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Rapid thermal desorption of di-atomic molecules: A theoretical study
195
Surface Science 213 (1989) 195-213 North-Holland, Amsterdam
RAPID THERMAL DESORPTION A THEORETICAL STUDY Joseph BLOCH Department Received
OF DI-ATOMIC
MOLECULES:
and Yehuda ZEIRI
of Physics, Nuclear Research Center-Negeu, 21 July 1988; accepted
for publication
P.O. Box 9001, Beer-Sheua,
25 October
Israel
1988
Rapid thermal desorption of a di-atomic molecule following irradiation of the surface by a short laser or electron beam pulse has been studied. The calculations were performed using a stochastic trajectory method in which the adsorbate motion is described by effective equations of motion. The simulations yield information about various distribution functions of the desorbates such as translational and internal energies, as well as angular and residence time. These distribution functions were computed for various adsorption geometries, molecular force constants and surface corrugation.
1. Introduction In the last decade is has been demonstrated in a number of studies that irradiation of an adsorbate-surface system by a laser or electron beam may induce various processes [l-3]. Among these are rapid surface heating (and melting), internal excitation (vibrational or electronic) of the adsorbate, electron-hole pair formation, etc. These different excitations may lead to the enhancement of various processes such as: reactions among adsorbates, surface diffusion, desorption and dissociative adsorption. Some of these phenomena play a major role in a number of industrially important processes, for example: heterogeneous catalysis [l-3], metal [4] and compound [5] decomposition, laser induced CVD [6], etching of surfaces [7] and others. It is expected that a detailed microscopic understanding of these surface phenomena may allow one to improve and to design new processes of industrial interest. In the present study, the dynamics of rapid thermal desorption of di-atomic molecules from a solid surface is examined. The desorption is induced here by rapid surface heating caused by an intense and short laser or electron beam pulse. In recent years, a number of studies were designed to measure the angular and velocity distributions of desorbates obtained in rapid thermal desorption [7e,8]. Some of these studies indicated that the desorbate distribution functions measured in rapid desorption experiments are quite different 0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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J. Bloch, Y Zeiri / Rapid thermal desorption of di-atomic molecules
than those obtained in programmed thermal desorption (TPD) experiments. For example, in some systems the angular distribution of desorbates was strongly peaked towards the surface normal as compared to a cosine type distribution obtained in TPD experiments. In addition, some systems [8a] showed non-Boltzmann velocity distributions of desorbates. Both angular and velocity distributions have been found to be very sensitive functions of the initial surface coverage [8]. Evidently, the measured distribution functions emerge from the nature of the desorption dynamics together with the effect of post-desorption gas-phase collisions among the desorbates [gal. The role of post-desorption gas-phase collisions on the desorbate distribution functions has been studied recently using Monte Carlo simulations [9]. In addition, the dynamics of rapid desorption processes was investigated recently [lO,ll] using the stochastic trajectory technique. In the present study it will be assumed that the initial surface coverage is low, hence gas-phase collisions among desorbates can be neglected. In this work, we shall present the results of a theoretical study in which the rapid desorption of CO molecules from an unreconstructed Si(100) is simulated. This system was chosen due to its importance in the understanding of metal deposition using metal carbonyl parent molecules [4]. The calculations were performed using a stochastic trajectory approach in which the motion of each adsorbate is described by an effective equation of motion [12]. The calculations were aimed to study the relationship between the desorbate distribution functions and various characteristics of the system, such as, adsorption geometry, strength of molecular vibrational force constant and surface corrugation. Since no accurate interaction potential between CO and the Si(100) surface is available, the simulations in this work can be regarded as a model system study. The rapid heating of the substrate by a pulse of a laser or electron beam was simulated by a continuous variation of the amplitude of the random force terms in the effective equations of motion (EEM) [12] of the adsorbate. This procedure enabled us to accurately describe the rapid temperature variation of the irradiated zone [lO,ll]. In the next section we shall briefly describe the calculational procedure, while section 3 will be devoted to a discussion of the results. The last section contains a short summary.
2. Desorption model 2.1. EEA4 approach The simulations of rapid desorption have been carried out using a stochastic trajectory method in which the time evolution of the adsorbate motion is
.I. Bloch, Y. Zeiri / Rapid thermal desorption ojdi-atomic molecules
197
followed. According to the EEM approach [12], the motion of each adsorbed atom is governed by a Langevin type equation of motion of the form
(1) where M, and R, are the mass and position vectors of the i th adsorbate. The potential V(R,, S) represents the interaction of the ith adsorbate with the surface, where the surface atoms are fixed at their lattice points, while V(R) represents the intramolecular potential. In writing V( R,, S) it was assumed that the adsorbed atom is interacting with a single fictitious surface particle whose mass was taken to be equal to the mass of a silicon atom (see discussion below). The last two terms in eq. (l), r(R) and f(t), are a friction term and Gaussian random force respectively. These two terms are related by the second ~uctuation-dissipation theorem (f(t)
f(O))
= 3kT,(t)
I’(&)
a(t),
(2)
where k is Boltzmann constant, 7”(t) is the time dependent surface temperature and ( ) denotes ensembles average [lo-121. The thermal motion of the surface atoms introduces, in the EEM method 1121, a modi~cation term, W(Ri), which alters the adsorbate-surface interaction potential. The functional form of W(R,) is [12] W(R,)
= 1 - Ci/2MsDi,
(3)
where MS is the surface particle mass and c, =
a2v’( Ri) s)/aRif
,
0, = Wz - W$‘i’Jf + C;/M,.
(44 (4b)
The various parameters used in eq. (4) can be obtained from the phonon mode density of the surface [13]. If the Debye model is used to describe the phonon density of the solid one obtains ]13]: Wi = 0.6W& W2 = 0.262Wk and pi = 0.577Wn where W, is the Debye frequency of the solid surface. In all the calculations reported here the silicon Debye temperature was taken to be equal to 0 = 600 K (a = W,/k). Thus, the correction term, W(R,), represents a modification of the adsorbate-surface interaction due to the thermal motion of the surface atoms. The friction term in eq. (l), F( R,), is given by [12] r( Ri) = ~W~C~/M*M~~~D~,
(5)
where p = 0.167~rWo if the Debye model is used to describe the surface phonon spectra [12,13]. Eq. (1) is an effective equation of motion which describes the time evolution of the position and velocity vectors of each adsorbed atom (which
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J. Bloch, Y. Zeiri / Rapid thermal desorption
of d&atomic
molecules
constitute the molecule). The two last terms together with W( R ;) represent the coupling of the adsorbate motion to the thermal motion of the surface atoms. Thus, the surface phonons are introduced in this approach in an average manner. Two points should be noted, first, if the surface temperature varies with time, so will the width of the Gaussian random force distribution, see eq. (2). The second point is related to the behaviour of the terms QR,) and W((R;) at Iarge adsorbate-surface separations. It is easy to see in eqs. (4) and (5) that both terms vanish when R, -+ co. Thus, at large particle-surface distances eq. (1) reduces to a deterministic Newtonian equation of motion. The main advantage of the EEM approach over more accurate methods, such as the one used in ref. [lo], is related to the large reduction in computation time. However, the energy exchange between the adsorbate and the surface is expected to be described less accurately when the EEM method is used. Thus, the discussion in the next section will emphasize the variation in relative magnitudes of the different quantities rather than their absolute value. A detailed derivation of eq. (1) together with a discussion of its accuracy are given in ref. 112). 2.2. Interaction potentials The present study was aimed at simulating the rapid thermal desorption of a di-atomic adsorbate at low initial surface coverage. Namely, it is assumed that the average distance between two adsorbates is large, hence, adsorbate-adsorbate interaction can be neglected. Consequently, the rapid thermal desorption of a single adsorbate was simulated. Unfortunately, very limited information is available in the literature about the CO/Si(lOO) system. However, the qualitative results of several experiments 1141 indicate that the binding of CO to the Si(100) surface is very weak. Since no quantitative information about the interaction potential between CO and the Si(100) is available, we have assumed that both the carbon and oxygen atoms interact with the surface via Morse-type potentials of the form y( R,, S) = De( x, y){,-~at~~~~r~-zoc~.~,l_
2
,-ptx.YMz-z,,(x.Y)l}.
