

s0 (Ts = 300 K) s0 (Ts = 600 K) s0 (Ts = 900 K)

<10−11

<10−10

2 × 10−9

5 × 10−8

2 × 10−6

1 × 10−5

2 × 10−5 1 × 10−4 –

EA A

0.87 ± 0.1 eV 7 × 10−2.0±0.5

0.75 ± 0.1 eV 1 × 10−1.0±0.5

0.09 ± 0.01 eV 4 ± 2 × 10−4

On Si(100)2×1 the overall sticking coefficients are by a factor of 2 to 10 higher than on Si(111)7×7 and the temperature dependence is slightly weaker. For both surfaces the sticking coefficients of the two isotopes H2 and D2 are of a similar absolute value and also their temperature dependence is quite alike (compare Sections 4.2.3 and 5.4). The observed temperature dependence can be parameterized by an Arrhenius law, s0 = A exp(−E A /kTs ), with activation energies and pre-factors given in Table 3 together with the absolute values of the sticking coefficient at three different surface temperatures. The table also includes data from vicinal Si(001) discussed in Section 2.2.2. It should be stressed that the Arrhenius law provides only a convenient parameterization of the measured sticking coefficient. The apparent activation energy can not be directly identified with the adsorption barrier E ads . In a somewhat simplified interpretation of the dynamical calculations the Arrhenius energy E A is the excitation energy of the silicon surface required to enable the incoming (cold) H2 molecule to adsorb without experiencing a large barrier. It is thus closely related to the lattice distortion in the transition state E s that will be introduced in connection with ab initio calculations below (Section 3.6). Only in special cases is this activation energy the same as the mean barrier height E 0 that is determined in molecular beam experiments as discussed in Section 4. 2.2.2. Reactivity of different surface sites The capability of SHG measurements to differentiate between reaction channels of different reactivity was first demonstrated for vicinal Si(001) surfaces [97,101]. It is also applicable on hydrogen pre-covered surfaces and the results have been very helpful for gaining insight into the microscopic mechanisms of H2 interaction with Si(001). In the inset of Fig. 13, a representative measurement on a Si(001) sample that was inclined from the [001] surface normal towards the [110] direction by 5.5◦ is displayed. The surface consists of Si(001) terraces separated by double-atomic height DB steps (compare Fig. 19 in Section 3.1) and was exposed to thermal H2 at a pressure of 10−3 mbar. Similar examples of molecular beam experiments are shown in Section 4 (Fig. 48(a)). One observes (2) a rapid drop of the surface nonlinear susceptibility χs responsible for the SHG signal immediately after admitting H2 gas to the chamber followed by a more gradual decay. The

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Fig. 13. Initial sticking coefficients s0 for a gas of H2 at room temperature on the steps (filled symbols) and terraces (open symbols) of vicinal Si(001) surfaces at various surface temperatures Ts . They were derived from the (2) decay of the nonlinear susceptibility χs during H2 exposure as shown in the inset. Numerical fits to an Arrhenius law s0 (Ts ) = A exp(−E A /kTs ) yield activation energies E A and prefactors A for step (terrace) adsorption of 0.09 ± 0.01 eV (0.76 ± 0.05 eV) and 4 ± 2 × 10−4 (∼10−1 ). Reprinted with permission from Kratzer et al. [101]. c 1998, APS.

(2)

two slopes of the χs (t) correspond to sticking probabilities of 1 × 10−4 and 1.4 × 10−8 . The fast hydrogen uptake saturates at a coverage that corresponds to the number of dangling bonds at the DB steps. It was thus identified with adsorption at special dissociation sites of the stepped surface. The slow signal decay yields very similar sticking coefficients as obtained for nominally flat Si(001) [56] and was attributed to adsorption on terrace sites. The results for both terrace adsorption and dissociation at the DB steps as obtained on Si surfaces that were systematically inclined with respect to the [001] surface by 2.5◦ , 5.5◦ and 10◦ ± 0.5◦ are summarized in Fig. 13. In general much higher sticking probabilities and a much lower activation of s0 with surface temperature is observed for sticking at step sites [101]. The identification of such a highly reactive adsorption channel for H2 on the DB steps provided the first clue to the inter-dimer transition state for H2 on Si(001) as discussed in Section 3. Furthermore, the fact that the reactivity of the steps is so much higher than on the terraces at room temperature makes it possible to prepare surfaces with all step sites saturated by atomic hydrogen while all the dangling bonds of the terraces are still empty [102]. This enables rather unique experiments to address diffusion processes across step sites [59,60]. Monitoring the step depletion as a function of temperature also allowed for the determination of binding energy differences between of hydrogen adsorbed at step and terrace sites [59,103]. Recently, a similar procedure was also applied to monitor electronic induced atomic motion on a metal

477

Fig. 14. Coverage dependence of the sticking coefficient of H2 on Si(111)7×7 at a surface temperature of Ts = 640 K. Reprinted with permission from Bratu et al. [106]. c 1996, APS.

surface by means of SHG, namely the diffusion of oxygen atoms from step sites onto terraces of Pt surfaces [104,105]. 2.2.3. Coverage dependence of sticking For comparison with theory the most interesting quantity is the sticking coefficient of the clean surface which in practice is extracted from data with a total hydrogen coverage θ ≤ 0.1 ML. With an appropriately calibrated SHG response it is also possible to extend these measurements to higher coverages. In particular under conditions where there is no desorption (Ts  Tdes ), the real-time monitoring of the surface coverage allows to determine the coverage dependence of the sticking coefficient s(θ ) = s0 f (θ ) in a straightforward manner. An example for H2 /Si(111)7×7 is shown in Fig. 14. The data clearly show that the slope −dθ/dt, which is proportional to the sticking coefficient s(θ ), increases as a function of exposure time and thus as a function of coverage. The observed behaviour is in contrast to the expected effect of site-blocking which in this coverage range should already result in a noticeable decrease of the sticking coefficient. A comparison with a fit to f (θ ) = (1 − θ )2 is shown as a dashed line in Fig. 14. In Ref. [106] the increase of the sticking coefficient with coverage was interpreted in terms of a slight decrease of the adsorption barrier for sites in the vicinity of adsorbed hydrogen. The 5-fold increase of the sticking coefficient, as compared to the (1 − θ )2 behaviour, corresponds roughly to a 10% reduction of the adsorption barrier between 0 and 0.4 ML. Such a small reduction of the adsorption barrier could be caused by several mechanisms: For example, the weakening of the adatom backbonds of Si(111)7×7 [107], which is likely to occur upon hydrogen adsorption, could decrease the amount of lattice distortion required to from the transition state. In addition, also purely electronic effects, such as bandflattening or redistribution of charge between the dangling

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bonds of Si(111)7×7, could reduce the adsorption barrier with increasing hydrogen coverage. It will be shown in Section 3.4.2 that on Si(001) preadsorption of atomic hydrogen leads to very reactive adsorption sites for molecular hydrogen. For this reason the coverage dependence of the sticking probability can be very strong on this surface under certain conditions (compare Ref. [108] and discussion in Section 3.7). 2.2.4. Comparison of measured sticking coefficients The results discussed above were subject to a considerable debate in the literature for several years. One reason was that early ab initio calculations for H2 /Si(001) did not find a large enough coupling of the adsorption barrier to the lattice degrees of freedom and because some of them predicted relatively low overall barrier heights (compare discussion in Section 3.3.1 and Table 5). The other reason was that other groups reported considerably higher experimental values for the sticking coefficients and a much weaker dependence on surface temperature [109,110]. Although these experimental discrepancies could subsequently be attributed to the influence of steps and defects [97,111] it is very important that independent experiments could confirm the small sticking probabilities measured by Bratu et al. [55,56]. Both of these experiments used SHG for the detection of H coverage as described above. Zimmermann and Pan [108] explored the sticking coefficient of H2 on Si(001) as function of gas pressure and extended the experiments of Ref. [56] to higher coverages as discussed in detail in Section 3.7. Mao et al. [78] reported slightly higher sticking coefficients and a slightly steeper Arrhenius curve (E A = 0.94) for H2 /Si(111)7×7 than Bratu et al. [55]. Given the difficulty of measuring very small sticking coefficients, the data of Refs. [55,78] for Si(111) as well as the data of Refs. [56] and [108] for Si(001) are in very good agreement. 2.3. Chemisorption energy To conclude this section on measurements of the basic properties of the hydrogen interaction with silicon surfaces, the determination of the chemisorption energy both of H on Si(111)7×7 and on Si(001)2×1 will be described. The chemisorption energy as a fundamental parameter of the potential energy surface of the H/Si system plays a decisive role for the discussion of reaction models in Sections 3–5. Again, a combination of several advantages of SHG made it possible to obtain reliable experimental values [26]. The procedural difficulty for determining the chemisorption energy for H2 /Si arises from the large barriers for recombinative desorption (2.4–2.5 eV) [24,25,33] and the small sticking coefficients for dissociative adsorption [55,56]. They require high temperatures and appreciable gas pressures to establish thermal equilibrium which prohibits the application of the conventional isosteric heat measurement technique [112] and also renders the method of adsorption microcalorimetry difficult [113]. The experimental setup used in Ref. [26] is a variant of the setup to determine the sticking coefficient for thermal H2

Fig. 15. Isothermal (T = 810 K) change of the nonlinear susceptibility of Si(111) with hydrogen pressure. Stepwise increase of the H2 flux leads to adjustments in the equilibrium coverage with the temporal behaviour as determined by the kinetics for ad- and desorption. Reprinted with permission from Raschke and H¨ofer [26]. c 2001, APS.

gas. The silicon samples were placed into a tube-shaped (Ø = 5 cm, l ' 25 cm) quartz cell rather than into a stainless steel UHV chamber. It was surrounded by a furnace and allowed to perform SHG experiments at equal gas and surface temperatures up to 1000 K. Fig. 15 shows the corresponding temporal change of the SH-response from Si(111). The data resemble those displayed in the previous subsection. However, here they are taken under the isothermal conditions TSi = TH2 = 810 K and the main interest was not in the adsorption or desorption rates. The kinetics for adsorption and desorption only determines the time required for the system to adjust to its equilibrium coverage. The pressure was increased in steps for low temperatures or slowly ramped up continuously in measurements at higher temperatures. The reaction was fully reversible and the desorption behaviour determined after the hydrogen flux was turned off was found to be in agreement with the desorption kinetics derived in previous experiments [24,25, 33]. The sticking coefficients were found to be about a factor of 5 to 10 higher compared to the experiments having used gas at 300 K as a consequence of the higher mean translational energy. The adsorption isotherms obtained after conversion of the SH-response to coverage are shown in Fig. 16 for different temperatures. From a series of these adsorption isotherms the isosteric heat of adsorption qst was derived evaluating the Clausius–Clapeyron equation [112] qst ∂ p = . (12) ∂ T θ T Vgas For that purpose, data pairs of temperature T and corresponding hydrogen pressure p leading to a constant surface coverage were taken from the results shown in Fig. 16 (left) as well as other isotherms and are plotted in Fig. 16 (right) in the form of an isosteric plot for some representative coverage values. When

M. D¨urr, U. H¨ofer / Surface Science Reports 61 (2006) 465–526 Table 4 Isosteric heat of adsorption qst for hydrogen on Si(111)7×7 and Si(001)2×1 derived for different equilibrium surface coverages. The corresponding individual Si–H bond energies are estimated as E Si–H = 21 (qst + E H−H ) with E H−H = 4.5 eV θ (ML)

Si(111)7×7 qst (eV)

E Si–H (eV)

Si(001)2×1 qst (eV)

E Si–H (eV)

0.1 0.15 0.2 0.3

1.52 ± 0.15 1.72 ± 0.15 1.77 ± 0.1 1.78 ± 0.1

3.01 3.11 3.14 3.14

1.83 ± 0.2 1.9 ± 0.25 2.0 ± 0.4 –

3.17 3.20 3.25 –

rewriting Eq. (12) in the form ∂ ln p qst =− , kB ∂ T1

In this equation  denotes energies associated with, e.g. adsorbate–adsorbate interactions as well as adsorbate induced changes in surface structure. The values for E Si–H given in Table 4 have been calculated with  = 0 and thus represent a lower limit for the individual bond energy. They may understate the actual value by a few tenths of an eV. These experimental values are very important for the comparison with theory and represent a crucial test for the consistency of the different adsorption models. This will be discussed in Sections 3 and 5 (cf. Table 5). Here we only note that the Si–H bond strengths of both, H/Si(111) and H/Si(001), are considerably weaker than hydrogen bonding in silanes. For comparison, the gas phase dissociation energies for the first Si–H bond for SiH4 and Si2 H6 are 3.92 eV and 3.74 eV, respectively [114].

(13) 3. Reaction pathways of H2 /Si(001)

θ

the slopes of these curves directly yield the isosteric heat of adsorption. Applying a similar procedure as described above for Si(111), corresponding data for Si(001) were obtained [26]. The resulting values for the isosteric heat of adsorption for both surface orientations are summarized in Table 4. After an initial increase, for coverages θ > 0.1 ML the values saturate at about (1.7–1.8) ± 0.1 eV for Si(111) and (1.9–2.0) ± 0.2 eV for Si(001), respectively. The error bars for qst are mainly due to the finite temperature range covered by the isosteric plot. The isosteric heat of adsorption is equivalent to the chemisorption energy, i.e., the total energy change resulting from the dissociative adsorption. It can be used to estimate the Si–H bond energy by considering the energy balance (comp. Fig. 3) 2 × E Si–H −  = qst + E H−H .

479

(14)

The surface reconstruction of silicon (001) is known in great detail and provides well defined adsorption sites for hydrogen. Nevertheless, the nature of the pathways for dissociative adsorption and recombinative desorption of H2 on clean, flat Si(001) was debated for more than one decade. In this section, we first briefly summarize the surface properties and the adsorption of atomic hydrogen on Si(001). Then, the various models for H2 adsorption that have been proposed over the years are presented. They differ in number and kind of silicon surface atoms involved in the process. In the main part, STM experiments which resolved the adsorption and desorption mechanisms in real space on flat Si(001) surfaces are discussed and the current theoretical understanding of the processes is summarized. Finally, the issues related to coverage dependence of adsorption and desorption rate and the unusual first-order desorption kinetics are addressed.

Fig. 16. Left: Representative adsorption isotherms for H/Si(111)7×7 for different temperatures. Discrete values for hydrogen coverage and their corresponding pressure were obtained for T = 787 K, 797 K and 810 K from data such as the ones displayed in Fig. 15. For T ≥ 826 K, data were acquired by slowly increasing the hydrogen pressure while monitoring the SH-response. Solid lines serve as guides to the eye. Right: Isosteric plot for different hydrogen coverages for Si(111) (top) and Si(001) (bottom). Solid lines represent numerical fits to the Clausius–Clapeyron equation (13) to derive the isosteric heat of adsorption. Reprinted with permission from Raschke and H¨ofer [26]. c 2001, APS.

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Fig. 17. Schematics of a hypothetical unreconstructed, the clean c(4×2)-reconstructed, and two hydrogen-terminated Si(001) surfaces. Filled grey circles indicate silicon atoms, empty circles indicate hydrogen atoms. The 2×1- and 3×1-reconstructions of H/Si(001) correspond to hydrogen coverages of 1 ML in the monohydride phase and 1.5 ML in a mixed mono- and dihydride phase, respectively.

3.1. Structure and electronic properties of Si(001) The Si(001)2×1 surface reconstruction was first discovered by Schlier and Farnsworth in 1959 using LEED [115]. One of the two dangling bonds per Si surface atom which are found on the non-reconstructed surface form a σ -like bond with one dangling-bond state of the neighboured silicon atom and the resulting dimers are arranged in rows parallel to the [110] direction of the Si crystal (Fig. 17). The driving force for the reconstruction is the reduction of the number of dangling bonds by a factor of two. The dimers have a bond length of ˚ [116–119] similar to the Si–Si distance in the bulk 2.2–2.4 A ˚ crystal (2.35 A). To further reduce the surface energy, the dimers are tilted by about 19◦ [119,120]. This Jahn-Teller-like distortion is favoured by approximately 0.14 eV per dimer when compared to the symmetrical configuration [117]. It opens a gap between the lowest unoccupied and the highest occupied surface states (Fig. 18). The filled states are then localized at the upper silicon atom and this dangling bond, denoted Dup in Figs. 17 and 18, exhibits more s-like character due to a hybridization close to sp3 . It is lower in energy than the dangling-bond state Ddown at the lower Si atom which is more of p-like character due to the lower atom’s hybridization being close to sp2 . It should be noted that the calculated bandstructure shown in Fig. 18 is that of a hypothetical 2×1 structure where all the dimers in one row would be tilted in the same direction. In reality, the dimers are alternatingly buckled due to elastic coupling. Additional weak coupling across the rows via the second and lower layers leads to a 4×2 superstructure (Fig. 17). Plotted in an extended Brillouin zone, the calculated band structure for Si(001)-c(4×2) [121] does not differ substantially from the one in Fig. 18. Experimentally, the c(4×2)-structure is observed only at temperatures below 200 K due to a fast dynamic flipping of the dimers from one to the other state already at room temperature [122–128]. Strong short-range dynamical correlation between neighboured dimers of the same row, however, persists at much higher temperatures [123,128,

Fig. 18. Band structure for Si(001)2×1 after Pollmann et al. [130]. The projected bulk states are hatched, the dangling bond induced states are indicated by Ddown and Dup for the unfilled and filled state, respectively (compare Fig. 17). The filled data points were measured by angle-resolved photoemission [131,132], open symbols refer to inverse photoemission data [133]. The characteristic points in the Brillouin zone are indicated in the inset.

129]. For the later discussion it is further important to note that there is considerable π -interaction between the two electrons of the dangling bonds also in the case of a symmetrical dimer [117]. In addition to adsorption on the flat Si(001) surface, adsorption at double-height atomic steps will be discussed in more detail in the following. Such steps can be prepared with high reproducibility when using crystals miscut with respect to one of the low index surfaces. As shown in the STM image in Fig. 19, the Si(001) surface miscut by 5.5◦ towards the [110] direction exhibits well-ordered, approximately 7-dimers-wide 2×1-terraces that are separated by steps perpendicular to the dimer rows. Most of the steps on this surface can be identified as double-height rebonded DB steps [134–137], which are characterized by the presence of an additional trigonally bonded Si atom at the step edge that serves to minimize the number of dangling bonds (compare sketches of Fig. 19).

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481

Fig. 19. Top left: Occupied-state STM image of the clean Si(001) 5.5◦ → [110] surface taken at a sample bias of U = −2.2 V and a tunnelling current of I = 0.7 nA. On the terraces, dimer rows perpendicular to the DB steps are observed, the end of a dimer row appears brighter than the other terrace dimers. The bright features between the terraces correspond to two of the buckled, rebonded step atoms. Top right: Sketch of the DB -step after Chadi [134]. Silicon atoms having dangling bonds are drawn white; the lower the position of the silicon atoms, the smaller the circles are drawn. The preferred adsorption site at the step atoms is indicated by a dashed oval. Bottom: Schematic side view of DB steps. Silicon atoms having dangling bonds are depicted as open circles, saturated silicon atoms are represented by filled circles.

3.2. Adsorption of atomic hydrogen Adsorption of moderate amounts of atomic hydrogen does not change the formation of dimer rows of Si(001) [10,138– 140]. STM images of well-prepared surfaces show a high degree of perfection of the 2×1 reconstruction for both the clean and the H-terminated surface (Fig. 20). In the monohydride phase, i.e. when the number of hydrogen atoms equals the number of Si surface atoms, each hydrogen atom quenches one dangling bond. The established chemical bond between hydrogen and silicon does not disrupt the Si–Si dimer bond. However, the interaction between the two dangling bonds of the two atoms at one dimer is disturbed. As a consequence, the buckling of the clean dimer is released as soon as one hydrogen atom adsorbs. The fully covered

H/Si(001) surface shows (2×1) reconstruction even at low temperatures [10] and no frozen buckling is observed. With hydrogen adsorbed, the bond length between the Si dimer atoms ˚ in comparison to is expected to enlarge by about 0.1–0.2 A the clean dimer (compare calculations referenced in Table 5). Since two hydrogen atoms on one dimer break only one π-bond between the dangling bonds in comparison to one broken πbond per hydrogen atom when the hydrogen atoms sit isolated on the dimers, the pairing of hydrogen atoms on one dimer is favoured by the energy of the π -bonding, i.e. by about 0.3 eV [142–145]. With further hydrogen dose, hydrogen coverages larger than 1 ML can be obtained at sample temperatures below 600 K. The adsorbing hydrogen atoms break the inter-silicon bonds of the respective dimers and Si-dihydrides are formed. Depending on

Fig. 20. STM topographies of clean (left image, negative sample voltage) and hydrogen saturated (right image, positive sample voltage) Si(001) surfaces. Each bright oval depicts one dimer unit. On the clean surface, monoatomic steps can be seen in the upper left corner. Adsorption of atomic hydrogen does not disturb the dimer row reconstruction visible in both images. In the right image, most dimers are saturated with one hydrogen atom per Si surface atom, i.e. the hydrogen coverage is very close to 1 ML. Only a few unsaturated dimers (bright) and dihydrides (small dark spots, [141]) are observed.

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Fig. 21. Schematics of (a) single-dimer, (b) two-dimer, and (c) dihydride reaction mechanism for hydrogen adsorption and desorption on Si(001). Grey circles depict silicon atoms, white circles depict hydrogen atoms. More realistic binding lengths are shown in Fig. 22.

hydrogen flux and surface temperature, a 3×1 reconstruction (alternating rows of hydrogen saturated Si dimers and Si dihydrides) or 1×1 reconstruction (neighbored rows of silicon dihydrides) equivalent to 1.5 and 2 ML hydrogen coverage, respectively, is formed [146–149]. 3.3. Models for dissociative adsorption In contrast to the adsorption of atomic hydrogen, which takes place at surface temperatures well below the onset of diffusion, the sticking coefficient of H2 on Si(001) at such temperatures is very low. This is the main reason why no direct information on the H2 adsorption sites was available for a comparably long time. The configurations observed after adsorption at higher temperatures as well as the configurations after thermal desorption are strongly influenced by surface diffusion. As a consequence, the models which were developed for those processes were not based on direct experimental evidence but on experiments on the kinetics and dynamics of ad- and desorption processes. Additionally, no common picture emerged from early ab initio calculations. High-level quantum chemical methods that included configuration interaction (CI) were restricted to very small cluster sizes that included only one dimer [150–159]. The results of density functional theory (DFT) differed substantially depending in the type of gradient corrections that were used to the local density approximation and whether periodic slabs or clusters were employed [159–165]. The main models derived from these calculations can be distinguished by the number and positions of the surface atoms which are involved in the process. Fig. 21 schematically displays the different reaction channels. Respective transitionstate geometries as calculated by Vittadini and Selloni [164] are shown in Fig. 22. In the single-dimer or intra-dimer pathway

(a), the H2 molecule interacts with the two silicon atoms of one dimer, whereas the two-dimer or inter-dimer pathway (b) involves two surface atoms on two silicon dimers. Dissociative adsorption or recombinative desorption via a dihydride state (c) occurs just over one single silicon surface atom. In the following, earlier experimental and theoretical results which supported one or the other model are reviewed mostly for historical reasons. Today, there is good overall agreement between experiment and theory hat the reaction follows the two-dimer pathway (b). For comparison, Table 5 summarizes the theoretical and experimental results of the most important energies for the different models. 3.3.1. Single-dimer mechanism Hydrogen dissociation over one single silicon dimer was thoroughly examined by means of various ab initio calculations [150–171,174–176]. This frequently called intradimer mechanism was favoured for a long time because it provides a straightforward explanation for the observed firstorder desorption kinetics via pre-paired hydrogen atoms on one silicon dimer. In more detail, isothermal measurements of the desorption kinetics by means of LITD [31,33] and SHG [25] exhibited first-order desorption kinetics for most of the high-coverage regime; i.e. the desorption rate decreases linearly with decreasing coverage, Rdes = −dθ/dt ∝ θ. This is in contrast to the second-order kinetics (Rdes ∝ θ 2 ) normally expected for an associative chemical reaction like recombinative desorption. A natural explanation for this observation is provided by the above mentioned pairing energy of H/Si(001) [25,33,177]. Prepairing of hydrogen atoms on the Si-dimers will naturally result in first-order desorption kinetics when the desorbing molecules start from one dimer, i.e. when a single-dimer desorption mechanism is operative. In that case the hydrogen atoms do not

Fig. 22. Transition states for (a) single-dimer and (b) two-dimer recombination on Si(001)2×1 and (c) H2 desorption from the dihydride phase of Si(001). Shaded and empty balls represent silicon and hydrogen atoms, respectively. Adopted with permission from Vittadini and Selloni [164]. c 1995, Elsevier.

