- Email: [email protected]
Surface diffusion kinetics of GaAs and AlAs metalorganic vapor-phase epitaxy
,. . . . . . . .
C R Y S T A L G R O W T H
ELSEVIER
Journal of Crystal Growth 170 (1997) 246-250
Surface diffusion kinetics of GaAs and AlAs metalorganic vapor-phase epitaxy Makoto Kasu *, Naoki Kobayashi NTT Basic Research Laboratories, 3-1 Morinosato Wakam~va, Atsugi, Kanagawa 243-01, Japan
Abstract We have investigated the surface kinetics during metalorganic vapor-phase epitaxy (MOVPE), using high-vacuum scanning tunneling microscopy (STM) observation of two-dimensional (2D) nuclei and denuded zones. Using Monte Carlo simulations based on the solid-on-solid model, from 2D nucleus densities we estimated the surface diffusion coefficients of GaAs and AlAs to be 2 × 10 6 and 1.5 × 10 7 c m 2 / s at 530°C, and the energy barriers for migration to be 0.62 and 0.8 eV, respectively. The 2D nucleus size in the [110] direction was about two times larger than that in the [i10] direction. The size anisotropy is caused primarily by a difference in the lateral sticking probability (P~) between steps along the [il0] direction (A steps) and steps along the [110] direction (B steps). The p, ratio was estimated to be more than 3: 1. Denuded zone widths on upper terraces were 2 __ 0.5 times wider than those on lower terraces. This showed that P~ at descending steps was 10 to 3 × 102 times larger than P~ at ascending steps.
1. Introduction
The surface kinetics, consisting of adsorption, surface diffusion of migrating species, nucleus formation, accommodation, and coalescence of nuclei, is one of the fundamental processes of epitaxial growth [1]. Investigation of the mechanism is very important, because it is closely related to the abrupt change in composition at heterointerfaces and thus affects device characteristics. Nevertheless, for metalorganic vapor-phase epitaxy (MOVPE) growth of I I I - V semiconductors, very few studies of surface kinetics have been done so far. Kasu et al. measured, from the step density dependence of the growth rate, the energy difference (0.6 to 0.7 eV) between desorption and migration [2]. Fuoss et al. observed in
* Corresponding author. E-mail: [email protected].
situ X-ray scattering intensity oscillation due to layer-by-layer growth, and regarded the measured long-range order period as a 2-dimensional (2D) nucleus separation to discuss the surface diffusion mechanism [3]. Previously we observed steps on vicinal surfaces [4] and 2D nuclei [5], using high-vacuum scanning tunneling microscopy (STM). STM observation was achieved by As passivation of MOVPE-grown sample surfaces in a vacuum chamber directly connected to an MOVPE system. STM observation gives realspace images of 2D nuclei and denuded zones on grown sample surfaces. A 2D nucleus is formed by accumulation of migrating species and, therefbre, its density is related to the surface diffusion coefficient, which is the area over which a species migrates in a unit time. A denuded zone, the area where few 2D nuclei exist near steps, is formed by migrating species sticking at steps before 2D nucleus formation. There-
0022-0248/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PH S0022-0248(96)00522-2
M. Kasu, . Kobayashi / Journal of CJystal Growth 170 (1997) 246-250
fore, investigation of 2D nuclei and denuded zones clarifies the surface diffusions of migrating species and the lateral sticking of migrating species at steps. So far these investigations have been progressed theoretically [6-8] and experimentally [6,9] by Lewis and Campbell [6], Venables [7], Ratsch et al. [8], and Mo et al. [9]. In this paper we investigated surface kinetics, such as the surface diffusion and the lateral sticking of GaAs and AlAs, quantitatively using STM observation of 2D nuclei and denuded zones of MOVPE surfaces.