In eq. (6) Z is the position of the i th atom along the surface normal while X and Y are its coordinates along the surface. The variation of the interaction potential along the surface is related to variations of the three Morse parameters. Once the lateral position of the ith atom is given, the three parameters in eq. (6) are determined according to the following relation: Q( X, Y) = A + B[cos(:!aX/a) + c cos(2nX/a)
+ cos(27iY/b)] cos(27rY/b),
199
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules Table 1 Morse parameters used in the different simulations; energy units are kcal/mol, cm -’ and distance in A Simulations
A, h C D, E, F G
H
Site
All All On-top Bridge Four-fold On-top Bridge Four-fold
frequency is in
Carbon
Oxygen
Q
R,
Q
we
R,
1.8 2.0 2.0 1.9 1.8 2.0 1.9 1.8
0.5 1.75 0.3 0.4 0.5 0.5 0.5 0.5
50 120 30 40 50 50 50 50
2.9283 2.0 3.1283 3.0283 2.9283 3.1283 3.0283 2.9283
3.0 1.75 2.6 2.8 3.0 1.8 2.0 3.0
a, 120 120 100 110 120 100 110 120
where Q stands for D,, p for 2, and the lattice constants are designated by a and b. The three coefficients in eq. (7) have the following form: 4A = 2Q(2) + Q(4) + Q(l),
@a)
4B = Q(4) - Q(l),
W)
4C = Q(4) + Q(I)
- 2Q(2),
(gc)
where Q(i), i = 1, 2, 4 are the values of the quantity Q over the on-top, bridge and four-fold sites respectively. Since the experimental TPD results [14] indicated that CO adsorption on Si(100) occurs at T, < 70 K, we assumed a total CO-Si(lO0) binding energy of 3.5 kcal/mol. The individual binding energies of the carbon and oxygen atoms to the surface were fixed according to the assumed adsorption geometry of the CO molecule. In all cases studied here, the sum of the individual binding energies at the best adsorption site was 3.5 kcal/mol. The interaction potential between the carbon and oxygen atoms, V(R), was assumed to be represented by a Morse function. The parameters used in the model potential function, described above, are listed in table 1. The various cases studied in this work differ in adsorption geometry, intramolecular force constant and surface corrugation, see table 1. In summary, the lack of quantitative information about the CO-Si(lO0) interaction leads us to use a model potential. Thus, the goal in these model calculations was to study the relationship between the dynamics of rapid desorption and the characteristics of the system. 2.3. Details of the calculations In order to simulate surface heating, a time dependent surface temperature, T,(t), was used in sampling the random force in eqs. (1) and (2). In all the
200
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
simulations described below, the time dependence of T, was assumed to have the form. T,(t)
= To+ T,[l -exp(-t/r)],
(9)
where To and T, are initial and final temperatures respectively, and r is a time constant. The functional form of T, in eq. (9) has been used in previous studies [lO,ll]. In the calculations performed in this work the following values for the constants in eq. (9) were used: To = 70 K, Tf = 2930 K and r = 0.25 ps. For each case 1000 trajectories were calculated with the integration time step value in the range (1-S) X lo-t6 s. In all the simulations the CO molecules were placed initially at their equilibrium positions with respect to the surface and at a C-O separation which corresponds to the gas-phase equilibrium distance (over the best adsorption site for corrugated potentials). The initial velocities were sampled from a canonical distribution at the surface temperature. Then, the system was allowed to equilibrate for 2000 integration steps before the surface heating was turned on according to eq. (9). A trajectory was terminated if the adsorbate-surface distance exceeded a value of 10 A or if 100000 integration steps were performed.
3. Results and discussion The present study summarizes the results of eight different simulations of rapid desorption. In all the calculations the gas-phase CO binding energy, De = 255.735 kcal/mol, and equilibrium distance, R, = 1.1283 A, were used [15]. These simulations were aimed to relate the desorption dynamics to the adsorption geometry, molecular force constant and surface corrugation. Table 2 summarizes the main features of the eight cases considered. Two adsorption geometries were considered: CO bound normal to the surface (with the carbon atom close to the surface, simulations A, B, C, G and H) and CO bound parallel to the surface (simulations D, E, and F). In addition, three oscillator frequencies were used, the gas-phase value [15] w, = 2169.81 cm-’ together with we = 1000 and 500 cm-‘. As shown in table 2, the first six simulations were performed on an uncorrugated surface, while in the last two cases different amounts of surface corrugation were introduced. All the parameters used for the adsorbate-substrate interaction potential are listed in table 1. It should be noted that in simulations G and H the four-fold site was assumed to be the best adsorption site. The average quantities of desorbate translational energy, (E), and its components along, ( Ep), and normal, (E,), to the surface are summarized in columns 2-4 in table 3. In addition, table 3 presents the average desorbate rotational, (E,), and vibrational, (E,), energies, as well as (cos 0) and (7”). Here, 8 is the angle between the direction of desorbate velocity vector and the
201
J. Bloch, Y. Zeiri / Rapid thermal desorptlon of di-atomic molecules Table 2 Parameters used in the different simulations; in all the calculations ps and maximum surface temperature was 3000 K Simulation
Surface corrugation (kcal/mol)
‘)
0.0 0.0 0.0 0.0 0.0 0.0 0.3 1.0
heating
time constant
Oscillator frequency (cm-‘)
Adsorbate geometry
2169.81 1000.00 500.00 2169.81 1000.00 500.00 500.00 500.00
Normal Normal Normal Parallel Parallel Parallel Normal Normal
was 0.25
a) Surface corrugation is measured as the difference in the CO binding energy over the four-fold and two-fold sites. These values measure the magnitude of the activation energy for diffusion from one four-fold site to the nearest neighbour four-fold site.
surface normal, while T, is the residence time of the desorbate on the surface. Note that the values of (E) are given in temperature units, i.e. the values in table 3 are obtained by dividing the calculated average translational energy by 2k. Inspection of table 3 shows that in all the cases considered, the average total desorbate translational energies are much lower than in the maximum surface temperature. Similar results were obtained in previous studies [lO,ll]. However, the values of (E) for CO adsorbed parallel to the surface (cases, D, E and F) are much larger than those obtained for normal adsorbates (cases A-C, G and H). Similar behaviour is obtained for (E,). Moreover, in all the simulations with a flat surface (cases A-F) a very small amount of energy is channeled into the desorbate motion parallel to the surface, ( Ep). Once Table 3 Average total, (E), normal, (E,), and vibrational, (E,), desorbates System
A B C D E F G H
(E)
(E,), and parallel, (En). translational energies; average rotational, energies and values of (cos 0) and the mean residence time, (T,) of
(En) (K)
(E,) (K)
(E,) (K)
(E,) (K)
(cos e>
(K)
R-) (PSI
296*11 300 * 10 313+12 511k19 5ooi19 472 + 17 278 f 15 343*17
571 f 22 579 + 19 606 f 24 1002&39 978 f 38 923 f 35 501 f 31 511+32
2150.6 21 f 0.6 21+0.6 20+0.6 21+ 0.6 22+0.6 56 f 6.0 176*11
282 k 16 325 f 16 314517 718f30 725 f 28 643+29 321+ 28 362+26
1148 f 49 1400 f 50 1393 + 54 804k 38 783 f 35 1080 + 44 1253 + 77 1207i63
0.95 f 0.027 0.94 k 0.023 0.95 k 0.025 0.97 + 0.012 0.96 + 0.027 0.96 + 0.027 0.90 * 0.038 0.79f0.022
8.2*0.11 10.0 f 0.16 10.0~0.21 4.0 * 0.08 3.9 f 0.08 4.0 + 0.09 11.0+0.42 11.0~0.31
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J. Bloch, Y. Zeiri / Rapid thermal desorption
of di-atomicmolecules
0 no corrugation a low corrugation
1
l
high corruoation
0.8 z _, 2
*
0.6
.
