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Complex diffusion mechanisms of a silicon adatom on hydrogenated Si(100) surfaces: on terraces and near steps
Surface Science 433–435 (1999) 481–485 www.elsevier.nl/locate/susc
Complex diffusion mechanisms of a silicon adatom on hydrogenated Si(100) surfaces: on terraces and near steps Sukmin Jeong *, Atsushi Oshiyama Institute of Physics, University of Tsukuba, Tennodai, Tsukuba 305, Japan
Abstract We present first-principles total-energy calculations which reveal microscopic mechanisms of silicon adatom diffusion on the flat terraces and near the single-layer steps of hydrogenated Si(100) surfaces. The diffusion of the silicon adatom is not a simple motion on a single potential-energy surface but a complex atomic reaction in which hydrogen-atom release and capture as well as adatom exchange are involved. The calculated diffusion barrier is sensitive to hydrogen coverage. Near the step edges, the hydrogen-atom capture and release are also crucial processes as on the terrace, and an additional activation barrier near the step edges (the Schwoebel effect) is absent. The S B step is found to be a deep sink for the adatom. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Anti-phase boundary; Epitaxy; Hydrogen; Schwoebel effect; Step; Substitutional adsorption; Surfactant
1. Introduction The hydrogenated Si(100) surface has been extensively studied because of its importance in both science and technology [1–9]. In homo- and heteroepitaxial growth using chemical vapor deposition or gas-source molecular-beam epitaxy (MBE ), the growth front is terminated by hydrogen [1–3]. In solid-source MBE, hydrogen is introduced intentionally to assist in epitaxial growth [4–7]. The morphology of overlayers indeed depends on hydrogen coverage [2,7], and even the growth mode is modified when using hydrogen as a surfactant in heteroepitaxy [4,5]. Little is known, however, about the microscopic processes, such as the adsorption and diffusion processes of an adatom, which lead to changes in the morphology and growth of the overlayers. * Corresponding author. Fax: +81-298-53-4492. E-mail address: [email protected] (S. Jeong)
In this paper, we present first-principles totalenergy calculations which reveal mechanisms of adatom diffusion on the flat terraces and near the single-layer (S) steps of hydrogenated Si(100) surfaces1. We find that the diffusion of the silicon adatom is not a simple motion on a single potential-energy surface but a complex atomic reaction in which capture and release of the hydrogen atom are rate-determining processes. An exchange process where the silicon adatom replaces a subsurface silicon atom during the diffusion is also found to be important. The calculated diffusion barrier is sensitive to hydrogen coverage. Near the step edges, the hydrogen capture and release are also crucial processes for adatom diffusion as on the terrace, and an additional activation barrier near the step edges (the Schwoebel effect) is absent. The S step is found to be a deep sink for the B 1 For the notations of various types of step, see Chadi [10].
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S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
adatom. Its implication for the morphology of overlayers is also discussed.
2. Calculational method All calculations have been performed by use of norm-conserving pseudopotentials, the local density (LDA) for the exchange-correlation energy, and the conjugate-gradient minimization technique. The surface is simulated by a repeating slab model. The size of the unit cell in the lateral directions is p(앀8×앀8)R45° for the flat terraces. To simulate steps, we use the periodic step arrays on the (100) surfaces with 2×n periodicities (n= 6, 8 and 10) and the (15,1,1) vicinal surfaces. The details of other calculational parameters can be found in [8].
potential-energy surface (PES) as a function of lateral coordinates of the adatom (refer to Fig. 3 of [8]). The most stable site is A, the adsorption geometry of which is shown in Fig. 2a. A striking feature of the geometry is the substitutional adsorption: the silicon adatom forms a bond with a substrate silicon atom (Si2) which releases a hydrogen atom, and the hydrogen atom is in turn bonded to the adatom. As shown in previous calculations [8,9], the energy barrier for the substitutional adsorption is absent. We take the geometry as the global minimum on the flat terrace since it is reached from a silicon vapor phase with no energy cost. The spontaneous substitutional adsorption takes place at many sites including metastable A
3. Results and discussion 3.1. Diffusion on flat terraces Fig. 1 shows (meta)stable sites (A and E) and saddle points (B, C and D) for a silicon adatom on the 2×1 monohydride phase [11], based on a
Fig. 1. Metastable adsorption sites and saddle points for a silicon adatom (represented by small dots) on the 2×1 monohydride Si(100). Black and open circles denote hyrdogen atoms and silicon atoms, respectively. Sites A and E are (meta)stable adsorption sites, and B, C and D are saddle points on the potential-energy surface (PES ) for the adatom. The subscripts to each letter are for discrimination of equivalent adsorption sites. Note that the PES has a fourfold symmetry, reflecting the substrate structure with symmetric dimers (before silicon adsorption).
