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Adsorption and diffusion of Ga, In and As adatoms on (001) and (111) GaAs surfaces: a computer simulation study
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Applied Surface Science 123/124 (1998) 653-657
Adsorption and diffusion of Ga, In and As adatoms on (001) and (111) GaAs surfaces" a computer simulation study C.C. Matthai *, G.A. Moran Department of Physics and Astronomy, University of Wales, Cardiff CF2 3YB, UK
Abstract
We have performed molecular dynamics simulations of the adsorption and diffusion of Ga, In and As adatoms on the (2 x 1) and (2 x 4) reconstructions of the GaAs(001) surfaces as well as on the unreconstructed (111)A and (111)B surfaces. For both (111) surfaces, the diffusion was found to be isotropic, whereas for the (001) surfaces the diffusion was primarily along the dimer rows. The As atoms were found to be the most mobile, on all the surfaces considered. The effects of strain on the activation energies was also investigated. © 1998 Elsevier Science B.V.
1. Introduction Crystal growth by epitaxial methods has formed the basis for the construction of a large number of devices and technologies. Growth is achieved in far from equilibrium conditions and the processes that are important to understand are kinetic in nature. However, the kinetic processes of growth and diffusion are still not well understood. Computer simulations provide a means of obtaining information about some of the factors that influence growth. In particular, it is possible to determine activation energies for surface diffusion, diffusion paths and diffusion constants and their dependence on species type, surface orientation and strain. From a knowledge of these dependencies, it is possible to alter growth parameters to ensure better quality epitaxial layers. The GaAs (001) surface exhibits a variety of surface reconstructions that are dependent on surface stoichiometry [1]. Experimentally, one finds that
* Corresponding author.
starting with the most 'As rich' phase, the surface is seen to have a c(4 X 4), (2 X 4) or c(2 X 8) symmetry. When As is driven from the system by heating the surface, it undergoes a number of transitions through various symmetries. Starting with the c(4 X 4), the surface changes to a set of (2 X 4) phases through a (3 X 1) and (2 X 6) phase before arriving at the 'Ga rich' phase [2]. As growth is usually done in an overpressure of As, we have focussed our attention on the (2 X 4) reconstructed surface and on the simpler unobserved (2 X 1) surface. We have also investigated the (111) A and B surfaces as a means of comparing them with the (100) orientation.
2. Simulation of diffusion The substrate was modelled by a block of atoms held by a fixed layer of atoms at the bottom and with periodic boundary conditions in the surface plane. The periodic surface unit cell was taken to be 20 X 20 planes, with the block being 10 units in the direction
0169-4332/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 ( 9 7 ) 0 0 4 4 2 - X
654
C,C. Matthai, G.A. Moran/Applied Sur/ace Science 123 / 124 (1998) 653-657
Table 1 Diffusion parameters for adatoms on GaAs reconstructcd surfaces Surface
Adatom species
Static energy barriers ( e V )
Activation energy(eV)
(001)2×4 (001)2×4 (001) 2×4 (I I 1) A ( 1I 1) A (111) A (111) B (I 11) B (I 11) B
As Ga In As Ga In As Ga In
1.08 2.04 2.03 0.57 0.99 0.94 1.56 1.76 1.88
0.14 0.22 0.35 0.19 0.23 0.25 0.07 0.14 0.29
The values for the (2× 1) and (2×4) surfaces are the same.
