- Email: [email protected]
Role of hydrogen for adsorption and diffusion of a Si adatom on monohydride and dihydride Si(0 0 1) surfaces
Surface Science 470 (2000) 89±105
www.elsevier.nl/locate/susc
Role of hydrogen for adsorption and diusion of a Si adatom on monohydride and dihydride Si(0 0 1) surfaces Seung Mi Lee a, Young Hee Lee a,b,*, Nam-gyun Kim c a
Department of Semiconductor Science and Technology, Semiconductor Physics Research Center, Jeonbuk National University, Jeonju 561 756, South Korea b Department of Physics, Jeonbuk National University, Jeonju 561 756, South Korea c Department of Bionics and Biomedical Engineering, Jeonbuk National University, Jeonju 561 756, South Korea Received 26 April 2000; accepted for publication 5 September 2000
Abstract We investigate adsorption and diusion of a Si adatom on monohydride and dihydride Si(0 0 1) surfaces using ®rst principles calculations. We ®nd that adsorption and diusion of a Si adatom on hydrogenated Si(0 0 1) surfaces are drastically altered from those on a clean surface in several ways. Both positions and number of adsorption sites vary with dierent coverages of hydrogen, leading to completely dierent diusion behavior from the clean surface. The Si adatom is stabilized by capturing surface hydrogen without potential barrier during adsorption. The H atom hops back and forth exothermally to the adatom during diusion and thus, the diusion species is no longer Si adatom itself. It reveals dierent diusion features that typical potential energy surface with a single adatom fails to describe. Dierences in the adsorption and diusion of Si adatom between monohydride and dihydride phases are discussed. The role of hydrogen as a surfactant on hydrogenated surface will be further discussed based on our calculations. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Low index single crystal surfaces; Adatoms; Chemisorption; Surface diusion
1. Introduction A surfactant has often been introduced in heteroepitaxial crystal growth of semiconductors and metals to suppress segregation of adsorbates to the growth surface [1±15]. The introduction of a surfactant prior to the deposition of adsorbates not only changes the surface free energy [16±19], but also alters kinetics signi®cantly [20,21] so as to * Corresponding author. Tel.: +82-63-270-3336; fax: +82-63270-3585. E-mail address: [email protected] (Y.H. Lee).
enhance exchange of adatoms to subsurface atoms in a concerted way over the simple surface diusion. This promotes layer-by-layer growth and thus, increases the abruptness at the interface. Prerequisite conditions for a surfactant are in general such that it should have (i) weaker binding energy and/or greater radius than adsorbates, (ii) low solid solubility, and (iii) shallow impurity levels (not to contribute to traps in case some remain in the epilayer after the growth). For instance, Ge atoms can easily segregate onto the front growing surface during Ge/Si growth, making less abrupt interface. Group V materials such
0039-6028/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 0 ) 0 0 8 4 5 - 1
90
S.M. Lee et al. / Surface Science 470 (2000) 89±105
as As, Sb, and Bi are good surfactants in order to suppress the Ge out-diusion since they all satisfy the above conditions. Such surfactants have led to a needle-like epitaxial growth along the dimer rows [16]. Several theoretical models for the exchange mechanism to explain the experimentally suggested needle-like epitaxial growth have been proposed, based on ®rst principles calculations [17±22]. However, the ion scattering measurements show disagreements with previously proposed theoretical models [23]. Unlike such typical surfactants of group V materials, the H atom has smaller atomic size than the most typical adsorbates and yet, behaves as a surfactant in many dierent systems [4±15]. When H atoms are introduced prior to the deposition of Ag on Si(1 1 1) surface, the growth mode changes drastically from the Stranski±Krastanow mode to the Frank±Van der Merwe mode, and the number of nucleation sites increases [7]. In spite of the high experimental temperature, where most hydrogen atoms are expected to desorb, abruptness of heterointerface is improved with exposure of the surface to an atomic hydrogen ¯ux [5]. H atoms can also anneal away Ge islands eciently similar to the typical group V surfactants [6,15]. Typical Ge overlayer deposition on Si(0 0 1) surface can lead to layer-by-layer growth up to about four monolayers, followed by island formation. Recent STM measurements with the dynamical supply of atomic hydrogens during Ge overlayer growth on the Si(0 0 1) surface clearly demonstrate that Ge islands do not grow in the presence of one monolayer of atomic hydrogen and furthermore, no needle-like step growth is observed [24]. The previous calculations showed that the Si adatom picks up the H atom on the hydrogenated Si(0 0 1) surface [25±27]. Although numerous experimental data exist, theoretical understanding for the role of H as a surfactant still lags far behind. The key issue here is to understand the adsorption and diusion of a Si adatom on hydrogenated surfaces and further, gain an intuitive picture for the role of the H atom as a surfactant. Since H is quite dierent from group V materials in Ge/Si epitaxial growth as mentioned above, we like to understand similarities and dierences of H
atoms from typical group V surfactants from atomic point of view. We particularly focus on adsorption and diusion of an adatom in the presence of H atoms, H hopping (or exchange) mechanism, and island suppression mechanism. The surface morphology of overlayer growth strongly depends on the hydrogen coverages. Therefore, adsorption and diusion on various hydrogen coverages should be further theoretically investigated in principle in order to completely understand the role of hydrogen in epitaxial growth. We choose in this paper two limits of hydrogen coverages, monohydride and dihydride surfaces. This should provide all the necessary informations for adsorption and kinetics of adatoms and further, provide physical intuition for the role of hydrogen as a surfactant. We ®nd from the ®rst principle calculations that (i) the presence of H atoms increases the number of adsorption sites by about three times on monohydride compared to that of a clean surface, whereas this value decreases on the dihydride, (ii) H atoms change the surface diusion to be isotropic compared to the clean Si(0 0 1) surface, leading to the disappearance of a needlelike step growth, (iii) the location of adsorption sites is signi®cantly altered on hydrogenated surface, (iv) the H atom lowers the surface free energy by hopping back and forth exothermally to adatoms from the preadsorbed surface, trying to saturate all possible dangling bonds of adatoms and surface atoms, and (v) the potential surface becomes rougher, particularly on the dihydride surface, delaying the onset of island growth. 2. Theoretical approaches Our calculations have been carried out using Car±Parrinello molecular dynamics approach [28]. In this scheme, ionic and electronic forces are derived separately from an eective Lagrangian based on the local-density approximation (LDA) of the density-functional theory. The interaction between ionic cores and valence electrons is described by a fully nonlocal norm-conserving pseudopotential with a separable form of s nonlocality for Si introduced by Kleinman and Bylander [29]. Similarly, the H atom is treated locally
S.M. Lee et al. / Surface Science 470 (2000) 89±105
[25±30]. The exchange-correlation energy is treated by Ceperly and Alder's scheme [31]. The electronic wave functions are expanded with a kinetic energy cuto of 8 Ry, and Bloch functions at C point of the supercell surface Brillouin zone are used. This choice of parameters with supercell geometry, which will be described later, gives reasonable accuracies in the energetics and local bonding con®gurations through the calculations compared with other theoretical results. Detailed comparisons will be given in the discussion. The preliminary test for silane molecule gives the Si±H bond and symmetric vibrational frelength of 1.54 A quency of 267 meV, compared to experimental and 271 meV [32], respectively. values of 1.48 A With the cuto of 20 Ry, these values are 1.52 A and 254 meV, in good agreement with the fact that the LDA approach usually underestimates vibrational frequencies [33±35]. The convergence test is also performed in a supercell geometry. The total energy for the 4 2 supercell is changed by 0.4 eV/atom when the cuto of 10 Ry was used. However, the relative energy dierence between two transients, adsorption points with larger cuto (16 Ry) is less than 0.15 eV and the bond length changes are negligible. Therefore, we estimate the energy dierence between dierent transient points to be approximately less than 0.2 eV. The size of the supercell may be of sources of errors. Doubling the size of supercell gives the energy dierence between dierent con®gurations to be of less than 0.1 eV [36]. We search for the electron energy minimization using a steepest decent approach for a given geometry. Ions are then moved by the fast relaxation scheme [37]. Remaining forces on sur in equiface atoms are less than 1:5 10ÿ3 Ry/A librium. The energy is converged to 1:0 10ÿ5 Ry through the calculations. The surface is simulated by a periodically repeated slab of Si atoms in which six atomic layers (each layer with 4 2 surface unit cell) are included, with the bottom surface terminated by hydrogens to emulate a bulk-like Si and the top Two surface followed by a vacuum region of 8 A. bottom Si layers and an additional H layer are ®xed to prevent any spurious forces by H atoms. Thus, this choice of supercell is usually sucient for most Si surface calculations [19,21,22,25,26].
91
3. Results and discussion Our aim here is to understand the microscopic picture of adsorption and diusion of Si adatoms on hydrogenated Si surface. Monohydride 2 1 phase, 3 1 phase (ordered mixture of monohydride and dihydride), and dihydride 1 1 phase are observed experimentally depending on the hydrogen coverage h [38±41]. In this paper, we choose two limits of coverage, monohydride h 1 and dihydride h 2 Si surfaces. This will provide enough physical intuition in understanding the microscopic role of hydrogen during the adsorption and diusion of adatoms on hydrogenated surfaces. Clean Si(0 0 1) surface is stabilized by forming p 2 2 or c 4 2 with an asymmetry of 0.69 A [42]. Signi®cant charges are transferred from the atoms in the second layer to the up atoms of dimer [43]. Three adsorption sites per 2 1 surface cell are found when bare Si adatoms are adsorbed on the dimerized Si(0 0 1) surface [44]. The diusion of Si adatom on the clean (without hydrogen) Si(0 0 1) surface is anisotropic, i.e., an activation energy of 0.6 eV is required for diusion parallel to the dimer rows and 1.0 eV for diusion perpendicular to the dimer rows [44]. It is our intention to understand how the diusion process of adatom changes on the hydrogenated surface. 3.1. Monohydride With one monolayer of H atoms on buckled p 2 2 surface, the buckling is completely removed with charges being neutralized in the up and down atoms, and the surface becomes 2 1 phase. Bond lengths of dimer and Si±H are 2.41 respectively, comparable to 2.40 and and 1.55 A, of previous LDA calculations [45]. 1.54 A 3.1.1. Adsorption We now add one Si adatom per 4 2 surface unit cell to ®nd stable adsorption sites. Si adatom is initially added on the surface at the relative dis away from adjacent surface tance of at least 2.8 A Si atoms. In order to draw the potential energy surface for Si adatom, we divide the surface primitive cell by 45 mesh points. The spacings between
92
S.M. Lee et al. / Surface Science 470 (2000) 89±105
in the x- and y- directions. mesh points are 0.48 A For a given planar point, the adatom is allowed to move along the z-direction while relaxing all the atoms in four sublayers. The potential energy surface is drawn with respect to the H point. The presence of hydrogen atoms modi®es notably the potential energy surface for Si adsorption, dierent from the clean surface as shown in Fig. 1.