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Table 5 Adsorption barriers E ads , desorption barriers E des and chemisorption energy qst for the dissociation of H2 on Si(001)2×1 as derived theoretically with different methods. In some cases also the substrate distortion energy E s in the transition state is given. The results are categorized according to the above-described adsorption models. For the two-dimer pathway, the desorption energy is based on the energy difference between two hydrogen atoms on one silicon dimer and the respective transition state. Experimental values are given for comparison Reference

E ads (eV)

Carter et al. [150–152] Jing & Whitten [153–156] Nachtigall et al. [157–159] Pai & Doren [160] Kratzer et al. [161,162] Pehlke & Scheffler [163] Vittadini & Selloni [164] Penev et al. [166] Steckel et al. [167] Tok & Kang [168] Okamoto [169] Filippi et al. [170] Kanai et al. [171]

0.7–1.2 1.15 0.85 1.0 0.4 0.3 0.6 0.5 0.55 0.65 0.70 0.75 0.4

Two-dimer (H2) (inter-dimer)

Vittadini & Selloni [164] Pehlke [172] Okamoto [169] Filippi et al. [170] Kanai et al. [171]

0.8 0.2 0.6 0.65 0.25

Defects/dihydrides

Wu et al. [151] Jing et al. [154] Nachtigall et al. [159] Radeke & Carter [152,173]

0.09 0.22 0.13 0.42

Single-dimer (intra-dimer)

E 0 (eV) Experiment (low coverage)

D¨urr et al. [111] Bratu et al. [56] H¨ofer et al. [25] Raschke et al. [26]

E s (eV)

0.1 0.15 ≈0.25

0.8 0.3

E A (eV)

E des (eV)

qst (eV)

Technique

3.6–4.1 3.75 3.25 2.95 2.5 2.4 2.5 2.45 2.80 2.95 3.0 2.96 2.34

2.9 2.6 2.4 1.95 2.15 2.1 1.9 1.95 2.25 2.3 2.3 2.2 1.94

CI, 2×1-cluster CI, 2×1-cluster CI/DFT, 2×1-cluster DFT, 2×1-cluster DFT, 2×1-slab DFT, 2×2-slab DFT, 4×4-slab DFT, 3×2-cluster DFT, 4×4-cluster DFT, 3×2-cluster DFT, 2×2-cluster QMC,√4×2-cluster √ DFT, 8 × 8-slab

2.7 2.15 2.9 2.9 2.2

1.9 1.95 2.3 2.3 1.95

DFT, 4×4-slab DFT, 2×4-slab DFT, 2×2-cluster QMC,√4×2-cluster √ DFT, 8 × 8-slab

2.4 2.3 2.5 2.5

2.3 2.1 2.35

CI, cluster DFT, cluster DFT, cluster CI, cluster

E des (eV)

qst (eV)

>0.6

have to ‘find’ their recombination partners by diffusive motion. Deviations from the first-order kinetics to lower coverages were interpreted as a result of an entropically driven increase in the number of un-paired hydrogen atoms [25,177]. The pairing energy deduced from this model was 0.25 ± 0.05 eV [25] which is very close to the recent result of 0.31 ± 0.01 eV based on STM measurements of the equilibrium distribution of H/Si(001) [144]. Whereas early cluster calculations [150–159] predicted much higher desorption barriers for the single-dimer reaction pathway than experimentally observed, the agreement between slab calculations and experiment was very good in this respect (compare Table 5). These DFT calculations, which made use of relatively large unit cells with up to 40 Si atoms, also allowed for a realistic treatment of the relaxation of the silicon surface during the adsorption process. [161–164,176]. An example of the lattice movement as obtained by Kratzer and co-workers [161] is shown in Fig. 23. Already during the adsorption process, the buckling angle of the silicon dimer is reduced towards the final configuration with an unbuckled dimer. In agreement with other calculations regarding the single-dimer pathway this movement of the silicon surface atoms, however, led to a comparably small influence of the silicon substrate on the reaction dynamics. As a quantitative measure, the energy

0.7 ± 0.2 2.5 ± 0.1 1.9 ± 0.2

SHG + mol. beam SHG SHG SHG

stored in the lattice distortion at the transition state, E s , can be compared to the adsorption barrier E ads . For all calculations, E s is small when compared to the adsorption barrier, e.g. E s ≈ 0.1 eV and E ads ≈ 0.4 eV in Refs. [161,162]. Dynamical calculations demonstrated that such a small energy stored in the lattice distortion only leads to a minor activation of sticking with surface temperature [174,175]. E.g. adsorption of 100 meV H2 molecules was found to be activated with surface temperature by only E A ∼ 0.3 eV [174] or less [175] whereas the experimental result is E A = 0.7 eV [56,111]. 3.3.2. Two-dimer mechanism The two-dimer or inter-dimer reaction pathway with the hydrogen molecule reacting over two neighboring silicon dimers as shown in Fig. 22(b) was treated theoretically only sporadically in the 1990s. It was first mentioned by Wu and Carter [150] to have a lower activation energy for desorption than the single-dimer pathway but later, due to difficulties in explaining the first-order desorption kinetics, it was abandoned in favour of a two-step process involving a dihydride intermediate [151]. Vittadini and Selloni who performed DFT calculations, reported comparable adsorption barriers for the single-dimer and the two-dimer pathways [164]. Considering their finding of substantially more energy being

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Fig. 23. Schematic side view of the silicon (big circles) dimer during hydrogen (small circles) dissociation via a hypothetical single-dimer pathway. The transition state is indicated by dotted lines, the final state configuration is shown with dashed lines. Reprinted with permission from Kratzer et al. [161]. c 1994, Elsevier.

stored in the distorted lattice of the two-dimer than of the single-dimer transition state [164], the two-dimer pathway should probably have attracted earlier theoretical attention. Instead it was only after strong experimental evidence in favour of the two-dimer pathway that the results of Ref. [164] were confirmed qualitatively and that different calculations agreed that this pathway has the lowest adsorption barrier [169–172]. Today, there is strong experimental and theoretical evidence for the two-dimer mechanism being operative over a wide range of reaction conditions. We will discuss this pathway in detail in Sections 3.4–3.6. 3.3.3. Dihydrides — defects In some of the early models of the dissociative desorption of hydrogen molecules from Si(001), minority sites were included [151,154,159]. They should reconcile the low sticking probabilities which were generally interpreted in terms of a high adsorption barrier with the low mean translational energy in desorption pointing towards a barrierless reaction channel. If only a small number of highly reactive sites was present on the surface, the sticking coefficient would be governed by their number and could be small, although the energetics at those sites do not exhibit a substantial adsorption barrier. If the defect sites were generated in a thermally activated process, they could also explain the increase of sticking probability with surface temperature. In reverse, desorption would also be governed by those reactive sites, leading to first order desorption kinetics and low translational energy of the desorbing molecules. The reaction via such defect sites was additionally favoured by the fact that calculations on the basis of relatively small silicon clusters could not reproduce realistic desorption energies on the basis of a reaction scheme on the defect-free surface. Results of such cluster calculations therefore correlated the reactive sites to non-dimerized, isolated Si atoms on the surface [151,152, 173,178]. An illustration of such a scenario with those sites being generated at step sites is shown in Fig. 24. The models based on adsorption mediated by static defect sites involve redistribution of the adsorbed hydrogen by

Fig. 24. Adsorption and desorption of H2 via the creation of isolated defect sites at SB -type steps on Si(001)2×1. Migration of the defect sites across the terraces allows then for both adsorption and desorption via formation of silicondihydrides. Reprinted with permission from Radeke and Carter [152]. c 1996, APS.

means of surface diffusion. Experiments on the adsorption and diffusion of hydrogen on silicon surfaces with a controlled number of steps or defect sites excluded static defects to dominate the adsorption behaviour on Si(001) [59,97,101]. Depending on structure and surface temperature, such defect sites indeed show a reactivity increase up to a factor of 106 when compared to adsorption on the clean, flat Si(001) surface [101]. However, for surface temperatures below 600 K, no significant diffusion from the defect sites to the undisturbed silicon dimers was observed and adsorption at static steps or defect sites could be separated from adsorption on the flat terraces [97]. The static defects therefore were shown not to be a relevant source of adsorption with respect to the flat surface. Additionally, recent data from molecular beam experiments on the adsorption of H2 on Si(001) as a function of beam energy and surface temperature are incompatible with both static and dynamic defect models for H2 interaction with Si surfaces [111]. In short, these data which are discussed in more detail in Section 4, show a strong activation of the sticking probability both with surface temperature and beam energy, as shown in Fig. 49. The observed activation with beam energy excludes the presence of a significant amount of highly reactive minority sites with negligible barriers for hydrogen dissociation. But also mechanisms involving short lived defect sites which are produced by thermal activation, e.g. with an activation energy E A at step sites, and which possess a small but finite adsorption barrier E 0 [152,173], can be excluded on the basis of those molecular beam data. The sticking coefficients of such a scenario would depend multiplicatively on the defect concentration on the surface, n(Ts ) ∝ exp(−E A /kTs ), and on the energy dependent reactivity of these sites, sˆ0 (E), i.e. s0 (E, Ts ) = n(Ts )ˆs (E). Consequently, the activation with surface temperature should be independent of the beam energy (leading to parallel lines if drawn in an Arrhenius plot) in contrast to the experimental findings (compare Fig. 50). As mentioned above, part of the motivation for introducing hydrogen adsorption at isolated silicon atoms was the overestimation of the desorption energy via the single-dimer pathway in cluster-based quantum chemical calculations. One

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should note at this point that the number of silicon atoms in one cluster was strongly restricted by the available computational power in earlier calculations. Apart from general problems of small clusters, typically consisting of 9 Si atoms, to describe the electronic ground state with a satisfactory degree of accuracy [166,179] these calculations cannot properly account for lattice distortions because the cluster configuration is fixed during the adsorption process. More recent calculations with bigger clusters find a systematic reduction of the barrier energies with cluster size [166–168]. In summary, although the defect model might provide a simple explanation of the reaction kinetics of the H2 /Si(001) system, the theoretical predictions are not consistent with the experimental results on the dynamics of H2 adsorption. Adsorption via defect states can therefore be ruled out as the dominant reaction pathway on well-prepared flat Si(001) surfaces. 3.4. Real space investigations of adsorption pathways Results obtained for the sticking of H2 at DB steps and H-precovered surfaces discussed in other parts of this review provided strong arguments against the single-dimer and in favour of the two-dimer pathway. The definitive answer to the question, whether the H2 molecule dissociates over one or two silicon dimers, was subsequently given by means of scanning tunnelling microscopy. In the following, these STM experiments are reviewed not in chronological order but start with the clean Si(001) surface and are followed by a discussion of the different configurations induced by hydrogen pre-coverage. Complementary experiments which have been performed by means of SHG as a probe of hydrogen adsorption are discussed in Section 4.

485

3.4.1. Adsorption on clean Si(001) As mentioned above, the observation of initial adsorption sites by means of scanning tunnelling microscopy requires surface temperatures below the onset of pronounced adatom diffusion on the surface, otherwise the initial adsorption sites might be lost due to rearrangement on the surface. On the other hand, the sticking probability is low for thermal hydrogen gas at these surface temperatures. Therefore, observation of the initial adsorption sites requires either the detection of very low sticking probabilities or the increase of s0 at a given surface temperature Ts ≤ 500 K by means of kinetic energy or vibrational excitation of the molecules [111,180]. In Ref. [181], both methods were employed in combination with room temperature scanning tunnelling microscopy. For dosing high-energy hydrogen molecules, a heatable nozzle was employed similar to that in Ref. [111]. It allowed for temperatures as high as 1300 K and stagnation pressures in the range of tenths of atmospheres. As a result of the almost supersonic-beam-like hydrogen dosing, an increased sticking probability on the clean surface allowed for the distinction between adsorption on a single dimer and adsorption on two neighboured dimers as illustrated in Fig. 25. In the negativesample-bias STM image taken after an exposure of 103 L H2 to the Si(001) surface, triangular shaped configurations are predominantly observed. These configurations are clearly identified as two hydrogen atoms adsorbed on two neighbored dimers by inspection of Fig. 25(c) where the two remaining dangling bonds appear as two bright spots in the positive sample bias image. As a consequence, they give strong evidence for the hydrogen molecules to adsorb via the two-dimer pathway. If in contrast hydrogen had dissociated via the single-dimer pathway it would appear in the STM images as a dark spot of the shape of one dimer both in positive and negative sample bias images.

Fig. 25. (a) Filled-state STM image (U = −2.2 V, I = 0.5 nA) of approximately 10 × 10 nm2 of a Si(001) surface after ≈103 L exposure of H2 through a nozzle at a temperature of 1300 K with the surface at a temperature of 450 K. Features of type A: isolated singly-occupied sites from the adsorption of H atoms produced by gas-phase dissociation in the 1300-K-beam. B: single-dimer sites, which are indistinguishable from surface defects. C: two-dimer configurations from the initial H2 adsorption. D: two doubly occupied dimers from a two-step H2 adsorption process. (b) and (c) show filled- and unfilled-state (U = +0.7 V, I = 0.5 nA) STM images of two neighboured H atoms (configuration C), for comparison. The two single unsaturated dangling bonds in (c) appear bright. Reprinted with permission from D¨urr et al. [181]. c 2002, APS.

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Fig. 26. Sketch of adsorption geometries and potential reaction pathways on a partially hydrogen pre-covered silicon dimer row. Unreacted silicon atoms are depicted as white disks, hydrogen covered silicon atoms are depicted as black disks.

3.4.2. Adsorption on hydrogen pre-covered Si(001) For the adsorption on clean Si(001) surfaces, strong evidence was found for thermally activated lattice distortions to account for the strong increase of reactivity with surface temperature [56,106]. As a main key to the understanding of this enhancement in reactivity, changed electronic properties which come along with the geometric distortions were discussed, especially a weaker interaction between the dangling bonds. An example where these distortions are not dynamic but static are DB step sites and, as will be discussed in more detail in Section 3.4.3, the changed electronic configuration at the DB step sites were found to enhance the sticking probability of molecular hydrogen by many orders of magnitude [101]. In an effort to further understanding the adsorption processes on silicon surfaces, similar electronic distortions were introduced on the dimer-row reconstructed Si(001) surface by pre-adsorption of atomic hydrogen. Indeed, such precovered surfaces were found to show an increased reactivity up to several orders of magnitude if compared to the clean surface, depending on the exact nature of the single configurations. The different configurations of preadsorbed hydrogen, the resulting adsorption pathways, and their labelling are summarized in Fig. 26. DFT calculations also revealed reduced adsorption barriers for hydrogen dissociation at partially precovered silicon dimers in the case of the two-dimer reaction schemes [172]. Experimentally, the pathways at configurations induced by preadsorbed hydrogen atoms were investigated with two complementary methods, scanning tunnelling microscopy [182, 183] and second-harmonic generation [184]. In combination with supersonic molecular beam techniques, the latter one allows for the measurement of the dynamics of each of the reaction channels on the surface. The results will be discussed in more detail in Section 4.2.4. Here, we will concentrate on the direct imaging of those reaction sites before and after hydrogen adsorption by means of STM. (i) Two-dimer reaction sites — H4 Biedermann et al. [182] in the group of Heinz were the first to observe the highly reactive H4 pathway with the STM by comparing images before and after exposure of a hydrogen precovered Si(001) surface to thermal H2 gas. An example for such an image demonstrating the creation of a H4 cluster is depicted in Fig. 27. The high reactivity of the H4 pathway and the predominance of the the two-dimer (H2) mechanisms for adsorption on the

Fig. 27. (a) STM image of Si(001) pre-covered with 0.05 ML of atomic hydrogen (positive sample bias). (b) The same area after dosing 1 × 106 L H2 . The arrow indicates the position of the initially unreacted H4 site (two dangling bonds on two neighbored dimers appear bright) which is quenched by H2 adsorption in (b).

clean surface is also evident from STM images taken after exposure of the clean Si(001) surface to thermal H2 gas at a sufficiently high gas flux [181]. They show almost only hydrogen atoms in the described configuration of four hydrogen atoms on two neighboured silicon dimers (Fig. 28). The gas flux in this experiment was 3000 ML/s. With a site specific sticking coefficient at the H4 sites of sˆ ≈ 10−3 it takes only about one second until a H4 cluster is formed once H2 has adsorbed at two neighbouring dimers and created two highly reactive dangling bonds [181]. If on the other hand H2 had initially dissociated over one dimer, there is no reason why only clusters of four Hquenched dangling bonds and not some clusters of 6 or 10 Hatoms etc. should appear. The STM images Fig. 28(b) and (c) are thus a clear fingerprint for the initial two-dimer adsorption of H2 , in addition to its direct observation using a heated H2 gas (Fig. 25). It should be noted that in the latter experiment the difference in reactivity between the H2 and H4 pathway is smaller due to the higher energy of the H2 molecules. Moreover, the gas flux was reduced to an extent that the formation of H4 cluster is less likely. Biedermann and co-workers evaluated the site specific sticking coefficient at the H4 sites at room temperature to be sˆ = (8 ± 2) × 10−4 [182]. Using molecular deuterium as adsorbate, they additionally could show that the H4∗ configuration depicted in Fig. 26 does not exhibit an increased sticking probability. Whereas thermal programmed desorption after exposure of D2 to the H4 sites leads to a pronounced HD peak due to D2 dissociation at H4, no HD peak was observed in the case when the H4 sites are transformed into the energetically favoured H4∗ sites by means of hydrogen diffusion at elevated surface temperatures Ts > 450 K (Fig. 29). This indicates that no measurable amount of deuterium was adsorbed at the H4∗ sites due to the low sticking probability at these sites [182]. (ii) Two-dimer reaction sites — H3 For the observation of adsorption at the H3 site, a much higher dose of hydrogen is necessary [184,186]. At room temperature, a quantitative reaction can be observed only after dosing thermal H2 gas in the order of 106 L. A small area image of such a H3 site before and after hydrogen dissociation is shown in Fig. 30. The site specific sticking coefficient was determined to be 1 × 10−8 at room temperature, in very good

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Fig. 28. Filled-state STM images (U = −2.2 V, I = 0.7 nA) of approximately 25 × 20 nm2 of a Si(001) surface ((a) and (b)). (a) The room-temperature surface was exposed to 106 L H2 by backfilling the chamber. (b) Same exposure as in (a) for a surface temperature of Ts = 500 K leads to enhanced dissociative adsorption of H2 . The dark features are mostly pairs of saturated dimers. (c) Close-up of three hydrogen clusters after exposure of 106 L H2 to a surface at a temperature comparable to that in (b). Comparison with silicon dimers in the adjacent rows clearly indicates a cluster size of 2 saturated dimers. (d) Schematic representation of the adsorption process. Top: clean dimer row before adsorption. Middle: after the adsorption of one H2 molecule in the two-dimer configuration. Bottom: final configuration after a second H2 molecule has been dissociatively adsorbed. Reprinted with permission from D¨urr et al. [181]. c 2002, APS.

Fig. 29. Adsorption of D2 on H predosed Si(100) as a function of annealing temperature. The thermal-desorption-specroscopy (TDS) signal for HD was taken as a measure of the dissociative adsorption of D2 . Also plotted as a function of annealing temperature is the density of H4 sites as it was obtained from STM images. Above Ts ≈ 450 K, H diffusion converts the H4 sites to empty and doubly occupied dimers (H4∗ sites). As a consequence, no D2 dissociation was observed for temperatures Ts > 500 K. Reprinted with permission from Biedermann et al. [182]. c 1999, APS.

agreement with the SHG measurements [184]. No reaction at the undisturbed dimers was observed under these conditions.

Fig. 30. STM images at positive sample bias of Si(001) pre-covered with 0.05 ML of atomic hydrogen (a) and the same area after dosing 5×106 L H2 (b). The arrow indicates the position of the initially isolated dangling bond (bright spot) at a Si dimer pre-covered with one hydrogen atom. After hydrogen dissociation, a new isolated dangling bond appears bright (b). In accordance with the illustration by the sketch in the bottom, it is situated at the neighboured dimer and on the opposite side of the dimer row. From D¨urr et al. [186].

In summary, not only for two clean silicon dimers, but also for configurations with one and two preadsorbed hydrogen atoms on one and two dimers, respectively, the dissociation of hydrogen was found to take place in the twodimer configuration. Moreover, an increased reactivity for the configurations with preadsorbed hydrogen was observed. The major influence for this change in reactivity can be tentatively attributed to the dangling-bond states on dimers with a preadsorbed hydrogen atom. These states possess a very

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Fig. 31. Panels (A) and (B): Filled- and empty-state images showing isolated bare dimer sites on a largely H-covered surface at 120 K. (C) Averaged STS data measured at dimer sites on clean surface and isolated bare dimers as in (A) and (B). Reprinted with permission from Chen and Boland [185]. c 2002, APS.

different electronic structure if compared to the clean dimer. In particular, the loss of dangling-bond state interaction will lead to a shift of the isolated dangling-bond states towards the Fermi level inducing a higher reactivity. A deeper insight into the interplay between electronic structure and reactivity could be obtained with the help of DFT calculations of which an overview is presented below in Section 3.6. (iii) Single-dimer reactions sites — isolated dimers Given the strong influence of H-preadsorption on the reactivity of the two-dimer reaction pathway, the question arises to what extent lattice distortions can influence the reactivity of a single dimer and whether the single-dimer path is perhaps a competitive reaction channel at very high coverages when few two-dimer reaction sites exist. Fig. 31 shows STM images of an almost H-saturated Si(001) surface with few isolated dimers taken in the group of Boland [185]. These dimers appear rather symmetrical even

at 120 K, either because they are stabilized at that position or because the barrier for flipping is reduced due to the lack of correlation with their neighbours. Scanning tunnelling spectroscopy (STS) data show that the filled and unfilled states of these isolated dimers are shifted in energy position with respect to those of the clean surface (Fig. 31). Upon exposure of a surface prepared in such a way D¨urr et al. found no enhanced reactivity at room temperature [183,186]. In the example depicted in Fig. 32 the H2 dosage was 107 Langmuir, i.e. each Si dimer was exposed to ∼4 × 107 H2 molecules. Only four out of ∼300 isolated dimers were found to have reacted. This corresponds to a site-specific sticking coefficient of sˆ0 < 10−9 , which is the detection limit of the experiment due to contaminants in the dosing gas. It must be pointed out that this negative result, although at variance with an earlier report by Buehler et al. [187] who found an increased sticking coefficient for those sites of about sˆ0 ≈ 10−4 , is in full accordance with the current understanding of H2 dissociation on Si(001). As will be discussed below (Section 3.6), effective hybridization of filled dangling bond states with the anti-bonding orbital of the hydrogen molecule is most vital to hydrogen dissociation and adsorption on Si(001). However, as clearly observed by means of STS in Fig. 31C and backed by quantum chemical calculations, the energy spacing between occupied and unoccupied orbitals of isolated dimers is even larger than the spacing between the corresponding Dup and Ddown states of the unperturbed asymmetrical dimers [185]. Apparently, the missing interaction of the dangling bond states of the isolated dimer with neighboured states leads to an increased π-interaction between them. It is thus not surprising that these sites do not show an enhanced reactivity. 3.4.3. Adsorption at DB step sites As already discussed in Section 2.2.2, SHG experiments at vicinal surfaces are able to distinguish between H2 adsorption at the step sites from adsorption on the terraces as long as the surface temperature is kept below 600 K to avoid diffusion from

Fig. 32. (a) and (b): Empty state images (U = +0.8 V, I = 0.5 nA) of Si(001)2×1-H of approximately 30 × 30 nm2 . As shown in the close-up in (c), most of the bright spots are single, doubly unoccupied dimers (labelled D) prepared by desorption and subsequent diffusion from (on) a monohydride surface at 700 K. Some single dangling bonds (S) are also detectable. (a): before H2 exposure. (b): after exposure of 107 L of H2 at Ts = 300 K. Only the 4 black circled dimers have been reacted. From D¨urr et al. [186].