Fig. 2. (a) Diffusion pathway of an adatom along the dimer rows and (b) the corresponding activation energies. Meshed, filled and open circles denote silicon adatoms, hydrogen atoms and silicon atoms, respectively. The arrow in each part of (a) indicates the direction of adatom migration towards the next stage. Values shown in (b) are the energies of the metastable or transition states in eV with respect to the monohydride geometry at site A. Note that the structures with the labels in Fig. 1 and in (a) may be different – i.e., at the same coordinates of the adatom, the total energy may vary, depending on the number of hydrogen atoms attached to the adatom.
S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
and E, but not on the sites such as saddle points B, C and D. The adatom may follow a pathway A B A C A … for the diffusion parallel to the 1 1 2 2 3 substrate dimer rows and a pathway A D A E 1 1 4 4 A … for the diffusion perpendicular to the dimer 5 rows. In order for the calculated PES to be suitable for assessment of the diffusion barriers, however, a spontaneous hydrogen release from the diffusion species is necessary as it travels along pathways on the PES: e.g., as the adatom from A (with a 1 hydrogen atom attached to the adatom) passes through site B (without the hydrogen atom 1 attached to the adatom). Thus, we have traced diffusion pathways of the monohydride from site A along the dimer rows and, at the same time, investigated throughly the hydrogen release from the diffusion species for several positions of the adatom. For this, we have performed a series of constrained minimizations with the x coordinate of the adatom as the reaction parameter and additionally with the x coordinate of the hydrogen atom to obtain the activation energy for the hydrogen release. Fig. 2 shows the adatom diffusion pathway thus obtained along the dimer rows (x direction) on the 2×1 monohydride phase along with the corresponding activation energies. The adatom– hydrogen unit starting from A increases the 1 energy as it proceeds, since the adatom–Si2 bond is weakened. Then, it is energetically favorable for the adatom to release the hydrogen atom (bonded to it) back to Si2 (~B in Fig. 2, where the tilde 1 means that the lateral position of the adatom roughly coincides with B ). As it proceeds further, 1 the adatom penetrates into the surface, making Si4 the outermost (C of Fig. 2). After that, the 2 adatom turns its direction (in the arrow direction) to make a dimer with Si3 ( E in Fig. 2) since the 3 straight movement costs too much energy. The energy barrier to form a metastable state at site E is only 0.3 eV. From now on, the diffusion 3 species is exchanged from the adatom to a dimer atom, Si4. Finally, the Si4–H unit goes from E 3 to A with a barrier of 0.5 eV. The process 3 A C , where the hydrogen release takes place, 1 2 is the rate-determining process, and we take its barrier (0.7 eV ) as the activation energy Q for d the diffusion along the dimer rows.
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A similar mechanism is expected for the diffusion perpendicular to the dimer rows; from A to 1 A passing through D , A and E , in which 5 1 4 4 hydrogen-atom release and capture by the adatom are involved along the pathway. We find that the activation energy for the adatom diffusion perpendicular to the dimer rows (Q ) is 1.1 eV. The ) exchange of silicon atoms does not occur in this case. As the hydrogen coverage H exceeds 1 ML, H the 3×1 and 1×1 phases appear (the 3×1 and 1×1 phases appear with increasing hydrogen dose or hydrogen chemical potential; for details see [11] for example). The spontaneous substitutional adsorption again takes place on the both phases, leading to formation of the adatom–H units (see, 2 for example, Fig. 5 of [8]). The dihydride geometries are extremely stable since the surface dangling bonds are all saturated there. (The binding energies are higher than that of A in Fig. 2 by 1.6 and 1 2.1 eV for the the 3×1 and 1×1 phases, respectively.) The activation energy for the adatom diffusion (i.e., the energy difference between the most stable and transition geometries) increases significantly for higher H , compared with the H 2×1 monohydride phase. This change in diffusion barrier is indeed observed in a recent study on silicon homoepitaxy which shows that epitaxial growth is eventually disrupted for H >1 ML [6 ]. H Now we consider the effect of a dihydride geometry on adatom diffusion on the 2×1 phase. We have found that when the adatom is located at sites B and E, stable adatom–H units are 2 formed. Both structures are more stable than A 1 by 0.7 eV, but an energy cost is required to reach them2. When the adatom is trapped on the geometries, the barriers – which are the energy differences between the stable and transition geometries – will become at least 1.4 and 1.8 eV for diffusion parallel and perpendicular to the dimer rows, respectively. These values are comparable to those of [9]. Even in this case, however, the diffusion mechanisms reported in the present study would be still valid.