0.4
10
20
30
40
50
60
70
80
90
@[Degrees]
Fig. 1. Desorbate angular distribution of normal CO for three values of surface corrugation (w, = 500 cm-‘). Marked points represent a statistical, cos 8, distribution.
surface corrugation is introduced, increased values of (E,) are obtained (simulations G and H). Thus, the coupling of the adsorbate parallel motion to the surface enhances energy transfer to this mode. Very similar results were obtained for atomic desorbates [ll]. The ratio between (E,) and (E,) determines the angular distribution of desorbates which is represented in table 3 by (cos 0). In the case of a statistical angular distribution (i.e. a cos 8 distribution), the mean value is (cos 9) = 0.667. All the values of (cos 8) in table 3 are larger than the statistical one, namely the corresponding distributions are highly peaked towards the surface normal. However, increased corrugation results in a significant decrease in the value of (cos 8), hence, to a broader angular distribution. The actual distributions obtained in simulations C, G and H are shown in fig. 1 (histograms) together with the statistical cos 0 distribution (marked points). The broadening of the angular distribution for increased surface corrugation is clearly seen in fig. 1. These results were numerically fitted to distributions of the form cos”8. The best fits were obtained for n values of 37, 26 and 9 for the no, low and high corrugation cases respectively. Comparison of the average residence times, for normal and parallel adsorbate, shows that the former corresponds to much larger values of (7”). In addition, residence time distributions for simulations A and D are shown in fig. 2, while fig. 3 presents the distributions obtained in cases C and F. The differences, discussed above, between (E) and (r,) values of adsorbates bound to the surface in a perpendicular and parallel geometry can be under-
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
203
0 . .’
j-
0.2
‘;: .z
Q
normal CO/Si(lOO)
.
parallel CO/Si(lOO)
0.2
5 ?
P
.r f l?L v
0.15
0.1
0.05
0
1
23
4
5
67
8
9
10 11
12
nun 13
14
15
Desorption T ime (psec)
Fig. 2. Residence time distribution for normal and parallel CO (w, = 2169 cm-).
stood by analyzing the desorption mechanism. In both situations the adsorbate interacts with a heat reservoir (the crystal). Thus, in both cases the adsorbate suffers random “kicks” due to the thermal fluctuations of the surface. We now assume that a large fraction of adsorbates desorbe when a single “kick” they obtain is larger than the adsorbate-surface binding energy [lo]. Consequently, in the case of normal CO the “kick” to break the C-surface bond should be much larger than the “kicks” needed to break the C-surface and O-surface bonds in parallel CO. The probability to obtain a “kick” of magnitude F, at a given time (or surface temperature) is given by
WI P(e) = (25~~)~‘~ exp( -4*/2a*),
(10)
where (I is the random force distribution width [16]. Since the C-surface bond, for perpendicularly bounded CO, is roughly twice the C-surface and O-surface bonds in parallel CO, the ratio between the strength of “kicks” to break these bonds will also be two. Thus, the corresponding ratio of “kicks” probability is P($)/P(2E;;)
= exp(3q2/2a2).
In other words, this probability
(11) ratio is proportional
to P(c.)-3
where
204
.I. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.3
0.25
0
normal CO/Si(lOO)
n
oarallel CO/Si(lOO)
0.2 :: .r 5 2 0.15 L " 2 4 F 0.1
0.05
0
1 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
16 17 18 19 20 21 22 23 24
Desorption Time[psecl
Fig. 3. Residence
time distribution
for normal
and parallel
CO (w, = 500 cm-‘).
0 < P(q) I 1. This discussion gives a qualitative understanding of the difference in (7”) values obtained for the two adsorption geometries. The fourth and fifth columns in table 3 describe the desorbate average rotational and vibrational energies respectively. It is clear from these results that variation of a oscillator frequency and surface corrugation leads only to minor changes in the values of (E,) and (E,). On the other hand, variation in the adsorption geometry leads to large changes in the magnitude of these quantities. For normal CO the values of (E,) are much smaller than those for parallel CO, while the opposite situation occurs in the case of average vibrational energy. This behaviour can be explained by the schematic description of the desorption event shown in fig. 4. For normal CO, fig. 4A, the force acting on the adsorbate, during the desorption, is mainly along the molecular axis. The results of such a situation is that energy can be channeled more efficiently into the vibrational mode rather than into the rotational one. On
205
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
A
Fig.
4. Schematic
description
of the desorption mechanism adsorbates.
for normal
(A) and
parallel
(B)
the other hand, for a parallel CO, fig. 4B, one atom-surface bond will break first while the other bond still exists. In such a situation, the adsorbate will exhibit a strong frustrated rotational motion which will be converted into free rotational when the desorption process is completed. The actual rotational and vibrational distributions for simulations C and F are shown in figs. 5 and 6 respectively. It is clear from these results that for parallel CO the rotational 0.5
q normal m
CO/Si(lOO)
parallel CO/Si(lOO
0.4 ‘;: .z ;
0.3
I .z g
0.2
0.1
2
m,
0.0 : 10
20
30
40
Quantum
Fig.
Rotational
for
and
CO
=
cm-‘).
206
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.6
c] normal CO/Si(lOO) m
0
12
3
45
67
parallel CO/Si(lOl
8
910
11
Vibrational Quantum Number
Fig, 6. Vibrational
distributions
for normal
and parallel
CO (we = 500 cm- ‘).
distribution is much wider than for normal CO (fig. 5) while in the case of the vibrational distributions the opposite behaviour is obtained (fig. 6). The discussion above is related also to the differences between the T, distributions of normal CO with two different oscillator frequencies (figs. 2 and 3). When the CO force constant is decreased, the cross section for energy transfer from the C-surface vibrational mode to the CO internal vibration is much larger than for an adsorbate with a high oscillator frequency. Thus, in the low frequency case, part of the energy transferred to the adsorbate-surface bond is redistributed in the adsorbate internal degrees of freedom. Consequently, increasing amounts of energy have to be transferred from the surface to cause desorption. The net result will be larger residence times for low frequency diatomic adsorbates as shown in figs. 2 and 3. It was noted above that the average values for the desorbate rotational and vibrational energies do not show a strong dependence on oscillator frequency and surface corrugation (see table 3). We now turn to the examination of the actual rotational and vibrational distributions and their dependence on the molecular force constant and surface corrugation. In figs. 7 and 8 the rotational distributions for normal CO are shown for the three oscillator frequencies studied (fig. 7) and for various degrees of surface corrugation (fig. 8). These results clearly show that the rotational distribution is independent of the molecular force constant and has only a weak dependence on the surface corrugation. Increased corrugation results in a slight broadening of the rotational distribution, fig. 8.
J. Bloch. Y. Zeiri / Rapid thermal desorption of di-atomic molecules
207
0.5
0.4
0.3
0.2
0.1
n 5
10
15
20
25
30
35
40
Rotational Quantum Number
Fig. 7. Rotational distribution of normal adsorbates for three adsorbate oscillator frequencies.
Similar examination of the vibrational distributions shows that these are more sensitive to a variation in oscillator frequency. Figs. 9 and 10 present the variation of the vibrational energy distributions as a function of oscillator frequency for normal and parallel CO respectively. These results show that also the average values of vibrational energy depend weakly on the molecular force constant, the actual distributions exhibit a clear broadening when the oscillator frequency is reduced. Thus, a decrease in w, results in the population
0I] ow corrugation m high corrugation
Rotational Quantum Number
Fig. 8. Rotational
distribution
of normal CO for three values of surface corrugation cm-‘).