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Fig. 33. (a) Occupied state image after a dose of 230 L H2 . One, two, and three of the bright features are quenched and an elongation of the adjoining bright spots is observed. (b) Unoccupied state image of the same frame as in (a). The bright features correspond to the last set of terrace dimers and the rebonded atoms of the step edge. Hydrogen reacts with the step sites located in line with the dimers of the upper terrace. The brightness of the first dimer of the upper terrace is also reduced upon hydrogen adsorption. Adopted with permission from D¨urr et al. [102]. c 2001, APS.

the step sites to the terraces [97,101]. At room temperature, sticking probabilities measured for the step sites exceeded those on the terraces and on flat surfaces by more than six orders of magnitude (compare Fig. 13). As shown in Fig. 33, STM images of step sites before and after dosing molecular hydrogen clearly identified that the hydrogen molecules dissociate over the rebonded step atoms [102]. A pair of step atoms in line with the upper dimer row is favoured for adsorption (compare Fig. 19, right panel, and Fig. 34) compared to the step pairs shifted by one inter-atom distance along the step. No adsorption with comparable sticking probability was found at the terrace atoms next to the step sites. No hint on dihydride formation or breaking of the backbond from the step atom to the upper terrace was observed [102]. For higher step coverage, the formation of chains of covered and uncovered step areas was observed [102]. Monte-Carlo simulations of the adsorption kinetics and hydrogen distribution led to the conclusion that the sticking probability at the uncovered step sites next to hydrogen covered step sites is increased by a factor of three (measured at room temperature).

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At higher surface temperature, adsorption at a pair of step atoms shifted by one inter-atom distance along the step when compared to the upper dimer row was also observed. The observation of an increased sticking probability at rebonded DB step sites with respect to the flat surface was in some point of view surprising. From adsorption on metal surfaces it is of course well known that step sites with undercoordinated surface atoms tend to exhibit a higher sticking probability [188,189]. However, in the case of the DB steps on Si(001) surfaces, the step atoms are not undercoordinated. They have three bonds to neighboured Si atoms and one dangling bond just as the dimer atoms of the reconstructed terraces. The coordination number can thus not account for the increased reactivity at the step sites. Step and dimer atoms differ, however, in the properties of their three neighbours. None of them has a dangling bond in case of a step atom whereas a dimer atom is bound to one Si atom with dangling bond, namely the second atom of the respective dimer. As will be discussed in more detail in Section 3.6.2, this difference results in a smaller interaction between the dangling bonds of adjacent step atoms as compared to the corresponding terrace atoms and ultimately in an higher reactivity of the step sites. 3.5. Real space investigations of desorption pathways Similar to the above described adsorption on Si(001), the direct observation of desorption sites after thermally programmed desorption seems to be impossible due to diffusion processes with a much lower diffusion barrier than the barrier for desorption and a resulting high diffusion rate. As a consequence, no desorption occurs at temperatures at which STM techniques can follow the motion of individual hydrogen adatoms. On the other hand, at temperatures at which desorption occurs, surface diffusion is so rapid that one cannot capture atomic positions by STM and no information about atomic pathways can be obtained. If the surface is examined after a conventional heating cycle that induced desorption, the resulting configuration will therefore reflect a situation

Fig. 34. Pseudo-3D-rendering of a negative-sample bias STM image of a partially hydrogen covered DB step edge and the corresponding ball-and-stick model with filled, half-filled, and empty dangling bond states at unreacted Si-atoms (large balls) as well as adsorbed hydrogen atoms (small balls). Adopted with permission from D¨urr et al. [102]. c 2001, APS.

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Fig. 35. Experimental setup of the laser-induced desorption measurement. A nanosecond laser pulse is used to heat the Si sample. A reference channel is provided by means of a beam splitter (BS) that permits beam characterization with photo diode (PD) and power meter (PM). The temperature rise of the surface (dots, not to scale) leads to recombinative desorption from the fully saturated monohydride surface. The STM images of the resulting surface (right side of figure) exhibit bright features where hydrogen molecules have been desorbed. More desorption is observed in regions nearer the centre of the laser beam where the peak surface temperature is higher. Reprinted with permission from D¨urr et al. [191]. c 2002, American Association for the Advancement in Science, AAAS.

close to the equilibrium arrangement of the surface. The initial configuration produced immediately after desorption will be lost to observation by means of STM due to fast diffusion of the adsorbates [190]. To overcome this very general limitations for observing desorption processes by means of scanning tunnelling microscopy, the combination of single-shot laser induced thermal desorption (LITD) with STM has been recently introduced [191]. The very fast heating and subsequent cooling of the surface due to thermal energy deposition by means of a single nanosecond laser pulse allows to freeze-in the processes dominant at high temperature. The obtained ‘snapshot’ of the surface reveals information of otherwise not observable reaction steps. The setup and procedure used for the experiment are sketched in Fig. 35. To induce desorption, the frequencydoubled output of a Nd:YAG laser with a wavelength of 532 nm and a pulse duration of 7 ns was focused on the silicon surface in a spot size of ≈500 µm diameter. The short penetration depth of the radiation leads to heating only within a thin region of the sample (≈1 µm) near the surface. Most important, thermal diffusion into the bulk material leads to cooling within ≈10 ns. If only a small fraction of the hydrogen is desorbed from the Si surface, the entire process must, because of the exponential dependence of desorption rate on temperature, occur at times when the surface is near its peak temperature. From the known desorption kinetics and the modelled heat flow in the substrate, it was found that the desorption occurs within a time window of just 3 ns. During this short time and for the given peak temperature, only little change in the configuration due to diffusion of the adsorbed hydrogen takes place.

Comparing the STM images before and after heating the surface by such a laser shot therefore revealed the initial desorption sites as demonstrated in Fig. 36. On the monohydride surface only a few unoccupied dangling bonds appear as bright features. In contrast, the adsorbate configuration following a nanosecond laser heating cycle showed many unoccupied silicon atoms (bright spots) with a preponderance of pairs of dangling bonds paired on adjacent dimers in the two-dimer configuration. Very few of the unsaturated dangling bonds were found in the single-dimer configuration. For comparison, desorbing a small fraction of a hydrogen monolayer by a conventional heating cycle (≈650 K for 100 s) resulted in a hydrogen distribution on the surface with the majority of the unoccupied dangling bonds paired on the same dimer, in agreement with earlier results [192]. In this configuration, the dangling bonds can form π -like bonds with an effective stabilization energy ≈0.3 eV per dimer [144]. The observed distribution after the conventional heating cycle therefore represents the situation close to the equilibrium at temperatures close to the desorption temperature or lower, depending on cooling rate [144]. Counting the number of each of the four configurations, shown in detail in Fig. 36, also quantitatively demonstrated a clear predominance of the two-dimer pathway (compare Fig. 37). Since hydrogen diffusion after desorption is expected to drive the system towards the thermal equilibrium, i.e. a broad distribution with a maximum occupancy of the single dimer configuration, the observed distribution with most of the dangling bonds in the two-dimer configuration can only be explained by a desorption process via the latter pathway. Indeed Monte-Carlo-simulations of the desorption and subsequent

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Fig. 36. STM images of the Si(001) surface taken at positive sample voltage (Ugap = +0.8 V, Itun = 0.5 nA). Upper left: Monohydride phase. After a conventional thermal desorption process (upper right), most of the dbs are paired on the same dimer (marked by red circles). In contrast, after heating by a laser pulse to ≈1350 K (lower left), pairs of dbs are found preferentially on adjacent Si dimers (marked by blue circles). The detailed images in the lower right show the different configurations of paired dangling bonds and the corresponding sketches of the structure (a filled circle denotes a hydrogen-terminated Si atom, an unfilled circle denotes a db): a pair of db on the same Si dimer (intra or single-dimer configuration), two db on neighboring Si dimers (inter or two-dimer configuration), as well as two db separated by one and by two saturated dimers. Reprinted with permission from D¨urr et al. [191]. c 2002, AAAS.

diffusion processes using the known rate laws [25,51] could match the experimental results of the LITD experiment only when based on desorption via the two-dimer pathway. Simulations based on the single-dimer desorption pathway were not able to reproduce the experimental findings (compare Fig. 37). More recent studies confirmed those findings. With multi-shot experiments Schwalb et al. [145] acquired STM images between single heating pulses and thus could take ‘snapshots’ of the fast equilibration processes of the danglingbond distributions. In conclusion, the LITD experiments clearly identified the two-dimer reaction pathway to be operative in desorption at high surface coverage. 3.6. Results of ab initio theory As reviewed above, it could be shown experimentally that dissociative adsorption and recombinative desorption of H2 takes place via the two-dimer reaction mechanism at different coverage and temperature regimes. For adsorption, it was found that the reactivity increases with the number of preadsorbed hydrogen atoms. This preadsorption of atomic hydrogen implies a major change of the electronic configuration of the silicon dimers on Si(001) since the π-bond between the dangling bonds of a single dimer is disrupted. Recent

theoretical investigations of the two-dimer reaction pathways, performed in parallel to the experiments, have shown that these changed electronic configurations are able to efficiently promote hydrogen dissociation [170,172,184]. By means of density functional calculations on the adsorption process, the two-dimer reaction channels were found to have generally lower adsorption barriers than the single-dimer processes [171, 172]. In the following, we will review the main results of these theoretical studies without going into the details of the calculations. 3.6.1. Terrace adsorption As mentioned earlier, a first theoretical indication that the two-dimer pathway might be worth a more serious consideration has been provided by the calculations of Vittadini and Selloni [164]. They reported the adsorption barrier E ads for the two-dimer pathway (0.8 eV) to be only slightly higher than for the single-dimer pathway (0.6 eV). Moreover, they calculated the energy stored in the lattice substrate for the transition state configuration, E s , to be much higher for the twodimer (0.8 eV) than for the single-dimer process (0.25 eV). As mentioned in Section 3.3.1, this figure is an important measure of the possibility of the substrate lattice to promote hydrogen dissociation. For the single-dimer mechanism, it was found

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Fig. 37. Measured and simulated distributions of pairs of unsaturated dangling bonds plotted as a function of their separation along the dimer row. Top: Initial condition (monohydride surface). Centre: Experimental distribution (cyan) after nanosecond laser-induced heating and simulation of the desorption process via the two-dimer pathway (blue). Bottom: Simulation of the desorption process via the single-dimer pathway. The different bars correspond to different diffusion times after desorption (dark: little diffusion; bright: more than an order of magnitude more diffusion steps than predicted). Reprinted with permission from D¨urr et al. [191]. c 2002, AAAS.

in all calculations to be too small to account for the strong activation of sticking probability with surface temperature. Pehlke performed systematic density functional total-energy calculations for the H2, H3, and H4 mechanisms [172,184]. In full agreement with the experimental results (cf. Section 4.2) he found a decreasing adsorption barrier with increasing number of hydrogen atoms preadsorbed and that a non-activated pathway exists for the H4 process. In contrast to the earlier result of Ref. [164] his more accurate calculations also clearly showed that the barrier of the two-dimer H2 process is actually lower than that of the single-dimer H2∗ mechanism. The distortion energy of the lattice E s was found to be comparable to the adsorption barrier E ads in the case of the two-dimer reaction mechanisms H3 and H2. In contrast, the single-dimer adsorption pathway H2∗ , despite its larger adsorption barrier, was shown to be associated with less substrate distortion in the transition state (E s < E ads /2) than the two-dimer pathway H2 (E s > E ads ) [172,184]. The corresponding numbers are collected in Table 7 in Section 4.2 together with the experimental values. Qualitatively, the results of Pehlke are not only in very good agreement with the experimental findings of an increased reactivity with increasing number of preadsorbed hydrogen atoms. As discussed in more detail below (Section 4) the high value of E s found for the two-dimer pathway H2 also explains the strong activation of sticking with surface temperature as observed experimentally [55,56]. To fully make use of the results of the density functional calculations, it is best to discuss the electronic states that are

involved in the reaction mechanism. Especially with respect to the ability of the relevant silicon atoms to provide reactive dangling-bond states for hybridization with the anti-bonding orbitals of the hydrogen molecule, the following reasoning was established: to dissociate the hydrogen molecule, the H–H bond must be weakened. This is accomplished by hybridizing the anti-bonding 1sΣu∗ H–H molecular orbital with two surface dangling-bond orbitals, which enter the hybrid orbital with opposite phases. The adsorption site shows a highly reactive character whenever the participating dangling-bond states lie close to the Fermi level: In this case the hybrid orbital may readily drop below the Fermi level and will be filled with electrons. For the relaxed surface configurations the energy separation between the dangling-bond states is not particularly small because of the Jahn–Teller splitting. To obtain high reactivity, however, it is sufficient for the energy gap between the dangling-bond states to become small when the substrate is distorted towards the transition geometry — provided that not too much energy has to be expended in distorting the lattice. This is the case for the two dangling bonds at the H4 site. The H3 site is intermediate between H4 and H2. It is very instructive to look more closely at the electronic states of this configuration as depicted in Fig. 38. Most relevant for hydrogen adsorption are the dangling bond orbitals at −0.52 eV and at the Fermi level. They hybridize effectively with the antibonding molecular orbital of the hydrogen molecule. However, when compared to the H4 mechanism, there is an extra electron that has to be transferred from the doubly occupied Dup state into the energetically unfavourable and previously unoccupied Ddown dangling bond, which renders the H3 site less reactive than the H4 site. For the H2 configuration the same electronic bond-breaking mechanism is still active. However, due to the interplay between the sp-rehybridization at large buckling angle of the Si dimers and the π-bond formation at small buckling angle there is no low-energy distortion that results in a small energy gap between the dangling-bond states. Hence the elastic energy needed to distort the substrate to create an electronically favourable configuration for hydrogen dissociation is comparatively large. This diminishes the reactivity of the H2 site and explains the strong activation with surface temperature. In Fig. 39 it can be seen that at the transition state, the dangling-bond orbitals relevant for the breaking of the H–H bond are again quite close to the Fermi energy. Additionally, the Si-atoms have approached each other (reduction of the Si–Si distance by 5%) in order to facilitate the H–H bond breaking. With respect to the difference between the single-dimer H2∗ and two-dimer reaction path H2 and why the latter one is energetically favoured both on clean and H-precovered surfaces, Kanai and co-workers reported on the application of first-principle molecular dynamics on the adsorption system of H2 /Si(001), both in the low- and high coverage regime [171]. To get a better insight into the driving forces of the reaction on the clean surfaces, Kanai et al. [171] analyzed the maximally localized Wannier functions (MLWFs) of replicas close to the transition state of both pathways (Fig. 40). They find an increased delocalization of these MLWFs for the two-dimer-

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Fig. 38. Contour surfaces of constant charge density (ρ = 0.005e− /bohr3 ) at the H3 site. Left hand side: electronic structure before H2 dissociation. Due to the single preadsorbed H atom, the dangling-bond orbital at the opposite side of the Si dimer is located at the Fermi energy and occupied by one electron. The orbitals relevant for the hybridization with the H2 molecule and their development during adsorption are indicated by arrows to the transition geometry shown in the middle panel. Right hand side: dangling bond at the Fermi level, occupied by a single electron, after dissociative H2 adsorption. The orbitals are labelled by their Kohn-Sham eigenvalues relative to the Fermi energy. Reprinted with permission from D¨urr et al. [184]. c 2001, APS.

Fig. 39. Atomic and electronic structure of the H2 configuration at the the twodimer transition state. Panels (a.1) and (a.2) show the frozen Si surface without the two hydrogen atoms; panel (b) shows the transition state including the stretched hydrogen molecule. For the wave function involved in the breaking of the H–H bond surfaces of constant charge density (ρ = 0.004e− /bohr3 ) are plotted. The eigenenergies measured with respect to the Fermi level are denoted in the panels. Reprinted with permission from Pehlke [172]. c 2000, APS.

transition state and conclude on a more efficient reduction of the HOMO–LUMO gap, where HOMO and LUMO stands for highest occupied and lowest unoccupied molecular orbitals, respectively. As a result, the potential energy curve for the two-dimer mechanism for the minimal energy pathway shows the lower maximum (Fig. 41). The ‘preparation’ of the

transition state for the two-dimer mechanism by means of lattice distortion can be seen in the earlier onset of the potential hill for the incoming H2 molecule when compared to the single-dimer mechanism. For the single-dimer mechanism, due to sp-rehybridization at large buckling angle and the π-bond formation at small buckling angle of the Si dimers, there is no low-energy distortion that results in a comparable reduction of the gap between the dangling-bond states. Thus, the MLWFs appear more localized in Fig. 40. In addition to the adsorption-energy barriers for H4 (0.0 eV), H2 (0.24 eV), and H2∗ (0.40 eV), which have been found to be comparable to the DFT-GGA calculations of Pehlke [172], Kanai et al. [171] calculated the adsorption barrier for H2 adsorption at an isolated dimer at high coverage. The barrier E ads = 0.45 eV is the highest found for all pathways under investigation. The slight increase when compared to the singledimer process on the clean surface was attributed to the fact that the hydrogenated surface tends to be more ‘rigid’ than the clean surface [171]. At this point, one should note that for both the calculations of Pehlke [172,184] and those of Kanai and co-workers [171] the absolute value of the adsorption barrier for H2 dissociation on the clean surface (0.2 eV and 0.35 eV respectively) is much lower than the experimental value of ≥0.6 eV. This deviation has been attributed mainly to the inaccuracy of the GGA for the exchange correlation functional, as the GGA tends to underestimate the adsorption-energy barrier up to a few hundred meV [193] as well as to dynamical effects due to the inability of the silicon atoms to follow the optimum reaction pathway assumed in the calculation because of the large mass mismatch between the reacting species [184]. Evidence for the first point has been published by Filippi and co-workers [170]. The authors applied quantum Monte Carlo

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Fig. 40. Isosurfaces (at 0.01 atomic units) of the electron density of the two relevant MLWF wavefunctions (maximum localized Wannier functions) for the single-dimer and two-dimer transition state, respectively. The latter one is shown by 90◦ rotated with respect to the former one. Adopted with permission from Kanai et al. [171]. c 2004, AIP.

Fig. 41. Potential energy profile along the minimum energy path for H2 adsorption on Si(001) for the single- (intradimer) and the twodimer (interdimer) pathway according to first-principles molecular dynamics calculations [171]. Energy zero corresponds to the noninteracting H2 molecule. The location of the saddle point (exact transition state) is indicated by a star. Adopted with permission from Kanai et al. [171]. c 2004, AIP.

methods to Si clusters to calculate reaction energies for the H2 /Si(001) system. They found a strong underestimation of the adsorption barriers by DFT-GGA and good agreement of their results calculated for the clean surface with the experimental values. The two-dimer mechanism with an adsorption barrier of E ads = 0.63 ± 0.09 eV is found to be favoured against the single-dimer mechanism with E ads = 0.75±0.05 eV. However, in variance to the experimental findings, a significantly higher desorption energy of 2.91 ± 0.09 eV was obtained for the H2 mechanism. 3.6.2. Adsorption at DB steps The adsorption of H2 at the step sites of rebonded, doubleatomic-height DB steps of vicinal Si(001) was the first reaction pathway for H2 dissociation on silicon surfaces which was clarified on a microscopic scale both theoretically [101] and experimentally [97,101,102]. It can be regarded as the first strong evidence for a reaction mechanism which does not take place at a single-dimer configuration. Additionally,

it mimics the situation on the flat surface but with the important parameters being restricted to an experimentally more accessible region. The resulting detailed insight in the driving forces therefore makes a more detailed discussion worthwhile. By means of DFT calculations it was shown that, similar to the ground state situation on the terraces, the two surface bands formed from the dangling orbitals located at the rebonded Si step atoms bracket the Fermi energy and are split by ≈1 eV due to the Jahn–Teller mechanism [101]. However, in contrast to the flat surface, the energy separation of the centres of the surface bands is reduced to 0.4 eV when the two rebonded Si atoms are forced to the same geometric height. The results of a calculation of the minimal energy path for hydrogen dissociation are then illustrated in Fig. 42. During adsorption of H2 a concerted motion of the H atoms and the two rebonded Si atoms towards a more symmetrical configuration of the Si atoms takes place. The Jahn–Teller like splitting showing up in the different height of the two rebonded Si atoms is therefore undone during the approach of the H2 molecule. Additionally, ˚ the two rebonded Si atoms move closer together by about 0.4 A during adsorption to assist in breaking the H–H bond. As a result, both for this optimum pathway and for the similar, but slightly less favourable pathway with the adsorption site shifted by one inter-atomic distance parallel to the step, the total energy was found to decrease monotonically when the H2 molecule approaches the surface (Fig. 42, right, full and dotted lines). Again, analogous to the adsorption on the flat surface, it seems to be most important for the dissociation of the hydrogen molecules that during adsorption the surface states with strongly reduced Jahn–Teller splitting can rehybridize and thus interact efficiently with the H2 molecular orbitals. This is the main difference to the surface band structure of the ideal Si(001) dimer reconstruction: At the Si dimers of the flat Si(001) surface, the strong π-interaction of the dangling bonds, either buckled or symmetrized, prevents the two band centres to come closer than 0.7 eV [125], while the dangling bonds of equivalent step edge Si atoms, similar to the H4 site, are almost degenerate. The theoretical findings on the importance of the interaction of the dangling-bond states and how much energy it costs to change this electronic interaction by atomic motion was experimentally illustrated by the STM images of hydrogen adsorption at partially covered steps shown in Fig. 34. The dangling-bond states of the pair of silicon step atoms next to saturated step atoms appear more symmetrical when compared to the frozen buckling of step atoms at the uncovered steps (Fig. 19). This might result either from a static symmetrization or from the fact that a fast flipping between two states make the atoms appear symmetrical in the STM images. Either way, the energy necessary for symmetrization of the step atoms and the resulting reduction of energy splitting is likely to be reduced. In perfect qualitative agreement to the above argumentation, this leads to an experimentally observed increase of the sticking probability [102]. Additional experiments on single-atomic-height steps further strengthened the picture of the interplay between