2 In a recent scanning tunneling microscopy study of Ge/Si heteroepitaxy [5], the germanium adatoms occupy site A at low temperature but sites E and B at high temperature.
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3.2. Diffusion near single-layer steps The local structures of the B-type steps are in sharp contrast with those on the clean surface: rearrangement of a bond network at the step edge (rebonding) that is a principal atomic relaxation on the clean surface is found to be energetically unfavorable on the hydrogenated surface3. This is a consequence of the existence of hydrogen atoms which terminate dangling bonds at the step edge. Fig. 3 presents the calculated diffusion pathways and activation energies for the silicon adatom near the non-rebonded S step. We present one of the B several pathways along which activation energies are found to be comparable. Near the step edge, a lot of metastable sites which are not seen on the flat surface are found. An adatom from the channel between dimer rows on the upper terrace reaches a local minimum at A , which is essentially the 1 same as the global minimum of the flat terrace (A in Fig. 3 or A in Figs. 1 and 2). Then the 0 adatom crosses the step edge following a pathway A PCDM (or A PBDM ), and finally reaches the 1 1 minimum site M which is larger than A in binding 0 energy by 1.6 eV. As addressed before, the hydrogen release and capture are the crucial processes in the adatom diffusion: the adatom captures a hydrogen atom (A P), then releases one 1 hydrogen atom to an upper-terrace dimer (PC ), and again captures another hydrogen atom (CDM ). The activation energy for the pathway is 0.8 eV by the PC step. The adatom from the dimer rows of the upper terrace follows a pathway E PCDM. The energy barrier is again 1 0.8 eV with PC as the rate-determining process. The energy barrier from the upper terrace to the lower one is comparable to the diffusion barrier along the dimer rows on the flat terrace (Q =0.7 eV ). Thus, there is no additional energy d barrier (Schwoebel barrier) in the vicinity of the step edge. On the other hand, the adatom from the lower terrace (from E ) can reach M with a 2 3 The energetics among various types of step is sensitive to the hydrogen chemical potential m , since each step structure H contains a different number of hydrogen atoms. The nonrebonded structure is more stable than the rebonded one for larger values of m , or for hydrogen coverages higher than the H saturation coverage of the rebonded structure.
Fig. 3. (a) Calculated diffusion pathways and activation energies for an adatom and (b) (meta)stable geometries near the nonrebonded S step (the upper terrace on the left). Meshed, black B and open circles denote silicon adatoms, hydrogen atoms and silicon atoms, respectively. Small dots in (a) represent metastable sites (note that the labels here are independent of the labels in Figs. 1 and 2). The structure shown in (a) is the equilibrium one without an adatom. Values shown in the lower panel of (a) are the energies of the (meta)stable or transition states in eV with respect to the global minimum on the flat terrace.
