- Email: [email protected]
Growth kinetics of non-planar substrates
Journal of Crystal Growth 127 (1993) 922—926 North-Holland
~
o~ CRYSTAL
GROWTH
Growth kinetics on non-planar substrates Niaz Haider, Mark R. Wilby
1
and Dimitri D. Vvedensky
The Blackett Laboratory, Imperial College, London SW7 2BZ, UK
We examine the temperature dependence of the growth kinetics on patterned (V-grooved) substrates by means of a Monte Carlo simulation of a solid-on-solid model. We have extended our previous model of MBE to include second nearest-neighbour interactions to incorporate facetting during growth. At high temperatures, surface diffusion of adatoms from one facet to the other leads to a distribution of growth rates on GaAs(OO1). However at low temperatures, where surface migration processes are rare, growth on such substrates proceeds in a shape preserving manner. This behaviour has been observed experimentally by scanning microprobe RHEED experiments on GaAs(OO1) near the (111) surface, where the growth rate is associated with the period of the specular intensity. Such variations of the growth rates on different facets may open avenues for optoelectronic devices, which exploits the higher mobility of Ga adatoms as compared to Al.
1. Introduction Growth by molecular-beam epitaxy (MBE) on non-planar substrates is of technological importance for the fabrication of low-dimensional devices [1]. Sakaki et al. have pointed out that quantum wires could give rise to enhanced properties such as high electron mobility [2], which could form the basis for novel device applications. An approach to the achievement of quanturn wires and related structures relies on the use of patterned substrates [12]. Such starting surfaces can be prepared, for example by chemical etching, to realize V-grooves. Current limitations on the etching and lithographic techniques only permit these V-grooved structures to be large and well separated. Most of the theoretical and experimental work to date on MBE and related growth techniques have focused upon singular and vicinal surfaces. However, MBE overgrowth on patterned substrates attracts interest in the growth mechanisms, because it shows peculiar features. One such feature is the lateral variations of the growth rate when growth occurs over non-planar sub-
strates, which has already been demonstrated on patterned substrates [71.GaAs grown on Vgrooved substrates presents a lateral variation of the thicknesses over different facets. Experimentally there are two mechanisms related to the MBE growth technique which are responsible for this lateral thickness variations. First the growth rate is limited by a geometric factor where the effective incident flux arriving at each facet is a function of the orientation of the facet [9]. The second mechanism influencing the local growth rate is the surface migration of the species from facet to facet [101.These phenomena are dependent on the crystallographic orientation of each facet, the growth parameters and the nature of the atoms on the surface. If the dimensions of the pattern are of the order of the surface diffusion length of the impinging species then it is possible for those adatoms to migrate to and incorporate in planes with lower surface energies. To design and fabricate high quality devices it is important to understand the principle processes that occur during facet growth. In this communication we study the growth kinetics, in particular the effect of surface migration, on an (001) surface with a facetted V-groove with respect to planar (001) surface) during MBE. This allows us to study the general features when (450
Also at: Department of Electrical and Electronic Engineering, University College, London WCIE 7JE, UK.
0022-0248/93/$06.OO © 1993
—
Elsevier Science Publishers B.V. All rights reserved
N. Haider et a!.
/ Growth
growth occurs on a facetted structure. As devices become smaller and smaller, where quantum size effects become noticeable, surface migration effects play a dominant role in the fabrication where atomic scale fluctuations in the morphology can degrade device performance. In most cases the morphology of the surfaces is the important factor, its evolution is governed by a balance between thermodynamics (surface energies) and kinetics (surface migration). Such a complex interplay can best be resolved by computer simulation techniques as described in section 2. Studies of reflection high-energy electron diffraction (RHEED) intensity oscillations on vicinal GaAs(001) provides a means of parameterizing the energy terms [6]. Neave et al. [51showed that the growth mode on a vicinal surface changes from two-dimensional nucleation to step flow as the temperature exceeds a critical value for a given flux. Such experiments can also be done for the (111) surface [11], but the parameterization process depends on whether the substrate is either an A surface or B surface. Combinations of parameters between the (001) and (111) surfaces are inequivalent when two or more distinct facets are exposed, since growth on a particular facet is influenced by the other facet. In the case of growth on patterned substrates there are no analogous experiments, thus we are forced to use estimates for the energy parameters as shown in table 1. These estimates are chosen as to resemble the behaviour of GaAs. Several models have been studied in the past to try to understand the facetting behaviour and its influence on the crystal morphology [141, but these have been restricted to the behaviour during equilibrium. These studies show that a nearest-neighbour interaction model shows little tendency of multiTable 1 . . . Energy parameters used during the simulation; case 1 and case 2 correspond to the (001) surface with (111)B and (111)A diagonal facets, respectively Energy parameters (eV) E~
E~
E2~
facetting which leads for the development of a model which incorporates more distant interactions, namely second nearest-neighbour interactions. However, growth during MBE occurs under far-from equilibrium conditions and by extending our previous model [4] to incorporate second nearest-neighbour interactions provides a means to study the facetting behaviour during far-from equilibrium conditions.