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Fig. 42. Left: Monohydride at a DB step (upper part) and motion of the highlighted step atoms during H2 dissociation (lower part). The reaction path is projected onto a (110) plane parallel to the DB step with different stages of dissociation marked by different colors. The insets show the motion of the rebonded Si atoms ˚ Right: Total energy of the H2 /surface system along the adsorption path shown on the left (full line). The dashed line comes from a separate (coordinates in A). calculation for the bare Si surface using the Si coordinates along the reaction path. The thin dotted line denotes the total energy along a similar reaction path, with the two H-adsorption sites translated by one inter-atomic distance along the step edge. Reprinted with permission from Kratzer et al. [101]. c 1998, APS.

lattice distortion and electronic structure and its influence on reactivity [183]. Rebonded, single-height SB steps (singleatomic-height steps perpendicular to the dimer rows on the upper terrace) show similar structural and electronic configuration as observed for the DB steps. As a consequence, also the measured adsorption coefficients are, within the error margins, identical. On the other hand, no increased reactivity could be measured for S A steps (single atomic height steps parallel to the dimer rows on the upper terrace) which do not have a rebonded step atom (all silicon atoms are found in dimer configuration) and consequently do not exhibit a pronounced distortion when compared to the flat surface atoms. In summary, the reactivity at step sites was shown to be highly increased when the electronic ground state configuration can be changed towards a more reactive configuration, i.e. filled states closer to the Fermi-level, without or with only little increase in the total energy. For the DB step sites, such a configuration is reached by de-buckling of the step atoms during hydrogen adsorption. The process was shown to be facilitated by a reduction of the energy which is necessary to de-buckle the step atoms, e.g. by already adsorbed hydrogen on step sites next to the reacting configuration. In this way, the situation at the step sites mimics the flat surface in a more limited energy range. On flat Si(001), the energy required for changing the clean dimers towards a reactive configuration is much higher. As a consequence, the mean adsorption barrier, and also the influence of preadsorbed hydrogen is much higher than at the step sites. 3.7. Kinetics of adsorption and desorption As discussed in 3.3.1 above, the observation of firstorder kinetics for recombinative desorption [25,31,33] was one reason why microscopic modelling of H2 /Si(001) concentrated on the single-dimer pathway H2∗ for many years. However, kinetic models are seldom unique and the fact that a certain

model agrees with experiment does not validate the underlying mechanism. On the other hand, with the correct microscopic model it should, of course, be possible to describe the kinetic data. In this subsection we will review the work of Zimmermann and Pan [108], D¨urr [183], and Brenig et al. [194] who showed that the desorption kinetics of H2 /Si(001) can be consistently modelled by the two-dimer processes H2 and H4. Most likely, the success of previous single-dimer desorption models was purely accidental. Desorption kinetics are generally classified as zero, first, or second order, depending on the power law which connects desorption rate and coverage   −E des dθ 0 Rdes (θ ) = − = θ m km = θ m νdes exp . (15) dt kTs This classification allows to determine the number of reactants involved in the rate limiting step [195]. For the recombinative desorption of H2 one consequently expects m = 2. However, Eq. (15) is only applicable under several assumptions, among others that there is only one adsorption site on the surface. Although this seems to be fulfilled for many systems, deviations from first- or second-order behaviour are also well known. For H2 /Si(111), e.g. desorption kinetics at low coverages have been described by an intermediate reaction order of m ' 1.5 [24]. This deviation from second-order desorption kinetics has been attributed to different H–Si binding energies and different H2 formation probabilities at adatom and restatom sites [24,28,29]. For the H2 /Si(001) system, isothermal desorption experiments performed by Sinniah et al. showed a first-order reaction [30,31]. This surprising result was one reason why the H/Si system attracted a lot of interest in the 1990s. It was soon confirmed (albeit with very different values for the activation energies for desorption E des ) by similar experiments conducted in the group of George [33] and by SHG experiments by H¨ofer et al. [25]. Fig. 43 displays isothermal desorption data of Ref. [25] recorded at Ts = 727 K. For θ > 0.05 ML

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θ2 (and consequently also θ1 ) can be calculated as function of the total coverage θ, surface temperature and pairing energy just as discussed in previous work considering single-dimer desorption [15,25,177]. The rate constants kH4 and kH2 differ due to different activation energies for desorption E des and possibly due to 0 (Eq. (15)). It is important to realize different prefactors νdes that the difference in E des is not only determined by the different H2 adsorption barriers E ads of both pathways but also by the number of π-bonds which are broken in the adsorbed state (Fig. 44). For this reason the H2 desorption sites have a significantly smaller heat of adsorption than the H4 sites. This can in fact overcompensate the presence of a finite barrier E ads in the desorption path of the H2 process and result in a larger desorption barrier for the H4 process, E des,H2 − E des,H4 = E ads − 2.

Fig. 43. Hydrogen coverage of Si(100)2×1 during the recombinative desorption at a surface temperature of 727 K. Dots: Experimental data from H¨ofer et al. [25]; solid line: prediction of the desorption model consisting of the two two-dimer processes H2 and H4 (Eq. (16)); dotted line: behaviour expected for simple 1st and 2nd order kinetics according to Eq. (15).

the semilogarithmic plot shows an exponential decrease of the coverage θ (t) = θ0 exp(−k1 t). This is the functional form obtained from Eq. (15) with m = 1. For lower coverages, the desorption process slows down; the kinetics gradually change over to second-order, θ (t) = θ0 (1 + k2 θ0 t)−1 . H¨ofer et al. analyzed these data under the assumption of the single-dimer pathway H2∗ being in operation [25]. They quantitatively related the transition to second-order kinetics to the finite value of the pairing energy  using the simple statistical mechanical consideration of D’Evelyn et al. [177]. Although the value of  = 0.25 ± 0.05 eV is very close to a recent more direct measurement by Hu et al. [144] ( = 0.31 ± 0.04 eV) it must be emphasized that the assumptions about the desorption mechanism made in Refs. [25,177] and in subsequent work [27,29,196] turned out to be incorrect. As discussed in detail in this review, the single-dimer process H2∗ is likely to play no role, neither at high nor at low coverages. For this reason it is of some interest whether kinetic models based on the two-dimer pathway are also consistent with the desorption experiments. In the most basic variant of a desorption model involving the two-dimer mechanisms one may neglect the H3 pathway due to a small prefactor (compare Fig. 55 in Section 4.2.4) and only include the H2 and H4 pathways. Since the number of H2 desorption sites is proportional to the square of the fraction of unpaired H atoms θ1 , whereas the number of H4 sites is proportional to the square of that fraction of H atoms θ2 which is paired at one dimer, one obtains for the total desorption rate: dθ = Rdes,H4 + Rdes,H2 = kH4 θ22 + kH2 θ12 , dt (θ = θ1 + θ2 ).

−

(16)

(17)

We note that for the calculation of the total activation of the desorption process, the energy for the formation of the sites with lower binding energy has to be taken into account (and this energy enters the activation energy when the desorption rate is measured as a function of surface temperature). Under the conditions of an isothermal desorption experiment, however, entropy drives the surface configurations out of the energetic minimum and the desorption rate from the single reaction sites is determined by the desorption energies E des,H4 and E des,H2 indicated in Fig. 44. This consideration also makes it clear, that once the temperature is high enough such that a considerable number of H2 desorption sites exist, it is highly unlikely that the H2∗ mechanism can contribute substantially to the desorption flux as suggested recently [197]. In order to be competitive, the adsorption barrier of the H2∗ pathway would have to be about  ' 0.3 eV lower than that of the H2 pathway whereas most calculations agree that it is in fact higher (compare Table 5). Additionally, one has to keep in mind that for the two-dimer pathway a larger distribution of barriers can be created dynamically by means of thermal excitations. As a consequence, most of the desorbing molecules will follow a pathway with lower adsorption barrier when compared to the mean adsorption barrier (compare Section 4.3.1). In the model, this is considered by an effective adsorption barrier E ads,eff , which is lower than the mean adsorption barrier. Its value is chosen close to the mean desorption energy of the desorbing molecules as obtained by means of time-of-flight measurements. We note that the usage of a reduced effective barrier for the H2 pathway is a major difference compared to recent kinetic models based on ab initio calculations of static barriers [197,198]. With a pairing energy of  = 0.25 eV, a desorption energy from H4, E des,H4 = 2.5 eV, and an effective adsorption barrier E ads,eff = 0.3 eV for desorption via H2 the experimental data of Ref. [25] are reproduced very well (Fig. 43). The relative contribution of the two reaction channels to the total desorption rate as function of coverage is plotted in Fig. 45. Obviously the reaction is dominated by the H4 process at high coverages and by the H2 processes at low coverages. With these parameters the crossover takes place at 0.3 ML.

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Fig. 44. One-dimensional energy potentials for the possible adsorption/desorption pathways of hydrogen on Si(001). Depending on the number of broken π -bonds, the heat of adsorption changes. The H4 shows the highest value. Contribution of the H2∗ channel to the desorption is regarded as unlikely due to its higher adsorption barrier and the much less efficient reduction of the barrier by means of thermally activated lattice distortions.

Fig. 45. Log–log plot of the calculated total desorption rate as function of coverage (solid line) and contributions of the H4 (dashed line) and H2 (dotdashed line) pathways. Reprinted from D¨urr [183].

Using nonequilibrium thermodynamics Brenig et al. [194] have worked out a more rigorous formulation of the kinetics based on the same general idea. They find the crossover from H4 to H2 to occur at a coverage around 0.5 up to 0.7 ML. The higher value is mainly a consequence of the inclusion of inter-dimer clustering interactions in their description [194]. This rather high cross-over coverage is consistent with recent coverage-dependent measurements of the translational energy of the desorbing H2 molecules that will be discussed in detail in Section 4.3 (compare Fig. 57). Finally, we note that this desorption model results in pure 2nd-order kinetics in two limits: very low and very high coverages. Whereas the low coverage limit is in good agreement with experiment (compare Fig. 43), the range of high coverages where 2nd-order kinetics applies is too small

to allow a meaningful comparison with available experimental data. For a wide range of coverage the presence of two competing reaction pathways lead to a coverage dependence of the desorption rate that is intermediate between 1st and 2nd order. Analogous to desorption, surface coverage is well known to influence the adsorption rate. In one of the most simple cases, site blocking by adsorbed species leads to a reduced reactivity with increasing surface coverage. In contrast, earlier measurements on Si(111) showed an increase of sticking probability with coverage (compare 2.2.3, Fig. 14). This increase in reactivity was attributed quite generally to the influence of already adsorbed hydrogen on the electronic occupation of the remaining dangling bonds [106]. Such an increase of reactivity with surface coverage was to be expected on Si(001), mostly due to the formation of the highly reactive H4-sites at higher coverages. This expectation was first confirmed by Raschke [199] by SHG measurements similar to those displayed in Fig. 14. His experiments as function of surface temperature could clearly correlate the formation of H4 sites with thermally activated H diffusion [199]. Systematic measurements of the sticking probability in an extended coverage range and as a function of hydrogen pressure as well as surface temperature were conducted by Zimmermann and Pan [108]. Their main experimental findings are depicted in Fig. 46 and can be summarized as follows: with increasing hydrogen coverage, the sticking probability increases. At lower surface temperature, the effect is more pronounced for lower hydrogen pressure. At higher surface temperature, no dependence on hydrogen pressure is found. At temperatures around 500 K and high hydrogen pressures, no increase of sticking probability is observed. The results are in qualitative agreement with the following scenario [108]: At higher surface coverage and elevated surface temperatures, H4-sites are created by thermally activated surface diffusion

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Fig. 46. Top: Arrhenius plot of the sticking probability of H2 on Si(001) at a hydrogen coverage of 0.4 ML for different H2 gas pressures. Bottom: Sticking probability as a function of H coverage for different pressures and surface temperatures. Symbols indicate experimental data, lines best fits based on a lattice gas model for the distribution of hydrogen atoms on the Si surface. Reprinted with permission from Zimmermann and Pan [108]. c 2000, APS.

leading to the increase of sticking probability. However, only at high surface temperature is this generation rate high enough to provide a sufficient number of reactive sites even at high hydrogen exposure. Therefore, in the mid-temperature regime a dependence on hydrogen pressure is observed. Zimmermann and Pan also performed isothermal desorption experiments and were able describe adsorption and desorption data with the same lattice gas model for the distribution of H atoms on the surface [108]. This model included clustering interactions between the occupied dimers on the same row [196]. According to their simulations, the H4 process dominates desorption in the high and mid-coverage regime and hydrogen clustering is the main reason for the deviation from second-order kinetics. Only at very low coverages (θ < 0.07 ML) is the reaction dominated by the H2 process [108]. We stress already at this point that this conclusion is at variance with many of the results concerning the reaction dynamics that

will be discussed below in Section 4. There is considerable experimental evidence for the presence of a sizable adsorption barrier for the interaction of H2 with Si(001) over a wide range of coverages. The notion put forward in Ref. [108] that adsorption and desorption proceed along two distinct microscopical pathways (H2, H4) and that this can explain the ‘barrier puzzle’ introduced in Section 1.2 thus can not be correct. In summary, one may conclude that the observed reaction kinetics are in good agreement with the existence of more than one reaction channel being operative. At low coverage, the H2 process is predominant, whereas at high coverage the H4 mechanism contributes most to hydrogen adsorption and desorption. The calculated crossover point between the two reaction channels depends on the applied model. However, based on experiments on coverage-dependent measurements of the dynamics of desorbing hydrogen molecules, the influence

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of the H4 mechanism in desorption seems to be restricted to coverages higher than 0.3–0.5 ML. As a consequence, at low coverage up to at least 0.3 ML the H2 mechanism is operative both in adsorption and desorption. The ‘barrier puzzle’ has therefore to be resolved by means of dynamic aspects of one single reaction channel, H2, rather than by the interplay between the H2 and H4 mechanisms. 4. Reaction dynamics of H2 /Si(001) 4.1. Introduction In this section, adsorption and desorption of the H2 /Si(001) system will be reviewed with focus on the underlying dynamics. As indicated already by the various reaction channels presented in the previous section, lattice distortions were found to play an important role. Kinetic energy and molecular vibrations further influence the reaction dynamics. Additionally, strong stereochemical effects have been observed when measuring the sticking probabilities as a function of the angle of incidence. Towards higher surface coverage, the influence of additional reaction channels and their dynamics is getting more important. All the experimental findings can be reconciled within the framework of phonon-assisted sticking. Comparison of the experimental results with calculations based on a model potential energy surface show quantitative agreement. The section is organized as follows: Firstly, the adsorption experiments both on the clean and hydrogen pre-covered surfaces by means of a combination of SHG and molecular beams are discussed with respect to kinetic energy, surface temperature, and molecular vibrations. These results are followed by complementary studies on recombinative desorption. The comparison of adsorption and desorption and the application of detailed balance is then discussed on the basis of a simple parametrization of the data. A separate paragraph has been reserved for angular resolved measurements, both in ad- and desorption, since a strong influence of the dangling bonds and thus the semiconductor’s properties of the silicon surface was observed. The section is concluded by a short overview of quantum dynamical calculations for the H2 /Si system and a comparison with the dynamics of hydrogen dissociation on copper surfaces.

Fig. 47. Experimental setup for the determination of sticking probabilities by means of a combination of supersonic molecular beam and optical secondharmonic generation techniques. The hydrogen beam is expanded from the continuous nozzle in chamber 1 (C1) and can be chopped by the chopper (Ch) in chamber 2 (C2) for time-of-flight measurements with the quadrupole mass spectrometer (QMS). After passing an additional differential pumping stage (C3) the beam enters the main chamber (C4). Chamber C5 can be used as a stagnation detector for the determination of the hydrogen flux in the beam when it is pumped only through its aperture [203,204]. For optical second-harmonic generation, pulsed laser light of the frequency ω shines on the sample under 45◦ . The specularly reflected signal at 2ω is detected after separation of the laser fundamental. Additional windows allow for angle dependent measurements of sticking coefficients.

Fig. 48(b), shows a strong increase of the adsorption speed with TN . For vicinal Si(001), Fig. 48(a), a clear separation between adsorption at step and terrace sites is observed, in addition to the increased reactivity on the terraces at high TN . By varying the temperature of the supersonic nozzle, the kinetic energy of H2 in the molecular beam is changed. Increasing nozzle temperature leads to an increased kinetic energy. However, the number of vibrationally excited molecules is increased at the same time. By admixing heavier rare gases to the hydrogen gas, the correlation between nozzle temperature and kinetic energy of the H2 molecules can be decoupled [202]. This so-called seeded beam technique allows then for the measurement of sticking probabilities as a function of kinetic energy for one fixed nozzle temperature and therefore a constant ratio between vibrationally excited and ground state molecules. 4.2. Adsorption experiments

4.1.1. Combination of SHG and molecular beam techniques Most of the adsorption measurements presented in this section have been performed by means of a combination of molecular beam techniques and optical second-harmonic generation [111,180,184,200]. The experimental setup is sketched in Fig. 47. The hydrogen beam was provided by a continuous, heatable supersonic nozzle consisting of a molybdenum tube with a hole of 30 µm in diameter [201]. Hydrogen gas with a purity of 99.9999% is passed through a cooled trap in order to freeze out residual H2 O. With a backing pressure of 11 bar and a nozzle–sample distance of 30 cm the apparatus allowed for a pure hydrogen flux on the surface as high as Φ = 2 × 1016 molecules/cm2 . The speed ratio S between the mean velocity and the width of the distribution was S = v/1v ¯ ≈ 10 at room temperature. Typical adsorption traces are shown in Fig. 48(a) and (b). Adsorption of flat Si(001),

In this section, we will firstly review the influence of surface temperature Ts , kinetic energy E kin , and molecular vibrations on the reaction dynamics at low coverage when the only reaction channel operative is dissociation over clean silicon dimers (H2). Secondly, the influence of Ts and E kin on the reaction dynamics at statically distorted adsorption sites, which were prepared by means of hydrogen pre-adsorption, is summarized. 4.2.1. Influence of surface temperature and beam energy From adsorption traces like those depicted in Fig. 48(b), the initial sticking coefficients s0 for adsorption on flat Si(001) can be deduced directly. The constant decrease of the SH signal when dosing with constant gas flux indicates the presence of one single reaction channel. It is possible to determine s0

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Fig. 48. (a) Determination of the sticking coefficients s0 for H2 adsorption on a vicinal surface with double-height atomic steps when being exposed to a supersonic (2) H2 beam created at various nozzle temperatures TN . Two different slopes of the nonlinear susceptibility χs for adsorption at the step sites (fast) and on the terraces (slow) can be distinguished per adsorption trace. Activation with beam energy for adsorption on the terraces is indicated by the increasing slope with increasing TN . (b) Determination of the sticking coefficients s0 for nominally flat Si(001). The coverage scale corresponds to the measurement with TN = 1096 K; an offset was added to the other data. The gas flux at this temperature was 8 × 1015 molecules cm−2 s−1 = 23 ML/s. Reprinted with permission from D¨urr et al. [111]. c 1999, AIP.

simply from the relationship (7) which is based on the linear (2) dependence between the nonlinear susceptibility χs and the hydrogen coverage for θ  1 ML, Eq. (5). The surface coverage was always kept low enough to avoid any influence of the H4 mechanism, which in principle can lead to a stronger decrease of the SH signal towards higher surface coverage, especially at higher Ts [199]. In Figs. 49 and 50, the sticking coefficients on flat Si(001) are shown for surface temperatures between 440 and 670 K and for nozzle temperatures ranging from 300 to 1800 K. s0 was found to change by almost three orders of magnitude in the investigated range of beam energies when measured at low surface temperatures (Fig. 49). For molecules with small kinetic energy a similarly strong dependence of s0 on surface temperature was obtained (Fig. 50), in agreement with the behaviour observed for thermal gas at room temperature [56] (compare Fig. 8). The higher absolute values of the beam data at TN = 297 K can be understood by means of a forwardpeaked angular distribution (compare Section 4.5, Fig. 60) and the still lower mean translational energy, hEi = 50 meV, of the thermal gas. High beam energies are seen to reduce the effect of surface temperature and vice versa. Figs. 49 and 50 demonstrate that hydrogen dissociation on flat Si(001) is a strongly activated process, both in terms of surface temperature and in terms of beam energy. The measured sticking coefficients require that both Si lattice and H2 molecular excitation can directly activate adsorption. This is indeed realized in the model of phononassisted sticking [44] and a detailed comparison with the potential energy surface for this process will be discussed in Section 4.6. However, already a simple parameterization using the commonly employed s-shaped adsorption energy functions [1–3] can give an idea of the key parameters of

Fig. 49. Initial sticking coefficients s0 as a function of nozzle temperature TN for various surface temperatures Ts on the terraces and at steps/defects of Si(001)2×1. Dashed lines are the results of best fits to Eq. (18), the dotted line indicates the estimated contribution from vibrationally excited H2 , solid lines are guides to the eye as a combination of both of them. Reprinted with permission from D¨urr et al. [111]. c 1999, AIP.

the dynamics of the H2 /Si system. The empirical character of these functions are demonstrated by the fact that either the tanh

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Fig. 51. S-shaped adsorption functions with mean adsorption barrier E 0 = 0.8 eV and width parameter of W = 100 meV (straight line) and 200 meV (dashed line). Inset: width parameter W as a function of surface temperature Ts when fitting the sticking probabilities according to Eq. (18) (filled squares). An additional data point from measurements with pre-covered surfaces (open square) was also taken into account. Straight line: linear fit to low coverage data. Dashed line: guide to the eyes. Fig. 50. Arrhenius plot of the initial sticking coefficients s0 for various nozzle temperatures TN . The dashed line represents the results obtained with thermal gas dosing as shown in Fig. 8 [56]. The dotted line is derived from Eq. (21). Reprinted with permission from D¨urr et al. [111]. c 1999, AIP.

or error function is applied in literature, depending on which function results in a better fit to the data. E.g. in the case of H2 /Cu the error function was employed very successfully. For the H2 /Si(001) system [205], the tanh function   A E kin − E 0 (18) s0 (E kin , Ts ) = 1 + tanh 2 W (Ts ) has proven to give the better fit to the data. The parameter E 0 is commonly identified as a mean energy barrier. Although such an interpretation might be misleading in some specific cases, comparison with calculations on a model PES show that this assumption is reasonable for hydrogen on silicon (compare Section 4.6). For fitting the H2 /Si(001) data, both E 0 and the saturation parameter A were kept constant but the width parameter W (Ts ) was varied as a function of surface temperature (compare Fig. 51). The latter can be then interpreted as a finite distribution of barriers for the dissociative adsorption at a given surface temperature. Since in the presented experiments the saturation value A is not reached, the mean energy barrier E 0 that is obtained when fitting Eq. (18) to the data has a relatively high uncertainty of ±0.2 eV. E 0 = 0.82(0.65, 1.0) eV was found for reasonable choices of A = 0.01(0.001, 0.1) [111]. The width W (Ts ) is insensitive to a change of A and E 0 . This can be rationalized when function (18) is approximated for small energies E kin and width parameters W (< E 0 ) by   E kin − E 0 s0 ' A exp W/2      E0 E kin = A exp − exp , (19) W/2 W/2

where both the exponential character and the independence of W on E 0 and A is easily recognized. The width parameter W was found to increase slightly superlinear as a function of Ts from 113 meV at 440 K to 193 meV at 670 K (inset of Fig. 51), independent of details of the parameterization. Here it should be noted that qualitatively similar results, but with higher absolute values for W (Ts ), were obtained when the error function erf [(E − E 0 )/W (Ts )] instead of tanh was used as the fit function (cf. Fig. 70 in 4.7). Additionally, it should be noted that a linear approximation of the experimental results would result in negative W values for small but finite surface temperatures. Therefore a flattening of the curve is expected towards lower temperatures. Indeed, an additional data point from measurements with precovered surfaces shows exactly this trend. Nonetheless, for a limited range of Ts , the linear dependence W (Ts ) = β + α × Ts

(20)

can be combined with the small energy approximation of Eq. (19). This leads to a dependence of s0 on surface temperature very similar to the experimentally observed Arrhenius dependence (compare Fig. 50), especially in the case of small values of β:     E kin − E 0 E kin − E 0 ≈ A exp . (21) s0 ' A exp (β + αTs )/2 αTs /2 On a first level, the strong activation of H2 dissociation on Si(001) with surface temperature and kinetic energy of the molecules can therefore successfully be described by the representation via s-shaped adsorption functions: Whereas a high mean adsorption barrier applies for all surface temperatures and causes the activation with kinetic energy, the activation with surface temperature can be described by an increase of the width of the adsorption functions with increasing Ts . Such an increase of W with Ts is then interpreted

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as an increased distribution of barriers on the surface which also results in a higher number of low-energy pathways and, as a consequence, a higher sticking probability for low-energy molecules. Such a widened barrier distribution is likely to be caused by thermally activated lattice distortions. The pronounced increase of the measured sticking probability s0 (E) for high beam energies E which deviates from the functional form of Eq. (18) was then attributed to vibrationally excited molecules that are more efficient in crossing the dissociation barrier when compared to ground state molecules. 4.2.2. Influence of molecular vibrations To probe the influence of molecular vibrations on the adsorption dynamics, seeded beam techniques were employed and mean adsorption barriers for the first and second excited state could be extracted [180]. In more detail, hydrogen was mixed with neon in the supersonic beam and sticking coefficients were measured at constant nozzle temperature but with varied gas mixture. If one neglects vibrational cooling during the supersonic expansion, the population of vibrational excited molecules is then given by the nozzle temperature TN . s0 (E kin ) therefore reflects the dependence of sticking probability on kinetic energy for a constant ratio between excited molecules and ground state molecules in the beam. For H2 /Si(001), such data are displayed in Fig. 52 for various nozzle temperatures TN and a surface temperature Ts = 90 K. The low surface temperature was chosen to minimize the effect of lattice excitation on the hydrogen dissociation. At low kinetic energies and high nozzle temperatures, the measured sticking coefficients are much higher than those of the unseeded beam and they show very little dependence on kinetic energy. This was attributed to the adsorption of atomic hydrogen [180]. Towards higher energies (E kin ≥ 150 meV), the sticking probability increases beyond this background. This effect is most pronounced for the lowest nozzle temperature (TN = 1268 K). It is due to the sticking of vibrationally excited molecules. In order to quantify the effect of vibrational excitation, the sticking coefficient was modelled as a function of kinetic energy and nozzle temperature using a model function that properly accounts for the relative population of vibrationally excited and dissociated molecules in the beam: X s0 (E kin , TN ) = FB (ν, TN )s0 (ν, E kin ) ν

+ αdiss (TN , p0 )s0,H .