(w, = 500
208
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.7 I7 we=2169 cm-l
q we=1000
0.6
cn-1
m we= 500 cm-l
1
2
3
4
5
6
7
8
9
10
11
12
Vibrational Energy [K] /lo00
Fig. 9. Vibrational
energy
distribution
of normal CO for three frequencies.
values
of adsorbate
oscillator
of higher internal vibrational states of the desorbates. Moreover, figs. 9 and 10 indicate that this broadening of the distributions for decreased values of W, is weakly dependent on the adsorption geometry. Fig. 11 presents the vibrational distributions for normal adsorbate (w, = 500 cm-‘) at three surface corrugation values (see table 2). Except for minor changes in the distribution, these results indicate that the vibrational distributions do not vary significantly when surface corrugation is changed. Comparison of the results obtained in the present simulation with those of ref. [lo] shows that all quantities except (E,) exhibit a similar range of values. There is a large discrepancy between the values of (E,) obtained in the two simulations. In the present work the amount of average vibrational energy of the desorbates is much larger than the values obtained in ref. [lo]. In addition, the calculations of Lucchese and Tully [lo] show a strong dependence of (E,) on o, where in the present study a much weaker dependence is found. One possible source for this discrepancy is related to the different calculational approaches used in the two simulations. As discussed above, the EEM method used here, is less accurate in describing adsorbate-surface energy transfer than the approach used in ref. [lo]. Thus, the discrepancy in (EY) values may be
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
209
0.8 Due=2169
cm-l
~~~~-1000
cm-l
0.6
0.4
0.2
0 Vibrational Energy (K)/lOOO Fig. 10. Same as fig. 9 for parallel adsorbate.
0
o'5r
no corrugatian
•I low corrugation I high corrugation
0.2
0.1
n
0
12
3
4
56
7
8
9
10
11
Vibrational Quantum Number
Fig. 11. Vibrational
distribution
of normal CO for three values of surface corrugation (we = 500 cm-‘).
210
J. Bfoch, Y. Zeiri / Rapid thermal desorption
ofdi-atomicmolecules
attributed in part to the unaccurate description of the system by the EEM method. However, if the crudeness of the approximations in the EEM approach is the source for this discrepancy in the values of (E,) one would expect similar disagreements in the magnitude of other quantities (e.g. average translational and rotational energies). Comparison of the (E) and (E,) values present in table 3 with those of table 1 in ref. [lo] show that these quantities exhibit similar values. Thus, the disagreement in the magnitude of (E,) in the two studies cannot be attributed only to the unaccuracy of the EEM approach. An additional major difference between the present study and the one presented in ref. [lo] is due to the adsorbate-surface interaction potential used in the two simulations. For example, the CO-Si(lO0) binding energy in the present work was taken to be 3.5 kcal/mol while the corresponding value for the NO-LiF(lOO) system in
0
Normal CO/Si(lOO)
a
Parallel CO/Si(lOO)
22 23 24 Residence time
Fig. 12. Variation
of average
vibrational energy parallel adsorbates
ipsecl
as a function of residence (w, = 1000 cm- ‘).
time for normal
and
J. Bloch, Y. Zeirz / Rapid thermal desorption of di-atomic molecules
211
ref. [lo] is 2.075 kcal/mol. In addition, the variations of the potential energy as a function of adsorbate orientation (the angle between the molecular axis and the surface normal) are quite different in the two simulations. A direct consequence of these differences in adsorbate-surface interaction potentials is the larger values of (T,) obtained in the present work. These long residence times may result in a larger degree of thermalization of the adsorbate vibrational mode at the elevated surface temperatures. The variation of ( EY) as a function of residence time for simulations B and E are shown in fig. 12 These results clearly indicate that the magnitude of (E,) increases for longer residence times. It should be noted that for small T, values (T, s 2 ps) the magnitude of (E,) agrees well with those of ref. [lo]. Moreover, the large increase in (E,) for long residence times, see fig. 12, may wash out the differences between simulations in which the molecular force constant was changed. Recently, Muckerman and Uzer [17] have studied the desorption dynamics of vibrationally excited adsorbed CO on an NaCl surface. In this study [17], the results of a one-dimensional quantum mechanical approach were compared to those of a classical calculation with and without the inclusion of the surface thermal motion. Despite the large discrepancy between the frequencies associated with the C-O and CO-surface bonds, efficient energy transfer between the two modes was obtained. The calculated average adsorbate lifetimes were of the order of 1 ps. Assuming microreversibility, these results substantiate our findings about vibrational thermalization of CO adsorbed on a hot surface. Furthermore, recent experiments [18] on laser induced desorption of NO from a Pt foil yield vibrationally hot desorbates with a vibrational temperature of 700 K. These results are in good agreement with the (E,) values obtained in the present study.
4. Summary A model study of rapid thermal desorption of diatomic molecules from a solid surfaces has been presented. The masses and some of the other quantities used in the calculations correspond to a CO molecule adsorbed on a Si(100) surface. However, the lack of information about the detailed CO-S1 interaction potential led us to the use of a model potential. This study was aimed at establishing the relationship between the desorption kinetics and various characteristics of the system. In particular, we were interested in the influence of adsorption geometry, oscillator frequency and surface corrugation on the desorption mechanism. It was found that increased surface corrugation has a large impact on the width of the desorbate angular distribution. Similar effect was found for atomic adsorbates [ll]. This suggests that if these rapid
212
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
desorption studies will be performed on different low Miller index surfaces of the same materials (different planes exhibit usually different corrugations), one would expect to obtain broader angular distributions for planes with higher corrugation. The most pronounced effect on the desorption kinetics was found to be related to the adsorption geometry. It was found that adsorption along the surface normal leads to larger amounts of energy channeled into the desorbate vibrational mode as compared to the rotational mode. The amount of average vibrational energy as well as the vibrational distributions were found to exhibit a weak dependence on the adsorbate oscillator frequency. For CO adsorbated parallel to the surface, a more efficient energy transfer into rotational modes was found. The differences in the amount of internal energies of normal and parallel adsorbates have been analyzed on the basis of a comparison between the two desorption mechanisms.
Acknowledgment This work has been partly supported by the Israeli and Development under contract No. 2564.
Council
for Research
References [I] T.J. Chuang, Surface Sci. Rept. 3 (1983) 1. [2] R.R. Aussenegg, A. Leitner and M.E. Lippitsch, Eds., Surface Studies with Lasers (Springer, Berlin, 1983). [3] R.B. Hall and A.B. Ellis, Eds., Chemistry and Structure at Interfaces, New Lasers and Optical Techniques (VCH, Deerfield Beach, 1986). [4] (a) D.J. Ehrlich, R.M. Osgood and T.F. Deutsch, Appl. Phys. Letters 38 (1981) 946: (b) T.H. Baum and C.R. Jones, Appl. Phys. Letters 47 (1985) 538; (c) T.H. Wood, J.C. White and B.A. Thacker, Appl. Phys. Letters 42 (1983) 408; (d) J. Ehrlich. R.M. Osgood and T.F. Deutsch, J. Vacuum Sci. Technol. 21 (1982) 23; (e) S. Matsui and K. Mori, Appl. Phys. Letters 51 (1987) 646. [5] (a) A. Glachantr and D. Saidi, J. Vacuum Sci. Technol. B 3 (1985) 895; (b) B.H. Chin and G. Ehrlich, Appl. Phys. Letters 38 (1981) 253; (c) M. Alonzo, J.L. Sacedon and F. Soria, Appl. Phys. Letters 45 (1984) 154. [6] (a) G.A. West, K.W. Beeson and A. Gupta, J. Vacuum Sci. Technol. A 3 (1985) 2278; (b) G.A. West, A. Gupta and K.W. Beeson, Appl. Phys. Letters 47 (1985) 476; (c) J. Nishizawa, H. Abe, T. Kurabayashi and N. Sokurai, J. Vacuum Sci. Technol. A 4 (1986) 706. [7] (a) G.C. Tirone and A.W. Johnson, Appl. Phys. Letters 42 (1983) 530; (b) W. Holber, G. Reckstein and R.M. Osgood, Appl. Phys. Letters 45 (1985) 231; (c) P.D. Brewer. D. McClure and R.M. Osgood, Appl. Phys. Letters 47 (1985) 310; (d) C.I.H. Ashby, Appl. Phys. Letters 46 (1985) 752; (e) W. Sesselmann, E.E. Mariner0 and T.J. Chuang, Appl. Phys. A 41 (1986) 209.