(a)
(b)
H
M
H’
M1
D M2
S
Fig. 1. (a) Potential energy surface of a Si adatom on the monohydride Si(0 0 1) surface and (b) its potential contour in two-dimensions. The heavy solid lines in (b) indicate the Si dimer bonds on the surface. The ®lled balls represent the Si atoms in dimer and the smaller empty balls indicate hydrogen atoms. The adatom±H pair is formed inside the dashed line. The energy dierence between lines is 0.1 eV. H0 , M1 , M2 are adsorption sites. H and M are shown for comparison with adsorption sites of the Si adatom on bare Si surface. D is the barrier point, and S is a saddle point. The respective adsorption points are explained in the text.
First of all, the adatom prefers to adsorb at H0 , M2 (new adsorption positions), and M1 sites near the dimer in the trough as shown in Fig. 1, different from H and M sites on the clean surface [44]. The corresponding con®gurations are shown in Figs. 2 and 3. The H site is a stable site for the clean surface, but now is shifted to the H0 site near the dimer on monohydride surface. Similarly, the M site is shifted to the M1 site in the trough. The S site is a saddle point, whereas the D site, on the center of the dimer, is the highest barrier point. We ®nd a new adsorption site of M2 located near the dimer atom, as shown in Fig. 1. Energies of the H0 , M1 , and M2 sites are lowered by picking up a hydrogen atom from the dimer atoms in the sublayer, as also observed in the previous reports [25± 27]. Note that the number of adsorption sites per 2 1 surface unit cell is increased to eight, about three times larger than that on the clean surface. The M1 site is the most stable adsorption site with a binding energy of ÿ3:9 eV whereas the H0 and M2 sites give slightly weaker binding energies by 0.2 eV than the M1 site does. It is interesting to see how the energy of these binding sites is lowered during the adsorption process. The energy gains near the H0 , M1 , and M2 sites are achieved by the hopping of the hydrogen atom to the adatom from the preadsorbed surface dimer. Fig. 2 illustrates the typical snapshots of the Si adatom approaching to one of the adsorption sites (M1 ) during the optimization process. When the Si adatom approaches to the hydrogenated surface, the H atom hops exothermally to the adatom in order to stabilize the lone electron of an adatom. In the mean time the adatom forms new bonds with one of the dimer atoms inducing an asymmetry as shown in Fig. 2(c), and ®nally with the subsurface atoms respectively, with bond lengths of 2.24 and 2.53 A, as shown in Fig. 2(d), resulting in a new p-bonded structure between them [17]. This is simply a manifestation of ¯oating bond that exists in the amorphous Si network, and is induced by the existence of dangling bonds of the adatom. Once the hopping is achieved, the dimer bond length is re from 2.41 A (Fig. 3(a)). Similarly, duced to 2.38 A the H0 and M2 sites are stabilized by hydrogen hopping, as shown in Fig. 3(b) and (c).
S.M. Lee et al. / Surface Science 470 (2000) 89±105
93
Fig. 2. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom at the M1 site in ball and stick forms. Bond lengths are in units of A.
The D site is the diusion barrier with a height of 1.4 eV with respect to the H0 . When approaching to the D site, the adatom cannot break the dimer while sustaining the bond length of 2.58 with its adjacent dimer atoms, as shown in Fig. A 3(d), due to the existence of energy barrier. 1 The adatom may then have probability to break the dimer at the typical experimental temperature. In fact, the dimer bond breaking actually strengthens the bondings of adatom with the surface dimer gaining energy by with bond length of 2.35 A, ÿ1:74 eV, as shown in Fig. 3(e). Note that the dimer atoms are completely hybridized with their
1
The D point is in good contrast with the E point in Refs. [25±27] which is the local minimum. We checked the energies with more mesh points near the D point. Adsorption energies near the D point (including D) vary very rapidly, as shown in Fig. 1, but the D site is still the barrier point, where the D point cannot possess H atoms and therefore, has higher adsorption energy. However, Si±H can be formed at very near the D site, having larger adsorption energy, as indicated by the dashed line in Fig. 1(b). We conjecture that the dierence may be due to the coarse meshes used in their works.
neighbor atoms including the H atom. We further tried the adatom picking up two hydrogen atoms from the preadsorbed surface dimer. This lowers the energy further to ÿ2:56 eV, as shown in Fig. 3(f ). In this case, however, the dimer formation in the subsurface is recovered, implying that higher H coverage may be detrimental to the surface morphology [12±14,24,46]. The adatom approaching to the D site also has a chance to diuse to the H0 site, picking up the H atom from the preadsorbed surface dimer which will be discussed later. Thus far we observed three dierent adsorption sites (H0 , M1 , M2 ). The energy gain by the adatom adsorption is achieved by H hopping mechanism from the surface dimer to the adatom. It increases the number of adsorption sites by a factor of 2.7 per surface primitive cell, compared to that on the clean surface. Adsorption at the M1 site should occur more frequently than at other sites due to its stronger binding energy. This is in excellent agreement with recent STM observations that most adsorption sites are placed near the dimer sites, and the M1 site is more probable than other sites (M2 and H0 ) [24].
94
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) no adatom 2.41 1.55
(b) H’ site
2.76
1.59 2.35
(c) M 2 site
(d) D site (0.0 eV)
1.60
1.60
2.58
2.34 2.45
2.44
(e) D site (-1.74 eV)
(f) D site (-2.56 eV)
1.56
1.55
2.35
2.33
2.44
Si adatom
bulk Si
H
Fig. 3. Various adsorption con®gurations in equilibrium. (a) The monohydride surface without an adatom, the local con®gurations when the Si adatom is at (b) the H0 site (local minimum site), (c) the M2 site (local minimum site), (d) the D site (barrier point), (e) when the dimer is broken at the barrier point, and (f ) when the adatom captures two hydrogen atoms from adjacent surface Si atoms. Bond lengths are in units of A.
3.1.2. Diusion We now study the diusion of adatom on monohydride surface. The potential contour upon the adsorption of a adatom (Fig. 1) in general gives rise to the estimation of the reasonable diffusion pathways. However, in adsorption of adatom on hydrogenated surface, it is reasonable to consider the diusion of Si±H, not the bare Si adatom, since the adsorption occurs via H hopping to adatom forming Si±H bond. In Fig. 4(a), we show the potential pro®le for several pathways. Escaping from the M1 site to diuse along the dimer row in the trough (path I) requires 0.5 eV (the M1 site is the reference point in this case) where the
barrier occurs at step (I-3). We note that at this barrier point, the H atom located at the adatom returns to the dimer position behind, as clearly visualized in the snapshots of Fig. 5. The Si±H cluster sees the preadsorbed the H atom on the next dimer and thus, is stabilized by capturing it (Fig. 5(a)). Once Si±H cluster captures the H atom, two H atoms in the cluster push back to each other sterically. The close distance from the dimer behind enables to accommodate exothermally the H atom hopping back to the original dimer as shown in Fig. 5(d). Then the con®guration in the step (I5) in Fig. 4(b) is identical to the M1 site (step (I-1) in Fig. 4(b)) in equilibrium. We should point out
S.M. Lee et al. / Surface Science 470 (2000) 89±105
95
Fig. 4. (a) Potential pro®les for various pathways. The lines are drawn by the cubic-spline method for eyes only. (b) The corresponding geometries of each pathway. The M1 site is taken here as a reference.