barrier of 0.4 eV. Once an adatom is captured at M, it hardly escapes from the site since the barriers towards the upper and lower terraces are as high as 1.8 and 2.0 eV, respectively. Therefore, the nonrebonded S step is a deep sink for the adatom. B The stability of M comes from the formation of the adatom–dihydride in which all surface dangling bonds are terminated (Fig. 3b). The adatom reaction and diffusion near the S A step show sharp differences from those near the non-rebonded S step. We have found only three B binding sites near the S step, which are energetiA cally similar to A . An adatom from the upper 0
S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
terrace migrates to the lower terrace with an energy barrier of about 1 eV, which is comparable to that for the adatom diffusion perpendicular to the dimer rows on the terrace (Q =1.1 eV ). Thus, the ) Schwoebel barrier is again absent. Since there is no deep binding site near the step edge, the S A step is a shallow sink for the adatom. The present finding that the S step is a deep B sink for the adatom gives a unified explanation of several observations in epitaxial experiments. First, a denuded zone, where the island density is much reduced compared with other places, appears near the upper terrace of the S step during the growth B [2]. Due to its anisotropic diffusion, as in the previous section and [8], the adatom from the upper terrace gets easier access to M than from the lower terrace near the S step edge. This leads B to a reduced island density on the upper terrace. Second, anti-phase boundaries that are generated when two epitaxial islands meet each other outof-phase (dimer rows of one island to troughs of the other and vice versa) are frequently observed in the growth using hydrogen [3]. The B-type antiphase boundaries, which are perpendicular to the dimer rows of the islands and thus structurally similar to the S step, are effective nucleation sites B [3]. We argue that this phenomenon is due to the preferential adatom adsorption at the S steps. B Finally, it was observed that hydrogen works as a surfactant in Ge/Si heteroepitaxy, suppressing the three-dimensional growth of the germanium overlayer [4,5]. Formation of the three-dimensional structures involves adatom aggregation onto
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islands via surface diffusion, which makes it necessary for adatoms to climb the step boundaries of the islands. On the clean Si(100) surface, the activation energies for silicon adatom climbing are 0.85 and 1.4 eV near the S and S steps, respecA B tively [12]. On the hydrogenated Si(100) surface, however, the adatom climbing is effectively prevented by larger energy barriers of 1.0 and 1.8 eV. Since the present results of silicon adsorption could be relevant to germanium adsorption, it is expected that the hydrogen atom works as a surfactant suppressing island formation.
References [1] J.J. Boland, Adv. Phys. 42 (1993) 129. [2] D.-S. Lin, E.S. Hirschorn, T.-C. Chiang, R. Tsu, D. Lubben, J.E. Greene, Phys. Rev. B 45 (1992) 3494. [3] M.J. Bronikowski, Y. Wang, R.J. Hammers, Phys. Rev. B 48 (1993) 12361. [4] A. Sakai, T. Tatsumi, Appl. Phys. Lett. 64 (1994) 52. [5] S.-J. Kahng, Y.H. Ha, J.-Y. Park, S. Kim, D.W. Moon, Y. Kuk, Phys. Rev. Lett. 80 (1998) 4931. [6 ] M. Copel, R.M. Tromp, Phys. Rev. Lett. 72 (1994) 1236. [7] J.E. Vasek, Z. Zhang, C.T. Salling, M.G. Lagally, Phys. Rev. B 51 (1995) 17207. [8] S. Jeong, A. Oshiyama, Phys. Rev. Lett. 79 (1997) 4425. [9] J. Nara, T. Sasaki, T. Ohno, Phys. Rev. Lett. 79 (1997) 4421. [10] D.J. Chadi, Phys. Rev. Lett. 59 (1987) 1691. [11] J.E. Northrup, Phys. Rev. B 44 (1991) 1419. [12] Q.-M. Zhang, C. Roland, P. Boguslawsky, J. Bernholc, Phys. Rev. Lett. 75 (1995) 101.
Complex diffusion mechanisms of a silicon adatom on hydrogenated Si(100) surfaces: on terraces and near steps Sukmin Jeong *, Atsushi Oshiyama Institute of Physics, University of Tsukuba, Tennodai, Tsukuba 305, Japan
Abstract We present first-principles total-energy calculations which reveal microscopic mechanisms of silicon adatom diffusion on the flat terraces and near the single-layer steps of hydrogenated Si(100) surfaces. The diffusion of the silicon adatom is not a simple motion on a single potential-energy surface but a complex atomic reaction in which hydrogen-atom release and capture as well as adatom exchange are involved. The calculated diffusion barrier is sensitive to hydrogen coverage. Near the step edges, the hydrogen-atom capture and release are also crucial processes as on the terrace, and an additional activation barrier near the step edges (the Schwoebel effect) is absent. The S B step is found to be a deep sink for the adatom. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Anti-phase boundary; Epitaxy; Hydrogen; Schwoebel effect; Step; Substitutional adsorption; Surfactant
1. Introduction The hydrogenated Si(100) surface has been extensively studied because of its importance in both science and technology [1–9]. In homo- and heteroepitaxial growth using chemical vapor deposition or gas-source molecular-beam epitaxy (MBE ), the growth front is terminated by hydrogen [1–3]. In solid-source MBE, hydrogen is introduced intentionally to assist in epitaxial growth [4–7]. The morphology of overlayers indeed depends on hydrogen coverage [2,7], and even the growth mode is modified when using hydrogen as a surfactant in heteroepitaxy [4,5]. Little is known, however, about the microscopic processes, such as the adsorption and diffusion processes of an adatom, which lead to changes in the morphology and growth of the overlayers. * Corresponding author. Fax: +81-298-53-4492. E-mail address: [email protected] (S. Jeong)
In this paper, we present first-principles totalenergy calculations which reveal mechanisms of adatom diffusion on the flat terraces and near the single-layer (S) steps of hydrogenated Si(100) surfaces1. We find that the diffusion of the silicon adatom is not a simple motion on a single potential-energy surface but a complex atomic reaction in which capture and release of the hydrogen atom are rate-determining processes. An exchange process where the silicon adatom replaces a subsurface silicon atom during the diffusion is also found to be important. The calculated diffusion barrier is sensitive to hydrogen coverage. Near the step edges, the hydrogen capture and release are also crucial processes for adatom diffusion as on the terrace, and an additional activation barrier near the step edges (the Schwoebel effect) is absent. The S step is found to be a deep sink for the B 1 For the notations of various types of step, see Chadi [10].
