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Modelling of silicon molecular beam epitaxy on Si(100)
14
Thin Solid Films, 215 (1992)
Modelling
of silicon molecular
beam epitaxy
14-18
on Si( 100)
H. J. Osten MRE
L.rrhorrrtor~ of tlw Institutc~ of Semiconductor
(Received
July 17. 1991; revised November
Physics.
W.-Korsing-Str.
25. 1991: accepted
January
2. 0- 1200 Frttnkfurt(Oder)
(Germany)
17, 1992)
Abstract A model for Si( 100) molecular beam epitaxy (MBE) based on Monte Carlo simulations is applied in order to study the influence of different parameters (substrate temperature. molecular flux density) on the growth kinetics by monitoring the step density of the simulated growth front. The existence of a minimum temperature for smooth two-dimensional film growth with a low step density is discussed. It is shown that such a temperature does not result from the model used. For a sufficiently low deposition rate smooth two-dimensional growth should be possible even at room temperature. The calculations yield an optimal temperature range for growth of low step density films which is in agreement with experimental findings for MBE growth of good quality crystalline layers.
1. Introduction Silicon molecular beam epitaxy (MBE) is playing a continuously increasing role in producing novel microelectronic devices (see for example refs. 1 and 2). A deeper understanding of the growth kinetics requires modelling of the first phase of layer deposition [3-g]. Two counteracting effects occur in MBE deposition, namely the supply of new silicon atoms arriving from a molecular beam and the migration of adatoms on the surface. A high molecular flux density can “pin down” the silicon adatoms, so that the migration is partly hampered. On the contrary, an increase in substrate temperature causes enhanced migration of adatoms but also an enhanced desorption from the surface [9]. It was found experimentally that for a typical growth rate temperature around of 1 monolayer s-’ a substrate 650 ‘C will yield the best crystalline quality of the growing silicon layer [ lo]. In this paper a model is presented for Si( 100) MBE that is capable of accounting for these different mechanisms. By applying a Monte Carlo computer simulation we will reveal the influence of the different growth parameters on the smoothness of the growing film. The quality of the layer is estimated by the step density of the growth front. This estimation gives only information on the surface quality of the grown layer and not explicitly on its crystalline quality such as perfection of epitaxial orientation and defect concentration. In particular, misorientations in epitaxial alignment are not considered in this model. Also, the model does not establish whether the layer is amorphous or crystalline. For epitaxial growth the step density can be easily correlated with the specular reflection high energy
0040-6090/92/$5.00
electron diffraction (RHEED) intensity, an experimental observation which gives an inside view on growth kinetics [ 111.
2. The model We used a version of a model presented by Clarke et al. [3-61. We will briefly review that model. For details the reader is referred to Clarke er ul’s papers. The substrate is modelled by a square, with each entry representing the height at that lattice point. Such a definition assumed a perfect surface; the formation of vacancies or overhangs is precluded. Assuming the substrate to be a square matrix means that all kinds of surface reconstructions are also neglected. Only deposition and migration of adatoms are included in the growth kinetics. All desorption processes are neglected because of the long residence time of surface atoms in comparison with the hopping frequency of adatoms along the surface. Deposition is modelled by randomly generating surface sites with a given rate. These surface sites are allowed to migrate modelled as a random nearest-neighbour hopping process with an Arrhenius rate k(E, T) = k, exp( -E/kT)
(1)
where T is the substrate temperature, k, = lOI ss’ is a vibrational frequency term, k is the Boltzmann constant and E is the barrier to diffusion. This surface migration model maximizes the number of nearest-neighbour bonds formed within an area bounded by a square region 2s + 1 lattice sites on a
,r” 1992 -
Elsevier
Sequoia.