(22)

The contributions s0 (ν, E kin ) of the molecules in the vibrational state ν are weighted by the Boltzmann factor FB (ν, TN ) for the state ν at temperature TN . Each state-resolved sticking coefficient s0 (ν, E kin ) was modelled by the above-introduced s-shaped functions   A(ν) E kin − E 0 (ν) 1 + tanh . (23) s0 (ν, E kin ) = 2 W (ν) Adsorption of atomic hydrogen was taken into account using a constant sticking coefficient s0,H ' 1 and a TN -dependent dissociation coefficient αdiss .

Fig. 52. Initial sticking coefficients on Si(001)2×1 at a surface temperature Ts = 90 K as a function of kinetic energy for three constant nozzle temperatures TN , i.e. three different populations of excited vibrational states (filled symbols) and as a function of nozzle temperature converted to E kin for the pure hydrogen beam (circles). Lines represent fits of the model functions Eqs. (22) and (23) to the data. In the inset, the obtained energy dependence of the sticking coefficient of H2 in the ν = 1 and the ν = 2 state is compared to that of groundstate molecules. For ν = 0, the dashed line indicates a width of the barrier distribution of 190 meV, as measured for a surface temperature of 670 K [111]. The solid line corresponds to W = 80 meV, the upper limit of W at Ts = 90 K. Reprinted with permission from D¨urr and H¨ofer [180]. c 2004, AIP.

The mean adsorption barriers E 0 (ν), the widths of the distributions W (ν), and saturation values A(ν) were obtained from the best fit of Eq. (22) to the full data set of Fig. 52. The resulting parameters are collected in Table 6, the solid lines in Fig. 52 indicate the calculated sticking coefficients. Although the number of the data points in Fig. 52 is limited, they impose severe restrictions on the most interesting fit parameters, i.e. the barriers E 0 (ν = 1) and E 0 (ν = 2). The estimated error bars of 30 meV and 50 meV, respectively [180] are considerably smaller than that of E 0 (ν = 0) as determined from the experiments presented in Section 4.2.1. This improved accuracy is a consequence of the fact that E 0 (ν = 1) and E 0 (ν = 2) are within the range of accessible beam energies whereas the mean adsorption barrier for ground state molecules, E 0 (ν = 0) ≥ 0.6 eV, is above this experimentally accessible energy range [111]. Also included in Table 6 is the parametrization used for the measurements at higher surface temperatures (compare Section 4.2.1). The contribution of the vibrationally excited hydrogen molecules at increased Ts are well described with the same mean adsorption barriers E 0 but with a somewhat increased width parameter W . As a consequence, the relative contributions of hydrogen atoms, molecules in the first excited state, and molecules in the second excited state to the total sticking probability of the unseeded beam depend on nozzle temperature. At low TN and

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503

Table 6 Adsorption barriers E 0 , width parameters W and saturation values A for the sticking of H2 in different vibrational states on Si(001)2×1 at different surface temperatures Ts Ts (K)

E ν (meV)

E 0 (meV) ≥600 390 ± 30 180 ± 50

90 90 90

ν=0 ν=1 ν=2

– 520 1020

487 670 540

ν=0 ν=0 ν=1

– – 520

820 ± 200 820 ± 200 390 ± 50

W (meV)

A

<80 40 40

0.01 0.03 0.015

125 190 70

0.009 0.009 0.006

therefore low kinetic energy, only the molecules in the second excited state may traverse their low adsorption barrier and therefore contribute to s0 . In the mid-temperature regime, the molecules in the first excited state contribute most to the overall sticking coefficients. This can be understood by the fact that the molecules in the second excited state have already reached the saturation value of the applied s-curve. Their contribution therefore follows a softer increase correlated to the number of excited molecules in the beam whereas the molecules in the first excited state reach their adsorption barrier with the consequence of a strongly increasing reactivity. Only for the highest temperatures close to TN = 2000 K, the influence of atomic hydrogen becomes comparable to that of the molecules in the first excited state. In a first approach for a qualitative discussion of the microscopic origin of the observed enhancement of the sticking probability by molecular vibrations, it is instructive to simply compare the relevant bond lengths. In case of the Si(001) interdimer pathway the Si–Si-distance of the reacting Si atoms and ˚ while thus the distance of the dissociated H atoms is 3.8 A ˚ Therefore, some of the the bond length of H2 is only 0.9 A. energy which is needed to overcome the adsorption barrier can be supplied by intra-molecular vibrations, provided that the incident molecules are oriented parallel to the surface. A further mechanism for effective energy transfer from the vibrational to the translational reaction coordinate, and vice versa, was suggested on the basis of the electronic structure of the reacting molecule [180]. With greater inter-atomic distance, the splitting of occupied σ and unoccupied σ ∗ states of H2 will be reduced. This might enable a more effective filling of the antibonding σ ∗ orbitals crucial for hydrogen dissociation [101, 172,180]. However, comparison of the amount of energy stored in the vibrational excitation with the respective reduction of the mean adsorption barrier shows that vibrational and kinetic energy cannot contribute equally to overcome the reaction barrier. Vibrational energy is less effective than translational energy. Moreover, the ν = 2 state is, relatively seen, less effective in reducing the adsorption barrier than the ν = 1 state. 4.2.3. Adsorption of D2 on Si(001) The large mass difference between the isotopes 1 H and 2 D makes it relatively easy to study the influence of the molecule’s mass on the adsorption dynamics of H2 /Si [180]. Fig. 53

Fig. 53. Initial sticking coefficients s0 as a function of nozzle temperature for deuterium on Si(001) at a surface temperature of Ts = 540 K. The connected line represents the fit of an s-function to the data, the dashed line shows the s-function for hydrogen under the same conditions. The same parameters for E 0 and A were used for H2 and D2 (cf. Table 6); the width parameters for D2 were W (ν = 0) = 140 meV, W (ν = 1, 2) = 50 meV, compared to W (ν = 0) = 150 meV, W (ν = 1, 2) = 70 meV for H2 . The thin dash-dotted lines indicate the contributions of the ν = 2 state for both isotopes. Reprinted with permission from D¨urr and H¨ofer [180]. c 2004, AIP.

compares results for H2 and D2 beams as a function of nozzle temperature at a surface temperature of 540 K. For low nozzle temperatures the sticking coefficient of D2 is about 50% smaller than that of H2 . This result is in agreement with measurements performed for thermal gas [56]. In this regime, the data can be fitted with the same E 0 and A values of the s-shaped model function as H2 but slightly reduced width parameter. However, an unchanged width parameter W in combination with a slightly increased E 0 is also compatible with the data. At TN ≥ 1000 K, s0 (TN ) exhibits a stronger increase for D2 and exceeds that of H2 at TN ≥ 1400 K. This increase can be fully accounted for by considering the lower energy of the first two D2 vibrational states (E ν=1 = 360 meV, E ν=2 = 700 meV). As a result, the population of vibrationally excited D2 molecules at a given nozzle temperature is higher than in the case of H2 . The effect is rather pronounced for the ν = 2 state which can significantly contribute to the sticking of D2 at intermediate nozzle temperatures whereas its effect is negligible in the case of H2 under the same conditions (Fig. 53). Among the possibilities how the molecules’ mass may influence the reaction dynamics aside from the different degree of vibrational excitation, adsorption via tunnelling through the adsorption barrier is the most prominent one [206]. However, as the mass enters the tunnelling rate exponentially, the 50% effect that shows up in the low energy regime of Fig. 53 appears to be too small to be associated with tunnelling.

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Fig. 54. SH response of Si(001) kept at Ts = 440 K during adsorption of thermal H2 (Tgas = 300 K). For preparation 0.15 ML atomic hydrogen was preadsorbed at 300 K and followed by annealing cycles for 400 s at 500 K for trace (B) and 600 K for trace (A). The corresponding surface precoverages are shown schematically on the right. Some of the dangling bonds (open circles) are quenched with hydrogen (filled circles). The respective reaction sites are labeled by rectangles. The inset shows the preparation of 0.2 ML H pre-coverage and the following saturation of the H4 sites with H2 . Reprinted with permission from D¨urr et al. [184]. c 2001, APS.

Two further possibilities were discussed in literature: On the one hand, the closer the molecules approach the surface, the more they experience the corrugation as a quantum trough [207]. The resulting zero point energy for the vibration of the centre of mass of the molecule in this quantum trough is higher for the lighter molecule and the difference adds to its adsorption barrier, i.e. the reactivity of the lighter H2 would be reduced, in contrast to the experimental results. On the other hand, the reduced ground state energy of the D2 molecule should lead to a higher adsorption barrier (in the order of 0.1 eV), in qualitative agreement with the observed lower sticking probability. 4.2.4. Dynamics at statically distorted adsorption sites The first experimental observation of an increased reactivity at distorted silicon configurations on silicon surfaces was reported for vicinal Si(001) miscut towards the [110] direction [97,101]. Those results as well as the observation of highly reactive adsorption sites induced by preadsorption of atomic hydrogen [182] have been discussed in detail in Section 3. Here, we would like to concentrate on the difference in the reaction dynamics of adsorption at those sites, mainly expressed by a different mean adsorption barrier E 0 , width of the adsorption function W , and activation with surface temperature E A . The reaction channels which have been discussed in literature are, according to the labelling in Fig. 26, DB -step sites, H4, H3, and H2 sites, the latter ones identical to the adsorption on the clean surface. The reaction dynamics at those sites were again investigated by means of a combined SHG and molecular beam experiment [184] which allows for a distinction of the

different reaction channels present on the surface. Whereas the type of step sites and the step density was chosen by means of direction and angle of miscut, respectively, the hydrogen induced reaction sites were prepared by preadsorption of atomic hydrogen (0.15–0.25 ML) and, if necessary, additional annealing cycles at elevated temperatures to allow hydrogen diffusion for a rearrangement of the adsorbed H-atoms. For illustration, adsorption traces typical for SHG experiments with preadsorbed H-atoms are displayed in Fig. 54. As for all the experiments, first the required H atoms were adsorbed at Ts < 350 K (Fig. 54 inset), a surface temperature at which the adsorbed H atoms are known to be immobile [51,53] and occupy dangling-bond sites in a largely random fashion as shown schematically in the lower right panel of Fig. 54. This leads to both H3 sites and, at a smaller number, H4 sites on the surface. Dissociation of hydrogen at H4 sites was identified in the SH adsorption data of trace C of Fig. 54 as the rapid initial drop in the SH signal. The subsequent slower adsorption was attributed to the H3 sites. When prior to H2 adsorption the hydrogen pre-covered surface is annealed at 500 K for 400 s, most of the reactive H4 channels are quenched by transformation of the H4 sites to a doubly occupied dimer [182] and the fast initial drop of the SH signal vanishes (Fig. 54, trace B). The sticking coefficient is identical to that one observed without annealing but after the initial saturation of the H4 sites, i.e. when only sticking at the remaining H3 sites contributes to the observed decrease of trace C. When the surface was annealed at a temperature of 600 K for 400 s (Fig. 54, trace A) the response showed a further reduced reactivity of s0 = 1.5 × 10−9 . It was attributed

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505

Fig. 55. Energy dependent sticking coefficients for the four main reaction channels on Si(001): (a) H4 at Ts = 350 K, (b) DB steps at Ts = 540 K, (c) H3 at Ts = 350 K (filled squares) and H2 at Ts = 350 K (filled circles) and Ts = 90 K (open circles). The open squares are the superposition of adsorption at the H2 ˆ and H3 sites at Ts = 350 K as determined in the experiment. The solid lines in (b) and (c) are fits to sˆ (E) = A/2[1 + tanh(E − E 0 )/W ], whereas the other lines are guides to the eye. Also shown as ball and stick models are the corresponding reaction sites with Si atoms comprising the top (lower) layer denoted as large dark (bright) balls. H atoms are small balls. Reprinted with permission from D¨urr et al. [184]. c 2001, APS.

to sticking at the H2 sites, similar to the reaction on the clean surface. At 600 K, the adsorbed hydrogen is mobile enough to reach thermodynamic equilibrium on the surface [51]. The equilibrium distribution for θ = 0.15 ML consists almost entirely of doubly occupied dimers [192], which have been shown not to exhibit any enhanced reactivity [182]. This assignment of the adsorption traces to the respective reaction channels allowed for the measurement of sticking coefficients as a function of the kinetic energy of the incident hydrogen molecules for each of the arrangements described above. The results are collected in Fig. 55, together with the results for adsorption at DB -step sites of vicinal Si(001) surfaces. For low kinetic energies, the sticking coefficient for the H4 sites was found to be the highest. However it decreases slightly with increasing beam energy (Fig. 55(a)). This behaviour indicates the presence of a barrierless reaction

pathway [208]. In contrast, H2 dissociation at the rebonded DB steps is clearly activated (Fig. 55(b)). The reactivity sˆ (E kin ) increases strongly as a function of beam energy until it saturates for E kin ' 100 meV. The data were fitted analogous to the data on the clean surface using the empirical s-shaped adsorption energy function (18). The adsorption barrier was determined to be E 0 = 0.08 ± 0.02 eV. The reaction at the H3 sites was found to be activated as well (Fig. 55(c)). The mean adsorption barrier associated with the H3 mechanism is E 0 = 0.19 ± 0.03 eV, about twice the value for dissociation at the steps. sˆH3 (E) shows a rather gradual increase for low beam energies, indicative of a wide distribution of barriers (W = 76 meV). The H2 channel is associated with the strongest activation of the sticking coefficient s0 (E kin ). As described earlier, it does not saturate within the range of available beam energies which translates into a barrier E 0 ≥ 0.6 eV [111].

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Table 7 Comparison of experimental and theoretical barrier heights E 0 , E ads , experimental substrate activation energies E A , calculated elastic energies in the transition state E s and energy splitting of the dangling bond (db) states in an unbuckled surface configuration for the different reaction pathways of H2 /Si(001), if applicable. Data collected from Refs. [56,184,199] H2∗

H2

H3

DB

H4

≥0.6 0.76

0.19 0.17

0.08 0.09

0 ≤0.01

0.20 0.33 0.7

0.06 0.08 –

– – 0.4

– –

Experiment

E 0 (eV) E A (eV)

– –

Theory

E ads (eV) E s (eV) db-splitting (eV)

0.35 0.15 0.7

0.35

In addition to the mean adsorption barrier E 0 , Raschke and D¨urr obtained experimental values for the energy E A for the adsorption of thermal hydrogen gas by measuring s0 as a function of surface temperature [183,199]. The values for the individual reaction channels are summarized in Table 7 together with the beam data and theoretical results of E ads and E s . Similar to the trend found for the adsorption barrier of the different adsorption sites, i.e. decreasing mean barrier E 0 with increasing degree of lattice distortion, the activation energy E A decreases from the H2 sites via H3 sites and DB -steps to the H4 configuration. Moreover, the absolute values of E 0 and E A are very similar for each of the adsorption sites. This is a further evidence that lattice distortion and kinetic energy can contribute to a similar extend to overcome the reaction barrier [184]. To quantify this statement, one can make again use of the above-introduced parametrization of the data via s-shaped adsorption functions. Expansion of the tanh functions together with the linear relationship between the width parameter W and surface temperature Ts lead to Eq. (21). Under the assumption of β = 0, Eq. (21) represents an Arrhenius behaviour as observed experimentally. The activation energy is then connected to the mean adsorption barrier through the proportionality constant α, E A = (2kB /α)(E 0 − E kin ), i.e. α determines the relationship between E 0 and E A . For example, for α = 2kB and small kinetic energy E kin of the incoming molecules, the activation energy E A then equals the mean adsorption barrier E 0 . On the other hand, the results of DFT calculations suggest that the height of the adsorption barrier changes with the amount of energy which is needed to create reactive dangling bonds. That is, although a configuration might be inert when frozen in the initial configuration, it readily can be active as long as only little energy is needed to create such a reactive configuration. This energy can be provided either by the reacting molecule’s movement or lattice excitation. Here, the DB step sites might serve again as a good example: With their relatively high energy splitting between occupied and unoccupied states, they show little reactivity in the frozen geometry. Little energy is, however, needed to reduce this splitting and therefore the step sites turn out to be rather reactive. Analogous to the step sites, the adsorption barrier of the operative reaction channels on the flat surface can be reduced by means of distortion of the silicon lattice. If this

distortion is induced by thermal activation of the silicon lattice, it leads to a broader distribution of adsorption barriers on the surface. This is observed experimentally in terms of an increasing width of the adsorption functions with increasing surface temperature. If one now assumes that the movements of the substrate’s atoms which lead to such a decrease of the adsorption barrier with respect to the mean adsorption barrier height are similar for all the reaction channels, regardless of the initial barrier height, the coupling between the width parameter W and surface temperature Ts is expected to be similar as well. Within the parametrization via s-shaped adsorption curves, this is then equivalent to a constant coupling parameter α and therefore the relationship between activation energy and adsorption barrier is fixed when the energy of the incoming molecules is kept constant: E A = const. × (E 0 − E kin ) = (2kB /α) × (E 0 − E kin ). In other words, a constant α tells us that the coupling between the lattice motions, which are effective in reducing the adsorption barrier, and the surface temperature stays constant for all reaction channels. It can be rationalized as follows: Although less energy is needed to thermally induce the lattice distortions which lower the adsorption barrier of the more reactive adsorption sites, e.g. DB steps, the reaction channels with higher mean adsorption barrier just need more distortion of the same kind. The strength of the coupling between surface temperature, lattice distortion and change of reactivity then determines the absolute value of α. In the case of H2 /Si(001), within this simple picture and limited range of parameters, it is found to be of the order of 2kB . 4.3. Desorption experiments In this subsection, we will review the desorption experiments concerning the dynamics of the H2 /Si system. They started in the early 1990s with the measurements of the population of rotational and vibrational degrees of freedom of hydrogen molecules desorbing from both Si(001) and Si(111) surfaces [209–212]. A few years later, the translational energy distribution of molecules desorbing from a laser-heated surface was also reported [35]. More recently, time of flight distributions were then measured for desorption induced by conventional surface heating [213,214]. As expected from the adsorption data, in the latter experiments the surface coverage was shown to be an important parameter for the desorption dynamics as well [214]. Analogous to the subsection on adsorption, first the translational and then the internal degrees of freedom will be reviewed in this subsection. A detailed comparison of the data on adsorption and desorption will then be given in Section 4.4. 4.3.1. Translational energy distribution of desorbing molecules Kolasinski and co-workers employed laser induced thermal heating of the silicon surface to measure time of flight distributions of the desorbing molecules [35]. By varying the flux of the incoming laser pulse (17 ns FWHM), temperatures up to ≈1500 K have been obtained on the surface. The desorbed molecules were then measured as a function of the time-offlight (TOF) as shown in Fig. 4 in the Introduction. Fitting

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Maxwell–Boltzmann distributions to the TOF spectra, fluxweighted mean translational energies were obtained. For the monohydride Si(001) surface, the desorption temperature was calculated to be Ts ' 920 K and the mean translational energy of the desorbing molecules was determined to be hE kin i = 166 ± 35 meV. For monohydride Si(111), the desorption temperature was Ts ' 1520 K and mean translational energy hE kin i = 224 ± 76 meV. In terms of the temperature of the desorbing molecules, those data transform to values only slightly above the surface temperature during the desorption process, e.g. 960 K for D2 desorbing from the Si(001) surface at Ts = 920 K. Although not investigated systematically, the experiment probed mainly desorption in the high coverage regime. The group of Namiki repeated this experiment under better defined experimental conditions [213,214]. They induced the desorption conventionally by temperature-programmed desorption (TPD) and used a stochastic mechanical chopper for the time-of-flight measurements of the continuously desorbing molecules with a quadrupole mass spectrometer [213]. Moreover, defined intervals of surface coverage could be probed [214]. This was accomplished by either starting the experiment with the monohydride covered surface but restricting the collected TOF data to a selected leading edge of the TPD peak or by starting at lower initial surface coverage θD0 and exploiting the whole TPD peak for the measurement of the respective TOF data. As depicted in Fig. 56, the following coverage intervals were probed with this concept: (i) 1.0–0.9 ML, (ii) 1.0–0.75 ML, (iii) 1.0–0.0 ML, (iv) 0.5–0.0 ML, and (v) 0.2–0.0 ML. The maximum of the desorption peak is located at about Ts = 780 K, well below the temperature probed by Kolasinski et al. [35]. Matsuno et al. [214] found that they could fit their data completely only when applying three different Maxwell fits with translational temperatures of 2500 K, 1500 K, and 800 K, respectively. More important, they observed the mean translational energy hE kin i to be shifted from hE kin i = 0.4 ± 0.04 eV to hE kin i = 0.2 ± 0.05 eV when increasing the averaged surface coverage probed in the respective experiment. This result is summarized in Fig. 57. Additionally, this graph shows the relative weight of the single fit functions for the fast, medium, and slow component of the desorbing molecules. The authors of Ref. [214] tentatively have assigned these three components to the three two-dimer reaction channels H2, H3, and H4 (the latter including the ν = 1 contribution which accounts for approx. 1% of the desorbing molecules), respectively, as they have been found in adsorption experiments. Whether such a close assignment between reaction channels in adsorption and desorption can be rationalized will be discussed in more detail in Section 4.4. Especially the fact that the saturation values for the different adsorption sites have been found to differ more than two orders of magnitude have raised the question on the importance of the H3 mechanism in desorption. In any case, the desorption experiments clearly show an increase of the mean translational energy of the desorbing molecules with decreasing coverage.