0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 01 1 7 -X
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S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
adatom. Its implication for the morphology of overlayers is also discussed.
2. Calculational method All calculations have been performed by use of norm-conserving pseudopotentials, the local density (LDA) for the exchange-correlation energy, and the conjugate-gradient minimization technique. The surface is simulated by a repeating slab model. The size of the unit cell in the lateral directions is p(앀8×앀8)R45° for the flat terraces. To simulate steps, we use the periodic step arrays on the (100) surfaces with 2×n periodicities (n= 6, 8 and 10) and the (15,1,1) vicinal surfaces. The details of other calculational parameters can be found in [8].
potential-energy surface (PES) as a function of lateral coordinates of the adatom (refer to Fig. 3 of [8]). The most stable site is A, the adsorption geometry of which is shown in Fig. 2a. A striking feature of the geometry is the substitutional adsorption: the silicon adatom forms a bond with a substrate silicon atom (Si2) which releases a hydrogen atom, and the hydrogen atom is in turn bonded to the adatom. As shown in previous calculations [8,9], the energy barrier for the substitutional adsorption is absent. We take the geometry as the global minimum on the flat terrace since it is reached from a silicon vapor phase with no energy cost. The spontaneous substitutional adsorption takes place at many sites including metastable A
3. Results and discussion 3.1. Diffusion on flat terraces Fig. 1 shows (meta)stable sites (A and E) and saddle points (B, C and D) for a silicon adatom on the 2×1 monohydride phase [11], based on a
Fig. 1. Metastable adsorption sites and saddle points for a silicon adatom (represented by small dots) on the 2×1 monohydride Si(100). Black and open circles denote hyrdogen atoms and silicon atoms, respectively. Sites A and E are (meta)stable adsorption sites, and B, C and D are saddle points on the potential-energy surface (PES ) for the adatom. The subscripts to each letter are for discrimination of equivalent adsorption sites. Note that the PES has a fourfold symmetry, reflecting the substrate structure with symmetric dimers (before silicon adsorption).
Fig. 2. (a) Diffusion pathway of an adatom along the dimer rows and (b) the corresponding activation energies. Meshed, filled and open circles denote silicon adatoms, hydrogen atoms and silicon atoms, respectively. The arrow in each part of (a) indicates the direction of adatom migration towards the next stage. Values shown in (b) are the energies of the metastable or transition states in eV with respect to the monohydride geometry at site A. Note that the structures with the labels in Fig. 1 and in (a) may be different – i.e., at the same coordinates of the adatom, the total energy may vary, depending on the number of hydrogen atoms attached to the adatom.