All rights
reserved
H. J. Osten / Si MBE on Si(lO0)
15
side. The barrier height E is taken as the sum of a surface term and a contribution from each nearest neighbour along the surface and perpendicular to it: E = Es + aE, + bE2
(2)
where E s is the surface term, E~ and Ez are the nearestneighbour bond energies perpendicular and parallel to the growth direction, and a and b are the numbers of such bonds formed. The quality of the grown layer is monitored by calculating the step density, projected onto an azimuthal direction ~b in the plane of the substrate:
8
1
S ( ~ ) = Z ~ {[1 - b(hi, j, hi+ ,,j)] c o s q~
+ [1 - 6(hg,j, hi.j+,)] sin q~}
(3)
where 6(a, b) is the Kronecker delta function and L is the number of lattice sites. The morphologically sensitive quantity S(~b) has been shown to provide a striking phenomenological representation of many aspects of specular R H E E D measurements [5, 6]. All the simulations were performed on a 70 × 70 lattice with infinitely high boundaries. The surface sites nearest to the boundaries were not included in the step density calculation. According to Clarke et al. [6] the surface bond energy E s was set to 1.3eV, and the different nearest-neighbour bond energies were chosen to be E~ = 0.454 eV and E2 = 0.045 eV. The evaluation of the step density is calculated in a projection onto the azimuthal direction q5 = 0 ° throughout this paper.
time
3. Results and discussion
Fig. 1. Calculated step density evolution in Si(100) MBE projected along the 0 ° azimuth for a growth rate of 1 monolayer s t and substrate temperatures of (a) 0 °C, (b) 500 °C and (c) 1000 °C (for other parameters see the text).
We applied the very simple model presented above in order to study the effect of different growth parameters on the kinetics. As a first set of simulations the influence of substrate temperature was investigated (Fig. 1). For a given growth rate (impinging flux density) of 1 monolayer s -l we changed the substrate temperature from 0 to 500 to 1000 °C. It can easily be seen that a certain temperature is necessary for two-dimensionallike growth to be obtained; the quality of the first monolayer is worse than that of the later monolayers because of the assumed high surface energy E s (especially visible for T = 500 °C, Fig. l(b)). At 1000 °C the step density for each completed layer is so small that smooth film growth can be assumed. There is no visible difference in the step density for the second and third layers grown at 500 °C and 1000 °C. As an effect of the high Es value, the first completed monolayer contains
more steps than the later monolayers, i.e. the relatively high step density is "growing out" in later monolayers (see Fig. l(b) and l(c)). In a second set of simulations we investigated the possibility of growing smooth layers at very low temperatures. In this context the question occurs as to whether there is a minimum temperature for the two-dimensional growtia of smooth layers of a given material or not. From our model assumption we see no reason for the existence of such a temperature. If the flux density is small enough, there is sufficient time for surface migration based formation of smooth monolayers even at low temperatures. We looked into the kinetics of the first phase of layer formation at 100 °C for different flux densities (Fig. 2). The growth rate r was varied from 1 monolayer s -~ down to 0.000l monolayer s -~. At the highest rate the step density
16
H. J. Osten / Si M B E on Si(lO0)
"7,
¢:
\S \J
v
time Fig. 2. Calculated step density evolution in Si(100) M B E projected along the 0 ~' azimuth for a substrate temperature of 100"C and different deposition rates: (a) 1 monolayer s ~; (b) 0.1 monolayer s ~: (c) 0.01 monolayer s i; (d) 0.001 monolayer s i; (e) 0.0001 monolayer s ~.