normal to the surface. The adsorption sites were determined by placing adatoms onto the surface and allowing the system to relax according to standard molecular dynamics (MD) techniques but with the adatom constrained to move only in the direction perpendicular to the surface plane. This was done for adatom positions on a grid of 100 points in the surface unit cell. By plotting the minimum energies for each lateral position, a surface potential energy contour map may be constructed and from this, both adatom adsorption sites (troughs in the contour plots) and static activation energies for surface diffusion (the heights of the barriers between troughs) may be obtained. In performing the M D simulations, we have used the Tersoff type coordination dependent potential of Sayed et al. [3] to model the interactions between the atoms. The dynamic s~rface diffusion properties (activation energies, diffusion paths and diffusion constants) of the adatoms were also obtained by the application of the MD method. In this case, an adatom was initially placed at one of the local minima on the contour energy surface and given some kinetic energy (temperature). The system was then allowed to evolve according to the MD equations of motion and the positions and velocities of all the atoms stored. The diffusion path is obtained by simply charting the path taken by the adatom on the substrate surface. The activation energy for diffusion can be obtained using the method of Matthai [4] or from knowledge of the temperature dependence of the diffusion coefficient [5]. The diffusion coefficients were determined from the velocity autocorre-
lation function which in turn was calculated from the stored velocities at each time step.
3. Results 3.1. GaAs(O01) (2 × 1) surface
Although the (2 × 1) reconstruction does not occur in the case of GaAs, it is nevertheless a useful structure to study as it forms the basis of the more important (2 × 4) surface. The (001) surface of the zinc-blende cell was As terminated and the surface atoms moved so as to form a (2 × 1) dimerised surface. In order to establish the minimum energy sites on the surface, In, As and Ga adatoms were then placed on the surface and the energy contour plots determined. The adsorption site for the As adatom was found to be over a bulk continued site. For both In and Ga adatoms, the energy minimum position was also found to be this position. In this instance, the As dimer bond below the Ga (In) adatom expands to 3.69 A giving a G a ( I n ) - A s bond length of 2.345 A which is very close to that in bulk
Fig. 1. Diffusion path for an adatom on the (2 × I) reconstructed GaAs(001 ) surface.
C.C. Matthai, G.A. Moran/Applied Surjhce Science 123/124 (1998) 653 657
(a)
ABOVE
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Fig. 2. Energy contour maps for an (a) As and (b) Ga adatom on the (2 × 4) reconstructed GaAs(001) surface.
655
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GaAs. From the energy contour plots, it is also possible to establish that the diffusion paths for the adatom would be over the As-dimer rows. The barriers encountered by the different adatoms in this diffusion process were determined by noting their heights from the contour maps and these are given in Table 1. Simulations of adatom pairs were then carried out. It was found that all three molecules, In 2, Ga 2 and A s 2, formed dimers perpendicular to the surface dimer orientation with the latter expanding from 2.42 to 3.22 A. This is in agreement with the view that both InAs and GaAs grow with alternate Ga (In) and As dimers along the (001) directions. For As adatoms on this As terminated surface, the configuration is thought to be the basis for the c(4 X 4) reconstructed surface. To simulate the dynamic diffusion process, the surface atoms a n d / o r the adatom was given a predetermined temperature (energy) and the positions and velocities of the atoms recorded at each time step. From this data it is possible to establish diffusion paths, activation energies and diffusion coefficients. An example of the diffusion of an adatom on the (2 × 1) surface is shown in Fig. 1. It can be seen that the adatom simply moves from one surface dimer to the next which open and close according to the position of the adatom. This motion is very similar to that observed on the Si(001) (2 X 1) reconstructed surface [6]. The activation energies determined from these diffusion events are also given in Table 1. It may be noted that the dynamically calculated barriers are much reduced compared to the static ones. One of the possible reasons for this is that the surface vibrations of the underlying lattice open up the dimers, resulting in a lowering of the barrier which allows the adatom through. It may be noted that the As adatoms are the most mobile reflecting the shallow minimum in the energy contour maps. The minimum energy sites for Ga and In adatoms on the other hand are fairly deep and testify to the strong bonding between the Ga (In) and As atoms. The barriers are therefore at least twice that found for the As adatoms. We have also examined the effects of strain on the diffusion barriers. It was found that when the GaAs (2 X 1) surface was under a 5% tensile strain, the diffusion barriers were increased by a factor of o
%g
kA
Fig. 3. Generic adsorption site for As 2, Ga 2 and In. molecule on the (2 X 4) reconstructed GaAs(001) surface.
three. Under an equivalent compressive strain, the barriers did reduce, but only by a few percent.