96
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) 0.0 eV (1.57, 1.59)
(b) -0.84 eV (1.69, 1.60)
(c) -1.32 eV (1.58, 1.70)
(d) -1.96 eV (1.58, 1.58)
Si adatom
bulk Si
H
Fig. 5. The snapshots (top views) of Si±H approaching to the next dimer during the diusion process. The numbers in parentheses represent the Si±H bond lengths as indicated by arrows. The bond lengths are in units of A.
that the position of Si adatom in the step (I-3) of Fig. 4(b) is dierent from that of Fig. 2(b) in Ref. [29]. The Si±H is stable in the middle of two dimers, which requires a barrier to detach the hydrogen atom, whereas in our case, a slightly misplaced Si±H from the middle does not require the barrier to exchange the hydrogen atom. There is another possibility of having dierent pathway from the step (I-3) by pushing down the adatom into the surface. This may result in the exchange adatom with surface Si atom, which was reported previously [25,26]. We also investigate dierent pathways, as shown in Fig. 4(b) (path II). Migration of Si±H from M1 along the dimer direction ®rst faces a potential barrier of 0.5 eV at the step (II-2) and then faces slightly higher barrier of 0.6 eV at the step (II-5), where most energy cost comes from with one of the dimer longer bond length (2.6 A) atoms behind. At the step (II-5), we note that Si±H does not pick up the H atom from the other side of the dimer, unlike the case of the step (I-3). This is understood by the directional dependence of the H bond on the dimer, the degree of freedom of the H atom on the adatom which can be freely rotated, and the long distance of the H atom from the dangling bond of the dimer atom behind. Since the
step (II-4) gives local minimum, we consider another pathway, path III, as shown in Fig. 4(b). Diusing on the dimer row along the direction of the dimer row (path III) requires a relatively high diusion barrier of 1.65 eV, since it involves creation of a dangling bond and severe bond angle distortions. The diusion pathways shown in Fig. 4 are somewhat dierent from those on the clean surface. Si±H diuses in the trough along the dimer row with a barrier height of 0.5 eV on the hydrogenated surface (path I), whereas on the clean surface the Si adatom diuses on top of the dimer row with a barrier height of 0.35 eV or in the trough along the dimer row with barrier height of 1.0 eV [44]. The Si±H diuses near the dimer perpendicularly to the dimer row (path II) with a barrier height of 0.6 eV on the hydrogenated surface while on the clean surface the Si adatom diffuses between the dimers across the dimer row with the same barrier height [44]. The diusion of the adatom becomes isotropic on the hydrogenated surface. Therefore, we expect that the surfactant (group V material)-induced needle-like step growth is unlikely to be observed at a moderate temperature range and at a low ¯ux rate of the incoming adatoms. We also note that the surface diusion
S.M. Lee et al. / Surface Science 470 (2000) 89±105
could be suppressed due to the higher diusion barrier. The tendency of suppressing the surface diusion in the presence of H atoms is in fact observed in many experiments [6,7,9,24,47]. This will lead to the delay of the onset of island formation. 3.2. Dihydride Dihydride is an ideal 1 1 phase where top Si dangling bonds are fully saturated by two hydrogen atoms. Fig. 6(a) shows the dihydride Si sur become shorter face. Si±H bond lengths of 1.53 A than those of monohydride surface. Since H±H strong distances between adjacent sites are 1.50 A, H±H repulsion forces do exist. Fig. 6(b) shows a more stable con®guration, the canted dihydride phase. Two hydrogen atoms are rotated so as to minimize H±H distances. The energy becomes lower by 0.1 eV per hydrogen atom, comparable to 0.09 eV from the previous pseudopotential calculations [45]. Now all H±H distances in the adjacent sites become maximized in the canted dihydride. We therefore use the canted dihydride in the next calculations in order to investigate the adsorption and diusion on two monolayer coverage of hydrogen. We also tried adsorption on an ideal dihydride. The potential surface was more symmetric but similar to that of the canted dihydride, and adsorption of the adatom near the preadsorbed hydrogen changed the surface structure to the canted phase after full relaxation.
(a) 0.0 eV 2.34 (2.33)
1.53 1.50 (1.50) 100 (1.51) (102 )
bulk Si
97
3.2.1. Adsorption We now bring a bare Si adatom onto the canted dihydride surface, which is similar to the monohydride surface, in order to draw the potential surface. Si adatom is initially added on the surface away at the relative distance of at least 1.75 A from adjacent surface H atoms. As illustrated in the dotted line in Fig. 7(b), we divide the surface primitive cell by 12 mesh points, as shown in the dashed line of Fig. 7(b). The spacings between in the x- and y-directions, mesh points are 0.96 A similar values to the previous calculations [25,26]. Long and short solid lines indicate the bonds of the top and bottom surface hydrogen atoms, respectively, in the canted phase. For a given planar point, the adatom is allowed to move along the zdirection, while relaxing all the atoms in four sublayers. The potential energy surface is drawn with respect to the B point. The potential surface of the dihydride phase is very dierent from monohydride phase. First of all, surface morphology becomes rougher than that in monohydride. The B site is the barrier point since the distances of adatom with its adjacent Si surface atoms are far and no energy gain by hydrogen hopping is involved. We can also see two dierent saddle points, S1 and S2 . The numbers in the dotted box indicate the number of hydrogen atoms hopping to the adatom from the preadsorbed surface. The M site is the adsorption site. We note that the M site is much deeper with adsorption energy of ÿ4:1 eV due to the capturing of two hydrogen atoms. Since the M site is the
(b) -1.62 eV 2.48 1.55 2.17 106 (2.46) (1.51) (2.21) (109 )
H
Fig. 6. The atomic geometries of (a) an ideal and (b) a canted dihydride model. The canted model has lower energy than the ideal dihydride by 1.62 eV/supercell. The numbers in parentheses are shown for comparison with pseudopotential calculations [44]. The bond lengths are in units of A.
98
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a)
(b) 0 1
0
0
1
1
1
1
1
1
M 2
B M
S1
2
S2
S1 M
Fig. 7. (a) Potential energy surface of the Si adatom on the canted dihydride Si(0 0 1) surface and (b) its potential contour in two-dimensions. The heavy solid lines in (b) indicate the Si±H bonds of the surface. The ®lled balls represent the surface Si atoms and the smaller empty balls indicate hydrogen atoms. The energy dierence between lines is 0.2 eV. The M site is the adsorption site. The B site is barrier position and S1 and S2 are saddle points. The numbers in the mesh indicate the number of hydrogen atoms which are adsorbed to the adatom from the preadsorbed surface.
only adsorption site, the number of adsorption sites per 2 1 surface unit cell is reduced to two, which is four times smaller than that of monohydride. Fig. 8 visualizes adsorption process of Si adatom at the M site, where hopping of two hydrogen atoms takes place. As the adatom approaches to the middle of two adjacent surface Si atoms, one hydrogen atom hops from the preadsorbed surface
to the adatom, gaining the energy of 1.8 eV, as shown in Fig. 8(b). The Si±H pair is further stabilized by forming another bond with the surface Si atom, as shown in Fig. 8(c). This process gains energy of 0.56 eV. Since the hydrogen atom, preadsorbed on the surface, is close to the adatom with the dangling bonds, this hydrogen atom hops to the adatom without an energy barrier. Finally, two hydrogen atoms saturate the dangling bonds of adatom forming a complete tetrahedral unit, as shown in Fig. 8(d). Note that two hydrogen atoms are bonded towards the front surface. This behavior is similar to the ¯oating of surfactants in group V materials on the growing surface in Ge/Si growth. Fig. 9 illustrates adsorption process of the Si adatom at the S1 site, where hopping of one hydrogen atom takes place. As the Si adatom approaches to the top H atom, the top hydrogen atom exchanges its position to the adatom. Since the top Si atom is still fully coordinated and one of the dangling bonds of the adatom is saturated by hydrogen atom, the energy gain of 2.35 eV is achieved, as shown in Fig. 9(c). The energy is further minimized by having a stronger bond between the adatom and the surface atom. The adsorption energy at the S1 site is ÿ2:67 eV, smaller than ÿ3:9 eV at the M1 site, where hopping of a single hydrogen atom is involved in monohydride. It is also smaller than ÿ4:04 eV at the M site, where hopping of two hydrogen atoms is involved. Saturation of the dangling bonds of the adatom is the key factor for the gain of adsorption energy. 3.2.2. Diusion The potential surface for Si adsorption on the dihydride was fully described in the previous paragraph. Since the SiH2 is formed after adsorption at the most stable site (M), the diusion species may not be a single Si adatom. Therefore, the above potential surface is no longer valid for diffusion. It is reasonable to choose the SiH2 as the most abundant diusion species, starting from the M site at the initial stage of the diusion. Figs. 10 and 11 show the potential pro®les and the corresponding pathways, respectively, for the diusion of the SiH2 on the dihydride surface.
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) 0.0 eV
99
(b) -1.81 eV
(c) -2.37 eV
(d) -4.04 eV
1.76 1.66
2.40
1.55
2.35
2.80
Si adatom
bulk Si
H
Fig. 8. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom on the M site in ball and stick forms. All bond lengths are in units of A.
(a) 0.0 eV
(b) -0.39 eV
(c) -2.35 eV
(d) -2.67 eV 1.60
1.59 2.55
Si adatom
2.41
bulk Si
H
Fig. 9. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom on the S1 site in ball and stick forms. All bond lengths are in units of A.
We ®rst consider the diusion pathway along the x-direction, as shown in Fig. 11(a). Moving the position of the adatom to the right distorts the
bond length and increases the total energy by 0.79 eV in the second step. Two dangling bonds are generated by moving the adatom further to the
100
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 10. Potential pro®les for various pathways. The lines are drawn by the cubic-spline method for eyes only. The corresponding geometries of each pathway are shown in Fig. 11. The energy of the M1 site is taken as a reference.
right, as shown in the third step, increasing the total energy to 2.53 eV, compared to the ®rst step. As the adatom passes the top Si surface atom in the fourth step, the SiH2 sees the another H atom at the front site and forms a completely hybridized SiH3 by hydrogen hopping. On the other hand, the front Si atoms try to share hydrogen atoms with its neighboring Si atom, as indicated by arrows, by sustaining a metastable form of Si±H bonds (1.6 This lowers the total energy by 1.3 eV and 1.9 A). from the previous barrier point. The diusion barrier is thus 2.53 eV, where the barrier occurs in the third path. We next consider the diusion pathway along the y-direction, as shown in Fig. 11(b). Extention increase the of surface Si adatom bonds to 2.43 A energy by 0.50 eV in the second step. We start again from the M point, as shown in the ®rst step. Moving further in direction towards the B point increases the total energy up to the third step by 2.2 eV, where the distortion is maximized. Moving the adatom further leaves two Si atoms with dangling bonds. These two Si atoms are stabilized by forming a monohydride unit, as shown in the fourth step. SiH2 sees a hydrogen atom in front Si, sharing the hydrogen atom with surface Si and forming again a metastable state, as indicated by an arrow in the fourth step. This lowers the energy by 0.7 eV, compared to the previous barrier step.