S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
and E, but not on the sites such as saddle points B, C and D. The adatom may follow a pathway A B A C A … for the diffusion parallel to the 1 1 2 2 3 substrate dimer rows and a pathway A D A E 1 1 4 4 A … for the diffusion perpendicular to the dimer 5 rows. In order for the calculated PES to be suitable for assessment of the diffusion barriers, however, a spontaneous hydrogen release from the diffusion species is necessary as it travels along pathways on the PES: e.g., as the adatom from A (with a 1 hydrogen atom attached to the adatom) passes through site B (without the hydrogen atom 1 attached to the adatom). Thus, we have traced diffusion pathways of the monohydride from site A along the dimer rows and, at the same time, investigated throughly the hydrogen release from the diffusion species for several positions of the adatom. For this, we have performed a series of constrained minimizations with the x coordinate of the adatom as the reaction parameter and additionally with the x coordinate of the hydrogen atom to obtain the activation energy for the hydrogen release. Fig. 2 shows the adatom diffusion pathway thus obtained along the dimer rows (x direction) on the 2×1 monohydride phase along with the corresponding activation energies. The adatom– hydrogen unit starting from A increases the 1 energy as it proceeds, since the adatom–Si2 bond is weakened. Then, it is energetically favorable for the adatom to release the hydrogen atom (bonded to it) back to Si2 (~B in Fig. 2, where the tilde 1 means that the lateral position of the adatom roughly coincides with B ). As it proceeds further, 1 the adatom penetrates into the surface, making Si4 the outermost (C of Fig. 2). After that, the 2 adatom turns its direction (in the arrow direction) to make a dimer with Si3 ( E in Fig. 2) since the 3 straight movement costs too much energy. The energy barrier to form a metastable state at site E is only 0.3 eV. From now on, the diffusion 3 species is exchanged from the adatom to a dimer atom, Si4. Finally, the Si4–H unit goes from E 3 to A with a barrier of 0.5 eV. The process 3 A C , where the hydrogen release takes place, 1 2 is the rate-determining process, and we take its barrier (0.7 eV ) as the activation energy Q for d the diffusion along the dimer rows.
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A similar mechanism is expected for the diffusion perpendicular to the dimer rows; from A to 1 A passing through D , A and E , in which 5 1 4 4 hydrogen-atom release and capture by the adatom are involved along the pathway. We find that the activation energy for the adatom diffusion perpendicular to the dimer rows (Q ) is 1.1 eV. The ) exchange of silicon atoms does not occur in this case. As the hydrogen coverage H exceeds 1 ML, H the 3×1 and 1×1 phases appear (the 3×1 and 1×1 phases appear with increasing hydrogen dose or hydrogen chemical potential; for details see [11] for example). The spontaneous substitutional adsorption again takes place on the both phases, leading to formation of the adatom–H units (see, 2 for example, Fig. 5 of [8]). The dihydride geometries are extremely stable since the surface dangling bonds are all saturated there. (The binding energies are higher than that of A in Fig. 2 by 1.6 and 1 2.1 eV for the the 3×1 and 1×1 phases, respectively.) The activation energy for the adatom diffusion (i.e., the energy difference between the most stable and transition geometries) increases significantly for higher H , compared with the H 2×1 monohydride phase. This change in diffusion barrier is indeed observed in a recent study on silicon homoepitaxy which shows that epitaxial growth is eventually disrupted for H >1 ML [6 ]. H Now we consider the effect of a dihydride geometry on adatom diffusion on the 2×1 phase. We have found that when the adatom is located at sites B and E, stable adatom–H units are 2 formed. Both structures are more stable than A 1 by 0.7 eV, but an energy cost is required to reach them2. When the adatom is trapped on the geometries, the barriers – which are the energy differences between the stable and transition geometries – will become at least 1.4 and 1.8 eV for diffusion parallel and perpendicular to the dimer rows, respectively. These values are comparable to those of [9]. Even in this case, however, the diffusion mechanisms reported in the present study would be still valid.
2 In a recent scanning tunneling microscopy study of Ge/Si heteroepitaxy [5], the germanium adatoms occupy site A at low temperature but sites E and B at high temperature.