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
213
[S] See, for example: (a) J.P. Cowin, D.J. Auerbach, C. Becker and L. Wharton, Surface Sci. 78 (1978) 545; (b) P. Taborek, Phys. Rev. Letters 48 (1982) 1737; (c) T.J. Chuang and I. Hussla, Phys. Rev. Letters 52 (1984) 2045; (d) A. Namiki, T. Kawai and K. Ichige, Surface Sci. 166 (1986) 129; (e) C.J.S.M. Simpson and J.P. Hordy, Chem. Phys. Letters 130 (1986) 175. [9] (a) I. NoorBatcha, R.R. Lucchese and Y. Zeiri, J. Chem. Phys. 86 (1987) 5816; (b) I. NoorBatcha, R.R. Lucchese and Y. Zeiri, Phys. Rev. B 36 (1987) 4978; (c) I. NoorBatcha, R.R. Lucchese and Y. Zeiri, Surface Sci., submitted. [lo] R.R. Lucchese and J.C. Tully, J. Chem. Phys. 61 (1984) 6313. [ll] Y. Zeiri, J. Chem. Phys. 88 (1988) 3981. [12] Y. Zeiri, J. Chem. Phys. 86 (1987) 7181. 1131 (a) S.A. Adelman, J. Chem. Phys. 71 (1979) 4471; (b) S.A. Adelman, Advan. Chem. Phys. 44 (1980) 143. [14] (a) C.E. Bartosch, J.A. Stroscio and W. Ho, in: Proc. Materials Research Society, December 2-6, 1985, p. 67; (b) J.R. Creighton, J. Appl. Phys. 59 (1986) 410; (c) N.S. Glucq, G.J. Wolga, C.E. Bartosch, W. Ho and Z. Ying, J. Appl. Phys. 61 (1987) 998. [lS] K.P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979). [16] J.C. Tully, G.H. Gilmer and M. Shugard, J. Chem. Phys. 71 (1979) 1630. [17] J.T. Muckerman and T. Uzer, J. Chem. Phys., in press. [18] D. Burgess, R.R. Cavanagh and D.S. King, J. Chem. Phys. 88 (1988) 6556.
Surface Science 213 (1989) 195-213 North-Holland, Amsterdam
RAPID THERMAL DESORPTION A THEORETICAL STUDY Joseph BLOCH Department Received
OF DI-ATOMIC
MOLECULES:
and Yehuda ZEIRI
of Physics, Nuclear Research Center-Negeu, 21 July 1988; accepted
for publication
P.O. Box 9001, Beer-Sheua,
25 October
Israel
1988
Rapid thermal desorption of a di-atomic molecule following irradiation of the surface by a short laser or electron beam pulse has been studied. The calculations were performed using a stochastic trajectory method in which the adsorbate motion is described by effective equations of motion. The simulations yield information about various distribution functions of the desorbates such as translational and internal energies, as well as angular and residence time. These distribution functions were computed for various adsorption geometries, molecular force constants and surface corrugation.
1. Introduction In the last decade is has been demonstrated in a number of studies that irradiation of an adsorbate-surface system by a laser or electron beam may induce various processes [l-3]. Among these are rapid surface heating (and melting), internal excitation (vibrational or electronic) of the adsorbate, electron-hole pair formation, etc. These different excitations may lead to the enhancement of various processes such as: reactions among adsorbates, surface diffusion, desorption and dissociative adsorption. Some of these phenomena play a major role in a number of industrially important processes, for example: heterogeneous catalysis [l-3], metal [4] and compound [5] decomposition, laser induced CVD [6], etching of surfaces [7] and others. It is expected that a detailed microscopic understanding of these surface phenomena may allow one to improve and to design new processes of industrial interest. In the present study, the dynamics of rapid thermal desorption of di-atomic molecules from a solid surface is examined. The desorption is induced here by rapid surface heating caused by an intense and short laser or electron beam pulse. In recent years, a number of studies were designed to measure the angular and velocity distributions of desorbates obtained in rapid thermal desorption [7e,8]. Some of these studies indicated that the desorbate distribution functions measured in rapid desorption experiments are quite different 0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
196
J. Bloch, Y Zeiri / Rapid thermal desorption of di-atomic molecules
than those obtained in programmed thermal desorption (TPD) experiments. For example, in some systems the angular distribution of desorbates was strongly peaked towards the surface normal as compared to a cosine type distribution obtained in TPD experiments. In addition, some systems [8a] showed non-Boltzmann velocity distributions of desorbates. Both angular and velocity distributions have been found to be very sensitive functions of the initial surface coverage [8]. Evidently, the measured distribution functions emerge from the nature of the desorption dynamics together with the effect of post-desorption gas-phase collisions among the desorbates [gal. The role of post-desorption gas-phase collisions on the desorbate distribution functions has been studied recently using Monte Carlo simulations [9]. In addition, the dynamics of rapid desorption processes was investigated recently [lO,ll] using the stochastic trajectory technique. In the present study it will be assumed that the initial surface coverage is low, hence gas-phase collisions among desorbates can be neglected. In this work, we shall present the results of a theoretical study in which the rapid desorption of CO molecules from an unreconstructed Si(100) is simulated. This system was chosen due to its importance in the understanding of metal deposition using metal carbonyl parent molecules [4]. The calculations were performed using a stochastic trajectory approach in which the motion of each adsorbate is described by an effective equation of motion [12]. The calculations were aimed to study the relationship between the desorbate distribution functions and various characteristics of the system, such as, adsorption geometry, strength of molecular vibrational force constant and surface corrugation. Since no accurate interaction potential between CO and the Si(100) surface is available, the simulations in this work can be regarded as a model system study. The rapid heating of the substrate by a pulse of a laser or electron beam was simulated by a continuous variation of the amplitude of the random force terms in the effective equations of motion (EEM) [12] of the adsorbate. This procedure enabled us to accurately describe the rapid temperature variation of the irradiated zone [lO,ll]. In the next section we shall briefly describe the calculational procedure, while section 3 will be devoted to a discussion of the results. The last section contains a short summary.
2. Desorption model 2.1. EEA4 approach The simulations of rapid desorption have been carried out using a stochastic trajectory method in which the time evolution of the adsorbate motion is
.I. Bloch, Y. Zeiri / Rapid thermal desorption ojdi-atomic molecules
197
followed. According to the EEM approach [12], the motion of each adsorbed atom is governed by a Langevin type equation of motion of the form
(1) where M, and R, are the mass and position vectors of the i th adsorbate. The potential V(R,, S) represents the interaction of the ith adsorbate with the surface, where the surface atoms are fixed at their lattice points, while V(R) represents the intramolecular potential. In writing V( R,, S) it was assumed that the adsorbed atom is interacting with a single fictitious surface particle whose mass was taken to be equal to the mass of a silicon atom (see discussion below). The last two terms in eq. (l), r(R) and f(t), are a friction term and Gaussian random force respectively. These two terms are related by the second ~uctuation-dissipation theorem (f(t)
f(O))
= 3kT,(t)
I’(&)
a(t),
(2)
where k is Boltzmann constant, 7”(t) is the time dependent surface temperature and ( ) denotes ensembles average [lo-121. The thermal motion of the surface atoms introduces, in the EEM method 1121, a modi~cation term, W(Ri), which alters the adsorbate-surface interaction potential. The functional form of W(R,) is [12] W(R,)
= 1 - Ci/2MsDi,
(3)
where MS is the surface particle mass and c, =
a2v’( Ri) s)/aRif
,
0, = Wz - W$‘i’Jf + C;/M,.