3.2. GaAs(O01) /3(2 X 4) surface The /3(2 X 4) surface is essentially a (2 X 1) surface, but with one missing As-dimer in four. For the Ga and In adatoms, the most favoured site from the energy contour maps is once again between the As atoms of a surface dimer. Rather more surprisingly, the As adatom also prefers to take up this position rather than move into one of the missing As sites (Fig. 2). This similarity with the (2 X 1) surface was also found to be the case for the In 2, Ga 2 and As 2 molecules (Fig. 3). When the diffusion of adatoms on the /3(2 X 4) surface was simulated, it was found that although the adatoms preferred to move over the As dimer rows, the diffusion paths were temperature dependent. For lower temperatures, once the adatom approached the vacancy row, they proceeded to diffuse along these vacancy rows. An example of such a diffusion event is displayed in Fig. 4. The activation energies for diffusion were found to be very similar to that found for the (2 X 1) surface. This is only to be expected when the main barrier which the adatom has to overcome is the same for both surface reconstructions. Interestingly, the activation energies of 1.2 and
c.c. Matthai, G.A. Moran/Applied Surface Science 123/124 (1998)653-657
657
The dynamic diffusion simulations showed that for both surfaces, the different adatom species underwent isotropic diffusion.
),
( 4. Conclusion
)
, (
LJ Fig. 4. Diffusion path for an adatom on the (2 × 4) reconstructed GaAs(001) surface. 1.5 eV along perpendicular directions for Ga adatoms on the (2 X 4) /3 2 surface as calculated by Kley and Scheffier using transition state theory [7] are in between the static and dynamic energy barriers as determined by us. The difference between the results is partly due to the different reconstructed surfaces that were considered. The diffusion coefficients for the As adatom on the /3(2 X 4) surface, as calculated from the velocity autocorrelation function, was found to be greater than for the In and Ga adatoms which is in keeping with its lower activation energy.
Simulations of diffusion events were performed on the various GaAs reconstructed surfaces. On both the (111) surfaces, the diffusion was fully isotropic, although there was some variation in the energy barriers and the activation energies for the different adatoms. By contrast, the diffusion on the (2 × l ) and (2 × 4) reconstructed (100) surfaces were highly anisotropic with the adatoms preferring to move over and along the As dimer rows. However, for the latter reconstruction, once the adatoms reached the vacancy sites, their motion was along the line of vacancies. The activation energy for diffusion for both these surfaces was essentially the same. In all the configurations, the As adatoms were found to be the most mobile of the adatom species, especially on As terminated surfaces. This is simply a reflection of the strong bonds that are formed between the Ga (In) adatoms and the As atoms on the surface. The activation energies for the Ga atoms were less than that for the In atoms and is probably due to lighter mass of the former.
References 3.3. G a A s ( l l l ) A and B surfaces For both the A and B (111) surfaces, the minimum energy position and therefore the adsorption site is directly above a surface atom. This is the case for all three adatom species investigated. The activation energy barriers determined for the 3 different adatoms on both surfaces are also given in Table 1. Once again, the As atoms diffuse most easily with the lowest barrier of all being on the (111)B surface.
[l] D.K. Biegelsen, R.D. Brigans. J.E. Northrup, L.E. Swartz, Phys. Rev. B 41 (1990) 5701. [2] B.A. Joyce, Rep. Prog. Phys. 48 (1985) 1637. [3] M. Sayed, J.M. Jefferson, A.B. Walker, A.G. Cullis, Nucl. Instr. Meth. Phys. Res. B 102 (1995) 218. [4] C.C. Matthai, Phil. Mag. A 52 (1985) 305. [5] P.W.M. Jacobs, Z.A. Rycerz. J. Moscinski, Adv. Solid State Chem. 2 (1991) 113. [6] P. Ashu, C.C. Matthai, Appl. Surf. Sci. 48/49 (1991) 39. [7] A. Kley, M. Scheffier, Proceedings of The Physics of Semiconductors - 23, vol. 2, World Scientific, 1996, p. 103l.