One may consider an intermediate pathway, as shown in Fig. 11(c). It can be conjectured from the potential surface in Fig. 7. Moving the SiH2 from the M site towards the S2 site form two ¯oating bonds between surface Si atoms and adatom with which again are stabilized by 2.49 and 2.46 A, as forming a dimer with bond length of 2.41 A, shown in the third step. It is worth noting that the Si adatom is completely hybridized with two hydrogen atoms and adjacent Si atoms, reducing the potential barrier height to 1.29 eV, smaller than those of previous pathways. In the fourth step, the SiH3 is formed similar to the previous case, but in this case a complete hybridization is achieved for all Si atoms on the surface. Thus the total energy is lowered further by 0.2 eV, relative to the M site. This is the most stable Si±H complex for the Si adatom on the dihydride surface. Note signi®cantly that the diusion barrier height of a single Si adatom on the dihydride is much higher, compared to those on the monohydride or clean surfaces [44]. One may also calculate the prefactor for the diusion using transition state theory. Since the height and width of the potential barriers of path I and path II are similar each other, as shown in Fig. 10, we expect the diusion constants to be similar to each other within numerical accuracy. 3.3. Role of hydrogen as a surfactant So far we have discussed the adsorption and the diusion of Si adatom on monohydride and the dihydride surfaces. The gain of adsorption energy is typically achieved by capturing H atoms from the preadsorbed surface to saturate the dangling bonds of adatom. In case of adsorption on monohydride, the number of equilibrium adsorption sites increases by about three times that of the clean surface with adsorption energies of ÿ3:9 and ÿ3:7 eV. In case of the dihydride, the number of equilibrium adsorption sites is reduced by four times that of monohydride. Only one deep adsorption site with an energy of 4.04 eV is formed. Therefore, the potential energy surface becomes much rougher than that of the monohydride or clean surface. Unlike a clean surface, the formation of the Si±H complex makes it dicult to
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11. Detailed top and side views of local geometries for various pathways of (a) path I, (b) path II, and (c) path III.
101
102
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11 (continued )
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11 (continued )
103
104
S.M. Lee et al. / Surface Science 470 (2000) 89±105
describe the diusion process on hydrogenated surfaces. For instance, Si±H is the diusion species in the monohydride surface, and the Si±H2 in the dihydride surface. While the adatom migrates, H atoms ¯oat to the top surface by hopping exothermally. Since the size of the H atom is much smaller than that of the host material, it is easy for the H atom to exchange its position with the adatom's position. When the next adatom is deposited, without loss of generality, we expect the H atom to hop easily to the adatom. This eect is similar to the exchange mechanism of typical group V materials as a surfactant. However, group V surfactants require usually relatively large activation barrier of about 1 eV [21]. In this sense, the H atom is more ecient in ¯oating to the surface to suppress the host materials. Of note, the diusion of the Si±H on monohydride surface becomes isotropic with an activation barrier of 0.5±0.6 eV. Therefore, no needle-like growth will be observed on the monohydride surface, unlike the clean surface. This has been con®rmed in the recent experiments [24]. Thus, at large atomic hydrogen ¯uxes we expect a dihydride surface. In this case, the number of adsorption sites is reduced but the diusion barrier height is increased. Therefore, the surface diusion will be severely suppressed. The surface should become rougher or more defective due to limited surface diusion compared to the monohydride surface. In this sense, large hydrogen doses are detrimental to the surface morphology and to further growth, as observed in experiments [14,24]. 4. Summary In summary, we performed the ®rst principles calculations to elucidate the role of H for adsorption and diusion of a Si adatom on hydrogenated surfaces. We ®nd that in case of monohydride, the adatom adsorbs particularly well near the dimer, being stabilized by the H hopping mechanism from the preadsorbed hydrogen on the dimer. The number of adsorption sites increases by about three times and the location of adsorption sites is signi®cantly altered on the hydrogenated surface. The diusion becomes
isotropic. While the adatom diuses, the H atom hops back and forth exothermally from the adatom to the dimer. In the case of the dihydride surface, the number of equilibrium adsorption sites is signi®cantly reduced compared to that of the monohydride surface, but the potential surface becomes rougher. The diusion barrier also is higher than that of clean surface or monohydride surfaces. This results in a rougher surface morphology than for the monohydride surface. The adsorption governs diusion on hydrogenated surfaces, and this delays the onset of island formation. With keen control of growth temperatures we expect the H atom as a surfactant to be more ecient than the typical group V surfactants. Acknowledgements We acknowledge ®nancial support by the Korea Science and Engineering Foundation and in part by the Korea Research Foundation through SPRC at JNU and BK21 program. References [1] M. Copel, M.C. Reuter, E. Kaxiras, R.M. Tromp, Phys. Rev. Lett. 63 (1989) 632. [2] N. Grandjean, J. Massies, V.H. Etgens, Phys. Rev. Lett. 69 (1992) 796. [3] W. Dondl, G. Leutiering, W. Wegscheider, J. Wilhelm, R. Schorer, G. Abstreiter, J. Cryst. Growth 127 (1993) 440. [4] H.J. Osten, J. Klatt, G. Lippert, B. Dietrich, E. Bugiel, Phys. Rev. Lett. 69 (1992) 450. [5] G. Ohta, S. Fukatsu, Y. Ebuchi, T. Hattori, N. Usami, Y. Shiraki, Appl. Phys. Lett. 65 (1994) 2975. [6] A. Sakai, T. Tatsumi, Appl. Phys. Lett. 64 (1994) 52. [7] K. Sumimoto, T. Kobayashi, F. Shoji, K. Oura, Phys. Rev. Lett. 66 (1991) 1193. [8] S. Fukatsu, H. Yoshida, A. Fujiwara, Y. Takahashi, Y. Shiraki, Appl. Phys. Lett. 61 (1992) 804. [9] K. Sakamoto, H. Matsuhata, K. Miki, T. Sakamoto, J. Cryst. Growth 157 (1995) 295. [10] B. Voigtlander, A. Zinner, Surf. Sci. Lett. 292 (1993) L775. [11] Y.J. Chun, Y. Okada, M. Kawabe, Jpn. J. Appl. Phys. 32 (1993) L1085. [12] M. Copel, R.M. Tromp, Phys. Rev. Lett. 72 (1994) 1236. [13] M. Copel, R.M. Tromp, Phys. Rev. Lett. 76 (1996) 2603. [14] M. Copel, R.M. Tromp, Appl. Phys. Lett. 58 (1991) 2648. [15] D.J. Eaglesham, F.C. Unterwald, D.C. Jacobson, Phys. Rev. Lett. 70 (1993) 966.
S.M. Lee et al. / Surface Science 470 (2000) 89±105 [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
R.M. Tromp, M.C. Reuter, Phys. Rev. Lett. 68 (1992) 954. B.D. Yu, A. Oshiyama, Phys. Rev. Lett. 71 (1993) 585. B.D. Yu, A. Oshiyama, Phys. Rev. Lett. 72 (1994) 3190. T. Ohno, Phys. Rev. Lett. 73 (1994) 460. C.W. Oh, E. Kim, Y.H. Lee, Phys. Rev. Lett. 76 (1996) 776. E. Kim, C.W. Oh, Y.H. Lee, Phys. Rev. Lett. 79 (1997) 4621. Y.-J. Ko, J.-Y. Yi, S.-J. Park, E.-H. Lee, K.J. Chang, Phys. Rev. Lett. 76 (1996) 3160. M.A. Boshart, A.A. Bailes III, L.E. Seiberling, Phys. Rev. Lett. 77 (1996) 1087. S.-J. Kahng, Y.H. Ha, J.-Y. Park, S. Kim, D.W. Moon, Y. Kuk, Phys. Rev. Lett. 80 (1998) 4931. S. Jeong, A. Oshiyama, Phys. Rev. Lett. 79 (1997) 4425. S. Jeong, A. Oshiyama, Phys. Rev. B 58 (1998) 12958. J. Nara, T. Sasaki, T. Ohno, Phys. Rev. Lett. 79 (1997) 4421. R. Car, M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. F. Buda, G.L. Chiarotti, R. Car, M. Parrinello, Phys. Rev. Lett. 63 (1989) 294. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. M. Cardona, Phys. Stat. Sol. (b) 118 (1983) 463.
105
[33] K.J. Chang, D.J. Chadi, Phys. Rev. B 42 (1990) 7651. [34] J.D. Joannopoulous, E. Kaxiras, Phys. Rev. B 37 (1988) 8842. [35] C.G. Van der Walle, P.J.H. Denteneer, Y. Bar-Yam, S.T. Pentelides, Phys. Rev. B 39 (1989) 10791. [36] T. Yamasaki, T. Uda, K. Terakura, Phys. Rev. Lett. 76 (1996) 2949. [37] C. Wang, Q.-M. Zhang, J. Bernholc, Phys. Rev. Lett. 69 (1992) 3789. [38] Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 53 (1984) 282. [39] Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 54 (1985) 1055. [40] S. Maruno, H. Iwasaki, K. Horioka, S.T. Li, S. Nakamura, Phys. Rev. 27 (1983) 4110. [41] T. Sakurai, H.D. Hagstrum, Phys. Rev. B 14 (1976) 1593. [42] J.E. Northrup, Phys. Rev. B 47 (1993) 10032. [43] D.H. Oh, Y.H. Lee, J. Kor. Phys. Soc. 28 (1995) S167. [44] G. Brocks, P.J. Kelly, R. Car, Phys. Rev. Lett. 66 (1991) 1729. [45] J.E. Northrup, Phys. Rev. B 44 (1991) 1419. [46] S.H. Wol, S. Wagner, J.C. Bean, R. Hull, J.M. Gibson, Appl. Phys. Lett. 55 (1989) 2017. [47] J.E. Vasek, Z. Zhang, C.T. Salling, M.G. Lagally, Phys. Rev. B 51 (1995) 17207.