2. Experimental procedure First we grew Si-doped ( n = 5 × 1017 c m - 3 ) GaAs on n+-(001) GaAs substrates at 700°C, which is above the range for step bunching [10]. The source materials were triethylgallium (TEG), triethylaluminum (TEA), arsine (ASH3), and silane (Sill4). The working pressure was 1 × l0 4 Pa. The growth rate was fixed at 1 / 6 monolayer ( M L ) / s . The AsH 3 partial pressure was 20 Pa, and the V / I I I ratio was 200. The use of the slow growth rate and the AsH 3 partial pressure results in a high V / l l I ratio. However, the As partial pressure used in the experiments was only about 10 times greater than that required to maintain the As-stabilized surface. For some samples, we inserted an (AIAs)4(GaAs) 4 short-period superlattice layer into the GaAs layer in order to suppress step bunching more effectively. Then we annealed the surface under the same AsH 3 partial pressure for 5 min at 700°C. The surface did not have any 2D nuclei in STM images. Next, we decreased the substrate temperature to that desired and deposited about a 1 / 6 ML of GaAs or AlAs in one second. From simulation results the 1 / 6 ML is within the range for 2D nucleus density saturation for 2D nucleus coverage [5]. Immediately after growth we cooled the sample down to room temperature (RT) at - 1.7°C/s under the same AsH 3 partial pressure. After As passivation in the vacuum chamber connected to the MOVPE system [5], we transferred the sample to the STM system and examined the surface. The STM observation was performed in a vacuum pressure of about 1 × 10 7 Pa. At 235°C the amorphous As cap layer evaporated, and reflection high-
247
energy electron diffraction patterns showed c(4 × 4) reconstruction [4] and we observed the surface at RT, using STM. In STM observations of denuded zones images were taken in a 1 btm 2 square area. To obtain the density of 2D nuclei grown under different surface diffusion coefficients and different lateral sticking probabilities, we performed Monte Carlo simulations based on the solid-on-solid model. An initial surface does not have any 2D nuclei. The migrating species adsorbs on the surface randomly. The rate was determined by the growth rate. Then, migration proceeds randomly on a surface at a rate determined by the surface diffusion coefficient D~ and finally sticks laterally, with a fixed probability P,, at steps around the 2D nuclei. When the denuded zone width Wd was investigated, we considered sticking of the migrating species at steps formed by substrate misorientation. We regarded the area where no 2D nuclei exist near steps as a denuded zone.
3. Results and discussion Fig. 1 shows STM images of 2D nuclei and denuded zones of GaAs (a) and AlAs (b) formed at 630°C. The 2D nucleus density N2D was 9 × 109 cm 2 for GaAs and 2 × l010 c m -2 for AlAs. Here N~D of AlAs was about twice as large as that of GaAs. The monolayer steps observed were caused by slight misorientation of the substrate. The temperature dependences of N2D for GaAs and AlAs, obtained from the STM images, are shown in Fig. 2. The slopes for AlAs and GaAs were similar. From simulations we obtained a relation between N2D (cm 2) the 2D nucleus density in the saturation region and D~ (cm'~/s) as log N2• =
-~log(DJR) + 9.16,
(1)
where R is the growth rate ( M L / s ) [5]. N2D depends on the coverage 0, but almost saturates when 0 > 1 / 2 0 ML. Then we defined N2D in the saturation region as N2~. In Eq. (1) we assumed a lateral sticking probability P, of unity. At higher temperatures our unity assumption for p~ may be invalid. Therefore, we entered N2~ of 6.5 × 10 ~° cm 2 for GaAs and 1.5 × 10 ~l cm -2 for AlAs at 530°C, the lowest temperature of our measurements, into Eq. (1), and obtained D, of 2 × 10 6 c m 2 / s for the Ga
248
M. Kasu, . Kobayashi / Journal of Crystal Growth 170 (1997) 246-250
(a) ,~[71o]2oonm ~Oown
(b) ~,['Tlo]200nm ~Down Fig. 1. High-vacuum STM images of the denuded zones near steps and of 2D nuclei of (a) GaAs and (b) AlAs. About a 1/6 ML amount of GaAs or AlAs was deposited on a very flat (001) GaAs surface at 630°C. The AlAs 2D nucleus density is about two times larger than that of GaAs. The 2D nucleus sizes in the [110] direction are about two times larger than those in the [110] direction. The denuded zone widths on upper terraces are about 2_+0.5 times wider than those on lower terraces.
N2~ depends on P, as well as on D~. We performed simulations to obtain a relation between N2o and P~ [12]. It was found that with the decrease in p, from 1 to 10 -2, N2~) remained almost constant. However, the decrease of P~ to 10 -3 and 10 4 resulted in N2~) increasing by factors of 2 and 5 respectively. In a lower p, range, migrating species form 2D nuclei less easily when 0 < l0 -2 ML, and NeD was lower. However, since N~D begins to saturate with a larger 0, N2D in the saturation range becomes higher. Actual growth is considered to proceed in the P, range from l to 10 -4, because when Ps < 10 -4 more than 50% of migrating species still migrate at 0 = 0.5 ML and layer-by-layer growth does not occur. If growth proceeds when p, = 10-3 and 10 -4, N2~ at P, = 1 should be multiplied by 2 and 5, respectively. Denuded zones, or areas with few 2D nuclei near steps, can be clearly observed in Fig. I. The widths of denuded zones on upper terraces, Wdu, were about 2 _+ 0.5 times greater than those on lower terraces, Wdl, for GaAs and A l A s in a temperature range of 530°C to 650°C. W~ for A and B steps were almost the same. To explain the difference in Wd between upper and lower terraces in terms of the difference in P, at descending and ascending steps, we performed simulations. We fixed the lateral sticking probability at descending steps, P~d, at unity, and changed the lateral sticking probability at ascending steps, P~a, as
700
Temperature T (°C) 650 600 550
E
O "~ 1011 Z
species and 5 × 10 -7 c m 2 / s for the Al species. W e estimated the energy barrier for migration E~ as 0.62 and 0.8 eV for Ga and A1 species, from D S = a2uexp(-E~/kT), where k is the Boltzmann constant and T is the temperature, assuming the hopping distance a = 0.4 nm, and the vibration frequency of an atom v = 10 ~3 s -1. The smaller D~ for AI species is considered to originate from stronger A 1 - A s bonds [11].