reaches a nearly constant value; no formation of individual monolayers can be observed. Already at r = 0.01 monolayer s-~ the step density as a function of deposition time exhibits an oscillation, i.e. the formation of at least the first monolayer can be seen. This effect becomes more pronounced at lower deposition rates. At r = 0.0001 monolayer s ~ the formation of each individual monolayer can be traced by following the step density as a function of time. However, it is interesting to notice that the numerical value for the relative step density at the time when a monolayer is completed is approximately as large as the constant value for growth with r = 1 monolayer s -~. This indicates that the over-
all quality of the layers grown at low temperature with small deposition rates is probably not very good [12]. Also, growth with such low rates is not practicable; for example, the growth of a 5 nm thick layer with a rate of 0.0001 monolayer s ~ used in the calculations will take several hours. We performed a third set of calculations in order to illustrate the counteraction of flux density and surface migration. For deposition rates of 1 and 0.5 monolayer s ~ we increased the substrate temperature by 50 °C steps beginning from 0 °C to 1000 aC. The results are shown in a three-dimensional form in Fig. 3. Two remarkable effects can be discerned. (i) The step density of the grown layers is generally higher for layers grown at the lower growth temperature. (ii) A peculiarity occurs between 600 and 700 ~'C. In this temperature region the step density does not increase as much as at higher or lower substrate temperatures after half a monolayer has grown; a local minimum in step density seems to occur. This effect can be understood by taking into consideration the two counteracting mechanisms (permanent supply of new adatoms and limited time for surface migration before the adatoms are "pinned down" by the next arriving atoms) which should lead to an optimum temperature region for a minimum step density for a certain molecular flux density. The optimum found (600-700 °C) for smooth layer growth with a low step density corresponds to experimental results for good quality epitaxial growth (see for example ref. 10). In silicon MBE growth processes on Si(100) substrates it was found that layers with very good crystalline properties could be grown at those temperatures; increasing or decreasing the substrate temperature leads to a decrease in crystalline quality.
4. Summary We demonstrated the ability of a very simple model to reproduce a wide range of experimental results for Si(100) MBE. Although the modelling approach is still largely phenomenological, it does highlight some fundamental issues in MBE. The calculations performed do not support the existence of a minimum temperature for two-dimensional smooth layer growth; we state that for low enough deposition rates smooth two-dimensional growth should be possible even at room temperature. For a given growth rate there always exists an optimum temperature range for smooth two-dimensional layer growth. The experimental findings of an optimum growth temperature region for good quality epitaxial growth are in agreement with our calculations for the step density.
H. J. Osten / Si M B E on Si(lO0)
17
° v.,~
¢D
~D (13
¢D
¢9
time Fig. 3. Calculated step density evolution in a three-dimensional representation for a growth rate of (a) 1 monolayer s-~ and (b) 0.5 monolayer s -t. The sabstrate temperature is increased in 50 °C steps starting from 0 °C to I000 °C.
The extension of our model calculation to non-perfect surfaces (behaviour of steps and kinks during the growth process) as well as to the influence of modifications to the energy of the growth process (for example by using surfactants) will be published later [13].
References 1 E. Kaspe~-, Springer, Ser. Mater. Sci., 13 (1989) 36. 2 Y. Shiraki, Proc. 3rd Int. Syrup. on Silicon MBE, 1987, p. 217. 3 S. Clarke, M. R. Wilby, D. D. Vvedensky and T. Kawamura, Thin Solid Films, 183 (1989) 221.
18
H. J. Osten / Si M B E on Si(lO0)
4 S. Clarke and D. D. Vvedensky, Phys. Rev. B, 6559. 5 S. Clarke and D. D. Vvedensky, J. Appl. Phys., 2272. 6 S. Clarke and D. D. Vvedensky, Appl. Phys. Lett., 340. 7 S. Ethier and L. J. Lewis, Mater. Res. Soc. Symp. (1990) 371. 8 J. E. Beeby, J. Cryst. Growth, 95 (1989) 48.
37 (1988) 63 (1988) 51 (1987) Proc., 202
9 R. A. Kubiak, W. Y. Leong, R. Houghton and E. H. C. Parker, in J. C. Bean, Proc. 1st Int. Symp. on Silicon MBE, 1985, p. 124. 10 E. Kasper and J. C. Bean (eds.), Silicon Molecular Beam Epitaxy, CRC Press, Boca Raton, FL, 1988. 11 G. S. Petrich, P. K. Pukite, A. M. Wowchak, G. J. Whaley, P. I. Cohen and A. S. Arrott, J. Cryst. Growth, 95 (1989) 23. 12 H. Jorke, H. Kibbel, F. Sch/iffler and H.-J. Herzog, Thin Solid Films, 183 (1989) 307. 13 H. J. Osten, in preparation.