www.elsevier.nl/locate/susc
Role of hydrogen for adsorption and diusion of a Si adatom on monohydride and dihydride Si(0 0 1) surfaces Seung Mi Lee a, Young Hee Lee a,b,*, Nam-gyun Kim c a
Department of Semiconductor Science and Technology, Semiconductor Physics Research Center, Jeonbuk National University, Jeonju 561 756, South Korea b Department of Physics, Jeonbuk National University, Jeonju 561 756, South Korea c Department of Bionics and Biomedical Engineering, Jeonbuk National University, Jeonju 561 756, South Korea Received 26 April 2000; accepted for publication 5 September 2000
Abstract We investigate adsorption and diusion of a Si adatom on monohydride and dihydride Si(0 0 1) surfaces using ®rst principles calculations. We ®nd that adsorption and diusion of a Si adatom on hydrogenated Si(0 0 1) surfaces are drastically altered from those on a clean surface in several ways. Both positions and number of adsorption sites vary with dierent coverages of hydrogen, leading to completely dierent diusion behavior from the clean surface. The Si adatom is stabilized by capturing surface hydrogen without potential barrier during adsorption. The H atom hops back and forth exothermally to the adatom during diusion and thus, the diusion species is no longer Si adatom itself. It reveals dierent diusion features that typical potential energy surface with a single adatom fails to describe. Dierences in the adsorption and diusion of Si adatom between monohydride and dihydride phases are discussed. The role of hydrogen as a surfactant on hydrogenated surface will be further discussed based on our calculations. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Low index single crystal surfaces; Adatoms; Chemisorption; Surface diusion
1. Introduction A surfactant has often been introduced in heteroepitaxial crystal growth of semiconductors and metals to suppress segregation of adsorbates to the growth surface [1±15]. The introduction of a surfactant prior to the deposition of adsorbates not only changes the surface free energy [16±19], but also alters kinetics signi®cantly [20,21] so as to * Corresponding author. Tel.: +82-63-270-3336; fax: +82-63270-3585. E-mail address: [email protected] (Y.H. Lee).
enhance exchange of adatoms to subsurface atoms in a concerted way over the simple surface diusion. This promotes layer-by-layer growth and thus, increases the abruptness at the interface. Prerequisite conditions for a surfactant are in general such that it should have (i) weaker binding energy and/or greater radius than adsorbates, (ii) low solid solubility, and (iii) shallow impurity levels (not to contribute to traps in case some remain in the epilayer after the growth). For instance, Ge atoms can easily segregate onto the front growing surface during Ge/Si growth, making less abrupt interface. Group V materials such
0039-6028/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 0 ) 0 0 8 4 5 - 1
90
S.M. Lee et al. / Surface Science 470 (2000) 89±105
as As, Sb, and Bi are good surfactants in order to suppress the Ge out-diusion since they all satisfy the above conditions. Such surfactants have led to a needle-like epitaxial growth along the dimer rows [16]. Several theoretical models for the exchange mechanism to explain the experimentally suggested needle-like epitaxial growth have been proposed, based on ®rst principles calculations [17±22]. However, the ion scattering measurements show disagreements with previously proposed theoretical models [23]. Unlike such typical surfactants of group V materials, the H atom has smaller atomic size than the most typical adsorbates and yet, behaves as a surfactant in many dierent systems [4±15]. When H atoms are introduced prior to the deposition of Ag on Si(1 1 1) surface, the growth mode changes drastically from the Stranski±Krastanow mode to the Frank±Van der Merwe mode, and the number of nucleation sites increases [7]. In spite of the high experimental temperature, where most hydrogen atoms are expected to desorb, abruptness of heterointerface is improved with exposure of the surface to an atomic hydrogen ¯ux [5]. H atoms can also anneal away Ge islands eciently similar to the typical group V surfactants [6,15]. Typical Ge overlayer deposition on Si(0 0 1) surface can lead to layer-by-layer growth up to about four monolayers, followed by island formation. Recent STM measurements with the dynamical supply of atomic hydrogens during Ge overlayer growth on the Si(0 0 1) surface clearly demonstrate that Ge islands do not grow in the presence of one monolayer of atomic hydrogen and furthermore, no needle-like step growth is observed [24]. The previous calculations showed that the Si adatom picks up the H atom on the hydrogenated Si(0 0 1) surface [25±27]. Although numerous experimental data exist, theoretical understanding for the role of H as a surfactant still lags far behind. The key issue here is to understand the adsorption and diusion of a Si adatom on hydrogenated surfaces and further, gain an intuitive picture for the role of the H atom as a surfactant. Since H is quite dierent from group V materials in Ge/Si epitaxial growth as mentioned above, we like to understand similarities and dierences of H
atoms from typical group V surfactants from atomic point of view. We particularly focus on adsorption and diusion of an adatom in the presence of H atoms, H hopping (or exchange) mechanism, and island suppression mechanism. The surface morphology of overlayer growth strongly depends on the hydrogen coverages. Therefore, adsorption and diusion on various hydrogen coverages should be further theoretically investigated in principle in order to completely understand the role of hydrogen in epitaxial growth. We choose in this paper two limits of hydrogen coverages, monohydride and dihydride surfaces. This should provide all the necessary informations for adsorption and kinetics of adatoms and further, provide physical intuition for the role of hydrogen as a surfactant. We ®nd from the ®rst principle calculations that (i) the presence of H atoms increases the number of adsorption sites by about three times on monohydride compared to that of a clean surface, whereas this value decreases on the dihydride, (ii) H atoms change the surface diusion to be isotropic compared to the clean Si(0 0 1) surface, leading to the disappearance of a needlelike step growth, (iii) the location of adsorption sites is signi®cantly altered on hydrogenated surface, (iv) the H atom lowers the surface free energy by hopping back and forth exothermally to adatoms from the preadsorbed surface, trying to saturate all possible dangling bonds of adatoms and surface atoms, and (v) the potential surface becomes rougher, particularly on the dihydride surface, delaying the onset of island growth. 2. Theoretical approaches Our calculations have been carried out using Car±Parrinello molecular dynamics approach [28]. In this scheme, ionic and electronic forces are derived separately from an eective Lagrangian based on the local-density approximation (LDA) of the density-functional theory. The interaction between ionic cores and valence electrons is described by a fully nonlocal norm-conserving pseudopotential with a separable form of s nonlocality for Si introduced by Kleinman and Bylander [29]. Similarly, the H atom is treated locally
S.M. Lee et al. / Surface Science 470 (2000) 89±105
[25±30]. The exchange-correlation energy is treated by Ceperly and Alder's scheme [31]. The electronic wave functions are expanded with a kinetic energy cuto of 8 Ry, and Bloch functions at C point of the supercell surface Brillouin zone are used. This choice of parameters with supercell geometry, which will be described later, gives reasonable accuracies in the energetics and local bonding con®gurations through the calculations compared with other theoretical results. Detailed comparisons will be given in the discussion. The preliminary test for silane molecule gives the Si±H bond and symmetric vibrational frelength of 1.54 A quency of 267 meV, compared to experimental and 271 meV [32], respectively. values of 1.48 A With the cuto of 20 Ry, these values are 1.52 A and 254 meV, in good agreement with the fact that the LDA approach usually underestimates vibrational frequencies [33±35]. The convergence test is also performed in a supercell geometry. The total energy for the 4 2 supercell is changed by 0.4 eV/atom when the cuto of 10 Ry was used. However, the relative energy dierence between two transients, adsorption points with larger cuto (16 Ry) is less than 0.15 eV and the bond length changes are negligible. Therefore, we estimate the energy dierence between dierent transient points to be approximately less than 0.2 eV. The size of the supercell may be of sources of errors. Doubling the size of supercell gives the energy dierence between dierent con®gurations to be of less than 0.1 eV [36]. We search for the electron energy minimization using a steepest decent approach for a given geometry. Ions are then moved by the fast relaxation scheme [37]. Remaining forces on sur in equiface atoms are less than 1:5 10ÿ3 Ry/A librium. The energy is converged to 1:0 10ÿ5 Ry through the calculations. The surface is simulated by a periodically repeated slab of Si atoms in which six atomic layers (each layer with 4 2 surface unit cell) are included, with the bottom surface terminated by hydrogens to emulate a bulk-like Si and the top Two surface followed by a vacuum region of 8 A. bottom Si layers and an additional H layer are ®xed to prevent any spurious forces by H atoms. Thus, this choice of supercell is usually sucient for most Si surface calculations [19,21,22,25,26].
91
3. Results and discussion Our aim here is to understand the microscopic picture of adsorption and diusion of Si adatoms on hydrogenated Si surface. Monohydride 2 1 phase, 3 1 phase (ordered mixture of monohydride and dihydride), and dihydride 1 1 phase are observed experimentally depending on the hydrogen coverage h [38±41]. In this paper, we choose two limits of coverage, monohydride h 1 and dihydride h 2 Si surfaces. This will provide enough physical intuition in understanding the microscopic role of hydrogen during the adsorption and diusion of adatoms on hydrogenated surfaces. Clean Si(0 0 1) surface is stabilized by forming p 2 2 or c 4 2 with an asymmetry of 0.69 A [42]. Signi®cant charges are transferred from the atoms in the second layer to the up atoms of dimer [43]. Three adsorption sites per 2 1 surface cell are found when bare Si adatoms are adsorbed on the dimerized Si(0 0 1) surface [44]. The diusion of Si adatom on the clean (without hydrogen) Si(0 0 1) surface is anisotropic, i.e., an activation energy of 0.6 eV is required for diusion parallel to the dimer rows and 1.0 eV for diusion perpendicular to the dimer rows [44]. It is our intention to understand how the diusion process of adatom changes on the hydrogenated surface. 3.1. Monohydride With one monolayer of H atoms on buckled p 2 2 surface, the buckling is completely removed with charges being neutralized in the up and down atoms, and the surface becomes 2 1 phase. Bond lengths of dimer and Si±H are 2.41 respectively, comparable to 2.40 and and 1.55 A, of previous LDA calculations [45]. 1.54 A 3.1.1. Adsorption We now add one Si adatom per 4 2 surface unit cell to ®nd stable adsorption sites. Si adatom is initially added on the surface at the relative dis away from adjacent surface tance of at least 2.8 A Si atoms. In order to draw the potential energy surface for Si adatom, we divide the surface primitive cell by 45 mesh points. The spacings between
92
S.M. Lee et al. / Surface Science 470 (2000) 89±105
in the x- and y- directions. mesh points are 0.48 A For a given planar point, the adatom is allowed to move along the z-direction while relaxing all the atoms in four sublayers. The potential energy surface is drawn with respect to the H point. The presence of hydrogen atoms modi®es notably the potential energy surface for Si adsorption, dierent from the clean surface as shown in Fig. 1.
