- Email: [email protected]
AlAs quantum wells by mobility measurement
348
Journal of Crystal Growth 111 (1991) 348—352 North-Holland
Characterization of lateral correlation length of interface roughness in MBE grown GaAs/AlAs quantum wells by mobility measurement T. Noda, M. Tanaka
*
and H. Sakaki
* *
Institute of Industrial Science, University of Tokyo, 7-22-1 Roppong4 Minato-ku Tokyo 106, Japan
The correlation length (A) of interface rougimess in GaAs/AlAs quantum wells (QWs) prepared by molecular beam epitaxy (MBE) was studied by measuring and analyzing the electron concentration dependences of mobilities. When the bottom AlAs barrier of QWs is prepared by alternate beam MSE and/or by the use of superlattice buffer beneath the QW, the mobility of two-dimensional electrons is substantially enhanced. The lateral correlation length A of such samples is found to become as large as 200—300 A. We have found that A of the bottom (GaAs-on-AlAs) interface of the QW is about 70 A when prepared by conventional MBE.
In a variety of quantum heterostructures, most of the electronic and optical properties are determined by the interaction of electrons with heterointerfaces [1]. Hence, the understanding of the atomic structures of interfaces and their controls is extremely important. Key parameters to characterize interface roughness are the amplitude and the lateral correlation length. Interfaces of GaAs/AlAs quantum wells (QWs) grown by conventional molecular beam epitaxy (MBE) have a roughness of monoatomic fluctuation. This results in the broadening of photoluminescence (PL) spectra [2,3] and a substantial decrease in mobility, particularly in the case of thin QWs [4]. From PL studies in GaAs/AlAs QWs, it is established that the GaAs surface or AlAs-on-GaAs (top) interface can be made atomically flat by growth interruption (GI), whereas the roughness on the AlAs surface or GaAs-on-AlAs (bottom) interface has a short correlation length A (<100 A) and is difficult to smooth out at the growth temperature
*
* *
Present address: Department of Electronic Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan. Also at Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153, Japan.
0022-0248/91/$03.50 © 1991
—
of 600°C[5].Our earlier mobility study has clarified that A of roughness at the bottom interface is typically 50—70 A [4]. We present in the first part of this paper our continuing effort to determine the correlation length by measuring and analyzing the mobility as a function of electron concentration. In the second part, we study the possibility of the enhancement of surface migration of adatoms by modification of MBEs. In particular, we evaluate the influence of the periodic reduction of arsenic pressure [6,7], referred to as alternate beam MBE or migration enhanced epitaxy [8] and the use of superlattice (SL) buffer. We show that these modifications are effective in enhancing A of the bottom interface to 200—300 A or more. In addition, we also discuss the dependence of the mobility on in-plane crystallographic orientation. Samples used are selectively doped GaAs/AlAs QWs with the well width L~ ranging from 17 monolayers (ML) to 30 ML. We prepared three sample groups (I, II, and III) on (001) Cr-doped semi-insulating GaAs at 590—600°C. Groups I and II were prepared by growing successively 8000 A-thick undoped GaAs, an SL buffer consisting of 21 periods of undoped AIAs(14 ML)/ GaAs(14 ML) with GI of 60 s prior to form the top interfaces, a 21-ML-thick undoped AlAs spacer, an
Elsevier Science Publishers B.V. (North-Holland)