C
"o 1010
o
0 p,
109 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.00
1.10 1.20 103/1- (K'I)
Fig. 2. Temperature dependences of 2D nucleus density, N2D, of AlAs and GaAs.
M. Kasu, . Kobayashi/ Journal of Co'stal Growth 170 (1997) 246-250
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~ P ~ P~'J"~ p ~ _ . ~ . ~._p~ T ~i:!:if:~~:::~.i~)::i:~~'i::!!.'.:ii!ii:.':::~i!=:!~........................ .LLL:k.................... .: I ~:::~:~:~i:::::::~::'::~:::~:~::::~:::5:::::2::::~:~:~:i::~:~::::::~:~:::~:::::~:::::::::::::::~::::~::~:::::::::~:::::::5:::: .'~---'~"g;~ :"-'~;~dl:
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............................. -T--
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. . . . . . . .
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I
10 ~
. . . . . . . .
I
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•
"
I .....
I
10 ~
Psd/Psa
Fig. 3. Denuded zone width ratios of upper terraces to lower terraces, W~, / W~I,for different lateral sticking probability ratios at the descending and the ascending steps, P,d/P~. Plots are simulation results assuming that P,d is fixed at unity and ~, at steps around 2D nuclei, is P~d. The experimentally obtained W~, / Wd~of about 2 _+0.5 is indicated by a broken line.
shown in the inset of Fig. 3. W e considered P, at steps around 2D nuclei to be the same as P~a- W e plotted simulation results of Wau/Wdl for different ratios of descending steps to ascending steps, i.e., P~d/P~a, as shown in Fig. 3. Wau/Wjl of 2 + 0.5 was obtained at a p,d/P,~ range of 10 to 3 × 10 2. That the migrating species sticks more easily at descending steps results in step separation instability, i.e., step bunching, as discussed by Schwoebel and Shipsey [13]. In fact the step bunching was observed on a GaAs vicinal surface during M O V P E growth [10,14]. Though Schwoebel and Shipsey [13] described some possible causes of preferentially sticking at descending steps, they were not able to explain preferentially sticking at descending steps in terms of only the energy barrier at the edge on an upper terrace, the so-called Schwoebel barrier. However, one possible origin are top-layer As trimer atoms at steps. At B steps each topqayer As trimer atom bonds with each other and with one 2nd-layer As atom, and prevents migrating group-III species from lower terraces, from sticking to the 2rid-layer As atoms. Migrating group-III species from upper terraces more easily cleave backbonds between top-layer As trimer atoms and 2nd-layer As atoms. A similar mechanism can be considered for A steps. From simulations, we obtained Wd c~ D~/6. The relation is similar to that between L2D, the 2D
249
nucleus separation, and D~, i.e., LZD (X D~/6, which is obtained from Eq. (1). But since the surface reconstruction on upper and lower terraces is the same, the difference in Wd between upper and lower terraces is not due to the difference in D~ [12]. Fig. 1 shows that G a A s and A l A s 2D nucleus sizes in the [110] direction were about 2 times larger than those in the [110] direction. The direction of elongation is opposite to that of molecular beam epitaxy grown GaAs [ 15]. W e performed simulations to obtain a relation between the 2D nucleus size ratio ([110] to [110] directions) and the p~ ratio (steps along [~10] direction, A steps, to steps along [1 10] directions, B steps), i.e., P~A/P~B" Here P~AP~B remained the same. The simulation results are also plotted in Fig. 4. The 2D nucleus size ratio increased, as psA/PsB increased. When P~A/P,B = 3, the 2D nucleus size ratio became 2, obtained from STM observations. But while a surface after growth was quenched to RT, 2D nuclei become nearly round due to the entropy, and therefore, during growth the 2D nucleus size ratio is thought to be more than 2 and P~A/P,B more than 3. In an MOVPE-grown GaAs vicinal surface, the A steps were about two times rougher than the B steps [4], and this is also
,
P
O
,
,
,
,
, , !
/P sA
sB
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Experimental
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0
I
I
I
i
,
,
i
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101
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Fig. 4. Closed circles; 2D nucleus size ratio ([ll0] direction to [110] direction) for different P~ ratios of steps along the [~10] direction (A steps) to steps along the [110] direction (B steps), i.e., P,A /P~B. Open circles; 2D nucleus size ratio for different D~ ratios ([110] direction to [~10] direction), i.e., D~[Ijo]/D~[TIo]. Simulation results are plotted. The experimentally obtained 2D nucleus size ratio of 2 is indicated by a broken line.