(44 (4b)
The various parameters used in eq. (4) can be obtained from the phonon mode density of the surface [13]. If the Debye model is used to describe the phonon density of the solid one obtains ]13]: Wi = 0.6W& W2 = 0.262Wk and pi = 0.577Wn where W, is the Debye frequency of the solid surface. In all the calculations reported here the silicon Debye temperature was taken to be equal to 0 = 600 K (a = W,/k). Thus, the correction term, W(R,), represents a modification of the adsorbate-surface interaction due to the thermal motion of the surface atoms. The friction term in eq. (l), F( R,), is given by [12] r( Ri) = ~W~C~/M*M~~~D~,
(5)
where p = 0.167~rWo if the Debye model is used to describe the surface phonon spectra [12,13]. Eq. (1) is an effective equation of motion which describes the time evolution of the position and velocity vectors of each adsorbed atom (which
198
J. Bloch, Y. Zeiri / Rapid thermal desorption
of d&atomic
molecules
constitute the molecule). The two last terms together with W( R ;) represent the coupling of the adsorbate motion to the thermal motion of the surface atoms. Thus, the surface phonons are introduced in this approach in an average manner. Two points should be noted, first, if the surface temperature varies with time, so will the width of the Gaussian random force distribution, see eq. (2). The second point is related to the behaviour of the terms QR,) and W((R;) at Iarge adsorbate-surface separations. It is easy to see in eqs. (4) and (5) that both terms vanish when R, -+ co. Thus, at large particle-surface distances eq. (1) reduces to a deterministic Newtonian equation of motion. The main advantage of the EEM approach over more accurate methods, such as the one used in ref. [lo], is related to the large reduction in computation time. However, the energy exchange between the adsorbate and the surface is expected to be described less accurately when the EEM method is used. Thus, the discussion in the next section will emphasize the variation in relative magnitudes of the different quantities rather than their absolute value. A detailed derivation of eq. (1) together with a discussion of its accuracy are given in ref. 112). 2.2. Interaction potentials The present study was aimed at simulating the rapid thermal desorption of a di-atomic adsorbate at low initial surface coverage. Namely, it is assumed that the average distance between two adsorbates is large, hence, adsorbate-adsorbate interaction can be neglected. Consequently, the rapid thermal desorption of a single adsorbate was simulated. Unfortunately, very limited information is available in the literature about the CO/Si(lOO) system. However, the qualitative results of several experiments 1141 indicate that the binding of CO to the Si(100) surface is very weak. Since no quantitative information about the interaction potential between CO and the Si(100) is available, we have assumed that both the carbon and oxygen atoms interact with the surface via Morse-type potentials of the form y( R,, S) = De( x, y){,-~at~~~~r~-zoc~.~,l_
2
,-ptx.YMz-z,,(x.Y)l}.
In eq. (6) Z is the position of the i th atom along the surface normal while X and Y are its coordinates along the surface. The variation of the interaction potential along the surface is related to variations of the three Morse parameters. Once the lateral position of the ith atom is given, the three parameters in eq. (6) are determined according to the following relation: Q( X, Y) = A + B[cos(:!aX/a) + c cos(2nX/a)
+ cos(27iY/b)] cos(27rY/b),
199
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules Table 1 Morse parameters used in the different simulations; energy units are kcal/mol, cm -’ and distance in A Simulations
A, h C D, E, F G
H
Site
All All On-top Bridge Four-fold On-top Bridge Four-fold
frequency is in
Carbon
Oxygen
Q
R,
Q
we
R,
1.8 2.0 2.0 1.9 1.8 2.0 1.9 1.8
0.5 1.75 0.3 0.4 0.5 0.5 0.5 0.5
50 120 30 40 50 50 50 50
2.9283 2.0 3.1283 3.0283 2.9283 3.1283 3.0283 2.9283
3.0 1.75 2.6 2.8 3.0 1.8 2.0 3.0
a, 120 120 100 110 120 100 110 120
where Q stands for D,, p for 2, and the lattice constants are designated by a and b. The three coefficients in eq. (7) have the following form: 4A = 2Q(2) + Q(4) + Q(l),
@a)
4B = Q(4) - Q(l),
W)
4C = Q(4) + Q(I)
- 2Q(2),
(gc)
where Q(i), i = 1, 2, 4 are the values of the quantity Q over the on-top, bridge and four-fold sites respectively. Since the experimental TPD results [14] indicated that CO adsorption on Si(100) occurs at T, < 70 K, we assumed a total CO-Si(lO0) binding energy of 3.5 kcal/mol. The individual binding energies of the carbon and oxygen atoms to the surface were fixed according to the assumed adsorption geometry of the CO molecule. In all cases studied here, the sum of the individual binding energies at the best adsorption site was 3.5 kcal/mol. The interaction potential between the carbon and oxygen atoms, V(R), was assumed to be represented by a Morse function. The parameters used in the model potential function, described above, are listed in table 1. The various cases studied in this work differ in adsorption geometry, intramolecular force constant and surface corrugation, see table 1. In summary, the lack of quantitative information about the CO-Si(lO0) interaction leads us to use a model potential. Thus, the goal in these model calculations was to study the relationship between the dynamics of rapid desorption and the characteristics of the system. 2.3. Details of the calculations In order to simulate surface heating, a time dependent surface temperature, T,(t), was used in sampling the random force in eqs. (1) and (2). In all the
200
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
simulations described below, the time dependence of T, was assumed to have the form. T,(t)
= To+ T,[l -exp(-t/r)],
(9)
where To and T, are initial and final temperatures respectively, and r is a time constant. The functional form of T, in eq. (9) has been used in previous studies [lO,ll]. In the calculations performed in this work the following values for the constants in eq. (9) were used: To = 70 K, Tf = 2930 K and r = 0.25 ps. For each case 1000 trajectories were calculated with the integration time step value in the range (1-S) X lo-t6 s. In all the simulations the CO molecules were placed initially at their equilibrium positions with respect to the surface and at a C-O separation which corresponds to the gas-phase equilibrium distance (over the best adsorption site for corrugated potentials). The initial velocities were sampled from a canonical distribution at the surface temperature. Then, the system was allowed to equilibrate for 2000 integration steps before the surface heating was turned on according to eq. (9). A trajectory was terminated if the adsorbate-surface distance exceeded a value of 10 A or if 100000 integration steps were performed.
3. Results and discussion The present study summarizes the results of eight different simulations of rapid desorption. In all the calculations the gas-phase CO binding energy, De = 255.735 kcal/mol, and equilibrium distance, R, = 1.1283 A, were used [15]. These simulations were aimed to relate the desorption dynamics to the adsorption geometry, molecular force constant and surface corrugation. Table 2 summarizes the main features of the eight cases considered. Two adsorption geometries were considered: CO bound normal to the surface (with the carbon atom close to the surface, simulations A, B, C, G and H) and CO bound parallel to the surface (simulations D, E, and F). In addition, three oscillator frequencies were used, the gas-phase value [15] w, = 2169.81 cm-’ together with we = 1000 and 500 cm-‘. As shown in table 2, the first six simulations were performed on an uncorrugated surface, while in the last two cases different amounts of surface corrugation were introduced. All the parameters used for the adsorbate-substrate interaction potential are listed in table 1. It should be noted that in simulations G and H the four-fold site was assumed to be the best adsorption site. The average quantities of desorbate translational energy, (E), and its components along, ( Ep), and normal, (E,), to the surface are summarized in columns 2-4 in table 3. In addition, table 3 presents the average desorbate rotational, (E,), and vibrational, (E,), energies, as well as (cos 0) and (7”). Here, 8 is the angle between the direction of desorbate velocity vector and the
201
J. Bloch, Y. Zeiri / Rapid thermal desorptlon of di-atomic molecules Table 2 Parameters used in the different simulations; in all the calculations ps and maximum surface temperature was 3000 K Simulation
Surface corrugation (kcal/mol)
‘)
0.0 0.0 0.0 0.0 0.0 0.0 0.3 1.0
heating
time constant
Oscillator frequency (cm-‘)
Adsorbate geometry
2169.81 1000.00 500.00 2169.81 1000.00 500.00 500.00 500.00
Normal Normal Normal Parallel Parallel Parallel Normal Normal
was 0.25
a) Surface corrugation is measured as the difference in the CO binding energy over the four-fold and two-fold sites. These values measure the magnitude of the activation energy for diffusion from one four-fold site to the nearest neighbour four-fold site.