Applied Surface Science 123/124 (1998) 653-657
Adsorption and diffusion of Ga, In and As adatoms on (001) and (111) GaAs surfaces" a computer simulation study C.C. Matthai *, G.A. Moran Department of Physics and Astronomy, University of Wales, Cardiff CF2 3YB, UK
Abstract
We have performed molecular dynamics simulations of the adsorption and diffusion of Ga, In and As adatoms on the (2 x 1) and (2 x 4) reconstructions of the GaAs(001) surfaces as well as on the unreconstructed (111)A and (111)B surfaces. For both (111) surfaces, the diffusion was found to be isotropic, whereas for the (001) surfaces the diffusion was primarily along the dimer rows. The As atoms were found to be the most mobile, on all the surfaces considered. The effects of strain on the activation energies was also investigated. © 1998 Elsevier Science B.V.
1. Introduction Crystal growth by epitaxial methods has formed the basis for the construction of a large number of devices and technologies. Growth is achieved in far from equilibrium conditions and the processes that are important to understand are kinetic in nature. However, the kinetic processes of growth and diffusion are still not well understood. Computer simulations provide a means of obtaining information about some of the factors that influence growth. In particular, it is possible to determine activation energies for surface diffusion, diffusion paths and diffusion constants and their dependence on species type, surface orientation and strain. From a knowledge of these dependencies, it is possible to alter growth parameters to ensure better quality epitaxial layers. The GaAs (001) surface exhibits a variety of surface reconstructions that are dependent on surface stoichiometry [1]. Experimentally, one finds that
* Corresponding author.
starting with the most 'As rich' phase, the surface is seen to have a c(4 X 4), (2 X 4) or c(2 X 8) symmetry. When As is driven from the system by heating the surface, it undergoes a number of transitions through various symmetries. Starting with the c(4 X 4), the surface changes to a set of (2 X 4) phases through a (3 X 1) and (2 X 6) phase before arriving at the 'Ga rich' phase [2]. As growth is usually done in an overpressure of As, we have focussed our attention on the (2 X 4) reconstructed surface and on the simpler unobserved (2 X 1) surface. We have also investigated the (111) A and B surfaces as a means of comparing them with the (100) orientation.
2. Simulation of diffusion The substrate was modelled by a block of atoms held by a fixed layer of atoms at the bottom and with periodic boundary conditions in the surface plane. The periodic surface unit cell was taken to be 20 X 20 planes, with the block being 10 units in the direction
0169-4332/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 ( 9 7 ) 0 0 4 4 2 - X
654
C,C. Matthai, G.A. Moran/Applied Sur/ace Science 123 / 124 (1998) 653-657
Table 1 Diffusion parameters for adatoms on GaAs reconstructcd surfaces Surface
Adatom species
Static energy barriers ( e V )
Activation energy(eV)
(001)2×4 (001)2×4 (001) 2×4 (I I 1) A ( 1I 1) A (111) A (111) B (I 11) B (I 11) B
As Ga In As Ga In As Ga In
1.08 2.04 2.03 0.57 0.99 0.94 1.56 1.76 1.88
0.14 0.22 0.35 0.19 0.23 0.25 0.07 0.14 0.29
The values for the (2× 1) and (2×4) surfaces are the same.
normal to the surface. The adsorption sites were determined by placing adatoms onto the surface and allowing the system to relax according to standard molecular dynamics (MD) techniques but with the adatom constrained to move only in the direction perpendicular to the surface plane. This was done for adatom positions on a grid of 100 points in the surface unit cell. By plotting the minimum energies for each lateral position, a surface potential energy contour map may be constructed and from this, both adatom adsorption sites (troughs in the contour plots) and static activation energies for surface diffusion (the heights of the barriers between troughs) may be obtained. In performing the M D simulations, we have used the Tersoff type coordination dependent potential of Sayed et al. [3] to model the interactions between the atoms. The dynamic s~rface diffusion properties (activation energies, diffusion paths and diffusion constants) of the adatoms were also obtained by the application of the MD method. In this case, an adatom was initially placed at one of the local minima on the contour energy surface and given some kinetic energy (temperature). The system was then allowed to evolve according to the MD equations of motion and the positions and velocities of all the atoms stored. The diffusion path is obtained by simply charting the path taken by the adatom on the substrate surface. The activation energy for diffusion can be obtained using the method of Matthai [4] or from knowledge of the temperature dependence of the diffusion coefficient [5]. The diffusion coefficients were determined from the velocity autocorre-
lation function which in turn was calculated from the stored velocities at each time step.