250
M. Kasu, . Koba.vashi / Journal of Crystal Growth 170 (1997) 246-250
explained by preferential sticking at kinks in the B steps, i.e., parts of A steps. Another possible origin of the anisotropy of 2D nucleus size is the anisotropy of D~. So we performed simulations to obtain a relation between the 2D nucleus size ratio ([1 10] direction to [1 10] directions) and the D, ratio ( [ l l 0 ] direction to [~10] directions), i.e., Ds[ll0]/Ds[Ti0l. Here Ds[ll0]/D~[Ti0] remained the same. The results are plotted in Fig. 4. The 2D nucleus size ratio increased to only 1.5 as D,[~Io]/D~[Tm I increased to 10. As a result, the 2D nucleus size anisotropy was not caused primarily by the anisotropy in D~. The anisotropy in 2D nucleus size is determined mainly by the lateral sticking rather than by the surface diffusion. This is because 2D nucleus size is determined by the direction in which migrating species sticks to the formed 2D nucleus, not by the direction in which the migration occurs over a wide range. The difference in the elongation direction of 2D nuclei between M O V P E and M B E has been considered to be due to the difference in reconstructions, c(4 × 4) in M O V P E and (2 × 4) in MBE [3]. Our results clarified further that the difference in the elongation direction is due to the difference in preferential sticking at A and B steps, rather than the difference in the direction of the fast surface diffusion. Probably it originates from the difference in step structures in M O V P E and MBE. This is reasonable, considering the difference in the surface reconstruction. We suppose that in M O V P E at B steps the top-layer As trimers that cover 2nd-layer As atoms prevent Ga species from sticking to the 2nd-layer As atoms; on the other hand, at A steps Ga species easily stick to top-layer As trimers. Therefore, the sticking probability of A steps is higher than that of B steps.
4. Conclusions We investigated surface kinetics during M O V P E from STM observation of 2D nuclei and denuded zones along steps. The surface diffusion coefficient was estimated to be 2 × 10 6 and 1.5 × 10 -7 c m 2 / s at 530°C for GaAs and AlAs, and the energy barrier
for migration to be 0.62 and 0.8 eV, respectively. We observed the denuded zone width on upper terraces is 2 _+ 0.5 times wider than that on lower terraces, suggesting that P, from upper terraces is 10 to 3 × 10 2 times larger than P~ from lower terraces. We observed that the 2D nucleus size in the [1 10] direction is about 2 times larger than that in the [-[ 10] direction. We attribute the anisotropy to the lateral sticking probability ratio at steps along [110] (A steps) and [I 10] directions (B steps) of more than 3+1.
Acknowledgements We thank Dr. Yoshiji Horikoshi for his s t i m u l a t ing discussions.
References [1] M.G. Lagally, Y.-W. Mo, R. Kariotis, B.S. Swartzcntruber and M.B. Webb, in: Kinetics of Ordering and Growth at Surfaces, Ed. M.G. Lagally (Plenum. New York, 1990) p. 145. [2] M. Kasu, H. Saito and T. FukuL J. Crystal Growth 115 (I991) 406. [3] P.H. Fuoss, D.W. Kisker, F.J. Lamelas, G.B. Stephenson, P. hnperatori and S. Brennan, Phys. Rev. Lett. 69 (1992) 2791. [4] M. Kasu, N. Kobayashi and H. Yamaguchi, Appl. Phys. Lett. 63 (1993) 678. [5] M. Kasu and N. Kobayashi, J. Appl. Phys. 78 (1995) 3026: 79 (I996) 1822. [6] B. Lewis and D.S. Campbell, J. Vac. Sci. Technol. 4 (1968) 209. [7] J.A. Venables, Philos. Mag. 27 (1973) 697. [8] C. Ratsch, A. Zangwill, P. Smilauer and D.D. Vvedensky, Phys. Rev. Lett. 72 (1994) 3194. [9] Y. W. Mo, J. Kleiner, M.B. Webb and M.G. Lagally. Phys. Rev. Lett. 66 (1991) 1998. [10] M. Kasu and N. Kobayashi, Jpn. J. Appl. Phys. 33 (1994) 712. [ll] M. Kasu and N. Kobayashi, Appl. Phys. Lett. 67 (1995) 2842. [12] M. Kasu and N. Kobayashi, Proc. 9th Int. Conf. Vapor Growth and Epitaxy (Vail, 1996); J. Crystal Growth, to be published. [13] R.L. Schwoebel and EJ. Shipsey, J. Appl. Phys. 37 (1966) 3682. [14] M. Kasu and T. Fukui, Jpn. J. Appl. Phys. 31 (1992) L864. [15] E.J. Heller and M.G. Lagally, Appl. Phys. Lett. 60 (1992) 2675.