Thin Solid Films, 215 (1992)
Modelling
of silicon molecular
beam epitaxy
14-18
on Si( 100)
H. J. Osten MRE
L.rrhorrrtor~ of tlw Institutc~ of Semiconductor
(Received
July 17. 1991; revised November
Physics.
W.-Korsing-Str.
25. 1991: accepted
January
2. 0- 1200 Frttnkfurt(Oder)
(Germany)
17, 1992)
Abstract A model for Si( 100) molecular beam epitaxy (MBE) based on Monte Carlo simulations is applied in order to study the influence of different parameters (substrate temperature. molecular flux density) on the growth kinetics by monitoring the step density of the simulated growth front. The existence of a minimum temperature for smooth two-dimensional film growth with a low step density is discussed. It is shown that such a temperature does not result from the model used. For a sufficiently low deposition rate smooth two-dimensional growth should be possible even at room temperature. The calculations yield an optimal temperature range for growth of low step density films which is in agreement with experimental findings for MBE growth of good quality crystalline layers.
1. Introduction Silicon molecular beam epitaxy (MBE) is playing a continuously increasing role in producing novel microelectronic devices (see for example refs. 1 and 2). A deeper understanding of the growth kinetics requires modelling of the first phase of layer deposition [3-g]. Two counteracting effects occur in MBE deposition, namely the supply of new silicon atoms arriving from a molecular beam and the migration of adatoms on the surface. A high molecular flux density can “pin down” the silicon adatoms, so that the migration is partly hampered. On the contrary, an increase in substrate temperature causes enhanced migration of adatoms but also an enhanced desorption from the surface [9]. It was found experimentally that for a typical growth rate temperature around of 1 monolayer s-’ a substrate 650 ‘C will yield the best crystalline quality of the growing silicon layer [ lo]. In this paper a model is presented for Si( 100) MBE that is capable of accounting for these different mechanisms. By applying a Monte Carlo computer simulation we will reveal the influence of the different growth parameters on the smoothness of the growing film. The quality of the layer is estimated by the step density of the growth front. This estimation gives only information on the surface quality of the grown layer and not explicitly on its crystalline quality such as perfection of epitaxial orientation and defect concentration. In particular, misorientations in epitaxial alignment are not considered in this model. Also, the model does not establish whether the layer is amorphous or crystalline. For epitaxial growth the step density can be easily correlated with the specular reflection high energy
0040-6090/92/$5.00
electron diffraction (RHEED) intensity, an experimental observation which gives an inside view on growth kinetics [ 111.
2. The model We used a version of a model presented by Clarke et al. [3-61. We will briefly review that model. For details the reader is referred to Clarke er ul’s papers. The substrate is modelled by a square, with each entry representing the height at that lattice point. Such a definition assumed a perfect surface; the formation of vacancies or overhangs is precluded. Assuming the substrate to be a square matrix means that all kinds of surface reconstructions are also neglected. Only deposition and migration of adatoms are included in the growth kinetics. All desorption processes are neglected because of the long residence time of surface atoms in comparison with the hopping frequency of adatoms along the surface. Deposition is modelled by randomly generating surface sites with a given rate. These surface sites are allowed to migrate modelled as a random nearest-neighbour hopping process with an Arrhenius rate k(E, T) = k, exp( -E/kT)
(1)
where T is the substrate temperature, k, = lOI ss’ is a vibrational frequency term, k is the Boltzmann constant and E is the barrier to diffusion. This surface migration model maximizes the number of nearest-neighbour bonds formed within an area bounded by a square region 2s + 1 lattice sites on a
,r” 1992 -
Elsevier
Sequoia.