surface normal, while T, is the residence time of the desorbate on the surface. Note that the values of (E) are given in temperature units, i.e. the values in table 3 are obtained by dividing the calculated average translational energy by 2k. Inspection of table 3 shows that in all the cases considered, the average total desorbate translational energies are much lower than in the maximum surface temperature. Similar results were obtained in previous studies [lO,ll]. However, the values of (E) for CO adsorbed parallel to the surface (cases, D, E and F) are much larger than those obtained for normal adsorbates (cases A-C, G and H). Similar behaviour is obtained for (E,). Moreover, in all the simulations with a flat surface (cases A-F) a very small amount of energy is channeled into the desorbate motion parallel to the surface, ( Ep). Once Table 3 Average total, (E), normal, (E,), and vibrational, (E,), desorbates System
A B C D E F G H
(E)
(E,), and parallel, (En). translational energies; average rotational, energies and values of (cos 0) and the mean residence time, (T,) of
(En) (K)
(E,) (K)
(E,) (K)
(E,) (K)
(cos e>
(K)
R-) (PSI
296*11 300 * 10 313+12 511k19 5ooi19 472 + 17 278 f 15 343*17
571 f 22 579 + 19 606 f 24 1002&39 978 f 38 923 f 35 501 f 31 511+32
2150.6 21 f 0.6 21+0.6 20+0.6 21+ 0.6 22+0.6 56 f 6.0 176*11
282 k 16 325 f 16 314517 718f30 725 f 28 643+29 321+ 28 362+26
1148 f 49 1400 f 50 1393 + 54 804k 38 783 f 35 1080 + 44 1253 + 77 1207i63
0.95 f 0.027 0.94 k 0.023 0.95 k 0.025 0.97 + 0.012 0.96 + 0.027 0.96 + 0.027 0.90 * 0.038 0.79f0.022
8.2*0.11 10.0 f 0.16 10.0~0.21 4.0 * 0.08 3.9 f 0.08 4.0 + 0.09 11.0+0.42 11.0~0.31
202
J. Bloch, Y. Zeiri / Rapid thermal desorption
of di-atomicmolecules
0 no corrugation a low corrugation
1
l
high corruoation
0.8 z _, 2
*
0.6
.
0.4
10
20
30
40
50
60
70
80
90
@[Degrees]
Fig. 1. Desorbate angular distribution of normal CO for three values of surface corrugation (w, = 500 cm-‘). Marked points represent a statistical, cos 8, distribution.
surface corrugation is introduced, increased values of (E,) are obtained (simulations G and H). Thus, the coupling of the adsorbate parallel motion to the surface enhances energy transfer to this mode. Very similar results were obtained for atomic desorbates [ll]. The ratio between (E,) and (E,) determines the angular distribution of desorbates which is represented in table 3 by (cos 0). In the case of a statistical angular distribution (i.e. a cos 8 distribution), the mean value is (cos 9) = 0.667. All the values of (cos 8) in table 3 are larger than the statistical one, namely the corresponding distributions are highly peaked towards the surface normal. However, increased corrugation results in a significant decrease in the value of (cos 8), hence, to a broader angular distribution. The actual distributions obtained in simulations C, G and H are shown in fig. 1 (histograms) together with the statistical cos 0 distribution (marked points). The broadening of the angular distribution for increased surface corrugation is clearly seen in fig. 1. These results were numerically fitted to distributions of the form cos”8. The best fits were obtained for n values of 37, 26 and 9 for the no, low and high corrugation cases respectively. Comparison of the average residence times, for normal and parallel adsorbate, shows that the former corresponds to much larger values of (7”). In addition, residence time distributions for simulations A and D are shown in fig. 2, while fig. 3 presents the distributions obtained in cases C and F. The differences, discussed above, between (E) and (r,) values of adsorbates bound to the surface in a perpendicular and parallel geometry can be under-
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
203
0 . .’
j-
0.2
‘;: .z
Q
normal CO/Si(lOO)
.
parallel CO/Si(lOO)
0.2
5 ?
P
.r f l?L v
0.15
0.1
0.05
0
1
23
4
5
67
8
9
10 11
12
nun 13
14
15
Desorption T ime (psec)
Fig. 2. Residence time distribution for normal and parallel CO (w, = 2169 cm-).
stood by analyzing the desorption mechanism. In both situations the adsorbate interacts with a heat reservoir (the crystal). Thus, in both cases the adsorbate suffers random “kicks” due to the thermal fluctuations of the surface. We now assume that a large fraction of adsorbates desorbe when a single “kick” they obtain is larger than the adsorbate-surface binding energy [lo]. Consequently, in the case of normal CO the “kick” to break the C-surface bond should be much larger than the “kicks” needed to break the C-surface and O-surface bonds in parallel CO. The probability to obtain a “kick” of magnitude F, at a given time (or surface temperature) is given by
WI P(e) = (25~~)~‘~ exp( -4*/2a*),
(10)
where (I is the random force distribution width [16]. Since the C-surface bond, for perpendicularly bounded CO, is roughly twice the C-surface and O-surface bonds in parallel CO, the ratio between the strength of “kicks” to break these bonds will also be two. Thus, the corresponding ratio of “kicks” probability is P($)/P(2E;;)
= exp(3q2/2a2).
In other words, this probability
(11) ratio is proportional
to P(c.)-3
where
204
.I. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.3
0.25
0
normal CO/Si(lOO)
n
oarallel CO/Si(lOO)
0.2 :: .r 5 2 0.15 L " 2 4 F 0.1
0.05
0
1 1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
16 17 18 19 20 21 22 23 24
Desorption Time[psecl
Fig. 3. Residence
time distribution
for normal
and parallel
CO (w, = 500 cm-‘).
0 < P(q) I 1. This discussion gives a qualitative understanding of the difference in (7”) values obtained for the two adsorption geometries. The fourth and fifth columns in table 3 describe the desorbate average rotational and vibrational energies respectively. It is clear from these results that variation of a oscillator frequency and surface corrugation leads only to minor changes in the values of (E,) and (E,). On the other hand, variation in the adsorption geometry leads to large changes in the magnitude of these quantities. For normal CO the values of (E,) are much smaller than those for parallel CO, while the opposite situation occurs in the case of average vibrational energy. This behaviour can be explained by the schematic description of the desorption event shown in fig. 4. For normal CO, fig. 4A, the force acting on the adsorbate, during the desorption, is mainly along the molecular axis. The results of such a situation is that energy can be channeled more efficiently into the vibrational mode rather than into the rotational one. On
205
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
A
Fig.
4. Schematic
description
of the desorption mechanism adsorbates.
for normal
(A) and
parallel
(B)
the other hand, for a parallel CO, fig. 4B, one atom-surface bond will break first while the other bond still exists. In such a situation, the adsorbate will exhibit a strong frustrated rotational motion which will be converted into free rotational when the desorption process is completed. The actual rotational and vibrational distributions for simulations C and F are shown in figs. 5 and 6 respectively. It is clear from these results that for parallel CO the rotational 0.5
q normal m
CO/Si(lOO)
parallel CO/Si(lOO
0.4 ‘;: .z ;
0.3
I .z g
0.2
0.1
2
m,
0.0 : 10
20
30
40
Quantum
Fig.
Rotational
for
and
CO
=
cm-‘).