(a)
(b)
H
M
H’
M1
D M2
S
Fig. 1. (a) Potential energy surface of a Si adatom on the monohydride Si(0 0 1) surface and (b) its potential contour in two-dimensions. The heavy solid lines in (b) indicate the Si dimer bonds on the surface. The ®lled balls represent the Si atoms in dimer and the smaller empty balls indicate hydrogen atoms. The adatom±H pair is formed inside the dashed line. The energy dierence between lines is 0.1 eV. H0 , M1 , M2 are adsorption sites. H and M are shown for comparison with adsorption sites of the Si adatom on bare Si surface. D is the barrier point, and S is a saddle point. The respective adsorption points are explained in the text.
First of all, the adatom prefers to adsorb at H0 , M2 (new adsorption positions), and M1 sites near the dimer in the trough as shown in Fig. 1, different from H and M sites on the clean surface [44]. The corresponding con®gurations are shown in Figs. 2 and 3. The H site is a stable site for the clean surface, but now is shifted to the H0 site near the dimer on monohydride surface. Similarly, the M site is shifted to the M1 site in the trough. The S site is a saddle point, whereas the D site, on the center of the dimer, is the highest barrier point. We ®nd a new adsorption site of M2 located near the dimer atom, as shown in Fig. 1. Energies of the H0 , M1 , and M2 sites are lowered by picking up a hydrogen atom from the dimer atoms in the sublayer, as also observed in the previous reports [25± 27]. Note that the number of adsorption sites per 2 1 surface unit cell is increased to eight, about three times larger than that on the clean surface. The M1 site is the most stable adsorption site with a binding energy of ÿ3:9 eV whereas the H0 and M2 sites give slightly weaker binding energies by 0.2 eV than the M1 site does. It is interesting to see how the energy of these binding sites is lowered during the adsorption process. The energy gains near the H0 , M1 , and M2 sites are achieved by the hopping of the hydrogen atom to the adatom from the preadsorbed surface dimer. Fig. 2 illustrates the typical snapshots of the Si adatom approaching to one of the adsorption sites (M1 ) during the optimization process. When the Si adatom approaches to the hydrogenated surface, the H atom hops exothermally to the adatom in order to stabilize the lone electron of an adatom. In the mean time the adatom forms new bonds with one of the dimer atoms inducing an asymmetry as shown in Fig. 2(c), and ®nally with the subsurface atoms respectively, with bond lengths of 2.24 and 2.53 A, as shown in Fig. 2(d), resulting in a new p-bonded structure between them [17]. This is simply a manifestation of ¯oating bond that exists in the amorphous Si network, and is induced by the existence of dangling bonds of the adatom. Once the hopping is achieved, the dimer bond length is re from 2.41 A (Fig. 3(a)). Similarly, duced to 2.38 A the H0 and M2 sites are stabilized by hydrogen hopping, as shown in Fig. 3(b) and (c).
S.M. Lee et al. / Surface Science 470 (2000) 89±105
93
Fig. 2. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom at the M1 site in ball and stick forms. Bond lengths are in units of A.
The D site is the diusion barrier with a height of 1.4 eV with respect to the H0 . When approaching to the D site, the adatom cannot break the dimer while sustaining the bond length of 2.58 with its adjacent dimer atoms, as shown in Fig. A 3(d), due to the existence of energy barrier. 1 The adatom may then have probability to break the dimer at the typical experimental temperature. In fact, the dimer bond breaking actually strengthens the bondings of adatom with the surface dimer gaining energy by with bond length of 2.35 A, ÿ1:74 eV, as shown in Fig. 3(e). Note that the dimer atoms are completely hybridized with their
1
The D point is in good contrast with the E point in Refs. [25±27] which is the local minimum. We checked the energies with more mesh points near the D point. Adsorption energies near the D point (including D) vary very rapidly, as shown in Fig. 1, but the D site is still the barrier point, where the D point cannot possess H atoms and therefore, has higher adsorption energy. However, Si±H can be formed at very near the D site, having larger adsorption energy, as indicated by the dashed line in Fig. 1(b). We conjecture that the dierence may be due to the coarse meshes used in their works.
neighbor atoms including the H atom. We further tried the adatom picking up two hydrogen atoms from the preadsorbed surface dimer. This lowers the energy further to ÿ2:56 eV, as shown in Fig. 3(f ). In this case, however, the dimer formation in the subsurface is recovered, implying that higher H coverage may be detrimental to the surface morphology [12±14,24,46]. The adatom approaching to the D site also has a chance to diuse to the H0 site, picking up the H atom from the preadsorbed surface dimer which will be discussed later. Thus far we observed three dierent adsorption sites (H0 , M1 , M2 ). The energy gain by the adatom adsorption is achieved by H hopping mechanism from the surface dimer to the adatom. It increases the number of adsorption sites by a factor of 2.7 per surface primitive cell, compared to that on the clean surface. Adsorption at the M1 site should occur more frequently than at other sites due to its stronger binding energy. This is in excellent agreement with recent STM observations that most adsorption sites are placed near the dimer sites, and the M1 site is more probable than other sites (M2 and H0 ) [24].
94
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) no adatom 2.41 1.55
(b) H’ site
2.76
1.59 2.35
(c) M 2 site
(d) D site (0.0 eV)
1.60
1.60
2.58
2.34 2.45
2.44
(e) D site (-1.74 eV)
(f) D site (-2.56 eV)
1.56
1.55
2.35
2.33
2.44
Si adatom
bulk Si
H
Fig. 3. Various adsorption con®gurations in equilibrium. (a) The monohydride surface without an adatom, the local con®gurations when the Si adatom is at (b) the H0 site (local minimum site), (c) the M2 site (local minimum site), (d) the D site (barrier point), (e) when the dimer is broken at the barrier point, and (f ) when the adatom captures two hydrogen atoms from adjacent surface Si atoms. Bond lengths are in units of A.
3.1.2. Diusion We now study the diusion of adatom on monohydride surface. The potential contour upon the adsorption of a adatom (Fig. 1) in general gives rise to the estimation of the reasonable diffusion pathways. However, in adsorption of adatom on hydrogenated surface, it is reasonable to consider the diusion of Si±H, not the bare Si adatom, since the adsorption occurs via H hopping to adatom forming Si±H bond. In Fig. 4(a), we show the potential pro®le for several pathways. Escaping from the M1 site to diuse along the dimer row in the trough (path I) requires 0.5 eV (the M1 site is the reference point in this case) where the
barrier occurs at step (I-3). We note that at this barrier point, the H atom located at the adatom returns to the dimer position behind, as clearly visualized in the snapshots of Fig. 5. The Si±H cluster sees the preadsorbed the H atom on the next dimer and thus, is stabilized by capturing it (Fig. 5(a)). Once Si±H cluster captures the H atom, two H atoms in the cluster push back to each other sterically. The close distance from the dimer behind enables to accommodate exothermally the H atom hopping back to the original dimer as shown in Fig. 5(d). Then the con®guration in the step (I5) in Fig. 4(b) is identical to the M1 site (step (I-1) in Fig. 4(b)) in equilibrium. We should point out
S.M. Lee et al. / Surface Science 470 (2000) 89±105
95
Fig. 4. (a) Potential pro®les for various pathways. The lines are drawn by the cubic-spline method for eyes only. (b) The corresponding geometries of each pathway. The M1 site is taken here as a reference.
96
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) 0.0 eV (1.57, 1.59)
(b) -0.84 eV (1.69, 1.60)
(c) -1.32 eV (1.58, 1.70)
(d) -1.96 eV (1.58, 1.58)
Si adatom
bulk Si
H
Fig. 5. The snapshots (top views) of Si±H approaching to the next dimer during the diusion process. The numbers in parentheses represent the Si±H bond lengths as indicated by arrows. The bond lengths are in units of A.