T. Noda et al.
/ Lateral correlation
length of interface roughness in MBE grown GaAs/A/As QWs
undoped GaAs QW with various L~, a 21-MLthick undoped AlAs spacer, a 800-A-thick Si-
P’r =
doped 7Al03Ga07As with aa donor density ND of cm~3,and finally 100-A-thick undoped 7 x iO’capping layer. For group III, the structure is GaAs
where V
the same as for groups I and II except that the buffer layers are 5000 A GaAs and 3. 2000 A Al0The 3Ga07As, and ND 1 x 1018 AlAs layer justisbelow the cm~ GaAs well was prepared by alternate beam MBE for group I, and by conventional MBE for groups II and III. In alternate beam MBE, the Al flux corresponding to 1 ML coverage and the As 4 flux for 5 s are alternately supplied with no for interval. The 2s~ Al and 8 Xbeam iO’4 flux is s~’ 1.4 for X 1014 cm~2 As cm~ 4. When the As4 cell shutter is closed, the beam equivalent pressure of As4 is reduced from 1 X 10~~ to 6 X iO—~Torr, or the 2 s1. In As4 about 5 X iO’~cm~ thesebeam thin flux QWs,of the roughness at the bottom interface plays a dominant role in the scattering process because the top interface prepared with Glof6osisexpectedtohavea Aofmorethan 1000 A and contributes little to the scattering [5]. The reduction of mobility due to possible contamination of growth surfaces during GI is negligibly small since the mobility of selectively doped single heterostructures with GI of 60 s exceeds i05 cm2/V s at 4.2 K. Typical growth rates in usual MBE growth are 0.55, 0.23 and 0.79 ~tm/h for GaAs, AlAs and Al 03Ga07As, respectively. It has been clarified [4,9] that interface roughness (IFR) scattering can be theoretically evaluated as long as the roughness is characterized by the height ~ and the lateral correlation length A of the Gaussian fluctuation. Since the fluctuation of the well width L~leads to the spatial fluctuation of the ground level E0,scattenng the potential fluctuation ~V responsible for the is given by
L~ const-~-g(A, N~,T)
349
(when V0
=
oo), (ib)
0 is the barrier height, and g is a function of A, the electron concentration and the ternperature Eq. ~1 (ib) indicates the dependence of 11r onT. L and N~is that separable and not interlinked. In particular, the N~dependence of ~tr is determined primarily by A, and independent of z~as long as T is constant. This is because the change of ~ with N~results mainly from the ~,
Fermi wavelength dependence of the scattering probability. We plot 4.2 K mobilities (it) of three sample groups, measured as a function of L~,in fig. 1. Closed circles are the data for group I, the closed triangle forsets group and closed for group III. These of II, mobility data squares are strongly dependent on L~, approximately proportional to L~,indicating that the mobilities are dominated ________________
io5
-
-
I
>~)4 -
A~250A
/ -
-
‘?i=70A
/ /
/ / 3 10
i0
I 20 40 70100 200 WELL WIDTH Lw (A)
Fig. 1. Calculated and measured mobilities at 4.2 K as a
L~V=(aE 0(L~,V0)/0L~) L~. Then, theexpressed roughness retically aslimited [4,9]. mobility I OE P~r=
I
) /
(j.& r)
is theo-
2
g(A, N~,T),
(la)
function of the well width L~.Closed circles are the data for group I, the closed triangle for group II and closed 2 squares for is shown in the following form N~(L~). For group I:10” 4.0(30 ML), 2.0(21 group III. N~ of each sample in the unit of cm ML), 2.7(19 ML), 1.6(17 ML). For group II: 4.2(17 ML). For group III: 4.3(23 ML), 1.9(21 ML), 3.2(19 ML), 3.1(17 ML). Solid and broken lines are the roughness dominated mobilities calculated for V 2. 0 = cc and V0 =1.2 eV, respectively, at N~= 2x 1011 cm
350
T. Noda et al.
/ Lateral correlation
length of interface roughness in MBE grown GaAs/AlAs QWs
by IFR scattering at the bottom interface and all other scattering mechanisms are far less important. Mobilities of group I are higher than those of group III, indicating that alternate beam MBE and/or the use of an SL buffer suppresses IFR scattering to some extent. When L~= 17 ML, p. of group II has an intermediate value, between those of groups I and III. This suggests that the use of an SL buffer alone enhances the
fig. 1, one cannot determine A and 4 separately only from the L~dependence of .t. The best way to determine A is to study the N~dependence of p. because it is determined by A, as indicated in eq. (1). As examples, we show by solid lines in fig. 2 the N~dependence of p.~for a QW with L~= 21 ML for various correlation lengths A. Note that the N~dependence of !.tr is primarily determined by A, and does not depend on V0 or 4. We also
mobility in thin QWs. For comparison, theoretical mobilities for inT=0 andtheN2 correlation = 2 X 1011 2 are (p.r) plotted fig. 1K for cm lengths A of 250 and 70 A; solid lines are for = ~ and 4 = 2.83 A, and broken lines for = 1.2 eV and 4 = 3.7 A. Note that the slope of p. versus L~at other values of N~is almost the same as that for N, = 2 x 1011 cm2 because 12r has a stronger dependence on L~than on N~(see fig. 2). Although the data have some spread, primarily due to the difference of N~in different sampies, the L~ dependence of p. is close to the theoretical prediction. Although a good agreement can be found in