All rights
reserved
H. J. Osten / Si MBE on Si(lO0)
15
side. The barrier height E is taken as the sum of a surface term and a contribution from each nearest neighbour along the surface and perpendicular to it: E = Es + aE, + bE2
(2)
where E s is the surface term, E~ and Ez are the nearestneighbour bond energies perpendicular and parallel to the growth direction, and a and b are the numbers of such bonds formed. The quality of the grown layer is monitored by calculating the step density, projected onto an azimuthal direction ~b in the plane of the substrate:
8
1
S ( ~ ) = Z ~ {[1 - b(hi, j, hi+ ,,j)] c o s q~
+ [1 - 6(hg,j, hi.j+,)] sin q~}
(3)
where 6(a, b) is the Kronecker delta function and L is the number of lattice sites. The morphologically sensitive quantity S(~b) has been shown to provide a striking phenomenological representation of many aspects of specular R H E E D measurements [5, 6]. All the simulations were performed on a 70 × 70 lattice with infinitely high boundaries. The surface sites nearest to the boundaries were not included in the step density calculation. According to Clarke et al. [6] the surface bond energy E s was set to 1.3eV, and the different nearest-neighbour bond energies were chosen to be E~ = 0.454 eV and E2 = 0.045 eV. The evaluation of the step density is calculated in a projection onto the azimuthal direction q5 = 0 ° throughout this paper.
time
3. Results and discussion
Fig. 1. Calculated step density evolution in Si(100) MBE projected along the 0 ° azimuth for a growth rate of 1 monolayer s t and substrate temperatures of (a) 0 °C, (b) 500 °C and (c) 1000 °C (for other parameters see the text).
We applied the very simple model presented above in order to study the effect of different growth parameters on the kinetics. As a first set of simulations the influence of substrate temperature was investigated (Fig. 1). For a given growth rate (impinging flux density) of 1 monolayer s -l we changed the substrate temperature from 0 to 500 to 1000 °C. It can easily be seen that a certain temperature is necessary for two-dimensionallike growth to be obtained; the quality of the first monolayer is worse than that of the later monolayers because of the assumed high surface energy E s (especially visible for T = 500 °C, Fig. l(b)). At 1000 °C the step density for each completed layer is so small that smooth film growth can be assumed. There is no visible difference in the step density for the second and third layers grown at 500 °C and 1000 °C. As an effect of the high Es value, the first completed monolayer contains
more steps than the later monolayers, i.e. the relatively high step density is "growing out" in later monolayers (see Fig. l(b) and l(c)). In a second set of simulations we investigated the possibility of growing smooth layers at very low temperatures. In this context the question occurs as to whether there is a minimum temperature for the two-dimensional growtia of smooth layers of a given material or not. From our model assumption we see no reason for the existence of such a temperature. If the flux density is small enough, there is sufficient time for surface migration based formation of smooth monolayers even at low temperatures. We looked into the kinetics of the first phase of layer formation at 100 °C for different flux densities (Fig. 2). The growth rate r was varied from 1 monolayer s -~ down to 0.000l monolayer s -~. At the highest rate the step density
16
H. J. Osten / Si M B E on Si(lO0)
"7,
¢:
\S \J
v
time Fig. 2. Calculated step density evolution in Si(100) M B E projected along the 0 ~' azimuth for a substrate temperature of 100"C and different deposition rates: (a) 1 monolayer s ~; (b) 0.1 monolayer s ~: (c) 0.01 monolayer s i; (d) 0.001 monolayer s i; (e) 0.0001 monolayer s ~.