2. The growth model The simulations are based on the solid-on-solid model (SOS) [3], whereby the substrate is represented as a simple cubic lattice, with neither vacancies nor overhangs permitted. This is expected to be a valid approximation where for low tilt angles the occurrence of overhangs or vacancies is small. The use of a monoatomic model emphasizes the kinetics of the group III species as being rate limiting, i.e. by comparison, the dissociative reaction kinetics and the subsequent migration of the As occur on a sufficiently short time scale as to be regarded as effectively instantaneous. This allows the use of a single species within the mean-field model where the As is present in sufficient quantities and only plays a stoichiometric role. Experimental evidence comes from the observation that the growth kinetics are only affected at low As pressure [131.The growth kinetics are described by two processes, the random deposition of atoms onto the surface and the migration of adatoms along the substrate. Desorption is neglected since for typical growth conditions in MBE of Ill—V compounds, the desorption flux of the group III species is negligible. The deposition site is chosen randomly with each site being chosen with equal probability. Migration is treated as a nearest-neighbour hopping process with the hopping rate given by the Arrhenius relation, k(E, T) k0 exp(—E/kBT), where k0 is the vibrational frequency of a surface =
atom (k0 2kBT/h), kB is the Boltzmann constant, T is the substrate temperature and E is the.. energy barrier to hopping, which depends on the environment of the active atom before hopping and h is Planck s constant. We have extended our =
E2~
Case 1 1.00 0.30 0.10 0.10 Case 2 0.30 0.10 0.375 0.375 __________________________________________
923
kinetics on non-planar substrates
.
,
924
N. Haider et a!.
E
/
Growth kinetics on non-planar substrates
substrate temperatures ranging from 700 to 850 K with an incident deposition flux of one monolayer per second. We consider the case with the first of energy
B
E2~
E~
E2~
E2, E
parameters given in table 1. Choosing E20 E2~
ft.
B.
E2,
Fig. i. Nearest-neighbour, second nearest-neighbour and surface bonding taken into account by the model.
previous model [4] to include second nearestneighbour interactions in the energy barrier. The hopping barrier has the following contributions, E E~+ pE2~+ nE~+ mE2~ where p 0,.. 4, n p, m n. The energy terms are illustrated in fig. 1, where E~is the substrate energy barrier, E2~is the second nearest-neighbour contribution from the substrate, E~is the nearest-neighbour contribution to the barrier, and E2~is the second nearest-neighbour contribution from, step structures. The hopping process is isotropic in that each of the four destination sites have equal probability of being chosen. Previous studies [14] showed that for a latticegas model with nearest-neighbour interactions (J1 > 0) the equilibrium crystal shape evolves from cubical (T 0 K) to spherical at high temperatures. During this transition facets remain which are separated by rounded regions with smooth edges. With second nearest-neighbour interaction (J2 RJ~,R > 0) the evolution is similar to the nearest-neighbour model except that (111) and (110) facets are found in addition to (001) facets For R <0 the equilibrium crystal shape remains cubical from T 0 K up to a finite temperature before rounded surfaces appear at the cube corners. In this case both smooth and sharp edges are found. These studies provide a basis for the need to include second nearest-neighbour interactions to incorporate facetting behaviour. =
=
. ,
=
=
://
=
\,
,‘,‘
Initial Lattice
20
!, ~.
_________
I 1)01
I SI)
L
3. Results and discussion The simulations were carried out on a 200 X 200 lattice with periodic boundary conditions at
Fig. 2. The projected effective growth rate after growth of 500 monolayers for the indicated substrate temperatures. The initial lattice is shown as a reference. In this case the adatom mobility is higher on the flat surface than on the diagonal surface.