that the position of Si adatom in the step (I-3) of Fig. 4(b) is dierent from that of Fig. 2(b) in Ref. [29]. The Si±H is stable in the middle of two dimers, which requires a barrier to detach the hydrogen atom, whereas in our case, a slightly misplaced Si±H from the middle does not require the barrier to exchange the hydrogen atom. There is another possibility of having dierent pathway from the step (I-3) by pushing down the adatom into the surface. This may result in the exchange adatom with surface Si atom, which was reported previously [25,26]. We also investigate dierent pathways, as shown in Fig. 4(b) (path II). Migration of Si±H from M1 along the dimer direction ®rst faces a potential barrier of 0.5 eV at the step (II-2) and then faces slightly higher barrier of 0.6 eV at the step (II-5), where most energy cost comes from with one of the dimer longer bond length (2.6 A) atoms behind. At the step (II-5), we note that Si±H does not pick up the H atom from the other side of the dimer, unlike the case of the step (I-3). This is understood by the directional dependence of the H bond on the dimer, the degree of freedom of the H atom on the adatom which can be freely rotated, and the long distance of the H atom from the dangling bond of the dimer atom behind. Since the
step (II-4) gives local minimum, we consider another pathway, path III, as shown in Fig. 4(b). Diusing on the dimer row along the direction of the dimer row (path III) requires a relatively high diusion barrier of 1.65 eV, since it involves creation of a dangling bond and severe bond angle distortions. The diusion pathways shown in Fig. 4 are somewhat dierent from those on the clean surface. Si±H diuses in the trough along the dimer row with a barrier height of 0.5 eV on the hydrogenated surface (path I), whereas on the clean surface the Si adatom diuses on top of the dimer row with a barrier height of 0.35 eV or in the trough along the dimer row with barrier height of 1.0 eV [44]. The Si±H diuses near the dimer perpendicularly to the dimer row (path II) with a barrier height of 0.6 eV on the hydrogenated surface while on the clean surface the Si adatom diffuses between the dimers across the dimer row with the same barrier height [44]. The diusion of the adatom becomes isotropic on the hydrogenated surface. Therefore, we expect that the surfactant (group V material)-induced needle-like step growth is unlikely to be observed at a moderate temperature range and at a low ¯ux rate of the incoming adatoms. We also note that the surface diusion
S.M. Lee et al. / Surface Science 470 (2000) 89±105
could be suppressed due to the higher diusion barrier. The tendency of suppressing the surface diusion in the presence of H atoms is in fact observed in many experiments [6,7,9,24,47]. This will lead to the delay of the onset of island formation. 3.2. Dihydride Dihydride is an ideal 1 1 phase where top Si dangling bonds are fully saturated by two hydrogen atoms. Fig. 6(a) shows the dihydride Si sur become shorter face. Si±H bond lengths of 1.53 A than those of monohydride surface. Since H±H strong distances between adjacent sites are 1.50 A, H±H repulsion forces do exist. Fig. 6(b) shows a more stable con®guration, the canted dihydride phase. Two hydrogen atoms are rotated so as to minimize H±H distances. The energy becomes lower by 0.1 eV per hydrogen atom, comparable to 0.09 eV from the previous pseudopotential calculations [45]. Now all H±H distances in the adjacent sites become maximized in the canted dihydride. We therefore use the canted dihydride in the next calculations in order to investigate the adsorption and diusion on two monolayer coverage of hydrogen. We also tried adsorption on an ideal dihydride. The potential surface was more symmetric but similar to that of the canted dihydride, and adsorption of the adatom near the preadsorbed hydrogen changed the surface structure to the canted phase after full relaxation.
(a) 0.0 eV 2.34 (2.33)
1.53 1.50 (1.50) 100 (1.51) (102 )
bulk Si
97
3.2.1. Adsorption We now bring a bare Si adatom onto the canted dihydride surface, which is similar to the monohydride surface, in order to draw the potential surface. Si adatom is initially added on the surface away at the relative distance of at least 1.75 A from adjacent surface H atoms. As illustrated in the dotted line in Fig. 7(b), we divide the surface primitive cell by 12 mesh points, as shown in the dashed line of Fig. 7(b). The spacings between in the x- and y-directions, mesh points are 0.96 A similar values to the previous calculations [25,26]. Long and short solid lines indicate the bonds of the top and bottom surface hydrogen atoms, respectively, in the canted phase. For a given planar point, the adatom is allowed to move along the zdirection, while relaxing all the atoms in four sublayers. The potential energy surface is drawn with respect to the B point. The potential surface of the dihydride phase is very dierent from monohydride phase. First of all, surface morphology becomes rougher than that in monohydride. The B site is the barrier point since the distances of adatom with its adjacent Si surface atoms are far and no energy gain by hydrogen hopping is involved. We can also see two dierent saddle points, S1 and S2 . The numbers in the dotted box indicate the number of hydrogen atoms hopping to the adatom from the preadsorbed surface. The M site is the adsorption site. We note that the M site is much deeper with adsorption energy of ÿ4:1 eV due to the capturing of two hydrogen atoms. Since the M site is the
(b) -1.62 eV 2.48 1.55 2.17 106 (2.46) (1.51) (2.21) (109 )
H
Fig. 6. The atomic geometries of (a) an ideal and (b) a canted dihydride model. The canted model has lower energy than the ideal dihydride by 1.62 eV/supercell. The numbers in parentheses are shown for comparison with pseudopotential calculations [44]. The bond lengths are in units of A.
98
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a)
(b) 0 1
0
0
1
1
1
1
1
1
M 2
B M
S1
2
S2
S1 M
Fig. 7. (a) Potential energy surface of the Si adatom on the canted dihydride Si(0 0 1) surface and (b) its potential contour in two-dimensions. The heavy solid lines in (b) indicate the Si±H bonds of the surface. The ®lled balls represent the surface Si atoms and the smaller empty balls indicate hydrogen atoms. The energy dierence between lines is 0.2 eV. The M site is the adsorption site. The B site is barrier position and S1 and S2 are saddle points. The numbers in the mesh indicate the number of hydrogen atoms which are adsorbed to the adatom from the preadsorbed surface.
only adsorption site, the number of adsorption sites per 2 1 surface unit cell is reduced to two, which is four times smaller than that of monohydride. Fig. 8 visualizes adsorption process of Si adatom at the M site, where hopping of two hydrogen atoms takes place. As the adatom approaches to the middle of two adjacent surface Si atoms, one hydrogen atom hops from the preadsorbed surface
to the adatom, gaining the energy of 1.8 eV, as shown in Fig. 8(b). The Si±H pair is further stabilized by forming another bond with the surface Si atom, as shown in Fig. 8(c). This process gains energy of 0.56 eV. Since the hydrogen atom, preadsorbed on the surface, is close to the adatom with the dangling bonds, this hydrogen atom hops to the adatom without an energy barrier. Finally, two hydrogen atoms saturate the dangling bonds of adatom forming a complete tetrahedral unit, as shown in Fig. 8(d). Note that two hydrogen atoms are bonded towards the front surface. This behavior is similar to the ¯oating of surfactants in group V materials on the growing surface in Ge/Si growth. Fig. 9 illustrates adsorption process of the Si adatom at the S1 site, where hopping of one hydrogen atom takes place. As the Si adatom approaches to the top H atom, the top hydrogen atom exchanges its position to the adatom. Since the top Si atom is still fully coordinated and one of the dangling bonds of the adatom is saturated by hydrogen atom, the energy gain of 2.35 eV is achieved, as shown in Fig. 9(c). The energy is further minimized by having a stronger bond between the adatom and the surface atom. The adsorption energy at the S1 site is ÿ2:67 eV, smaller than ÿ3:9 eV at the M1 site, where hopping of a single hydrogen atom is involved in monohydride. It is also smaller than ÿ4:04 eV at the M site, where hopping of two hydrogen atoms is involved. Saturation of the dangling bonds of the adatom is the key factor for the gain of adsorption energy. 3.2.2. Diusion The potential surface for Si adsorption on the dihydride was fully described in the previous paragraph. Since the SiH2 is formed after adsorption at the most stable site (M), the diusion species may not be a single Si adatom. Therefore, the above potential surface is no longer valid for diffusion. It is reasonable to choose the SiH2 as the most abundant diusion species, starting from the M site at the initial stage of the diusion. Figs. 10 and 11 show the potential pro®les and the corresponding pathways, respectively, for the diusion of the SiH2 on the dihydride surface.
S.M. Lee et al. / Surface Science 470 (2000) 89±105
(a) 0.0 eV
99
(b) -1.81 eV
(c) -2.37 eV
(d) -4.04 eV
1.76 1.66
2.40
1.55
2.35
2.80
Si adatom
bulk Si
H
Fig. 8. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom on the M site in ball and stick forms. All bond lengths are in units of A.
(a) 0.0 eV
(b) -0.39 eV
(c) -2.35 eV
(d) -2.67 eV 1.60
1.59 2.55
Si adatom
2.41
bulk Si
H
Fig. 9. The typical snapshots (side views) of H hopping mechanism during the adsorption of the Si adatom on the S1 site in ball and stick forms. All bond lengths are in units of A.
We ®rst consider the diusion pathway along the x-direction, as shown in Fig. 11(a). Moving the position of the adatom to the right distorts the
bond length and increases the total energy by 0.79 eV in the second step. Two dangling bonds are generated by moving the adatom further to the
100
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 10. Potential pro®les for various pathways. The lines are drawn by the cubic-spline method for eyes only. The corresponding geometries of each pathway are shown in Fig. 11. The energy of the M1 site is taken as a reference.
right, as shown in the third step, increasing the total energy to 2.53 eV, compared to the ®rst step. As the adatom passes the top Si surface atom in the fourth step, the SiH2 sees the another H atom at the front site and forms a completely hybridized SiH3 by hydrogen hopping. On the other hand, the front Si atoms try to share hydrogen atoms with its neighboring Si atom, as indicated by arrows, by sustaining a metastable form of Si±H bonds (1.6 This lowers the total energy by 1.3 eV and 1.9 A). from the previous barrier point. The diusion barrier is thus 2.53 eV, where the barrier occurs in the third path. We next consider the diusion pathway along the y-direction, as shown in Fig. 11(b). Extention increase the of surface Si adatom bonds to 2.43 A energy by 0.50 eV in the second step. We start again from the M point, as shown in the ®rst step. Moving further in direction towards the B point increases the total energy up to the third step by 2.2 eV, where the distortion is maximized. Moving the adatom further leaves two Si atoms with dangling bonds. These two Si atoms are stabilized by forming a monohydride unit, as shown in the fourth step. SiH2 sees a hydrogen atom in front Si, sharing the hydrogen atom with surface Si and forming again a metastable state, as indicated by an arrow in the fourth step. This lowers the energy by 0.7 eV, compared to the previous barrier step.