reaches a nearly constant value; no formation of individual monolayers can be observed. Already at r = 0.01 monolayer s-~ the step density as a function of deposition time exhibits an oscillation, i.e. the formation of at least the first monolayer can be seen. This effect becomes more pronounced at lower deposition rates. At r = 0.0001 monolayer s ~ the formation of each individual monolayer can be traced by following the step density as a function of time. However, it is interesting to notice that the numerical value for the relative step density at the time when a monolayer is completed is approximately as large as the constant value for growth with r = 1 monolayer s -~. This indicates that the over-
all quality of the layers grown at low temperature with small deposition rates is probably not very good [12]. Also, growth with such low rates is not practicable; for example, the growth of a 5 nm thick layer with a rate of 0.0001 monolayer s ~ used in the calculations will take several hours. We performed a third set of calculations in order to illustrate the counteraction of flux density and surface migration. For deposition rates of 1 and 0.5 monolayer s ~ we increased the substrate temperature by 50 °C steps beginning from 0 °C to 1000 aC. The results are shown in a three-dimensional form in Fig. 3. Two remarkable effects can be discerned. (i) The step density of the grown layers is generally higher for layers grown at the lower growth temperature. (ii) A peculiarity occurs between 600 and 700 ~'C. In this temperature region the step density does not increase as much as at higher or lower substrate temperatures after half a monolayer has grown; a local minimum in step density seems to occur. This effect can be understood by taking into consideration the two counteracting mechanisms (permanent supply of new adatoms and limited time for surface migration before the adatoms are "pinned down" by the next arriving atoms) which should lead to an optimum temperature region for a minimum step density for a certain molecular flux density. The optimum found (600-700 °C) for smooth layer growth with a low step density corresponds to experimental results for good quality epitaxial growth (see for example ref. 10). In silicon MBE growth processes on Si(100) substrates it was found that layers with very good crystalline properties could be grown at those temperatures; increasing or decreasing the substrate temperature leads to a decrease in crystalline quality.
4. Summary We demonstrated the ability of a very simple model to reproduce a wide range of experimental results for Si(100) MBE. Although the modelling approach is still largely phenomenological, it does highlight some fundamental issues in MBE. The calculations performed do not support the existence of a minimum temperature for two-dimensional smooth layer growth; we state that for low enough deposition rates smooth two-dimensional growth should be possible even at room temperature. For a given growth rate there always exists an optimum temperature range for smooth two-dimensional layer growth. The experimental findings of an optimum growth temperature region for good quality epitaxial growth are in agreement with our calculations for the step density.
H. J. Osten / Si M B E on Si(lO0)
17
° v.,~
¢D
~D (13
¢D
¢9
time Fig. 3. Calculated step density evolution in a three-dimensional representation for a growth rate of (a) 1 monolayer s-~ and (b) 0.5 monolayer s -t. The sabstrate temperature is increased in 50 °C steps starting from 0 °C to I000 °C.
The extension of our model calculation to non-perfect surfaces (behaviour of steps and kinks during the growth process) as well as to the influence of modifications to the energy of the growth process (for example by using surfactants) will be published later [13].
References 1 E. Kaspe~-, Springer, Ser. Mater. Sci., 13 (1989) 36. 2 Y. Shiraki, Proc. 3rd Int. Syrup. on Silicon MBE, 1987, p. 217. 3 S. Clarke, M. R. Wilby, D. D. Vvedensky and T. Kawamura, Thin Solid Films, 183 (1989) 221.
18
H. J. Osten / Si M B E on Si(lO0)
4 S. Clarke and D. D. Vvedensky, Phys. Rev. B, 6559. 5 S. Clarke and D. D. Vvedensky, J. Appl. Phys., 2272. 6 S. Clarke and D. D. Vvedensky, Appl. Phys. Lett., 340. 7 S. Ethier and L. J. Lewis, Mater. Res. Soc. Symp. (1990) 371. 8 J. E. Beeby, J. Cryst. Growth, 95 (1989) 48.
37 (1988) 63 (1988) 51 (1987) Proc., 202
9 R. A. Kubiak, W. Y. Leong, R. Houghton and E. H. C. Parker, in J. C. Bean, Proc. 1st Int. Symp. on Silicon MBE, 1985, p. 124. 10 E. Kasper and J. C. Bean (eds.), Silicon Molecular Beam Epitaxy, CRC Press, Boca Raton, FL, 1988. 11 G. S. Petrich, P. K. Pukite, A. M. Wowchak, G. J. Whaley, P. I. Cohen and A. S. Arrott, J. Cryst. Growth, 95 (1989) 23. 12 H. Jorke, H. Kibbel, F. Sch/iffler and H.-J. Herzog, Thin Solid Films, 183 (1989) 307. 13 H. J. Osten, in preparation.