C R Y S T A L G R O W T H
ELSEVIER
Journal of Crystal Growth 170 (1997) 246-250
Surface diffusion kinetics of GaAs and AlAs metalorganic vapor-phase epitaxy Makoto Kasu *, Naoki Kobayashi NTT Basic Research Laboratories, 3-1 Morinosato Wakam~va, Atsugi, Kanagawa 243-01, Japan
Abstract We have investigated the surface kinetics during metalorganic vapor-phase epitaxy (MOVPE), using high-vacuum scanning tunneling microscopy (STM) observation of two-dimensional (2D) nuclei and denuded zones. Using Monte Carlo simulations based on the solid-on-solid model, from 2D nucleus densities we estimated the surface diffusion coefficients of GaAs and AlAs to be 2 × 10 6 and 1.5 × 10 7 c m 2 / s at 530°C, and the energy barriers for migration to be 0.62 and 0.8 eV, respectively. The 2D nucleus size in the [110] direction was about two times larger than that in the [i10] direction. The size anisotropy is caused primarily by a difference in the lateral sticking probability (P~) between steps along the [il0] direction (A steps) and steps along the [110] direction (B steps). The p, ratio was estimated to be more than 3: 1. Denuded zone widths on upper terraces were 2 __ 0.5 times wider than those on lower terraces. This showed that P~ at descending steps was 10 to 3 × 102 times larger than P~ at ascending steps.
1. Introduction
The surface kinetics, consisting of adsorption, surface diffusion of migrating species, nucleus formation, accommodation, and coalescence of nuclei, is one of the fundamental processes of epitaxial growth [1]. Investigation of the mechanism is very important, because it is closely related to the abrupt change in composition at heterointerfaces and thus affects device characteristics. Nevertheless, for metalorganic vapor-phase epitaxy (MOVPE) growth of I I I - V semiconductors, very few studies of surface kinetics have been done so far. Kasu et al. measured, from the step density dependence of the growth rate, the energy difference (0.6 to 0.7 eV) between desorption and migration [2]. Fuoss et al. observed in
* Corresponding author. E-mail: [email protected].
situ X-ray scattering intensity oscillation due to layer-by-layer growth, and regarded the measured long-range order period as a 2-dimensional (2D) nucleus separation to discuss the surface diffusion mechanism [3]. Previously we observed steps on vicinal surfaces [4] and 2D nuclei [5], using high-vacuum scanning tunneling microscopy (STM). STM observation was achieved by As passivation of MOVPE-grown sample surfaces in a vacuum chamber directly connected to an MOVPE system. STM observation gives realspace images of 2D nuclei and denuded zones on grown sample surfaces. A 2D nucleus is formed by accumulation of migrating species and, therefbre, its density is related to the surface diffusion coefficient, which is the area over which a species migrates in a unit time. A denuded zone, the area where few 2D nuclei exist near steps, is formed by migrating species sticking at steps before 2D nucleus formation. There-
0022-0248/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PH S0022-0248(96)00522-2
M. Kasu, . Kobayashi / Journal of CJystal Growth 170 (1997) 246-250
fore, investigation of 2D nuclei and denuded zones clarifies the surface diffusions of migrating species and the lateral sticking of migrating species at steps. So far these investigations have been progressed theoretically [6-8] and experimentally [6,9] by Lewis and Campbell [6], Venables [7], Ratsch et al. [8], and Mo et al. [9]. In this paper we investigated surface kinetics, such as the surface diffusion and the lateral sticking of GaAs and AlAs, quantitatively using STM observation of 2D nuclei and denuded zones of MOVPE surfaces.
2. Experimental procedure First we grew Si-doped ( n = 5 × 1017 c m - 3 ) GaAs on n+-(001) GaAs substrates at 700°C, which is above the range for step bunching [10]. The source materials were triethylgallium (TEG), triethylaluminum (TEA), arsine (ASH3), and silane (Sill4). The working pressure was 1 × l0 4 Pa. The growth rate was fixed at 1 / 6 monolayer ( M L ) / s . The AsH 3 partial pressure was 20 Pa, and the V / I I I ratio was 200. The use of the slow growth rate and the AsH 3 partial pressure results in a high V / l l I ratio. However, the As partial pressure used in the experiments was only about 10 times greater than that required to maintain the As-stabilized surface. For some samples, we inserted an (AIAs)4(GaAs) 4 short-period superlattice layer into the GaAs layer in order to suppress step bunching more effectively. Then we annealed the surface under the same AsH 3 partial pressure for 5 min at 700°C. The surface did not have any 2D nuclei in STM images. Next, we decreased the substrate temperature to that desired and deposited about a 1 / 6 ML of GaAs or AlAs in one second. From simulation results the 1 / 6 ML is within the range for 2D nucleus density saturation for 2D nucleus coverage [5]. Immediately after growth we cooled the sample down to room temperature (RT) at - 1.7°C/s under the same AsH 3 partial pressure. After As passivation in the vacuum chamber connected to the MOVPE system [5], we transferred the sample to the STM system and examined the surface. The STM observation was performed in a vacuum pressure of about 1 × 10 7 Pa. At 235°C the amorphous As cap layer evaporated, and reflection high-
247
energy electron diffraction patterns showed c(4 × 4) reconstruction [4] and we observed the surface at RT, using STM. In STM observations of denuded zones images were taken in a 1 btm 2 square area. To obtain the density of 2D nuclei grown under different surface diffusion coefficients and different lateral sticking probabilities, we performed Monte Carlo simulations based on the solid-on-solid model. An initial surface does not have any 2D nuclei. The migrating species adsorbs on the surface randomly. The rate was determined by the growth rate. Then, migration proceeds randomly on a surface at a rate determined by the surface diffusion coefficient D~ and finally sticks laterally, with a fixed probability P,, at steps around the 2D nuclei. When the denuded zone width Wd was investigated, we considered sticking of the migrating species at steps formed by substrate misorientation. We regarded the area where no 2D nuclei exist near steps as a denuded zone.