N. Haider et a!.
/
925
Growth kinetics on non-planar substrates
sion length of the adatoms. At higher temperatures it can be seen that the flat terrace experiences a large negative growth rate, since free adatoms, which are much more mobile than on the diagonal facet, are diffusing across the terrace over to the diagonal facet. On arriving onto the diagonal surface these adatoms become much less mobile due to the stronger bond energies. This can be seen in the early stages of high temperature growth or at intermediate temperatures where the lower half of the diagonal facet experiences a negative growth rate, due to the transfer of adatoms into the filling of the apex. This is because the diffusing adatoms from the flat terrace migrate very slowly down the diagonal facet. Hence the point of maximum supersaturation occurs at the top of the diagonal facet resulting in the formation of a “lip”. A closer examination reveals that the diagonal facet tries to maintain a constant gradient during growth. This means that multi-facet formation does not occur, On further growth the size of the “lip” increases as these adatoms diffuse down the facet thus resulting in a positive growth rate deep in the groove. If growth is continued indefinitely this will result in planarization of the growth front as the two diagonal facets merge together. Experimental evidence for this type of behaviour comes from real time scanning microprobe RHEED measurements on GaAs(001) near (11 1)B surface [81.These studies showed that the period of the specular intensity increased on the (001) surface near the (11 1)B surface implying a slower growth rate. The relative growth rate dereases exponentially as a function of the distance from the edge of the interface. The gradients of the decreases are smaller at higher growth temperatures. This is in agreement with the observed projected morphology in fig. 2, since the gradients reflect the inverse of the diffusion length. However, at these higher temperatures long periods of post-growth relaxation leads to a uniform distribution of material on the surfaces. This occurs because adatoms at the top of the groove migrate down into the groove and fill the apex. Considering the case with the second set of energy parameters given in table 1. Reversing the
no
_______
~
.J
_______
‘\
7.
2)1-
1
_________
~
irnitaaiitce
‘°. - - 50
T = 850 K Ml
L
Fig. 3. The projected effective growth rate after growth of 500 monolayers for the indicated substrate temperatures. The initial lattice is shown as a reference. In this case the adatom .. mobility is lower on the flat surface than on the diagonal surface.
above case and imposing E2~ E2~> E~,ensures a greater adatom activity on the diagonal surface as compared with the (001) surface. To keep a similar temperature scale for both cases requires a change in the value of E~.This change of parameters is required since the (11 1)A surface is Ga terminated which reduces “stickness” of this surface as compared to the (11l)B surface which is As terminated. At low temperatures, growth occurs in a shape preserving manner as in the previous case and occurs for the same reasons. At higher temperatures during growth, as shown in fig. 3, the groove experiences a negative growth rate, since adatoms migrate from the groove to the flat terrace. However, to maintain the gradient of the diagonal facet, adatoms must migrate from the lower-half of the groove. This is done by the filling of the apex, but since there is no flat base these diagonal facets tend to separate, contrary to the above case. When adatoms migrate from the groove to the flat surface they become much less mobile due to the stronger bond energies. This leads to a maximum in the supersaturation at the edge of the flat surface resulting in the formation of a “lip”. However, if growth is continued indefinitely this will lead to the planarization of the growth front as the two diagonal facets diverge. This behaviour is the opposite to the case discussed above. This effect can be seen =
926
N. Haider et al.
/ Growth kinetics on non-planar substrates
in the comparison of the surface profiles at 800 and at 850 K where the position of the “lip” moves down to allow the morphology to planarize to the average height (37k). Evidence for this kind of behaviour can again be seen from real time scanning microprobe RHEED measurements on GaAs(001) near (111)A surface, where the period of the specular intensity decreased implying a higher growth rate. The relative growth rate increases exponentially as a function of the distance from the edge of the interface. The gradients of the increases are smaller at higher growth temperatures. Again, at the higher growth temperatures long periods of of post-growth relaxation leads to a uniform distribution of material on the surfaces. This implies that adatoms, from the point of maximum supersaturation, migrate along the flat terrace.
4. Summary To summarize, our simple model, which includes deposition and surface migration, has qualitatively reproduced the morphological behaviour of MBE growth on GaAs(001) near (111) surfaces as observed from scanning microprobe RHEED experiments. The distribution of growth rates observed is a direct consequence of the surface diffusion of Ga. In each case, growth on such V-groove structures always leads to planarization of the growth front. The development of a “lip” is found to be an artifact of the difference in the surface energies of the two surfaces coupled with surface diffusion during growth. However, our approach is limited in the sense that the appearance or growth of new facets cannot be easily distinguished.