One may consider an intermediate pathway, as shown in Fig. 11(c). It can be conjectured from the potential surface in Fig. 7. Moving the SiH2 from the M site towards the S2 site form two ¯oating bonds between surface Si atoms and adatom with which again are stabilized by 2.49 and 2.46 A, as forming a dimer with bond length of 2.41 A, shown in the third step. It is worth noting that the Si adatom is completely hybridized with two hydrogen atoms and adjacent Si atoms, reducing the potential barrier height to 1.29 eV, smaller than those of previous pathways. In the fourth step, the SiH3 is formed similar to the previous case, but in this case a complete hybridization is achieved for all Si atoms on the surface. Thus the total energy is lowered further by 0.2 eV, relative to the M site. This is the most stable Si±H complex for the Si adatom on the dihydride surface. Note signi®cantly that the diusion barrier height of a single Si adatom on the dihydride is much higher, compared to those on the monohydride or clean surfaces [44]. One may also calculate the prefactor for the diusion using transition state theory. Since the height and width of the potential barriers of path I and path II are similar each other, as shown in Fig. 10, we expect the diusion constants to be similar to each other within numerical accuracy. 3.3. Role of hydrogen as a surfactant So far we have discussed the adsorption and the diusion of Si adatom on monohydride and the dihydride surfaces. The gain of adsorption energy is typically achieved by capturing H atoms from the preadsorbed surface to saturate the dangling bonds of adatom. In case of adsorption on monohydride, the number of equilibrium adsorption sites increases by about three times that of the clean surface with adsorption energies of ÿ3:9 and ÿ3:7 eV. In case of the dihydride, the number of equilibrium adsorption sites is reduced by four times that of monohydride. Only one deep adsorption site with an energy of 4.04 eV is formed. Therefore, the potential energy surface becomes much rougher than that of the monohydride or clean surface. Unlike a clean surface, the formation of the Si±H complex makes it dicult to
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11. Detailed top and side views of local geometries for various pathways of (a) path I, (b) path II, and (c) path III.
101
102
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11 (continued )
S.M. Lee et al. / Surface Science 470 (2000) 89±105
Fig. 11 (continued )
103
104
S.M. Lee et al. / Surface Science 470 (2000) 89±105
describe the diusion process on hydrogenated surfaces. For instance, Si±H is the diusion species in the monohydride surface, and the Si±H2 in the dihydride surface. While the adatom migrates, H atoms ¯oat to the top surface by hopping exothermally. Since the size of the H atom is much smaller than that of the host material, it is easy for the H atom to exchange its position with the adatom's position. When the next adatom is deposited, without loss of generality, we expect the H atom to hop easily to the adatom. This eect is similar to the exchange mechanism of typical group V materials as a surfactant. However, group V surfactants require usually relatively large activation barrier of about 1 eV [21]. In this sense, the H atom is more ecient in ¯oating to the surface to suppress the host materials. Of note, the diusion of the Si±H on monohydride surface becomes isotropic with an activation barrier of 0.5±0.6 eV. Therefore, no needle-like growth will be observed on the monohydride surface, unlike the clean surface. This has been con®rmed in the recent experiments [24]. Thus, at large atomic hydrogen ¯uxes we expect a dihydride surface. In this case, the number of adsorption sites is reduced but the diusion barrier height is increased. Therefore, the surface diusion will be severely suppressed. The surface should become rougher or more defective due to limited surface diusion compared to the monohydride surface. In this sense, large hydrogen doses are detrimental to the surface morphology and to further growth, as observed in experiments [14,24]. 4. Summary In summary, we performed the ®rst principles calculations to elucidate the role of H for adsorption and diusion of a Si adatom on hydrogenated surfaces. We ®nd that in case of monohydride, the adatom adsorbs particularly well near the dimer, being stabilized by the H hopping mechanism from the preadsorbed hydrogen on the dimer. The number of adsorption sites increases by about three times and the location of adsorption sites is signi®cantly altered on the hydrogenated surface. The diusion becomes
isotropic. While the adatom diuses, the H atom hops back and forth exothermally from the adatom to the dimer. In the case of the dihydride surface, the number of equilibrium adsorption sites is signi®cantly reduced compared to that of the monohydride surface, but the potential surface becomes rougher. The diusion barrier also is higher than that of clean surface or monohydride surfaces. This results in a rougher surface morphology than for the monohydride surface. The adsorption governs diusion on hydrogenated surfaces, and this delays the onset of island formation. With keen control of growth temperatures we expect the H atom as a surfactant to be more ecient than the typical group V surfactants. Acknowledgements We acknowledge ®nancial support by the Korea Science and Engineering Foundation and in part by the Korea Research Foundation through SPRC at JNU and BK21 program. References [1] M. Copel, M.C. Reuter, E. Kaxiras, R.M. Tromp, Phys. Rev. Lett. 63 (1989) 632. [2] N. Grandjean, J. Massies, V.H. Etgens, Phys. Rev. Lett. 69 (1992) 796. [3] W. Dondl, G. Leutiering, W. Wegscheider, J. Wilhelm, R. Schorer, G. Abstreiter, J. Cryst. Growth 127 (1993) 440. [4] H.J. Osten, J. Klatt, G. Lippert, B. Dietrich, E. Bugiel, Phys. Rev. Lett. 69 (1992) 450. [5] G. Ohta, S. Fukatsu, Y. Ebuchi, T. Hattori, N. Usami, Y. Shiraki, Appl. Phys. Lett. 65 (1994) 2975. [6] A. Sakai, T. Tatsumi, Appl. Phys. Lett. 64 (1994) 52. [7] K. Sumimoto, T. Kobayashi, F. Shoji, K. Oura, Phys. Rev. Lett. 66 (1991) 1193. [8] S. Fukatsu, H. Yoshida, A. Fujiwara, Y. Takahashi, Y. Shiraki, Appl. Phys. Lett. 61 (1992) 804. [9] K. Sakamoto, H. Matsuhata, K. Miki, T. Sakamoto, J. Cryst. Growth 157 (1995) 295. [10] B. Voigtlander, A. Zinner, Surf. Sci. Lett. 292 (1993) L775. [11] Y.J. Chun, Y. Okada, M. Kawabe, Jpn. J. Appl. Phys. 32 (1993) L1085. [12] M. Copel, R.M. Tromp, Phys. Rev. Lett. 72 (1994) 1236. [13] M. Copel, R.M. Tromp, Phys. Rev. Lett. 76 (1996) 2603. [14] M. Copel, R.M. Tromp, Appl. Phys. Lett. 58 (1991) 2648. [15] D.J. Eaglesham, F.C. Unterwald, D.C. Jacobson, Phys. Rev. Lett. 70 (1993) 966.
S.M. Lee et al. / Surface Science 470 (2000) 89±105 [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
R.M. Tromp, M.C. Reuter, Phys. Rev. Lett. 68 (1992) 954. B.D. Yu, A. Oshiyama, Phys. Rev. Lett. 71 (1993) 585. B.D. Yu, A. Oshiyama, Phys. Rev. Lett. 72 (1994) 3190. T. Ohno, Phys. Rev. Lett. 73 (1994) 460. C.W. Oh, E. Kim, Y.H. Lee, Phys. Rev. Lett. 76 (1996) 776. E. Kim, C.W. Oh, Y.H. Lee, Phys. Rev. Lett. 79 (1997) 4621. Y.-J. Ko, J.-Y. Yi, S.-J. Park, E.-H. Lee, K.J. Chang, Phys. Rev. Lett. 76 (1996) 3160. M.A. Boshart, A.A. Bailes III, L.E. Seiberling, Phys. Rev. Lett. 77 (1996) 1087. S.-J. Kahng, Y.H. Ha, J.-Y. Park, S. Kim, D.W. Moon, Y. Kuk, Phys. Rev. Lett. 80 (1998) 4931. S. Jeong, A. Oshiyama, Phys. Rev. Lett. 79 (1997) 4425. S. Jeong, A. Oshiyama, Phys. Rev. B 58 (1998) 12958. J. Nara, T. Sasaki, T. Ohno, Phys. Rev. Lett. 79 (1997) 4421. R. Car, M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. F. Buda, G.L. Chiarotti, R. Car, M. Parrinello, Phys. Rev. Lett. 63 (1989) 294. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. M. Cardona, Phys. Stat. Sol. (b) 118 (1983) 463.
105
[33] K.J. Chang, D.J. Chadi, Phys. Rev. B 42 (1990) 7651. [34] J.D. Joannopoulous, E. Kaxiras, Phys. Rev. B 37 (1988) 8842. [35] C.G. Van der Walle, P.J.H. Denteneer, Y. Bar-Yam, S.T. Pentelides, Phys. Rev. B 39 (1989) 10791. [36] T. Yamasaki, T. Uda, K. Terakura, Phys. Rev. Lett. 76 (1996) 2949. [37] C. Wang, Q.-M. Zhang, J. Bernholc, Phys. Rev. Lett. 69 (1992) 3789. [38] Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 53 (1984) 282. [39] Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 54 (1985) 1055. [40] S. Maruno, H. Iwasaki, K. Horioka, S.T. Li, S. Nakamura, Phys. Rev. 27 (1983) 4110. [41] T. Sakurai, H.D. Hagstrum, Phys. Rev. B 14 (1976) 1593. [42] J.E. Northrup, Phys. Rev. B 47 (1993) 10032. [43] D.H. Oh, Y.H. Lee, J. Kor. Phys. Soc. 28 (1995) S167. [44] G. Brocks, P.J. Kelly, R. Car, Phys. Rev. Lett. 66 (1991) 1729. [45] J.E. Northrup, Phys. Rev. B 44 (1991) 1419. [46] S.H. Wol, S. Wagner, J.C. Bean, R. Hull, J.M. Gibson, Appl. Phys. Lett. 55 (1989) 2017. [47] J.E. Vasek, Z. Zhang, C.T. Salling, M.G. Lagally, Phys. Rev. B 51 (1995) 17207.