3. Results and discussion Fig. 1 shows STM images of 2D nuclei and denuded zones of GaAs (a) and AlAs (b) formed at 630°C. The 2D nucleus density N2D was 9 × 109 cm 2 for GaAs and 2 × l010 c m -2 for AlAs. Here N~D of AlAs was about twice as large as that of GaAs. The monolayer steps observed were caused by slight misorientation of the substrate. The temperature dependences of N2D for GaAs and AlAs, obtained from the STM images, are shown in Fig. 2. The slopes for AlAs and GaAs were similar. From simulations we obtained a relation between N2D (cm 2) the 2D nucleus density in the saturation region and D~ (cm'~/s) as log N2• =
-~log(DJR) + 9.16,
(1)
where R is the growth rate ( M L / s ) [5]. N2D depends on the coverage 0, but almost saturates when 0 > 1 / 2 0 ML. Then we defined N2D in the saturation region as N2~. In Eq. (1) we assumed a lateral sticking probability P, of unity. At higher temperatures our unity assumption for p~ may be invalid. Therefore, we entered N2~ of 6.5 × 10 ~° cm 2 for GaAs and 1.5 × 10 ~l cm -2 for AlAs at 530°C, the lowest temperature of our measurements, into Eq. (1), and obtained D, of 2 × 10 6 c m 2 / s for the Ga
248
M. Kasu, . Kobayashi / Journal of Crystal Growth 170 (1997) 246-250
(a) ,~[71o]2oonm ~Oown
(b) ~,['Tlo]200nm ~Down Fig. 1. High-vacuum STM images of the denuded zones near steps and of 2D nuclei of (a) GaAs and (b) AlAs. About a 1/6 ML amount of GaAs or AlAs was deposited on a very flat (001) GaAs surface at 630°C. The AlAs 2D nucleus density is about two times larger than that of GaAs. The 2D nucleus sizes in the [110] direction are about two times larger than those in the [110] direction. The denuded zone widths on upper terraces are about 2_+0.5 times wider than those on lower terraces.
N2~ depends on P, as well as on D~. We performed simulations to obtain a relation between N2o and P~ [12]. It was found that with the decrease in p, from 1 to 10 -2, N2~) remained almost constant. However, the decrease of P~ to 10 -3 and 10 4 resulted in N2~) increasing by factors of 2 and 5 respectively. In a lower p, range, migrating species form 2D nuclei less easily when 0 < l0 -2 ML, and NeD was lower. However, since N~D begins to saturate with a larger 0, N2D in the saturation range becomes higher. Actual growth is considered to proceed in the P, range from l to 10 -4, because when Ps < 10 -4 more than 50% of migrating species still migrate at 0 = 0.5 ML and layer-by-layer growth does not occur. If growth proceeds when p, = 10-3 and 10 -4, N2~ at P, = 1 should be multiplied by 2 and 5, respectively. Denuded zones, or areas with few 2D nuclei near steps, can be clearly observed in Fig. I. The widths of denuded zones on upper terraces, Wdu, were about 2 _+ 0.5 times greater than those on lower terraces, Wdl, for GaAs and A l A s in a temperature range of 530°C to 650°C. W~ for A and B steps were almost the same. To explain the difference in Wd between upper and lower terraces in terms of the difference in P, at descending and ascending steps, we performed simulations. We fixed the lateral sticking probability at descending steps, P~d, at unity, and changed the lateral sticking probability at ascending steps, P~a, as
700
Temperature T (°C) 650 600 550
E
O "~ 1011 Z
species and 5 × 10 -7 c m 2 / s for the Al species. W e estimated the energy barrier for migration E~ as 0.62 and 0.8 eV for Ga and A1 species, from D S = a2uexp(-E~/kT), where k is the Boltzmann constant and T is the temperature, assuming the hopping distance a = 0.4 nm, and the vibration frequency of an atom v = 10 ~3 s -1. The smaller D~ for AI species is considered to originate from stronger A 1 - A s bonds [11].