Acknowledgements N.H. would like to thank the UK Science and Engineering Research Council for their financial assistance. The support of Imperial College and the Research Development Corporation of Japan under the auspices of the “Atomic Arrangement: Design and Control for New Materials” Joint Research Program is also gratefully acknowledged.
References [i] Y. Nakamura, S. Koshiba, M. Tsuchiya, H. Kano and H Sakaki, AppI. Phys. Letters 59 (1991) 6. [2] H. Sakaki, J. AppI. Phys. 19 (1980) L375. [3] iD. Weeks and G.H. Gilmer, Advan. Chem. Phys. 40 (1979) 157. [4] S. Clarke and D.D. Vvedensky, Phys. Rev. Letters 58 (1987) 2235. [51J.H. Neave, P.J. Dobson, BA. Joyce and J. Zhang, AppI. Phys. Letters 47 (1985) 100.
16]
T. Shitara, D.D. Vvedensky, MR. Wilby, J. Zhang, J.H. Neave and BA. Joyce, AppI. Phys. Letters 60 (1992) 1504.
[7] J.S. Smith, P.L. Derry, S. Margalit and A. Yariv, AppI. Phys. Letters 47 (1985) 712. [81 M. Hata, T. Isu, A. Watanabe and Y. Katayama, J. Vacuum Sci. Technol. B 8 (1990) 692. [9] W.T. Tsang and A. Cho, AppI. Phys. Letters 30 (1977) 293. [10] E. Kapon, MC. Tamargo and D.M. Hwang, AppI. Phys. Letters 50 (1987) 347.
[11] T. Shitara, E. Kondo and T. Nishinaga, J. Crystal Growth 99 (1990) 530. [121Y. Nakamura, S. Koshiba, M. Tsuchiya, H. Kano and H. Sakaki, Appi. Phys. Letters 59 (1991) 700. [13] M. Hata, A. Watanabe and T. Isu, J Crystal Growth 111 (1991) 83. [141C. Rottman and M. Wortis, Phys. Rev. B 29 (1984) 328.
~
o~ CRYSTAL
GROWTH
Growth kinetics on non-planar substrates Niaz Haider, Mark R. Wilby
1
and Dimitri D. Vvedensky
The Blackett Laboratory, Imperial College, London SW7 2BZ, UK
We examine the temperature dependence of the growth kinetics on patterned (V-grooved) substrates by means of a Monte Carlo simulation of a solid-on-solid model. We have extended our previous model of MBE to include second nearest-neighbour interactions to incorporate facetting during growth. At high temperatures, surface diffusion of adatoms from one facet to the other leads to a distribution of growth rates on GaAs(OO1). However at low temperatures, where surface migration processes are rare, growth on such substrates proceeds in a shape preserving manner. This behaviour has been observed experimentally by scanning microprobe RHEED experiments on GaAs(OO1) near the (111) surface, where the growth rate is associated with the period of the specular intensity. Such variations of the growth rates on different facets may open avenues for optoelectronic devices, which exploits the higher mobility of Ga adatoms as compared to Al.
1. Introduction Growth by molecular-beam epitaxy (MBE) on non-planar substrates is of technological importance for the fabrication of low-dimensional devices [1]. Sakaki et al. have pointed out that quantum wires could give rise to enhanced properties such as high electron mobility [2], which could form the basis for novel device applications. An approach to the achievement of quanturn wires and related structures relies on the use of patterned substrates [12]. Such starting surfaces can be prepared, for example by chemical etching, to realize V-grooves. Current limitations on the etching and lithographic techniques only permit these V-grooved structures to be large and well separated. Most of the theoretical and experimental work to date on MBE and related growth techniques have focused upon singular and vicinal surfaces. However, MBE overgrowth on patterned substrates attracts interest in the growth mechanisms, because it shows peculiar features. One such feature is the lateral variations of the growth rate when growth occurs over non-planar sub-
strates, which has already been demonstrated on patterned substrates [71.GaAs grown on Vgrooved substrates presents a lateral variation of the thicknesses over different facets. Experimentally there are two mechanisms related to the MBE growth technique which are responsible for this lateral thickness variations. First the growth rate is limited by a geometric factor where the effective incident flux arriving at each facet is a function of the orientation of the facet [9]. The second mechanism influencing the local growth rate is the surface migration of the species from facet to facet [101.These phenomena are dependent on the crystallographic orientation of each facet, the growth parameters and the nature of the atoms on the surface. If the dimensions of the pattern are of the order of the surface diffusion length of the impinging species then it is possible for those adatoms to migrate to and incorporate in planes with lower surface energies. To design and fabricate high quality devices it is important to understand the principle processes that occur during facet growth. In this communication we study the growth kinetics, in particular the effect of surface migration, on an (001) surface with a facetted V-groove with respect to planar (001) surface) during MBE. This allows us to study the general features when (450
Also at: Department of Electrical and Electronic Engineering, University College, London WCIE 7JE, UK.