3. Results 3.1. GaAs(O01) (2 × 1) surface
Although the (2 × 1) reconstruction does not occur in the case of GaAs, it is nevertheless a useful structure to study as it forms the basis of the more important (2 × 4) surface. The (001) surface of the zinc-blende cell was As terminated and the surface atoms moved so as to form a (2 × 1) dimerised surface. In order to establish the minimum energy sites on the surface, In, As and Ga adatoms were then placed on the surface and the energy contour plots determined. The adsorption site for the As adatom was found to be over a bulk continued site. For both In and Ga adatoms, the energy minimum position was also found to be this position. In this instance, the As dimer bond below the Ga (In) adatom expands to 3.69 A giving a G a ( I n ) - A s bond length of 2.345 A which is very close to that in bulk
Fig. 1. Diffusion path for an adatom on the (2 × I) reconstructed GaAs(001 ) surface.
C.C. Matthai, G.A. Moran/Applied Surjhce Science 123/124 (1998) 653 657
(a)
ABOVE
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Fig. 2. Energy contour maps for an (a) As and (b) Ga adatom on the (2 × 4) reconstructed GaAs(001) surface.
655
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656
GaAs. From the energy contour plots, it is also possible to establish that the diffusion paths for the adatom would be over the As-dimer rows. The barriers encountered by the different adatoms in this diffusion process were determined by noting their heights from the contour maps and these are given in Table 1. Simulations of adatom pairs were then carried out. It was found that all three molecules, In 2, Ga 2 and A s 2, formed dimers perpendicular to the surface dimer orientation with the latter expanding from 2.42 to 3.22 A. This is in agreement with the view that both InAs and GaAs grow with alternate Ga (In) and As dimers along the (001) directions. For As adatoms on this As terminated surface, the configuration is thought to be the basis for the c(4 X 4) reconstructed surface. To simulate the dynamic diffusion process, the surface atoms a n d / o r the adatom was given a predetermined temperature (energy) and the positions and velocities of the atoms recorded at each time step. From this data it is possible to establish diffusion paths, activation energies and diffusion coefficients. An example of the diffusion of an adatom on the (2 × 1) surface is shown in Fig. 1. It can be seen that the adatom simply moves from one surface dimer to the next which open and close according to the position of the adatom. This motion is very similar to that observed on the Si(001) (2 X 1) reconstructed surface [6]. The activation energies determined from these diffusion events are also given in Table 1. It may be noted that the dynamically calculated barriers are much reduced compared to the static ones. One of the possible reasons for this is that the surface vibrations of the underlying lattice open up the dimers, resulting in a lowering of the barrier which allows the adatom through. It may be noted that the As adatoms are the most mobile reflecting the shallow minimum in the energy contour maps. The minimum energy sites for Ga and In adatoms on the other hand are fairly deep and testify to the strong bonding between the Ga (In) and As atoms. The barriers are therefore at least twice that found for the As adatoms. We have also examined the effects of strain on the diffusion barriers. It was found that when the GaAs (2 X 1) surface was under a 5% tensile strain, the diffusion barriers were increased by a factor of o
%g
kA
Fig. 3. Generic adsorption site for As 2, Ga 2 and In. molecule on the (2 X 4) reconstructed GaAs(001) surface.
three. Under an equivalent compressive strain, the barriers did reduce, but only by a few percent.