507

Fig. 56. TOF density spectra of D2 molecules desorbed from the D/Si(100) surface for various surface coverages. TOF data were collected for the coverage windows (i) 1.0–0.9 ML, (ii) 1.0–0.75 ML, (iii) 1.0–0.0 ML, (iv) 0.5–0.0 ML, and (v) 0.2–0.0 ML, as indicated by the hatched area of the TPD spectra in the insets. The thick solid lines show the best results when fitting the sum of three TOF functions to the data, i.e. a fast, a medium, and a slow component (thin lines). Reprinted with permission from Matsuno et al. [214]. c 2005, AIP.

When conventionally heating the surface to Ts,peak = 780 K, the values of hE kin i range from 0.2 eV for high surface coverage to 0.4 eV for low surface coverage. A value of hE kin i = 0.17 eV was reported for the experiments with laser-induced thermal heating of the surface to Ts = 920 K. Within the error margins and under the assumption that the LITD experiment mainly probed the high coverage regime, the experimental results can therefore be seen as consistent. On the other hand, a substantial contribution of the single-dimer process in desorption as recently suggested by Shi and coworkers [197] can be safely excluded on the basis of these results. The single-dimer path is calculated not only to have a higher adsorption barrier but, more important at this point, the barrier is difficult to reduce by means of lattice distortions [164, 172]. The mean translational energy in desorption is therefore expected to be similar to the mean adsorption barrier for this process, i.e. at least 0.6 eV or higher (compare also Section 4.4).

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Fig. 57. Mean translational energy hE kin i as a function of the five coverage windows (i) to (v), and thus of increasing average coverage. Additionally, the relative weight of the applied fit functions, denoted 2H, 3H, and 4H for fast, medium, and slow component, respectively, is shown for each of the probed coverage regime. Adopted with permission from Matsuno et al. [214]. c 2005, AIP.

4.3.2. Vibrational and rotational energy distribution of desorbing molecules Internal-state-resolved measurements of H2 , HD, and D2 desorbing from Si(001)2×1 may be regarded as the first experiments on the dynamics of hydrogen on silicon surfaces [209–212]. On Si(001)2×1 both the relative population of the rotational states [209] as well as of the ro-vibrational states [210] have been measured by Kolasinski et al. by means of temperature-programmed desorption of the hydrogen molecules using resonance-enhanced multiphoton ionization (REMPI) for the state-resolved detection of the desorbing molecules. In detail, a (2 + 1) REMPI scheme utilizing the E, F 1 Σg+ state as intermediate state was employed with a Nd:YAG-pumped dye laser producing the required ultraviolet radiation in the wavelength range of 200–215 nm. Maximum desorption was observed at 780 K ≤ Ts ≤ 800 K in agreement with earlier reported results (see above). A Boltzmann analysis of the rotational populations of hydrogen in the vibrational ground state and first excited vibrational state is shown in Fig. 58. When plotting the natural logarithm of the ion signal, which has been divided by the rotational state degeneracy (2J + 1) and the nuclear spin degeneracy (gN ), as a function of rotational energy, the slope of a straight line would indicate the temperature of the respective Boltzmann distribution. However, since the data in Fig. 58 do not unambiguously indicate such a distribution, Kolasinski and co-workers calculated the vibrational state dependent mean rotational energy , X X hE rot i(ν) = Nν J E J Nν J (24) J

J

with Nν J being the the population of the rotational state J in arbitrary units and E J being the rotational energy of that state. The reported values for hE rot i(ν = 0) are 345 ± 83 K, 451 ± 77 K, and 332 ± 57 K for H2 , HD, and D2 , respectively, and 348 ± 95 K, 385 ± 70 K, and 330 ± 54 K for hE rot i(ν = 1). These values indicate for all isotopes similar and significant

Fig. 58. Boltzmann plot of H2 thermally desorbed from Si(100)2×1. The data has been corrected for background contributions, surface temperature was Ts = 780–800 K. Solid lines are guides to the eye. The top dashed line represents a thermal rotational population of ν = 0 at 800 K. The lower dashed line represents the population of ν = 1 that would be expected for an 800 K distribution relative to the ν = 0 distribution. Vibrational heating is clearly observed. Reprinted with permission from Shane et al. [211]. c 1992, AIP.

rotational cooling (Trot ≈ 12 Ts ) of the desorbing molecules when compared to the desorption temperature Ts = 780 K. The strong rotational cooling was explained in the framework of the potential energy surface of the H2 /Si system: the frequencies responsible for the frustration of rotations decrease to zero towards the gas side. This leads to an adiabatic expansion in desorption and a corresponding cooling of the rotational degree of freedom [207]. The deviation from Boltzmann statistics can be explained best by considering the reverse process, i.e. adsorption of rotationally excited

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molecules [7]: At low J , steering helps to overcome the adsorption barrier. For intermediate J values, this effect is reduced because increased molecular rotation leads to an increased probability to turn the molecules out of the preferential orientation for dissociation. For high J values, increased translation–rotation coupling again increases the adsorption probability: Towards the transition state, the H–H distance is increased and as a consequence, for a given J , E rot is decreased. The excess energy is transferred to translational energy which helps to overcome the barrier in adsorption. As a consequence, in desorption the rotational cooling is strongest in the regime of medium J values [207]. With respect to the comparison of the mean rotational energies of H2 , HD, and D2 , similar values are expected for the symmetrical molecules H2 and D2 : If one neglects energy transfer to the substrate degrees of freedom, molecules of the same energy follow the same classical trajectories if they move on the same potential energy surface, regardless of the molecules’ mass [215]. For the asymmetrical HD molecule, however, a different potential surface applies and changes in the dynamics are expected. This is in agreement with the experiments of Kolasinski et al. [209], where indeed similar values for H2 and D2 and a higher mean rotational energy for HD molecules were reported. At this point, one should mention that the assumption of negligible energy transfer to the substrate of course does not apply in the case of the H2 /Si system. However, the difference between H2 and D2 might be small because of the pronounced mass mismatch between hydrogen and silicon as well as the stiffness of the silicon lattice. The population ratio Pν=1 /Pν=0 between the ν = 1 and ν = 0 state was obtained by integration over the populations of the J levels for these two vibrational states separately (considering the relative ionization probabilities of these states [216]). For H2 , HD, and D2 , Pν=1 /Pν=0 was found to be 0.0116 ± 0.005, 0.021 ± 0.015, and 0.081 ± 0.040, respectively. When compared to the vibrational population ratio as expected for a Boltzmann distribution, Pν=1 /Pν=0 = exp(−E(ν = 1)/kTs ), an enhancement of the experimentally determined Pν=1 /Pν=0 ratio by a factor of 25 ± 10, 17 ± 12, and 20 ± 10 for H2 , HD, and D2 , respectively, was observed [210]. Strong vibrational heating is known from various other adsorption systems, including H2 /Cu(111) and H2 /Cu(110) with similar vibrational enhancement reported [2,205]. It is generally explained in terms of an early barrier in desorption, i.e. the hydrogen molecule is significantly elongated in the transition state and the vibrational energy cannot be transferred completely to the translational degrees of freedom. Such a scenario was assumed to be likely for the H2 /Si system as well, the more as the initial separation ˚ for the inter-dimer of the hydrogen atoms is as high as 3.8 A configuration. It might be worth to note that the authors of Ref. [210] applied both, full peak integration and peak-height analysis to their data. Whereas the former one averages over the entire accessible coverage range, i.e. 0–1 ML, the latter probes a smaller coverage range around half the saturation coverage. Within the error bars, no difference for the rotational distributions was observed. However, unfortunately

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no comment was made on the effect on the vibrational distributions. The vibrational heating indicates a substantial energy barrier which has to be overcome by the desorbing molecules. Similar to the results obtained from measurements of the mean translational energy as a function of coverage (see Section 4.3), which suggest that molecules desorbing from midcoverage still have to overcome a barrier comparable to that when desorbing from low coverage, such a coverage dependent measurement of the internal state distribution would be of high additional value. Shane, Kolasinski and Zare also measured rotational and vibrational population of molecules desorbing from the dihydride surface [212]. They made use of the dihydride desorption peak in TPD at Ts = 660 K and found for this temperature a rotational distribution very similar to desorption from H/Si(100)2×1. A mean rotational energy equivalent to 345 ± 85 K was evaluated. The first vibrational state was found to be populated with 0.2% of the desorbing molecules. This is less than the value found for desorption from the monohydride surface, however the desorption temperature is lower for the dihydride and the overpopulation was found to be again about a factor of 20, close to the result on the monohydride surface [209,212]. From this observation, the authors of Refs. [209,212] concluded on a similar transition state for dihydrides and monohydrides. However, it should be noted that, e.g. calculations both for the single- and the two-dimer reaction pathway for the desorption from the monohydride surface can reproduce the vibrational heating in desorption equally well [174,217], although they are very different in the reaction scheme. Therefore such an observation seems to be a rather weak indication for a specific reaction mechanism. Moreover, recent results for desorption via the dihydride state have shown that this process may occur also via a pathway with a elongated H2 molecule in the transition state [218], thus it is not surprising to find vibrationally excited molecules after desorption. 4.4. Comparison of adsorption and desorption — detailed balance As already pointed out in Section 1.2, there is no doubt about the validity of detailed balance as such since it is a consequence of time reversibility of the investigated scattering problem. This time reversibility is also the major appeal point of the concept of detailed balance: From one direction of the reaction, one can directly conclude on the reverse process, and, moreover, discuss the problem in the direction which fits best our analytical tools and scientific intuition. The textbook example for this is well known: If we start a desorbing molecule on the saddle point of the respective PES, i.e. the transition state, and the curvature of the PES leads to a vibrationally excited molecule after desorption, detailed balance tells us that in the reverse process, i.e. adsorption from the gas phase, vibrational excitation will help to overcome the adsorption barrier, since the PES allows a good coupling between vibrational and translational degree of freedom. Such considerations have been applied with much success in gas-surface dynamics, e.g. for the H2 /Cu system [2].

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As we have seen in the previous sections, adsorption and desorption experiments are, however, rarely conducted under similar conditions and even much more rarely under equilibrium conditions, for which detailed balance again directly applies. As a consequence, comparison via detailed balance might be misleading. If comparison of adsorption and desorption via detailed balance leads to a contradiction at a first glance, one might therefore (a) check the applicability under the given experimental conditions (b) make sure that the correlation expected from detailed balance does not oversimplify the situation. The earlier discussions on hydrogen on silicon have indeed overlooked both points: The mostly debated observation of the H2 /Si system was the low mean translational energy of the desorbing molecules as reported in Ref. [35] in a seemingly contradiction to the high adsorption barrier as concluded from extremely low sticking probabilities at low surface temperature [17] and the high activation with increasing surface temperature [55,56]. This so-called barrier puzzle provoked many discussions on the applicability of detailed balance in the form discussed in Section 1.2 [35,44,173,175]. However, the two simple rules as stated above were not always correctly applied: Firstly, the desorption experiments were performed far off the experimental conditions applied for typical adsorption experiments, especially the surface coverage was very different. Secondly, the assumption that a high mean barrier in adsorption must lead to hot molecules in desorption is, even without detailed knowledge of the underlying PES, too naive as can be easily illustrated with the help of differently shaped adsorption functions, all having the same (high) mean adsorption barrier [111,180]. Whereas a narrow distribution of barriers around the mean adsorption barrier E 0 indeed leads to a mean translational energy in desorption which is comparable to E 0 , a broad distribution of barriers is found to result in mean translational energy in desorption that is strongly reduced compared E 0 . As in the preceding subsections, we will start this summary on the application of detailed balance first by comparing the effect of translational energy in adsorption and desorption in the low coverage regime. Further, the implications of low-barrier adsorption pathways on the desorption dynamics at higher coverage are discussed. At last, the limited data on the influence of internal degrees of freedom in adsorption and desorption are compared. 4.4.1. Translational energy According to Eq. (1) differential desorption flux Φdes (E kin ) and sticking probability s(E kin ) are connected via Φdes (E kin ) ∝ E kin exp(−E kin /kTs )s(E kin )

(25)

when measured perpendicular to the surface (normal incidence). In Fig. 59(a) sticking coefficients s0 (E kin ) obtained at Ts = 670 K on the clean surface are shown after conversion to desorption flux via Eq. (25). As a result, a mean energy of the desorbing H2 molecules of hE kin i = 0.27 eV is calculated, considerably lower than the derived adsorption barrier of E 0 ' 0.8 eV and comparable to the experimental value of Matsuno et al. for their lowest coverage range probed,

Fig. 59. (a) Differential desorption flux as obtained by applying detailed balance to sticking coefficients of H2 on clean Si(001)2×1 at Ts = 670 K (dots, cf. Fig. 49 [111]). The solid line represents the converted s-shaped adsorption function with a mean adsorption barrier of E 0 = 0.82 eV and a width of W = 193 meV, the dotted curve shows a distribution with same E 0 but smaller width W = 80 meV. The dashed line indicates a Maxwell–Boltzmann distribution with a mean desorption energy of hE kin i = 0.4 eV, thus comparable to the experimental results measured in desorption at low coverage and Ts = 780 K (cf. Fig. 57 [214]). For better comparison, the converted adsorption data have been extrapolated to Ts = 800 K and are also shown (dot-dashed curve). (b) Converted adsorption data for H2 dissociation at H4 sites on hydrogen pre-covered Si(001)2×1 at Ts = 350 K (dots, cf. Fig. 55 [184]). The solid line represents the converted adsorption function of the form sH4 = s1 + s2 exp(−E kin /W ) which fits the adsorption data very well. The dashed line indicates a Maxwell–Boltzmann distribution with a mean desorption energy of hE kin i = 0.2 eV, thus comparable to the experimental results at high coverage and Ts = 780 K (cf. Fig. 57 [214]). For better comparison, the converted adsorption data have been extrapolated to Ts = 780 K and are also shown (dot-dashed curve) together with the results obtained by Kolasinski et al. at Ts = 920 K (dotted curve, cf. Fig. 4 [35]).

hE kin i = 0.4 eV [214]. For a better comparison, a Maxwell distribution with hE kin i = 0.4 eV is also indicated in Fig. 59(a). The good agreement is obvious as well as the fact that most of the discrepancy can be attributed to the high energy part of the desorption flux, a range inaccessible to the adsorption experiment and therefore subject to higher error bars. To demonstrate the influence of the width of the adsorption function, a converted s-curve with mean adsorption barrier E 0 = 0.8 eV, but lower width parameter W = 80 meV is also shown in Fig. 59(a). It is clearly observable that only for such a small width parameter W the desorption flux is peaked around the adsorption barrier, thus leading to translationally hot molecules in desorption. A larger width parameter is a consequence of a larger distribution of barriers available on the surface, in the case

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of clean Si(001) due to thermally activated configurations with a higher reactivity. In thermal desorption, these thermally activated low-barrier pathways contribute much more to the desorption flux than the larger number of high-barrier pathways. This is understood in terms of the energy of the adsorbed hydrogen atoms being described by a Boltzmann distribution with surface temperature which strongly favours the low barrier channels. In other words, although many high energy pathways are present on the surface, only a few molecules possess the required energy and therefore most of them desorb via low-barrier pathways. Towards higher surface coverage, a shift of the mean translational energy in desorption towards smaller values was observed. For the coverage range between 0.9 and 1.0 ML, hE kin i ≈ 0.2 eV was reported [214]. A comparable Maxwell–Boltzmann distribution is shown in Fig. 59(b) together with the converted sticking coefficients for the H4 mechanism, which was shown to be operative in adsorption in the high coverage regime [191]. Also in this case, one observes the measured values for the desorption flux at in average higher energies than the converted adsorption data. The mean translational energies hE kin i range from 0.12 eV for the converted sticking data (calculated at Ts = 780 K and under the assumption that the sticking probability of the barrierless reaction channel does not change significantly with temperature) over 0.13 eV for thermal equilibration of the desorbing molecules with the surface, 0.17 eV for the desorption experiments performed at 920 K by means of LITD [35], and 0.2 eV obtained by TPD of the first 10% of surface coverage [214]. We note that (1) the values for the laser-induced desorption are lower than those of the TPD experiments, although they are obtained at higher temperature and presumably lower average surface coverage. (2) When we extrapolate the data of Ref. [214] to 1 ML coverage, we obtain hE kin i = 0.13 eV, which is in perfect agreement with the converted adsorption data. We therefore conclude that the adsorption and desorption experiments are, within the experimental error bars, in good agreement when detailed balance is applied to results from a limited surface coverage range. In the regime of very low coverage, ad- and desorption via the H2 pathway leads to a high mean adsorption barrier but a broad distribution of barriers at higher temperatures. Thus, in desorption, the molecules possess only little translational energy when compared to the mean adsorption barrier. Most of them desorb via thermally generated low-barrier reaction channels. Excess energy is stored in the substrate. Towards higher surface coverage, statically distorted adsorption sites induced by already adsorbed hydrogen lead to a higher sticking probability. Analogous, even lower mean translational energy is observed in desorption. In the extreme case of θ = 1 ML, desorption must proceed via the H4 mechanism because no H2 paths are accessible. The corresponding energy distribution of the desorbing molecules can be calculated from the energy dependent sticking coefficients for this process (hE kin i = 0.12 eV) and is in good agreement with the extrapolated value from desorption experiments (hE kin i = 0.13 eV). A more difficult scenario

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applies for the intermediate coverage range. Even at a given coverage, adsorption and desorption do not have to proceed via the same reaction channels, unless thermal equilibrium with the gas phase is established. The reason for this is the following: For adsorption via the H4 path the number of sites with two neighboring, singly occupied dimers is rate determining. However, for desorption via this channel, the number of sites with two neighboring doubly occupied dimers determines the desorption rate. Adsorption and desorption data can therefore only be compared via modeling the hydrogen distribution on the surface (compare Section 3.7). We note that Matsuno et al. [214] included a third desorption channel in the interpretation of their data. It was associated with the H3 adsorption site. Although this site shows a low mean adsorption barrier, the absolute sticking probabilities were found to be low. According to detailed balance, one consequently expects a low prefactor for the desorption probability. However, this might be overcompensated by a higher number of those sites and a lower desorption energy when compared to the H2 and H4 site. Matsuno et al. additionally suggested that excitation of the Si–H vibrations modes after diffusion might change the effective desorption barriers [214]. One should also note that so far we neglected in the discussion the molecules which are vibrationally excited after desorption. Although they are expected to possess a lower translational energy when compared to molecules in the ground state, the relative population was found to be only 1% at typical desorption temperatures of 780 K. For this temperature, and also for Ts = 920 K as applied for the LITD experiments, no significant contribution of vibrationally excited molecules to the TOF spectra is therefore expected. On the basis of the good agreement between experimental desorption and converted adsorption data, we do not see any indication which makes the introduction of defects, steps, or other minority sites for the interpretation of the desorption from Si(001)2×1 necessary. Further support for this conclusion, at least with respect to step sites, comes from experiments on the desorption kinetics on vicinal Si(001) surfaces. Raschke compared desorption from surfaces with different step density but did not observe any difference in the desorption kinetics [199]. One possible explanation for this observation might be found in experiments and calculations on the binding energy at DB sites. They were shown to exhibit an increased binding energy when compared to the flat surface [59,103]. Together with a lower prefactor, this might explain a minor contribution of those sites to the desorption process. Furthermore, the experimental results can be described without introducing electronic excitations, e.g. such as longlived electron–hole pairs [41]. 4.4.2. Molecular excitations Similar to the comparison of sticking functions and desorption flux for the molecules in the ground state, such a comparison is possible for vibrationally excited hydrogen molecules. However, for desorption, only data integrated over the whole range of translational energy are available.

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Nonetheless, the observed vibrational heating and the resulting ratio of molecules found in the ν = 1 state to those found in the ν = 0 state can be compared to the enhanced reactivity of excited molecules in adsorption via   Pν=1 E ν=1 = exp − Pν=0 kTs R∞√ E exp(−E/kTs )s(ν = 1, E)dE (26) × R0∞ √ E exp(−E/kTs )s(ν = 0, E)dE 0 which is applicable for molecules desorbing perpendicular to the surface [219]. As shown in Section 4.3.2, Kolasinski et al. [209,211] found Pν=1 /Pν=0 ≈ 1% at a surface temperature of Ts = 780 K. Since no adsorption data for this temperature are available, width parameters W (ν = 0) = 200 meV and W (ν = 1) = 80 meV for the adsorption functions of the ground and first excited state of the hydrogen molecules were used in Ref. [180] to reproduce this value of Pν=1 /Pν=0 . The values of the width parameter are in good agreement with the results obtained at the highest temperature realized in the adsorption experiment, Ts = 670 K [180]. Although the desorption measurements of Ref. [209,211] probed a surface in the mid-coverage regime and the adsorption measurements were performed at a coverage below 5%, detailed balance seems to be applicable in this case. This might be interpreted in two ways: Either two different reaction channels are operative in the two coverage regimes but show comparable dynamics with respect to the vibrational degrees of freedom. Alternatively, the same reaction mechanism might be operative predominantly both in the low- and mid-coverage regime. From the results of the energy resolved adsorption and desorption experiments discussed above, no great influence of the low-barrier pathways is expected in the low- and mid-coverage regime and the latter possibility is strongly favoured. No experimental information on the influence of rotations on the adsorption behaviour is available. 4.5. Angular distributions measured in adsorption and desorption Angular dependent measurements are a good tool to obtain information on the corrugation of the potential energy surface. In the case of the silicon surface with its highly localized dangling bonds, a pronounced effect was expected. In this subsection, first angular distributions measured in adsorption and desorption on the flat (001)-surface are reviewed and compared. A high directionality of the reaction is observed. Second, the angular distributions at step sites are discussed with focus on the correlation between angular distribution and kinetic energy of the incoming molecules. 4.5.1. Angular resolved sticking probabilities on flat surfaces Since many forms of surface relaxation and reconstruction tend to form domains which are rotated with respect to each other, angular resolved measurements often average over these domains. This would be true for flat Si(001) as well, since

monoatomic steps, which are always present on the nominally flat Si(001) surface, lead to a rotation of the dimer rows by 90◦ . However, with the help of vicinal surfaces, a pronounced predominance of one domain can be obtained [220]. In Ref. [200] such single-domain surfaces were used to measure the angular resolved sticking probability both parallel and perpendicular to the silicon dimer. In detail, the highly reactive adsorption sites at DB steps were pre-covered by dissociation of molecular hydrogen at Ts = 300 K which then takes place only at the step sites. Between the double-atomic height steps, the dimer rows are all arranged in parallel (compare Fig. 19). The angular dependence of the sticking coefficient at those terrace dimers was then measured at Ts = 500 K [200]. At this temperature, hydrogen diffusion from step to terrace sites is still negligible on the time scale of an adsorption experiment but the sticking probability is high enough to measure reduced sticking probabilities under glancing incidence. The results are summarized in the form of polar plots in Fig. 60 together with sketches of the corresponding surface geometry. In case of the H2 beam being incident parallel to the Si dimers (indicated by black bars in the sketches), the angular distribution is broad and has its maximum at the surface normal (Fig. 60(a)). Perpendicular to the dimers, in contrast, the distribution is sharply peaked and tilted by about 5◦ from the surface normal (Fig. 60(b)). This tilt is simply a consequence of the particular geometry of the vicinal surfaces in the way that it reflects the incline of the terraces with respect to the optical surface. Fitting cosine distributions to the data resulted in cos3 (ϑ) and cos12 (ϑ +5.5◦ ) parallel and perpendicular to the dimers, respectively [200]. The anisotropy reflected by the different exponentials is also apparent in Fig. 60(c) where the azimuthal dependence of s0 is plotted for a beam incident under a polar angle ϑ 0 = 45◦ with respect to the (001) direction. Many activated adsorption systems, especially H2 on metal surfaces, show a sharply forward-peaked angular distribution of sticking coefficients. In some cases, it was explained as a consequence of normal energy scaling [2], i.e. if only the component of the translational energy normal to the surface is relevant for overcoming the barrier, molecules hitting the surface under an angle have a smaller chance to stick. This means that the effective energy for the adsorption process is given by E eff = E kin cosn (ϑ) with n = 2 in the case of normal energy scaling. In earlier publications this relation was attributed to a smooth PES. Within this framework, n < 2 then represents the case where momentum parallel to the surface enhances sticking. It is generally correlated to a geometric corrugation of the PES, i.e. the distance between the (constant) adsorption barrier and the averaged surface varies. On the other hand, n > 2 is then correlated to an energetic corrugation of the PES, i.e. a variation of the barrier height as a function of the lateral position on the surface. However, a more detailed examination has shown that frequently both cases are combined and can lead to the case of ‘balanced corrugation’ with n close to 2 although the PES shows strong corrugation, both with respect to geometry and energetics [6].