0022-0248/93/$06.OO © 1993
—
Elsevier Science Publishers B.V. All rights reserved
N. Haider et a!.
/ Growth
growth occurs on a facetted structure. As devices become smaller and smaller, where quantum size effects become noticeable, surface migration effects play a dominant role in the fabrication where atomic scale fluctuations in the morphology can degrade device performance. In most cases the morphology of the surfaces is the important factor, its evolution is governed by a balance between thermodynamics (surface energies) and kinetics (surface migration). Such a complex interplay can best be resolved by computer simulation techniques as described in section 2. Studies of reflection high-energy electron diffraction (RHEED) intensity oscillations on vicinal GaAs(001) provides a means of parameterizing the energy terms [6]. Neave et al. [51showed that the growth mode on a vicinal surface changes from two-dimensional nucleation to step flow as the temperature exceeds a critical value for a given flux. Such experiments can also be done for the (111) surface [11], but the parameterization process depends on whether the substrate is either an A surface or B surface. Combinations of parameters between the (001) and (111) surfaces are inequivalent when two or more distinct facets are exposed, since growth on a particular facet is influenced by the other facet. In the case of growth on patterned substrates there are no analogous experiments, thus we are forced to use estimates for the energy parameters as shown in table 1. These estimates are chosen as to resemble the behaviour of GaAs. Several models have been studied in the past to try to understand the facetting behaviour and its influence on the crystal morphology [141, but these have been restricted to the behaviour during equilibrium. These studies show that a nearest-neighbour interaction model shows little tendency of multiTable 1 . . . Energy parameters used during the simulation; case 1 and case 2 correspond to the (001) surface with (111)B and (111)A diagonal facets, respectively Energy parameters (eV) E~
E~
E2~
facetting which leads for the development of a model which incorporates more distant interactions, namely second nearest-neighbour interactions. However, growth during MBE occurs under far-from equilibrium conditions and by extending our previous model [4] to incorporate second nearest-neighbour interactions provides a means to study the facetting behaviour during far-from equilibrium conditions.
2. The growth model The simulations are based on the solid-on-solid model (SOS) [3], whereby the substrate is represented as a simple cubic lattice, with neither vacancies nor overhangs permitted. This is expected to be a valid approximation where for low tilt angles the occurrence of overhangs or vacancies is small. The use of a monoatomic model emphasizes the kinetics of the group III species as being rate limiting, i.e. by comparison, the dissociative reaction kinetics and the subsequent migration of the As occur on a sufficiently short time scale as to be regarded as effectively instantaneous. This allows the use of a single species within the mean-field model where the As is present in sufficient quantities and only plays a stoichiometric role. Experimental evidence comes from the observation that the growth kinetics are only affected at low As pressure [131.The growth kinetics are described by two processes, the random deposition of atoms onto the surface and the migration of adatoms along the substrate. Desorption is neglected since for typical growth conditions in MBE of Ill—V compounds, the desorption flux of the group III species is negligible. The deposition site is chosen randomly with each site being chosen with equal probability. Migration is treated as a nearest-neighbour hopping process with the hopping rate given by the Arrhenius relation, k(E, T) k0 exp(—E/kBT), where k0 is the vibrational frequency of a surface =
atom (k0 2kBT/h), kB is the Boltzmann constant, T is the substrate temperature and E is the.. energy barrier to hopping, which depends on the environment of the active atom before hopping and h is Planck s constant. We have extended our =
E2~
Case 1 1.00 0.30 0.10 0.10 Case 2 0.30 0.10 0.375 0.375 __________________________________________
923
kinetics on non-planar substrates
.