3.2. GaAs(O01) /3(2 X 4) surface The /3(2 X 4) surface is essentially a (2 X 1) surface, but with one missing As-dimer in four. For the Ga and In adatoms, the most favoured site from the energy contour maps is once again between the As atoms of a surface dimer. Rather more surprisingly, the As adatom also prefers to take up this position rather than move into one of the missing As sites (Fig. 2). This similarity with the (2 X 1) surface was also found to be the case for the In 2, Ga 2 and As 2 molecules (Fig. 3). When the diffusion of adatoms on the /3(2 X 4) surface was simulated, it was found that although the adatoms preferred to move over the As dimer rows, the diffusion paths were temperature dependent. For lower temperatures, once the adatom approached the vacancy row, they proceeded to diffuse along these vacancy rows. An example of such a diffusion event is displayed in Fig. 4. The activation energies for diffusion were found to be very similar to that found for the (2 X 1) surface. This is only to be expected when the main barrier which the adatom has to overcome is the same for both surface reconstructions. Interestingly, the activation energies of 1.2 and
c.c. Matthai, G.A. Moran/Applied Surface Science 123/124 (1998)653-657
657
The dynamic diffusion simulations showed that for both surfaces, the different adatom species underwent isotropic diffusion.
),
( 4. Conclusion
)
, (
LJ Fig. 4. Diffusion path for an adatom on the (2 × 4) reconstructed GaAs(001) surface. 1.5 eV along perpendicular directions for Ga adatoms on the (2 X 4) /3 2 surface as calculated by Kley and Scheffier using transition state theory [7] are in between the static and dynamic energy barriers as determined by us. The difference between the results is partly due to the different reconstructed surfaces that were considered. The diffusion coefficients for the As adatom on the /3(2 X 4) surface, as calculated from the velocity autocorrelation function, was found to be greater than for the In and Ga adatoms which is in keeping with its lower activation energy.
Simulations of diffusion events were performed on the various GaAs reconstructed surfaces. On both the (111) surfaces, the diffusion was fully isotropic, although there was some variation in the energy barriers and the activation energies for the different adatoms. By contrast, the diffusion on the (2 × l ) and (2 × 4) reconstructed (100) surfaces were highly anisotropic with the adatoms preferring to move over and along the As dimer rows. However, for the latter reconstruction, once the adatoms reached the vacancy sites, their motion was along the line of vacancies. The activation energy for diffusion for both these surfaces was essentially the same. In all the configurations, the As adatoms were found to be the most mobile of the adatom species, especially on As terminated surfaces. This is simply a reflection of the strong bonds that are formed between the Ga (In) adatoms and the As atoms on the surface. The activation energies for the Ga atoms were less than that for the In atoms and is probably due to lighter mass of the former.
References 3.3. G a A s ( l l l ) A and B surfaces For both the A and B (111) surfaces, the minimum energy position and therefore the adsorption site is directly above a surface atom. This is the case for all three adatom species investigated. The activation energy barriers determined for the 3 different adatoms on both surfaces are also given in Table 1. Once again, the As atoms diffuse most easily with the lowest barrier of all being on the (111)B surface.
[l] D.K. Biegelsen, R.D. Brigans. J.E. Northrup, L.E. Swartz, Phys. Rev. B 41 (1990) 5701. [2] B.A. Joyce, Rep. Prog. Phys. 48 (1985) 1637. [3] M. Sayed, J.M. Jefferson, A.B. Walker, A.G. Cullis, Nucl. Instr. Meth. Phys. Res. B 102 (1995) 218. [4] C.C. Matthai, Phil. Mag. A 52 (1985) 305. [5] P.W.M. Jacobs, Z.A. Rycerz. J. Moscinski, Adv. Solid State Chem. 2 (1991) 113. [6] P. Ashu, C.C. Matthai, Appl. Surf. Sci. 48/49 (1991) 39. [7] A. Kley, M. Scheffier, Proceedings of The Physics of Semiconductors - 23, vol. 2, World Scientific, 1996, p. 103l.