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Fig. 60. Polar plots of the relative initial sticking coefficients s0 on the terraces of Si(001) as a function of incident polar angle ϑ and azimuthal angle ϕ. (a) Parallel to the dimers (ϕ = 0◦ ): the dashed line represents cos3.2 ϑ, solid lines indicate cos8 (ϑ ± 19◦ ) and the superposition of these curves. (b) Perpendicular to the dimers: the solid line describes cos11.6 (ϑ + 5.5◦ ), the dashed line indicates the distribution expected from normal energy scaling of the values from Ref. [111] (compare Fig. 49). (c) Azimuthal dependence obtained by rotating the sample around the normal of the terraces at ϑ 0 = 45◦ , i.e. ϑ = 39.5◦ for ϕ = 90◦ (filled dots); open circles indicate the variation of s0 for rotation around the optical surface normal; lines are guides to the eye. Reprinted with permission from D¨urr and H¨ofer [200]. c 2002, APS.

If one applies normal energy scaling to the energy dependent sticking coefficients for adsorption on flat Si(001) [111], these data result in the angular distribution indicated as a dashed line in Fig. 60(b). For comparison with the angular resolved measurements parallel to the dimer rows, this distribution has to be tilted by 5.5◦ to compensate for the inclined terrace surface normal in case of the vicinal normal. It is then only slightly broader than the observed angular dependence parallel to the dimer rows. This good agreement can be understood in terms of a balanced corrugation with both energetic and geometric corrugation of the PES along the rows. However, the energetic corrugation which narrows the impact area and causes focusing of the distribution along the surface normal of the terraces [106] seems to have a slightly stronger influence. On the other hand, geometric corrugation appears to be dominating in the case of the angular distribution perpendicular to the dimer rows since the measured angular dependence is considerably broader than the distribution expected for normal energy scaling [200]. In the approximation of pure geometric corrugation, the angular distributions of s0 can be traced back to specific shapes of the surface corrugation [221]. In the case of H2 /Si(001), the contribution of geometric corrugation was explained in a qualitative way on the basis of the directionality of the dangling bonds on the Si(001) surfaces [200]. If one assumes the tilt of the dangling bonds to correspond to the H–Si–Si-angle of the adsorbed hydrogen, i.e. to be close to the 109◦ of a tetrahedron [140], and further assumes that the most efficient pathway for H2 molecules to overcome the dissociation barrier is the movement in the direction of these dangling bonds then asymmetrical angular distributions are to be expected for the reactive subunits of two neighboured silicon dimers on terraces. Indeed, the broad angular distribution of Fig. 60(a)

can be well described by the superposition of two narrow distributions, each tilted by 19◦ as illustrated in Fig. 61. The tilted distributions on the flat surface are again compatible with the distribution measured parallel to the dimer rows, hence with normal energy scaling. They might be interpreted as the result of a ‘balanced corrugation’ with respect to the direction of the dangling bonds, i.e. with respect to a very local surface normal. The interpretation of the broad angular distribution as a superposition of two tilted, narrow distributions was further backed by the direct observation of such asymmetrical angular distributions for hydrogen dissociation at the steps sites of vicinal Si(001) [200]. Additionally, measurements of the sticking coefficient as a function of polar angle for flat, two-domain surfaces were conducted [200]. The angular distribution was found to be proportional to cos6–7 (ϑ) at Ts = 600 K and TN = 815 K. No pronounced dependence on surface temperature and beam energy for 600 K < Ts < 670 K and 500 K < TN < 1100 K was observed. Comparison with the superposition of the two distributions determined for the single domain surface, which yields a distribution very close to cos7 (ϑ), confirmed the measurements on the single-domain surface. 4.5.2. Angular resolved sticking at step sites A representative set of data for a relatively broad angular sticking distribution at sites with low mean adsorption barrier was found when measuring the sticking probabilities at the reactive sites of double-atomic height DB steps as a function of polar angle [200,222]. For a beam energy of 0.07 eV and a surface temperature of 500 K, e.g., a distribution significantly broader than on the terraces was observed, both, parallel and perpendicular to the steps [200]. Interestingly, for

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Fig. 61. Sketch of a pair of symmetrized dimers with two reactive subunits on the right and on the left. The respective angular distributions of the sticking probability are also included.

the beam incident parallel to the step edges the distribution was found to be forward-peaked and symmetrical. In the direction perpendicular to the steps, however, the distribution is asymmetrical and exhibits a clear preference for the adsorption of molecules incident from the direction of the lower terrace (Fig. 62). Moreover, a clear difference was observed in the energy scaling parallel and perpendicular to the surface [222]. The sticking probabilities parallel to the step edges follow normal energy scaling for kinetic energies smaller than the mean adsorption barrier (E 0 = 0.08 eV) and depart from this behaviour only for energies higher than E 0 . For the latter condition, a sharply forward-peaked angular distribution was observed representing n > 2. Such a behaviour with a transition

from n = 2 to n > 2 for increasing kinetic energy of the incoming molecules is indicative of the predominance of an energetic corrugation parallel to the step edges. In contrast, the sticking probabilities measured perpendicular to the step edges as shown in Fig. 62 exhibit extremely broad angular distributions for kinetic energies below the mean adsorption barrier, i.e. n < 2 (Fig. 62(b)). The resulting transition of the energy scaling from n < 2 at low energies to n > 2 for beam energies well above the adsorption barrier (Fig. 62(a)) indicates a clear predominance of geometric corrugation in the direction perpendicular to the step edges [222]. In summary, direct indication for both energetic and geometric corrugation was observed for the H2 /Si system. Both on the flat surface as well as at the step sites of Si(001), the covalent character of the broken bonds leads to a strong directionality of the H2 dissociation reaction. In the case of adsorption at the dimers of the flat Si(001) surface, this directionality can lead to a preferential adsorption on one side of the dimer, depending on the angle of incidence; in other words the reaction can be stereochemically controlled [200]. 4.5.3. Angular resolved desorption from flat surfaces and comparison with adsorption The reported angular resolved measurements of the desorption flux lack in part the level of detail of the adsorption measurements since they have been performed on two-domain surfaces [21,223]. Nonetheless, combined with time-resolved detection of the desorbing molecules, they give complementary information to the adsorption data. In an early experiment, Park and co-workers [21] investigated thermal desorption of H2 /Si(001) in the coverage regime θ = 1 ML to θ = 0.6 ML. They reported cosm (ϑ) distributions with m = 3.9 to 5.2 for θ = 1 ML to θ = 0.6 ML, respectively. According to detailed balance, the desorption flux

Fig. 62. Initial sticking coefficients s0 on the DB step sites of Si(001) as a function of incident polar angle ϑ perpendicular to the step edges (ϕ = 90◦ ), (a) E kin = 0.35 eV, (b) E kin = 0.03 eV. The solid lines indicate a dependence s0 (ϑ) ∝ cos3.5 (ϑ − 6◦ ) in (a) and s0 (ϑ) ∝ cos0...1.2 (ϑ) in (b). The dashed line shows a distribution peaked along the (001) direction, cos3.5 (ϑ + 5.5◦ ) in (a) and cos1.2 (ϑ + 5.5◦ ) in (b), for better comparison. From Stanciu et al. [222].

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very similar to the data of Park et al. at a surface coverage of θ = 0.6 ML [21]. 4.6. Quantum dynamics calculations

Fig. 63. Experimentally determined angular distributions of D2 desorption yield Y (ϑ) (dots [223]). The dot-dashed line, cos5.2 ϑ, represents the experimental data from [213]. The solid line is a fit of equations (1) and (18) to the data of Ref. [223] using the parameterization of Ref. [111] for s0 (E kin ) with W (780 K) = 0.195 eV and n = 1.4 for the energy scaling. The dashed line represent a cos ϑ distribution, for comparison. Reprinted with permission from Shibataka et al. [223]. c 2003, APS.

Φdes at a given energy can be calculated from the adsorption data via Φdes (ϑ) ∝ cos(ϑ) × s(ϑ).

(27)

With this, the measured adsorption data translate to Φdes ∝ cos7–8 (ϑ) for desorption in the limit of low coverages (θ ≤ 0.1). If we neglect the fact that the measured distribution in desorption integrated over a range of energies, the larger exponent resulting from the adsorption experiments thus confirms the trend towards a sharpening of the distribution with reduced coverages that is apparent in the desorption experiments [21]. The broader distributions found at higher coverage might be interpreted as a further indication that the additional, low-barrier reaction channels (H3, H4), present at higher coverage, contribute substantially to the measured desorption flux and therefore lead to an angular distribution with a less pronounced dependence of s0 on the angle of incidence ϑ. In a more recent experiment, Shibataka and co-workers measured time-of-flight spectra of D2 molecules desorbing from Si(001) as a function of polar angle [223]. The experiment averaged over a surface coverage between 0.8 ML and 0.1 ML. The mean translational energy was found to decrease with increasing angle off the surface normal, similar to the results on Cu surfaces [38]. The authors of [223] applied detailed balance to the adsorption data of Ref. [111] and could reconcile the two sets of data when using n = 1.4 for the energy scaling E eff = E kin cosn (ϑ) (Fig. 63). However, a relatively wide spread of 1 < n < 2 is acceptable within the error bars of the experimental data. The low exponential for the energy scaling goes along with a relatively broad angular distribution of the desorption yield when the data were integrated over all energies, which was found to be proportional to cos5.2 (ϑ),

Up to now most of the theoretical results concerning the dynamics of the H2 /Si system have been obtained by calculations based on model potential energy surfaces (PES). In this subsection we give an overview of the main results. For a more detailed discussion the reader is referred to the comprehensive review by Brenig and Hilf [207]. Calculations based on ab initio derived PES’s [174,175] and ab initio molecular dynamics calculations [176,224,225] will only be touched very briefly as they have been exclusively performed for the one-dimer or the dihydride pathway but not for the twodimer reaction mechanism. So far in this review, the adsorption dynamics on clean Si(001) and the pronounced dependence of sticking probability on surface temperature has been discussed in terms of thermally activated surface configurations which exhibit a lower adsorption barrier when compared to the mean adsorption barrier. To fully account for such a situation theoretically, the coupling between the molecule’s degrees of freedom and the lattice excitations of the surface have to be taken into account. Brenig and co-workers were the first ones to rationalize the importance of lattice distortion for hydrogen dissociation and included a lattice degree of freedom besides a general reaction coordinate in their model potential for hydrogen adsorption on Si surfaces [44]. This work was initially motivated by the ‘barrier puzzle’ and the seeming contradiction of low sticking probabilities at moderate surface temperatures and only little translational heating in desorption. The results of their earlier calculations based on a two-dimensional PES have been presented in the introductory Section 1.3. Subsequently, Brenig and co-workers added the H–H distance to their model potential and also investigated the influence of a one-dimensional surface corrugation [106, 226]. Hilf and Brenig then performed quantum mechanical dynamics calculations with a five-dimensional (5D) model potential, including the H2 -surface distance, the H–H distance, a displacement of the substrate lattice, and two coordinates for the surface corrugation [217]. They adjusted the parameters of the model potential such that they could fit the experimental data of s0 (E kin ) from the respective molecular beam experiment [111] (cf. Fig. 49 in Section 4.2.1) as well as the vibrational heating measured for desorbing molecules [210]. The good agreement between experiment and theory is illustrated in Fig. 64; the adsorption barrier of the respective model potential was E ads = 0.72 eV [217]. The final 7D model potential also includes molecular orientation [207]. With such an optimized potential energy surface, the influence of the various degrees of freedom are then inspected best by low dimensional cuts through the PES: The importance of the lattice substrate on the reaction dynamics is illustrated in Fig. 65 where the wave function density of the incoming and outgoing molecules is shown on 2D contour plots of the model PES as function of the reaction path coordinate s and

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Fig. 64. Comparison of calculated sticking coefficients (lines) and experimental beam data (symbols, cf. Fig. 49, Ref. [111]) as a function of kinetic energy for three different surface temperatures. Thin lines correspond to the adsorption of molecules in the vibrational ground state (ν = 0), calculations indicated by thick lines additionally account for vibrationally assisted sticking with Tvib = TNozzle . Adopted with permission from Hilf and Brenig [217]. c 2000, AIP.

the lattice displacement. s is a function of the H–H distance and the H2 -surface distance. An incident molecule with 0.2 eV translational energy is seen to be almost completely reflected as indicated by the interference pattern in the entrance channel (Fig. 65(a)). The small transmitted component is many orders of magnitude lower and invisible in the plot. The corresponding plot for desorption starts with a translational energy of 0.1 eV on the barrier (Fig. 65(b)). During desorption only a small part of the potential energy at the barrier is converted into centre-ofmass kinetic energy, but most of it remains as excitation energy

in the lattice showing up in Fig. 65(b) as a large-amplitude oscillation of the wave function. A typical elbow-shaped equipotential contour plot that illustrates the effect of molecular vibrations is reproduced in Fig. 66. The barrier is at an intermediate elongation of the H–H inter-atomic distance of 35% above the gas phase value, the value calculated in Ref. [162] for the single-dimer pathway. The density plot of the desorption wave function shows a strong coupling between molecular vibrations in the ν = 1 state and the centre-of-mass movement in the exit channel. Related to this vibrational heating in desorption is vibrational assisted sticking as discussed above [207]. The surface corrugation results in a strongly forward-peaked distribution as illustrated in Fig. 67. It shows the desorption wave function obtained from a 3D calculation involving the two dominant coordinates s and y as well as one lateral coordinate x projected onto the two coordinates s and y. Obviously, only a small fraction of the unit cell contributes to desorption. In line with the results of direct conversion of sticking probabilities to desorption flux distributions, Brenig and Hilf [207] inferred a higher mean desorption energy of about twice the thermal energy in very good agreement with the recently published data [213]. Additionally, they could show that molecular rotations can be treated by a reduced prefactor for the sticking probabilities, known as the so-called ‘pinhole effect’, when they compared their results to 5D calculations without corrugation but including molecular rotations. When comparing the results of the rovibrational population of the desorbing molecules to the experimental data, they find almost perfect agreement with respect to the rotational cooling and the non-Boltzmann behaviour (cf. Section 4.3.2). Calculations at lower dimensions (3D) but based on ab initio derived potential energy surfaces [174,175] were so far performed exclusively for the intra-dimer reaction pathway [161,162]. A general result of these calculations was that there is some lattice energy stored in the transition state, a

Fig. 65. 2D Contour plots of the model PES as function of the reaction path coordinate s and the Si displacement with the density of a projected 3D wave function (including molecular vibrations v). (a) Adsorption and (b) desorption. The spacing between the contours is 100 meV. Reprinted with permission from Brenig and Hilf [207]. c 2001, IOPP, Institute of Physics Publishing.

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did not change this picture substantially. In retrospect, these theoretical findings are in good agreement with the more recent experimental results, that the intra-dimer reaction pathway is not operative under standard experimental conditions. Lattice distortions are not as effective in lowering the adsorption barrier for this pathway as for the inter-dimer reaction channel. 4.7. Comparison of H2 /Si and H2 /Cu Table 8 Adsorption barriers E 0 for the sticking of D2 /H2 in different vibrational states ν on Cu(111) [236] and on Si(001)2×1 [180], respectively. Ts was 120 K for Cu and 90 K for Si

H2 /Cu(111) H2 /Si(001) Fig. 66. Density plot of a desorption wave as a function of the H2 -surface distance and the H–H inter-atomic distance obtained from a 3D calculation. Reprinted with permission from Brenig and Hilf [207]. c 2001, IOPP.

Fig. 67. Density plot of a desorption wave as a function of the reaction coordinate s and the lateral coordinate y extending over one unit cell as obtained from a 3D calculation. Reprinted with permission from Brenig and Hilf [207]. c 2001, IOPP.

finding which was attributed to the de-buckling of the silicon dimer during the adsorption process. Moreover, as a very important result, it could be shown that such a substrate energy leads to the activation of sticking probability with surface temperature. However, the effect was found to be small in all the investigations. Kratzer and co-workers, e.g. calculated an activation of sticking with surface temperature of E A = 0.3 eV for 100 meV molecules [174]. In the calculations by Luntz and Kratzer the influence of surface temperature was even weaker with E A = 0.04 eV for 250 meV molecules [175]. Both calculations were based on an ab initio derived PES with an adsorption energy barrier of 0.4 eV, but only 0.1 eV stored in the substrate lattice at the transition state [162]. Ab-initio molecular dynamics calculations with supercells [176] and clusters [224]

E 0 (ν = 0) (meV)

E 0 (ν = 1) (meV)

E 0 (ν = 2) (meV)

630 ≥600

290 390 ± 30

100 180 ± 50

The adsorption system of molecular hydrogen on copper surfaces, especially on Cu(111), has been investigated by means of molecular beam techniques since more than 30 years [39,227]. Within this long period, the system has emerged as a cornerstone on the way of a clear understanding and interpretation of molecular beam experiments and results. This is especially true with respect to the influence of vibrationally excited molecules on the sticking probabilities when being measured with supersonic molecular beams from hot nozzle sources [228–231]. Other new techniques in gas surface dynamics research [232,233] as well as theoretical methods [6– 8] were also pioneered with the H2 /Cu system and it can be therefore seen as the model system for activated dissociation on metal surfaces. In comparison with the H2 /Si system, some surprising similarities were found despite the very different surface properties which are expected when a metal surface with highly delocalized electrons is compared to a semiconductor system, which is governed by the localized covalent bonds and their breaking at the surface. In the following, experimental results, obtained for both systems are compared as far as comparable sets of data are available. The differences of the two systems are highlighted. They were found to be most pronounced with respect to the influence of surface temperature on the reaction dynamics. 4.7.1. Energy dependence of sticking and influence of vibrational excitations The influence of translational and vibrational energy of the impinging hydrogen molecules was measured most comprehensively by means of seeded molecular beam techniques by Rettner and co-workers [231]. The results are depicted in Fig. 68. Clear activation with translational energy is observed. Moreover, a reduced adsorption barrier with respect to translational energy for vibrational excited molecules was evaluated from the data when applying the adsorption functions of Eq. (23). The results are summarized in Table 8 and compared to the results for H2 /Si(001)2×1. Apparently, both systems show a similar height of the mean adsorption

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Fig. 68. Initial sticking coefficients s0 for D2 on Cu(111) as a function of normal energy. The data were obtained by the use of seeded beam techniques and varying angle of incidence. The solid lines represent fits of Eq. (23) to the data. Reprinted with permission from Rettner et al. [231]. c 1992, APS.

barriers E 0 and a comparable reduction of E 0 for vibrationally excited molecules. In general, the barriers for D2 /Cu(111) are somewhat lower than for H2 /Si(001). It is also worth noting that the saturation value for the former system was found to be 0.2, whereas for the latter one values approximately one order of magnitude smaller were reported. Although detailed calculations for the H2 /Cu system have shown that on metal surfaces a strong energetic corrugation also exists [234, 235] (for a more detailed discussion, see also below), the difference in saturation values may point towards an even stronger restriction on active-site-area for the H2 /Si system. The reduction of barrier height for vibrationally excited molecules in both systems indicates a late barrier in adsorption for H2 /Cu and H2 /Si. 4.7.2. Energy distribution in desorption Since much of the interest in the H2 /Si system was based on the seeming discrepancy between high adsorption barrier and low excess energy in desorption, such a comparison is also of interest for the H2 /Cu system. Murphy and Hodgson measured state-resolved time-of-flight distributions of hydrogen desorbing from Cu(111) by means of REMPI. Typical data are depicted in Fig. 69 for three different desorption temperatures. The distributions for molecules in the vibrational ground state are all peaked between 400 and 500 meV, with mean desorption energies around 550 meV, close to the mean adsorption barrier as determined by adsorption measurements [231].

Fig. 69. Flux weighted translational energy distributions P(E) for H2 (ν = 0, J = 1) as a function of Ts . The solid curves through the data are the results of fitting P(E)(E > 200 meV) using s-shaped adsorption functions s0 (E) as in Eq. (18) but using the error function instead of tanh. Reprinted with permission from Murphy and Hodgson [237]. c 1998, AIP.