C
"o 1010
o
0 p,
109 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.00
1.10 1.20 103/1- (K'I)
Fig. 2. Temperature dependences of 2D nucleus density, N2D, of AlAs and GaAs.
M. Kasu, . Kobayashi/ Journal of Co'stal Growth 170 (1997) 246-250
5 4
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~ P ~ P~'J"~ p ~ _ . ~ . ~._p~ T ~i:!:if:~~:::~.i~)::i:~~'i::!!.'.:ii!ii:.':::~i!=:!~........................ .LLL:k.................... .: I ~:::~:~:~i:::::::~::'::~:::~:~::::~:::5:::::2::::~:~:~:i::~:~::::::~:~:::~:::::~:::::::::::::::~::::~::~:::::::::~:::::::5:::: .'~---'~"g;~ :"-'~;~dl:
Calculated
_
3 "~--.~
Experimental
2
............................. -T--
I
0
. . . . . . . .
10 0
I
10 ~
. . . . . . . .
I
10 2
•
"
I .....
I
10 ~
Psd/Psa
Fig. 3. Denuded zone width ratios of upper terraces to lower terraces, W~, / W~I,for different lateral sticking probability ratios at the descending and the ascending steps, P,d/P~. Plots are simulation results assuming that P,d is fixed at unity and ~, at steps around 2D nuclei, is P~d. The experimentally obtained W~, / Wd~of about 2 _+0.5 is indicated by a broken line.
shown in the inset of Fig. 3. W e considered P, at steps around 2D nuclei to be the same as P~a- W e plotted simulation results of Wau/Wdl for different ratios of descending steps to ascending steps, i.e., P~d/P~a, as shown in Fig. 3. Wau/Wjl of 2 + 0.5 was obtained at a p,d/P,~ range of 10 to 3 × 10 2. That the migrating species sticks more easily at descending steps results in step separation instability, i.e., step bunching, as discussed by Schwoebel and Shipsey [13]. In fact the step bunching was observed on a GaAs vicinal surface during M O V P E growth [10,14]. Though Schwoebel and Shipsey [13] described some possible causes of preferentially sticking at descending steps, they were not able to explain preferentially sticking at descending steps in terms of only the energy barrier at the edge on an upper terrace, the so-called Schwoebel barrier. However, one possible origin are top-layer As trimer atoms at steps. At B steps each topqayer As trimer atom bonds with each other and with one 2nd-layer As atom, and prevents migrating group-III species from lower terraces, from sticking to the 2rid-layer As atoms. Migrating group-III species from upper terraces more easily cleave backbonds between top-layer As trimer atoms and 2nd-layer As atoms. A similar mechanism can be considered for A steps. From simulations, we obtained Wd c~ D~/6. The relation is similar to that between L2D, the 2D
249
nucleus separation, and D~, i.e., LZD (X D~/6, which is obtained from Eq. (1). But since the surface reconstruction on upper and lower terraces is the same, the difference in Wd between upper and lower terraces is not due to the difference in D~ [12]. Fig. 1 shows that G a A s and A l A s 2D nucleus sizes in the [110] direction were about 2 times larger than those in the [110] direction. The direction of elongation is opposite to that of molecular beam epitaxy grown GaAs [ 15]. W e performed simulations to obtain a relation between the 2D nucleus size ratio ([110] to [110] directions) and the p~ ratio (steps along [~10] direction, A steps, to steps along [1 10] directions, B steps), i.e., P~A/P~B" Here P~AP~B remained the same. The simulation results are also plotted in Fig. 4. The 2D nucleus size ratio increased, as psA/PsB increased. When P~A/P,B = 3, the 2D nucleus size ratio became 2, obtained from STM observations. But while a surface after growth was quenched to RT, 2D nuclei become nearly round due to the entropy, and therefore, during growth the 2D nucleus size ratio is thought to be more than 2 and P~A/P,B more than 3. In an MOVPE-grown GaAs vicinal surface, the A steps were about two times rougher than the B steps [4], and this is also
,
P
O
,
,
,
,
, , !
/P sA
sB
(Calculated) ~ o .N
(/) ¢~
Experimental
_o O =3
z O4
1~
D s[11o]/ D s[T1oi (Calculated)
0
I
I
I
i
,
,
i
= I
101
10 0 P
/P sA
or D sB
/D s[110]
slY10]
Fig. 4. Closed circles; 2D nucleus size ratio ([ll0] direction to [110] direction) for different P~ ratios of steps along the [~10] direction (A steps) to steps along the [110] direction (B steps), i.e., P,A /P~B. Open circles; 2D nucleus size ratio for different D~ ratios ([110] direction to [~10] direction), i.e., D~[Ijo]/D~[TIo]. Simulation results are plotted. The experimentally obtained 2D nucleus size ratio of 2 is indicated by a broken line.