206
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.6
c] normal CO/Si(lOO) m
0
12
3
45
67
parallel CO/Si(lOl
8
910
11
Vibrational Quantum Number
Fig, 6. Vibrational
distributions
for normal
and parallel
CO (we = 500 cm- ‘).
distribution is much wider than for normal CO (fig. 5) while in the case of the vibrational distributions the opposite behaviour is obtained (fig. 6). The discussion above is related also to the differences between the T, distributions of normal CO with two different oscillator frequencies (figs. 2 and 3). When the CO force constant is decreased, the cross section for energy transfer from the C-surface vibrational mode to the CO internal vibration is much larger than for an adsorbate with a high oscillator frequency. Thus, in the low frequency case, part of the energy transferred to the adsorbate-surface bond is redistributed in the adsorbate internal degrees of freedom. Consequently, increasing amounts of energy have to be transferred from the surface to cause desorption. The net result will be larger residence times for low frequency diatomic adsorbates as shown in figs. 2 and 3. It was noted above that the average values for the desorbate rotational and vibrational energies do not show a strong dependence on oscillator frequency and surface corrugation (see table 3). We now turn to the examination of the actual rotational and vibrational distributions and their dependence on the molecular force constant and surface corrugation. In figs. 7 and 8 the rotational distributions for normal CO are shown for the three oscillator frequencies studied (fig. 7) and for various degrees of surface corrugation (fig. 8). These results clearly show that the rotational distribution is independent of the molecular force constant and has only a weak dependence on the surface corrugation. Increased corrugation results in a slight broadening of the rotational distribution, fig. 8.
J. Bloch. Y. Zeiri / Rapid thermal desorption of di-atomic molecules
207
0.5
0.4
0.3
0.2
0.1
n 5
10
15
20
25
30
35
40
Rotational Quantum Number
Fig. 7. Rotational distribution of normal adsorbates for three adsorbate oscillator frequencies.
Similar examination of the vibrational distributions shows that these are more sensitive to a variation in oscillator frequency. Figs. 9 and 10 present the variation of the vibrational energy distributions as a function of oscillator frequency for normal and parallel CO respectively. These results show that also the average values of vibrational energy depend weakly on the molecular force constant, the actual distributions exhibit a clear broadening when the oscillator frequency is reduced. Thus, a decrease in w, results in the population
0I] ow corrugation m high corrugation
Rotational Quantum Number
Fig. 8. Rotational
distribution
of normal CO for three values of surface corrugation cm-‘).
(w, = 500
208
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
0.7 I7 we=2169 cm-l
q we=1000
0.6
cn-1
m we= 500 cm-l
1
2
3
4
5
6
7
8
9
10
11
12
Vibrational Energy [K] /lo00
Fig. 9. Vibrational
energy
distribution
of normal CO for three frequencies.
values
of adsorbate
oscillator
of higher internal vibrational states of the desorbates. Moreover, figs. 9 and 10 indicate that this broadening of the distributions for decreased values of W, is weakly dependent on the adsorption geometry. Fig. 11 presents the vibrational distributions for normal adsorbate (w, = 500 cm-‘) at three surface corrugation values (see table 2). Except for minor changes in the distribution, these results indicate that the vibrational distributions do not vary significantly when surface corrugation is changed. Comparison of the results obtained in the present simulation with those of ref. [lo] shows that all quantities except (E,) exhibit a similar range of values. There is a large discrepancy between the values of (E,) obtained in the two simulations. In the present work the amount of average vibrational energy of the desorbates is much larger than the values obtained in ref. [lo]. In addition, the calculations of Lucchese and Tully [lo] show a strong dependence of (E,) on o, where in the present study a much weaker dependence is found. One possible source for this discrepancy is related to the different calculational approaches used in the two simulations. As discussed above, the EEM method used here, is less accurate in describing adsorbate-surface energy transfer than the approach used in ref. [lo]. Thus, the discrepancy in (EY) values may be
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
209
0.8 Due=2169
cm-l
~~~~-1000
cm-l
0.6
0.4
0.2
0 Vibrational Energy (K)/lOOO Fig. 10. Same as fig. 9 for parallel adsorbate.
0
o'5r
no corrugatian
•I low corrugation I high corrugation
0.2
0.1
n
0
12
3
4
56
7
8
9
10
11
Vibrational Quantum Number
Fig. 11. Vibrational
distribution
of normal CO for three values of surface corrugation (we = 500 cm-‘).
210
J. Bfoch, Y. Zeiri / Rapid thermal desorption
ofdi-atomicmolecules
attributed in part to the unaccurate description of the system by the EEM method. However, if the crudeness of the approximations in the EEM approach is the source for this discrepancy in the values of (E,) one would expect similar disagreements in the magnitude of other quantities (e.g. average translational and rotational energies). Comparison of the (E) and (E,) values present in table 3 with those of table 1 in ref. [lo] show that these quantities exhibit similar values. Thus, the disagreement in the magnitude of (E,) in the two studies cannot be attributed only to the unaccuracy of the EEM approach. An additional major difference between the present study and the one presented in ref. [lo] is due to the adsorbate-surface interaction potential used in the two simulations. For example, the CO-Si(lO0) binding energy in the present work was taken to be 3.5 kcal/mol while the corresponding value for the NO-LiF(lOO) system in
0
Normal CO/Si(lOO)
a
Parallel CO/Si(lOO)
22 23 24 Residence time
Fig. 12. Variation
of average
vibrational energy parallel adsorbates
ipsecl
as a function of residence (w, = 1000 cm- ‘).
time for normal
and
J. Bloch, Y. Zeirz / Rapid thermal desorption of di-atomic molecules
211
ref. [lo] is 2.075 kcal/mol. In addition, the variations of the potential energy as a function of adsorbate orientation (the angle between the molecular axis and the surface normal) are quite different in the two simulations. A direct consequence of these differences in adsorbate-surface interaction potentials is the larger values of (T,) obtained in the present work. These long residence times may result in a larger degree of thermalization of the adsorbate vibrational mode at the elevated surface temperatures. The variation of ( EY) as a function of residence time for simulations B and E are shown in fig. 12 These results clearly indicate that the magnitude of (E,) increases for longer residence times. It should be noted that for small T, values (T, s 2 ps) the magnitude of (E,) agrees well with those of ref. [lo]. Moreover, the large increase in (E,) for long residence times, see fig. 12, may wash out the differences between simulations in which the molecular force constant was changed. Recently, Muckerman and Uzer [17] have studied the desorption dynamics of vibrationally excited adsorbed CO on an NaCl surface. In this study [17], the results of a one-dimensional quantum mechanical approach were compared to those of a classical calculation with and without the inclusion of the surface thermal motion. Despite the large discrepancy between the frequencies associated with the C-O and CO-surface bonds, efficient energy transfer between the two modes was obtained. The calculated average adsorbate lifetimes were of the order of 1 ps. Assuming microreversibility, these results substantiate our findings about vibrational thermalization of CO adsorbed on a hot surface. Furthermore, recent experiments [18] on laser induced desorption of NO from a Pt foil yield vibrationally hot desorbates with a vibrational temperature of 700 K. These results are in good agreement with the (E,) values obtained in the present study.
4. Summary A model study of rapid thermal desorption of diatomic molecules from a solid surfaces has been presented. The masses and some of the other quantities used in the calculations correspond to a CO molecule adsorbed on a Si(100) surface. However, the lack of information about the detailed CO-S1 interaction potential led us to the use of a model potential. This study was aimed at establishing the relationship between the desorption kinetics and various characteristics of the system. In particular, we were interested in the influence of adsorption geometry, oscillator frequency and surface corrugation on the desorption mechanism. It was found that increased surface corrugation has a large impact on the width of the desorbate angular distribution. Similar effect was found for atomic adsorbates [ll]. This suggests that if these rapid
212
J. Bloch, Y. Zeiri / Rapid thermal desorption of di-atomic molecules
desorption studies will be performed on different low Miller index surfaces of the same materials (different planes exhibit usually different corrugations), one would expect to obtain broader angular distributions for planes with higher corrugation. The most pronounced effect on the desorption kinetics was found to be related to the adsorption geometry. It was found that adsorption along the surface normal leads to larger amounts of energy channeled into the desorbate vibrational mode as compared to the rotational mode. The amount of average vibrational energy as well as the vibrational distributions were found to exhibit a weak dependence on the adsorbate oscillator frequency. For CO adsorbated parallel to the surface, a more efficient energy transfer into rotational modes was found. The differences in the amount of internal energies of normal and parallel adsorbates have been analyzed on the basis of a comparison between the two desorption mechanisms.
Acknowledgment This work has been partly supported by the Israeli and Development under contract No. 2564.
Council
for Research
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