Therefore, in contrast to the H2 /Si system, hydrogen molecules desorbing from the copper surface experience a much more accelerating potential and most of the excess energy in the transition state is transferred to the molecular degrees of freedom, especially the translational energy of the molecules. From this observation, one can conclude on a different coupling between the lattice degrees of freedom and the desorbing molecules when comparing the metal–hydrogen system with the semiconductor–hydrogen system. 4.7.3. Influence of surface temperature on sticking probability The first time that an influence of surface temperature on the sticking probability was considered for the H2 /Cu(111) system dates back to 1992. Michelsen and co-workers introduced the idea of an increasing width of the s-shaped adsorption functions with increasing surface temperature, in order to reconcile sticking probabilities measured at low surface temperature with angular distributions of hydrogen desorbing from Cu(111) at elevated temperature [238]. Qualitatively similar results, but with a stronger dependence of W on Ts have been reported more recently by Murphy and Hodgson [237] who fitted converted sticking functions   A E kin − E 0 s0 (E kin , Ts ) = 1 + erf (28) 2 W (Ts ) to their measured desorption data. Here it might be again worth mentioning that both tanh and error function are used in literature to represent s-shaped adsorption curves. In the case of H2 on copper, it was found that the error function with its stronger decrease towards lower energies represents the data

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better than the tanh function [205]. For hydrogen on silicon the opposite applies, i.e. the tanh with its exponential increase of s0 at low energies represents the measured adsorption data best [111]. For the H2 /Si system, the increase of W with surface temperature was interpreted as an indicator of the strong interaction between surface motion and adsorption barrier and the broad adsorption functions explained on the other hand the low mean translational energy in desorption. The more surprising it is at a first glance that on copper not only the width parameter increases with surface temperature but, moreover, the calculated activation energy for promoting sticking of low-energy molecules with surface temperature was found to be comparable to the mean adsorption barrier. Murphy and Hodgson calculated comparable activation with surface temperature and gas temperature for low surface temperature and translational gas temperatures above 500 K [237]. This raises the question of whether the influence of the surface atom motion on the reaction dynamics is, against intuition, of the same importance for metal and semiconductor surfaces. To shed light on the problem, width parameters for both systems are plotted as a function of temperature in Fig. 70. Although the silicon data are better reproduced by tanh functions, fitting the error function also yields reasonable results [111] and the respective width parameters are used in this figure for better comparison. For both systems, a linear dependence is observed. However, H2 /Cu exhibits a much smaller slope and a positive value for W (Ts = 0). H2 /Si, on the other hand, exhibits the higher W values, a stronger dependence on Ts and a negative value for W (Ts = 0) when extrapolating the data. With respect to the latter point, it was argued that towards lower surface temperatures a flattening of W (Ts ) can be expected [111]. From the comparison of W (Ts ) it becomes clear that indeed the coupling between the barrier distribution on the surface and the surface temperature is much more pronounced in the case of the semiconductor surface. As a result, the broad distributions, which correlate to the large width parameters, lead to the shift of the mean translational energy in desorption to values much lower than the mean adsorption barrier, in contrast to comparable values of hE kin i and E 0 in the case of hydrogen adsorption on copper. So how can the activation energy for surface-motion-assisted sticking then be so similar for the silicon and copper surface, i.e. E A (E kin = 50 meV) = 0.545 eV for H2 on Cu(111), and E A (E kin = 70 meV) = 0.66 eV for H2 on Si(001)? Here one has to note that the activation energies are evaluated from a limited range of surface temperature. Fig. 71 depicts the dependence of log(s0 ) as a function of inverse temperature using the linear dependence of W (Ts ) in combination with Eqs. (18) and (28). Although the depicted temperature range is larger than typically plotted, for the copper system the whole range is covered by experimental values, assuming that the saturation value A does not change with temperature (A has been chosen arbitrarily but constant in Fig. 71). For the H2 /Si system the experimentally accessible range is much smaller, nonetheless the difference between the two systems

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Fig. 70. Width parameter W as a function of surface temperature for H2 /Cu (ν = 0, J = 1; 3; 5) [2,237] and H2 /Si (ν = 0) [111]. Since for both data sets the error function was used for the parameterization of s0 (E kin ), the values for H2 /Si deviate from those shown in Fig. 51 where the tanh function was applied.

is obvious. Whereas between 400 and 700 K both curves can be approximated by a straight line, clear deviations can be seen for lower temperatures. The similar activation energies reported for H2 /Cu and H2 /Si therefore might be regarded rather as a coincidence than it can be taken as an indicator for similar coupling between the motion of the surface atoms and reaction dynamics for both systems. 4.7.4. Influence of molecular rotations Measurements of the rotational state distributions have shown qualitative similarities between the H2 /Cu(111) [205, 239] and the H2 /Si(001) [211] system. In both cases, rotational cooling and deviations from a Boltzmann distribution were

Fig. 71. Arrhenius plot with s0 (E kin = 50 meV) as obtained from the linear dependence of W on Ts for H2 /Cu and H2 /Si. Inset: close up of the experimentally most accessible temperature range.

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observed. The latter effect was explained in Section 4.3.2 for the H2 /Si(001) system and the same explanation was strengthened in the case of H2 /Cu(111) by means of measurements of time-of-flight distributions for the different ro-vibrational states [205]. With respect to the rotational cooling, a stronger effect was observed in the case of H2 /Si(001), i.e. Trot ≈ 0.5Ts , whereas for H2 /Cu(111), the effect is less pronounced, Trot ≈ 0.8–0.9Ts . This difference might be rationalized within the explanation that the rotational cooling is a consequence of the fact that the rotations are frustrated at the transition state. On the copper surface, the frustration of rotational motion in the transition state might be less pronounced than in the case of the covalently bound silicon surface which then leads to a less pronounced rotational cooling for the former system as well. 4.7.5. Surface corrugation and angular distribution of sticking probabilities The successful application of normal energy scaling to the angular resolved sticking measurements of H2 on Cu(111) [231] was earlier interpreted as the result of a rather smooth potential energy surface with respect to lateral variations of the H2 -surface interaction. The broadening of the strongly forward-peaked distributions of desorbing molecules at higher desorption temperatures was correlated to the increase of the width of the adsorption functions [238]. However, DFT calculations suggested a strongly corrugated PES [234, 235] and the results were reconciled with the experimental observations by means of the concept of ‘balanced corrugation’, i.e. counterbalancing effects of energetic and geometric corrugation [6]. More recently, by analyzing their energy resolved desorption measurements and by comparison of transformed adsorption functions with earlier reported angular resolved desorption distributions [238], Murphy and Hodgson concluded on an energy-dependent energy scaling with n < 2 for low energies and n ≥ 2 for energies above the mean adsorption barrier [237]. This behaviour was interpreted as an indicator for geometric corrugation of the surface dominating the adsorption–desorption dynamics at low energy. Direct evidence for such a geometric corrugation was also observed for H2 /Si(001) when measuring the angular distribution of sticking probabilities perpendicular to the dimer rows [181]. It was tentatively interpreted as a direct result of the strong directionality of the Si–H bond and a correlated angular dependence of the reactivity of the dangling bonds prior to adsorption of hydrogen. On the other hand, parallel to the dimer rows a dominance of energetic corrugation was observed. For hydrogen dissociation at DB steps on Si(001), geometric corrugation was observed perpendicular to the step edges by comparison of angular distributions of s0 at beam energies well below, around, and well above the mean adsorption barrier. Parallel to the step edges, energetic corrugation was found to be dominant. In summary, whereas the strong directionality of the dangling bonds on the silicon surface lead to a change between energetic and geometric corrugation depending on dimer orientation, a geometric corrugation seems to be dominant in the case of the copper surface with its delocalized electrons.

5. Hydrogen on Si(111)7×7 In distinct contrast to the rather simple 2×1 or c(4×2) reconstructions of the Si(001) surface, Si(111) reorganizes in a complicated 7×7 unit cell which has become the textbook example of semiconductor surface reconstruction. It is well understood in the framework of the dimer-adatom-stackingfault (DAS) model of Takayanagi and co-workers [107,240]. The originally 49 dangling bonds of the 7×7 unit cell are reduced by more than a factor of two to 19 dangling bonds by adatoms, the formation of dimers and the introduction of a stacking fault. The resulting structure, which is stable up to more than 1100 K, is shown in Fig. 72. With respect to the reactivity towards molecular hydrogen, this very different surface reconstruction might be seen as a good test for the general applicability of the dynamical features observed for Si(001). Indeed, time and again, comparison between H2 reaction on Si(111) and on Si(001) has been applied to determine whether the rather pronounced difference in reconstruction also influences the reactivity of the surface with respect to molecular hydrogen. Different desorption kinetics, e.g. led to models specific to the respective reconstruction [15]. On the other hand, similarities in the desorption dynamics [211] as well as comparable activation of sticking with surface temperature [55,56] was used to argue in favour of a transition state more or less independent on surface reconstruction. In the following, adsorption and desorption dynamics of H2 on Si(111)7×7 are summarized and the possible adsorption pathways are reviewed. A short comparison with H2 /Si(001) is presented. 5.1. Dynamics of adsorption A combined molecular beam and SHG experiment similar to that one used for the measurement of sticking coefficients of H2 on Si(001) was used to measure s0 for hydrogen dissociation on Si(111) [180]. The respective sticking probabilities are shown as a function of nozzle temperature in Fig. 73 for four different surface temperatures. For comparable surface temperatures, s0 on Si(111) is in general smaller than on Si(001), in agreement with the results reported for adsorption of thermal gases [56]. Similar to the behaviour on Si(001), two regimes were distinguished. At TN ≥ 1200 K, the sticking coefficient increases strongly with nozzle temperature due to the onset of vibrational assisted sticking. The mean barrier E 0 (ν = 1) and saturation value A(ν = 1) were found to be similar to those of Si(001) but a smaller width parameter W (ν = 1) ≈ 40 meV was obtained. A less pronounced dependence of s0 on nozzle temperature at lower nozzle temperatures was attributed to the influence of kinetic energy of the ground state molecules. In this low energy regime, the sticking coefficients on Si(111) exhibit a strong dependence on surface temperature Ts . For higher Ts , one observes a higher overall sticking probability and in general a lower activation with kinetic energy. In the case of Si(001), the whole data set was well described by using s-shaped model functions (23) with width parameters W (ν = 0) that monotonously increase as a function of surface

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Fig. 72. Schematic representation (top view and side view) of the Si(111) surface when reconstructed in the 7×7 unit cell as described by the DAS model.

temperature [111]. For Si(111), the correlation between the sticking coefficient as a function of kinetic energy and surface temperature is not as simple. The energy dependence of the data, e.g., is smaller for Ts = 600 K than for Ts = 666 K. A description via s-shaped adsorption functions with one common mean adsorption barrier E 0 and only the width of the distribution being dependent on surface temperature matches the data in this region rather poorly (Fig. 73). The data were nonetheless fitted by such a set of s-shaped adsorption functions with E 0 = 0.8 eV and a saturation value A = 10−2 . A linear increase of the width parameter with surface temperature from W = 120 meV at Ts = 535 K to W = 230 meV at Ts = 727 K was derived. The comparison with the results of Si(001) (see inset of Fig. 73) shows that in the experimentally accessible range of Ts the temperature dependence of W is stronger in the case of Si(111). The differences between the results of Si(001) and Si(111) can be further illustrated with the help of an Arrhenius plot (Fig. 74) of the sticking coefficients. Within the limited range of accessible sticking coefficients, the activation of s0 with surface temperature is lower for TN = 297 K (apparent activation energy E A = 0.7 eV) than for TN = 815 K (E A = 0.9 eV). However, for TN = 297 K and Ts = 535 K the value of s0 is below 10−8 , the detection limit of the experiment. As a consequence, we conclude that the data for TN = 297 K cannot exactly follow the Arrhenius law in the given temperature range, in contrast to Si(001), where for all nozzle temperatures a good Arrhenius-like dependence on surface temperature was found. Activation with Ts for TN = 297 K should therefore actually be higher than the value extracted from Fig. 74. This would then be in agreement with the results obtained for the adsorption of thermal gas [55,56,106] where the activation with surface temperature was found to be higher in the case of Si(111) (E A ' 0.9 eV) than for Si(001) (E A ' 0.7 eV).

Fig. 73. Initial sticking coefficients of H2 on Si(111)7×7 as a function of nozzle temperature TN for various surface temperatures Ts . The solid lines are fits of s-shaped adsorption functions (Eq. (18)) with a common mean barrier E 0 (ν = 0) = 820 meV and E 0 (ν = 1) = 390 meV. The inset shows the strong dependence of the width parameters W (ν = 0) for Si(111)7×7 (filled squares) on surface temperature in comparison to Si(001) (open squares). Reprinted with permission from D¨urr and H¨ofer [180]. c 2004, AIP.

5.2. Dynamics of desorption Laser-induced thermal desorption of H2 from Si(111) by Kolasinski and co-workers revealed a mean translational energy

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Fig. 74. Arrhenius plots of initial sticking probability s0 of H2 on Si(111) (filled symbols) and on Si(001) (open symbols). For Si(111) the dependence on surface temperature is compared to the results obtained with thermal gas (dashed line) [55]. Reprinted with permission from D¨urr and H¨ofer [180]. c 2004, AIP.

of the desorbing molecules of hE kin i = 225 ± 70 meV at Ts = 1520 K [35]. This value can be compared to the adsorption data by application of detailed balance to the latter ones. When the converted adsorption data are fitted by a fluxweighted Maxwell distribution Φ ∝ E exp(−E/kTM ) a mean translational energy in desorption of hE kin i = 2kTM = 400 meV is evaluated for Ts = 727 K [180]. Due to the uncertainty of the shape of the distribution in the high energy tail, this value should be regarded as an upper limit. A converted s-shaped adsorption function yields hE kin (Ts = 727 K)i = 345 meV for the same data [180]. Like the LITD result, these values are considerably lower than the mean adsorption barrier. However, the converted adsorption data yield higher mean translational energies than the LITD experiments. This can be explained in part by the fact that, again, adsorption experiments were performed in the low coverage regime but the desorption experiments averaged over a wider range of surface coverage. From earlier adsorption measurements with thermal gas, it is known that the sticking probability increases with surface coverage on Si(111) (compare Fig. 14). These results were interpreted in terms of a reduced barrier with increasing coverage due to next neighbor correlations [106]. Such a reduced adsorption barrier could in turn also account for the lower translational energies in desorption as found in the LITD experiment. Unfortunately, time-of-flight measurements for different coverages, as available for Si(001), do not exist for Si(111) to back this explanation. For such measurements, application of detailed balance would predict an increase of translational heating with decreasing surface coverage for the Si(111) surface, comparable to the H2 /Si(001) system.

Fig. 75. Boltzmann plot of H2 thermally desorbed from the Si(100)2×1 and Si(111)7×7 surfaces. The rotational distributions are shown for both the ν = 0 and ν = 1 vibrational states. The relative positions of the H2 (ν = 0) and the H2 (ν = 1) rotational distributions accurately represent the measured H2 (ν = 0) to H2 (ν = 1) population ratio. Reprinted with permission from Shane et al. [211]. c 1992, AIP.

When measuring the ro-vibrational population of hydrogen molecules desorbing from Si(111), very similar results as on Si(001) were obtained by Shane et al. [211] (Fig. 75). The mean rotational energy was found to be 385 ± 65 K and 300 ± 70 K for the ground and first vibrationally excited state, respectively, well below the desorption temperature Ts = 800 K. The population of the first vibrational state was found to be enhanced by a factor of 20±10 over the thermal distribution. This overpopulation is very similar to Si(001) and in qualitative agreement with the vibrationally-assisted sticking found in the adsorption measurements [180]. 5.3. Microscopic reaction pathways Although the number of experimental studies on the adsorption of atomic hydrogen on Si(111)7×7 is high [10], so far only little effort has been undertaken to reveal the initial adsorption sites for dissociation of molecular hydrogen on this surface. Theoretical work based on density functional calculations has identified pairs of ad- and restatoms to be the preferred places of hydrogen dissociation on Si(111) [241,242]. Two different mechanisms, a direct one [241] as well as dissociation via a dihydride state [242] are found in the calculations, as had been proposed earlier [106]. Both reaction mechanisms include high lattice distortions during the adsorption process. For the direct dissociation, one Si–Si-bond of the involved adatom is (nearly) broken during the adsorption/desorption process. As depicted in Fig. 76, this allows for a strong reduction of the distance between the two reacting Si atoms in the transition state, lowering the adsorption barrier significantly [241].

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Fig. 76. Schematic illustration of the H2 desorption process. (a) Si–Si and Si–H bond lengths and H–H distance in the monohydride state. (b) Breaking of one adatom backbond and motion of the adatom which brings two H atoms close to the H–H bonding distance. (c) Desorption of the H2 molecule and subsequent reformation of the broken adatom backbond. Reprinted with permission from Cho et al. [241]. c 1997, APS.

E ads was found to be 0.8 eV. The corresponding desorption energy was calculated to be 2.4 eV in good agreement with experimental data [24]. Although at first sight very different, dissociation via a dihydride state at the adatom [242] can be seen as an extension of the concept of barrier reduction by lattice distortion. For the formation of a SiH2 sub-unit, one Si–Si bond has to be broken completely. For this dihydride pathway, adsorption barrier, desorption energy, and energy stored in the lattice distortion at the transition state were calculated to be E ads = 1.0 eV, E des = 2.4 eV and E s = 0.6 eV, respectively. The latter one is remarkably high and could account for the activation of s0 with Ts and the low mean translational energy of the desorbing hydrogen molecules [35], comparable to the situation on Si(001). 5.4. Comparison Si(111)–Si(001) From the the very similar behaviour for molecules desorbing from Si(001) and Si(111), Shane et al. concluded that the transition state for the two surfaces is similar, despite the very different reconstruction [211]. Since also desorption from the dihydride state resulted in similar rotational and vibrational H2 distributions [212] they suggested a dihydride transition state to be operative both on Si(001) and Si(111). Indeed such a

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dihydride state is expected to be rather insensitive on surface reconstruction. Moreover, for Si(111), Vittadini and Selloni found a transition state with two hydrogen atoms localized at one Si surface atom [242]. However, no indication of such a dihydride intermediate state was found for Si(001). Today, both theory and experiments favour a direct ad- and desorption mechanism via the two-dimer reaction pathway. For Si(111), additional calculations have shown that adsorption via a direct reaction pathway is also possible [241]. For Si(111), both the dihydride as well as the direct adsorption pathway are in good agreement with the strong activation with surface temperature. So how can the similarities on the one hand and the differences on the other hand be understood? On both surfaces, thermally activated lattice distortions are assumed to lead to broad adsorption functions due to the distribution of adsorption barriers on the surface. On Si(001), the strong lattice distortion during adsorption is connected with the creation of sites with reactive dangling bonds since the totally filled and unfilled states of the buckled dimer configuration turn out to be highly unreactive (compare Section 3.6). On Si(111), such reactive sites exist in principle in the form of partially filled dangling bonds at the adatoms of the 7×7 reconstruction. However, for an effective reduction of the adsorption barrier, ad- and restatom have to get much closer to each other, again resulting in strong lattice distortions (compare Refs. [106,241] and Fig. 76). In both cases, the transition state shows a high amount of energy stored in the substrate lattice. However, since the shape of the single adsorption functions at constant surface temperature depends strongly on the curvature of the PES, some deviation between the adsorption functions s(E kin ) of H2 /Si(111) and H2 /Si(100) is to be expected, as observed experimentally. Nonetheless, with respect to the angular momentum of the desorbing molecules and the vibrational excitation, the transition state can be very similar on both surfaces since the inter-atomic distance between ˚ and the two silicon atoms involved in the reaction is 3.8 A ˚ on Si(001) and Si(111), respectively, i.e. in both cases 4.4 A a considerable stretching of the hydrogen molecule in the transition state is expected. In summary, one could draw the following picture: the adatom with its partially filled dangling bond and the correlated U1 /S1 states close to the Fermi level acts as the reactive centre. Comparable to the situation on the Si(001) surface, e.g. for the isolated dangling bond of the H3 site, effective hybridization with the hydrogen orbitals occurs at the adatom. However, for the successful dissociation, a site with two reactive Si-atoms has to be created. Due to the long distance between ad- and restatom, this includes high lattice distortions. Reorganization of the involved electrons (the dangling bond of the restatom is filled with two electrons but only one is needed for the Si–H bond) costs additional energy. This is again very similar to the H3 site on Si(001). However, the latter is more reactive, presumably, among other reasons, due to the smaller distance between the involved Si atoms. The increase of reactivity with surface coverage on Si(111)7×7 [106] can then be attributed, e.g., to the change of local electronic structure. Such a change has to occur since with

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increasing coverage, the occupancy of the adatom dangling bonds with electrons has to increase to keep the average number of electrons per dangling bond constant. Acknowledgements The achieved level of understanding of hydrogen adsorption on silicon is the result of the effort of many outstanding scientists. In particular, the authors would like to thank Peter Bratu, Markus Raschke, Michael Hartmann, Georg Schmidt, Carsten Voelkmann, Catrinel Stanciu, Karl Kompa, Tony Heinz, Alfred Biedermann, Zonghai Hu, Wilhelm Brenig, Axel Groß, Ralf Russ, Moritz Hilf, Peter Kratzer, Eckhard Pehlke, and Matthias Scheffler for enjoyable collaboration. We also benefitted greatly from discussions with Emily Carter, Eckhart Hasselbrink, Ken Jordan, Kurt Kolasinski, Akira Namiki, Annabella Selloni, and Frank Zimmermann. We gratefully acknowledge support by the Deutsche Forschungsgemeinschaft through SFB 338 and HO2235/1, by the Deutsche Akademische Austauschdienst, by the Max-Planck-Institute for Quantum Optics and by the Marburg Centre for Optodynamics. One of us (UH) is indebted to Prof. K. Tanimura and the Institute for Scientific and Industrial Research of Osaka University for hospitality during composing parts of this review. References [1] A. Winkler, K.D. Rendulic, Int. Rev. Phys. Chem. 11 (1992) 101. [2] H.A. Michelsen, C.T. Rettner, D.J. Auerbach, in: R.J. Madix (Ed.), Surface Reactions, Springer Verlag, Berlin, 1994, pp. 185–237. [3] A. Hodgson, Progr. Surf. Sci. 63 (2000) 1. [4] H. Zacharias, Internat. J. Modern Phys. B 4 (1990) 45. [5] G.O. Sitz, Rep. Progr. Phys. 65 (2002) 1165. [6] G.R. Darling, S. Holloway, Rep. Progr. Phys. 58 (1995) 1595. [7] A. Gross, Surf. Sci. Rep. 32 (1998) 291. [8] G.J. Kroes, Progr. Surf. Sci. 60 (1999) 1. [9] J.M. Jasinski, S.M. Gates, Acc. Chem. Res. 24 (1991) 9. [10] J.J. Boland, Adv. Phys. 42 (1993) 129. [11] H.N. Waltenburg, J.T. Yates, Chem. Rev. 95 (1995) 1589. [12] K. Oura, V.G. Lifshits, A.A. Saranin, A.V. Zotov, M. Katayama, Surf. Sci. Rep. 35 (1999) 1. [13] A.J. Mayne, D. Riedel, G. Comtet, G. Dujardin, Progr. Surf. Sci. 81 (2006) 1. [14] K.W. Kolasinski, Internat. J. Modern Phys. B 9 (1995) 2753. [15] U. H¨ofer, Appl. Phys. A 63 (1996) 533. [16] D.J. Doren, Adv. Chem. Phys. 95 (1996) 1. [17] J.T. Law, J. Chem. Phys. 30 (1959) 1568. [18] I. Langmuir, J. Amer. Chem. Soc. 37 (1915) 417. [19] G. Schulze, M. Henzler, Surf. Sci. 124 (1983) 336. [20] M. Liehr, C.M. Greenlief, M. Offenberg, S.R. Kasi, J. Vac. Sci. Technol. A 8 (1990) 2960. [21] Y.-S. Park, J.-S. Bang, J. Lee, Surf. Sci. 283 (1993) 209. [22] G. Herzberg, A. Monfils, J. Mol. Spectrosc. 5 (1960) 482. [23] B.P. Stoicheff, Canad. J. Phys. 79 (2001) 165. [24] G.A. Reider, U. H¨ofer, T.F. Heinz, J. Chem. Phys. 94 (1991) 4080. [25] U. H¨ofer, L. Li, T.F. Heinz, Phys. Rev. B 45 (1992) 9485. [26] M.B. Raschke, U. H¨ofer, Phys. Rev. B 63 (2001) 201303(R). [27] M.C. Flowers, N.B.H. Jonathan, Y. Liu, A. Morris, J. Chem. Phys. 99 (1993) 7038. [28] M.C. Flowers, N.B.H. Jonathan, Y. Liu, A. Morris, J. Chem. Phys. 102 (1995) 1034.

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