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3.2. Diffusion near single-layer steps The local structures of the B-type steps are in sharp contrast with those on the clean surface: rearrangement of a bond network at the step edge (rebonding) that is a principal atomic relaxation on the clean surface is found to be energetically unfavorable on the hydrogenated surface3. This is a consequence of the existence of hydrogen atoms which terminate dangling bonds at the step edge. Fig. 3 presents the calculated diffusion pathways and activation energies for the silicon adatom near the non-rebonded S step. We present one of the B several pathways along which activation energies are found to be comparable. Near the step edge, a lot of metastable sites which are not seen on the flat surface are found. An adatom from the channel between dimer rows on the upper terrace reaches a local minimum at A , which is essentially the 1 same as the global minimum of the flat terrace (A in Fig. 3 or A in Figs. 1 and 2). Then the 0 adatom crosses the step edge following a pathway A PCDM (or A PBDM ), and finally reaches the 1 1 minimum site M which is larger than A in binding 0 energy by 1.6 eV. As addressed before, the hydrogen release and capture are the crucial processes in the adatom diffusion: the adatom captures a hydrogen atom (A P), then releases one 1 hydrogen atom to an upper-terrace dimer (PC ), and again captures another hydrogen atom (CDM ). The activation energy for the pathway is 0.8 eV by the PC step. The adatom from the dimer rows of the upper terrace follows a pathway E PCDM. The energy barrier is again 1 0.8 eV with PC as the rate-determining process. The energy barrier from the upper terrace to the lower one is comparable to the diffusion barrier along the dimer rows on the flat terrace (Q =0.7 eV ). Thus, there is no additional energy d barrier (Schwoebel barrier) in the vicinity of the step edge. On the other hand, the adatom from the lower terrace (from E ) can reach M with a 2 3 The energetics among various types of step is sensitive to the hydrogen chemical potential m , since each step structure H contains a different number of hydrogen atoms. The nonrebonded structure is more stable than the rebonded one for larger values of m , or for hydrogen coverages higher than the H saturation coverage of the rebonded structure.
Fig. 3. (a) Calculated diffusion pathways and activation energies for an adatom and (b) (meta)stable geometries near the nonrebonded S step (the upper terrace on the left). Meshed, black B and open circles denote silicon adatoms, hydrogen atoms and silicon atoms, respectively. Small dots in (a) represent metastable sites (note that the labels here are independent of the labels in Figs. 1 and 2). The structure shown in (a) is the equilibrium one without an adatom. Values shown in the lower panel of (a) are the energies of the (meta)stable or transition states in eV with respect to the global minimum on the flat terrace.
barrier of 0.4 eV. Once an adatom is captured at M, it hardly escapes from the site since the barriers towards the upper and lower terraces are as high as 1.8 and 2.0 eV, respectively. Therefore, the nonrebonded S step is a deep sink for the adatom. B The stability of M comes from the formation of the adatom–dihydride in which all surface dangling bonds are terminated (Fig. 3b). The adatom reaction and diffusion near the S A step show sharp differences from those near the non-rebonded S step. We have found only three B binding sites near the S step, which are energetiA cally similar to A . An adatom from the upper 0
S. Jeong, A. Oshiyama / Surface Science 433–435 (1999) 481–485
terrace migrates to the lower terrace with an energy barrier of about 1 eV, which is comparable to that for the adatom diffusion perpendicular to the dimer rows on the terrace (Q =1.1 eV ). Thus, the ) Schwoebel barrier is again absent. Since there is no deep binding site near the step edge, the S A step is a shallow sink for the adatom. The present finding that the S step is a deep B sink for the adatom gives a unified explanation of several observations in epitaxial experiments. First, a denuded zone, where the island density is much reduced compared with other places, appears near the upper terrace of the S step during the growth B [2]. Due to its anisotropic diffusion, as in the previous section and [8], the adatom from the upper terrace gets easier access to M than from the lower terrace near the S step edge. This leads B to a reduced island density on the upper terrace. Second, anti-phase boundaries that are generated when two epitaxial islands meet each other outof-phase (dimer rows of one island to troughs of the other and vice versa) are frequently observed in the growth using hydrogen [3]. The B-type antiphase boundaries, which are perpendicular to the dimer rows of the islands and thus structurally similar to the S step, are effective nucleation sites B [3]. We argue that this phenomenon is due to the preferential adatom adsorption at the S steps. B Finally, it was observed that hydrogen works as a surfactant in Ge/Si heteroepitaxy, suppressing the three-dimensional growth of the germanium overlayer [4,5]. Formation of the three-dimensional structures involves adatom aggregation onto
485
islands via surface diffusion, which makes it necessary for adatoms to climb the step boundaries of the islands. On the clean Si(100) surface, the activation energies for silicon adatom climbing are 0.85 and 1.4 eV near the S and S steps, respecA B tively [12]. On the hydrogenated Si(100) surface, however, the adatom climbing is effectively prevented by larger energy barriers of 1.0 and 1.8 eV. Since the present results of silicon adsorption could be relevant to germanium adsorption, it is expected that the hydrogen atom works as a surfactant suppressing island formation.
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