,
924
N. Haider et a!.
E
/
Growth kinetics on non-planar substrates
substrate temperatures ranging from 700 to 850 K with an incident deposition flux of one monolayer per second. We consider the case with the first of energy
B
E2~
E~
E2~
E2, E
parameters given in table 1. Choosing E20 E2~
ft.
B.
E2,
Fig. i. Nearest-neighbour, second nearest-neighbour and surface bonding taken into account by the model.
previous model [4] to include second nearestneighbour interactions in the energy barrier. The hopping barrier has the following contributions, E E~+ pE2~+ nE~+ mE2~ where p 0,.. 4, n p, m n. The energy terms are illustrated in fig. 1, where E~is the substrate energy barrier, E2~is the second nearest-neighbour contribution from the substrate, E~is the nearest-neighbour contribution to the barrier, and E2~is the second nearest-neighbour contribution from, step structures. The hopping process is isotropic in that each of the four destination sites have equal probability of being chosen. Previous studies [14] showed that for a latticegas model with nearest-neighbour interactions (J1 > 0) the equilibrium crystal shape evolves from cubical (T 0 K) to spherical at high temperatures. During this transition facets remain which are separated by rounded regions with smooth edges. With second nearest-neighbour interaction (J2 RJ~,R > 0) the evolution is similar to the nearest-neighbour model except that (111) and (110) facets are found in addition to (001) facets For R <0 the equilibrium crystal shape remains cubical from T 0 K up to a finite temperature before rounded surfaces appear at the cube corners. In this case both smooth and sharp edges are found. These studies provide a basis for the need to include second nearest-neighbour interactions to incorporate facetting behaviour. =
=
. ,
=
=
://
=
\,
,‘,‘
Initial Lattice
20
!, ~.
_________
I 1)01
I SI)
L
3. Results and discussion The simulations were carried out on a 200 X 200 lattice with periodic boundary conditions at
Fig. 2. The projected effective growth rate after growth of 500 monolayers for the indicated substrate temperatures. The initial lattice is shown as a reference. In this case the adatom mobility is higher on the flat surface than on the diagonal surface.
N. Haider et a!.
/
925
Growth kinetics on non-planar substrates
sion length of the adatoms. At higher temperatures it can be seen that the flat terrace experiences a large negative growth rate, since free adatoms, which are much more mobile than on the diagonal facet, are diffusing across the terrace over to the diagonal facet. On arriving onto the diagonal surface these adatoms become much less mobile due to the stronger bond energies. This can be seen in the early stages of high temperature growth or at intermediate temperatures where the lower half of the diagonal facet experiences a negative growth rate, due to the transfer of adatoms into the filling of the apex. This is because the diffusing adatoms from the flat terrace migrate very slowly down the diagonal facet. Hence the point of maximum supersaturation occurs at the top of the diagonal facet resulting in the formation of a “lip”. A closer examination reveals that the diagonal facet tries to maintain a constant gradient during growth. This means that multi-facet formation does not occur, On further growth the size of the “lip” increases as these adatoms diffuse down the facet thus resulting in a positive growth rate deep in the groove. If growth is continued indefinitely this will result in planarization of the growth front as the two diagonal facets merge together. Experimental evidence for this type of behaviour comes from real time scanning microprobe RHEED measurements on GaAs(001) near (11 1)B surface [81.These studies showed that the period of the specular intensity increased on the (001) surface near the (11 1)B surface implying a slower growth rate. The relative growth rate dereases exponentially as a function of the distance from the edge of the interface. The gradients of the decreases are smaller at higher growth temperatures. This is in agreement with the observed projected morphology in fig. 2, since the gradients reflect the inverse of the diffusion length. However, at these higher temperatures long periods of post-growth relaxation leads to a uniform distribution of material on the surfaces. This occurs because adatoms at the top of the groove migrate down into the groove and fill the apex. Considering the case with the second set of energy parameters given in table 1. Reversing the
no
_______
~
.J
_______
‘\
7.