250
M. Kasu, . Koba.vashi / Journal of Crystal Growth 170 (1997) 246-250
explained by preferential sticking at kinks in the B steps, i.e., parts of A steps. Another possible origin of the anisotropy of 2D nucleus size is the anisotropy of D~. So we performed simulations to obtain a relation between the 2D nucleus size ratio ([1 10] direction to [1 10] directions) and the D, ratio ( [ l l 0 ] direction to [~10] directions), i.e., Ds[ll0]/Ds[Ti0l. Here Ds[ll0]/D~[Ti0] remained the same. The results are plotted in Fig. 4. The 2D nucleus size ratio increased to only 1.5 as D,[~Io]/D~[Tm I increased to 10. As a result, the 2D nucleus size anisotropy was not caused primarily by the anisotropy in D~. The anisotropy in 2D nucleus size is determined mainly by the lateral sticking rather than by the surface diffusion. This is because 2D nucleus size is determined by the direction in which migrating species sticks to the formed 2D nucleus, not by the direction in which the migration occurs over a wide range. The difference in the elongation direction of 2D nuclei between M O V P E and M B E has been considered to be due to the difference in reconstructions, c(4 × 4) in M O V P E and (2 × 4) in MBE [3]. Our results clarified further that the difference in the elongation direction is due to the difference in preferential sticking at A and B steps, rather than the difference in the direction of the fast surface diffusion. Probably it originates from the difference in step structures in M O V P E and MBE. This is reasonable, considering the difference in the surface reconstruction. We suppose that in M O V P E at B steps the top-layer As trimers that cover 2nd-layer As atoms prevent Ga species from sticking to the 2nd-layer As atoms; on the other hand, at A steps Ga species easily stick to top-layer As trimers. Therefore, the sticking probability of A steps is higher than that of B steps.
4. Conclusions We investigated surface kinetics during M O V P E from STM observation of 2D nuclei and denuded zones along steps. The surface diffusion coefficient was estimated to be 2 × 10 6 and 1.5 × 10 -7 c m 2 / s at 530°C for GaAs and AlAs, and the energy barrier
for migration to be 0.62 and 0.8 eV, respectively. We observed the denuded zone width on upper terraces is 2 _+ 0.5 times wider than that on lower terraces, suggesting that P, from upper terraces is 10 to 3 × 10 2 times larger than P~ from lower terraces. We observed that the 2D nucleus size in the [1 10] direction is about 2 times larger than that in the [-[ 10] direction. We attribute the anisotropy to the lateral sticking probability ratio at steps along [110] (A steps) and [I 10] directions (B steps) of more than 3+1.
Acknowledgements We thank Dr. Yoshiji Horikoshi for his s t i m u l a t ing discussions.
References [1] M.G. Lagally, Y.-W. Mo, R. Kariotis, B.S. Swartzcntruber and M.B. Webb, in: Kinetics of Ordering and Growth at Surfaces, Ed. M.G. Lagally (Plenum. New York, 1990) p. 145. [2] M. Kasu, H. Saito and T. FukuL J. Crystal Growth 115 (I991) 406. [3] P.H. Fuoss, D.W. Kisker, F.J. Lamelas, G.B. Stephenson, P. hnperatori and S. Brennan, Phys. Rev. Lett. 69 (1992) 2791. [4] M. Kasu, N. Kobayashi and H. Yamaguchi, Appl. Phys. Lett. 63 (1993) 678. [5] M. Kasu and N. Kobayashi, J. Appl. Phys. 78 (1995) 3026: 79 (I996) 1822. [6] B. Lewis and D.S. Campbell, J. Vac. Sci. Technol. 4 (1968) 209. [7] J.A. Venables, Philos. Mag. 27 (1973) 697. [8] C. Ratsch, A. Zangwill, P. Smilauer and D.D. Vvedensky, Phys. Rev. Lett. 72 (1994) 3194. [9] Y. W. Mo, J. Kleiner, M.B. Webb and M.G. Lagally. Phys. Rev. Lett. 66 (1991) 1998. [10] M. Kasu and N. Kobayashi, Jpn. J. Appl. Phys. 33 (1994) 712. [ll] M. Kasu and N. Kobayashi, Appl. Phys. Lett. 67 (1995) 2842. [12] M. Kasu and N. Kobayashi, Proc. 9th Int. Conf. Vapor Growth and Epitaxy (Vail, 1996); J. Crystal Growth, to be published. [13] R.L. Schwoebel and EJ. Shipsey, J. Appl. Phys. 37 (1966) 3682. [14] M. Kasu and T. Fukui, Jpn. J. Appl. Phys. 31 (1992) L864. [15] E.J. Heller and M.G. Lagally, Appl. Phys. Lett. 60 (1992) 2675.