2)1-
1
_________
~
irnitaaiitce
‘°. - - 50
T = 850 K Ml
L
Fig. 3. The projected effective growth rate after growth of 500 monolayers for the indicated substrate temperatures. The initial lattice is shown as a reference. In this case the adatom .. mobility is lower on the flat surface than on the diagonal surface.
above case and imposing E2~ E2~> E~,ensures a greater adatom activity on the diagonal surface as compared with the (001) surface. To keep a similar temperature scale for both cases requires a change in the value of E~.This change of parameters is required since the (11 1)A surface is Ga terminated which reduces “stickness” of this surface as compared to the (11l)B surface which is As terminated. At low temperatures, growth occurs in a shape preserving manner as in the previous case and occurs for the same reasons. At higher temperatures during growth, as shown in fig. 3, the groove experiences a negative growth rate, since adatoms migrate from the groove to the flat terrace. However, to maintain the gradient of the diagonal facet, adatoms must migrate from the lower-half of the groove. This is done by the filling of the apex, but since there is no flat base these diagonal facets tend to separate, contrary to the above case. When adatoms migrate from the groove to the flat surface they become much less mobile due to the stronger bond energies. This leads to a maximum in the supersaturation at the edge of the flat surface resulting in the formation of a “lip”. However, if growth is continued indefinitely this will lead to the planarization of the growth front as the two diagonal facets diverge. This behaviour is the opposite to the case discussed above. This effect can be seen =
926
N. Haider et al.
/ Growth kinetics on non-planar substrates
in the comparison of the surface profiles at 800 and at 850 K where the position of the “lip” moves down to allow the morphology to planarize to the average height (37k). Evidence for this kind of behaviour can again be seen from real time scanning microprobe RHEED measurements on GaAs(001) near (111)A surface, where the period of the specular intensity decreased implying a higher growth rate. The relative growth rate increases exponentially as a function of the distance from the edge of the interface. The gradients of the increases are smaller at higher growth temperatures. Again, at the higher growth temperatures long periods of of post-growth relaxation leads to a uniform distribution of material on the surfaces. This implies that adatoms, from the point of maximum supersaturation, migrate along the flat terrace.
4. Summary To summarize, our simple model, which includes deposition and surface migration, has qualitatively reproduced the morphological behaviour of MBE growth on GaAs(001) near (111) surfaces as observed from scanning microprobe RHEED experiments. The distribution of growth rates observed is a direct consequence of the surface diffusion of Ga. In each case, growth on such V-groove structures always leads to planarization of the growth front. The development of a “lip” is found to be an artifact of the difference in the surface energies of the two surfaces coupled with surface diffusion during growth. However, our approach is limited in the sense that the appearance or growth of new facets cannot be easily distinguished.
Acknowledgements N.H. would like to thank the UK Science and Engineering Research Council for their financial assistance. The support of Imperial College and the Research Development Corporation of Japan under the auspices of the “Atomic Arrangement: Design and Control for New Materials” Joint Research Program is also gratefully acknowledged.
References [i] Y. Nakamura, S. Koshiba, M. Tsuchiya, H. Kano and H Sakaki, AppI. Phys. Letters 59 (1991) 6. [2] H. Sakaki, J. AppI. Phys. 19 (1980) L375. [3] iD. Weeks and G.H. Gilmer, Advan. Chem. Phys. 40 (1979) 157. [4] S. Clarke and D.D. Vvedensky, Phys. Rev. Letters 58 (1987) 2235. [51J.H. Neave, P.J. Dobson, BA. Joyce and J. Zhang, AppI. Phys. Letters 47 (1985) 100.
16]
T. Shitara, D.D. Vvedensky, MR. Wilby, J. Zhang, J.H. Neave and BA. Joyce, AppI. Phys. Letters 60 (1992) 1504.
[7] J.S. Smith, P.L. Derry, S. Margalit and A. Yariv, AppI. Phys. Letters 47 (1985) 712. [81 M. Hata, T. Isu, A. Watanabe and Y. Katayama, J. Vacuum Sci. Technol. B 8 (1990) 692. [9] W.T. Tsang and A. Cho, AppI. Phys. Letters 30 (1977) 293. [10] E. Kapon, MC. Tamargo and D.M. Hwang, AppI. Phys. Letters 50 (1987) 347.
[11] T. Shitara, E. Kondo and T. Nishinaga, J. Crystal Growth 99 (1990) 530. [121Y. Nakamura, S. Koshiba, M. Tsuchiya, H. Kano and H. Sakaki, Appi. Phys. Letters 59 (1991) 700. [13] M. Hata, A. Watanabe and T. Isu, J Crystal Growth 111 (1991) 83. [141C. Rottman and M. Wortis, Phys. Rev. B 29 (1984) 328.