show, by a broken line in fig. 2, p.~for a QW with L~ 23 of ML, V0 = 1.2 eV and 4we= plot 3.4 A. show the =role impurity scattering, by To a dotted line the mobility for a QW with L~= 21 ML dominated by ionized donors in A1GaAs. Now we plot in fig. 2 the measured p. at 4.2 K as a function of /~for three samples (a, b-i and b-2) of group III. Closed squares are for a QW (sample a) with L~= 21 ML and N~was changed by using the persistent photoconductivity (PPC) effect. The current is along the (110) direction. Closed and open circles are the mobilities measured for QWs (samples b-i and b-2) with L~= 23 ML and N~was changed by a gate electric field in a FET configuration. The current directions are along the (110) direction for sample b-i and along (110) for sample b-2. We first discuss p. of sample a (shown by closed squares), which is almost constant when /sç <4 x 1011 crn2 and gradually increases with increase of N,. This N~dependence of ~A agrees very well with a theoretical prediction of IFR scattering only when we assume A = 70 A. To achieve the corn-
10~
‘/
‘
// I~N/
/
/
/
/
/‘‘
,A:300A ~200 A
N100A
/
/
// ~70A
plete fit in A since V the absolute magnitude, we find 4 4.2 0 = 1.2 eV. These values of 4 and A are consistent with our previous results obtained from the p.—T characteristic [4]. To avoid ambiguities due to the PPC effect, we also examine p. of
• Sample a • Sample b-i
sample b (closed and open circles). The measured p. of this sample is a little more strongly depen-
,~
/
/“
-
/
—50 A
O&
0
Sample b-2
2)
1012
Ns (cm Fig. 2. The 1V~dependences of mobilities of group III. Measured data are plotted by closed squares for a QW (sample a) with L~= 21 ML, closed and open circles for QWs (samples b-i and b-2) with L = 23• ML. Solid, .•• broken and chained lines are the roughness dominated mobilities calculated at 0 K. Dotted line is the impurity dominated mobility calculated at 0 K.
dent on N,. By adopting the same process, we find that 4A isis 3.4 100A A for for(110) bothchannel samples. orientation We find also and 4 = 3.8 A for (110) channel orientation. These values are close to those of sample a. The reason for finding a larger value of A and a smaller value of 4 is probably due to small changes in the growth condition, such as the As 4 flux or the substrate temperature. We find from these results
T Noda er al.
/ Lateral correlation length
of interface roughness in MBE grown GaAs/AlAs
that the roughness at the bottom interface of group III has a typical correlation length A of 70—100 A and a effective height 4 of 1—1.5 ML. Next, we study whether or not A is enhanced by alternate beam MBE and/or the use of SL buffer. Mobilities of three samples (c, d-i and d-2) of group I are plotted in fig. 3. Closed circles are measured p. for a QW (sample c) with L~= 21 ML with current flowing along (110) direction. Closed and open squares are measured p. for QWs (samples d-1 and d-2) with L~= 21 ML with current flowing along (110) for sample d-1 and (110) for sample d-2. In samples d-1 and d-2, not only the bottom AlAs but also the central GaAs well layer is prepared by alternate beam MBE. However, the main feature of bottom interfaces is the same as sample c because the top interface contributes little to the scattering process. Note in these samples (c, d-i and d-2) that p. is strongly dependent on N~,suggesting that the nature of bottom interfaces has changed as compared with those of group III. Although the ionized impurity
I
//
oN//
.
~
/,~$ /
c~io~
351
(ION) scattering plays some role, particularly at high N~,the mobility is still mostly affected by IFR scattering. This indicates that a steep p.—N~ characteristic of samples c, d-1 and d-2 originates from the interface with A larger than that of group III. By analyzing the data, A is estimated to be 200 A or longer. Note that the N, dependence of p. is no longer sensitive to A when A exceeds 200 A and the exact determination of A gets difficult. Hence, one may conclude that A is 250— 300 A if we assume 4 = 4.2 A (broken lines), and A is about 200 A if 4 = 2.83 A (chained lines). A similar conclusion is obtained for group I with L~= 19 ML. This implies that A of bottom interfaces prepared by modified MBE with alternate supply of beams and SL buffer becomes about three times larger than those prepared by the usual MBE. Further study is necessary to clarify which of the two modifications has a major contribution. In conclusion, we have determined the correlation length A of roughness at the bottom interface by measuring and analyzing the p.—N~characteristics. It is shown that A of the bottom interface is short (70—100 A when prepared with conventional MBE but A can be enhanced to 200—300 A by the use of alternate beam MBE and/or SL buffer layer. In addition, we have clanfied the depen-
________________ .•
/
Q Ws
iooA
-
dence of the mobility on intraplane orientation. This work is supported by a Grant in Aid from the Ministry of Education and by the Research ~ the
5qA
70A References
• Sample c • Sample d-i a Sample d-2 I
10
Ns (cmz)
101
Fig. 3. The N~dependences of mobilities of group I with L~= 21 ML. Measured data are plotted by closed circles (sample c), and closed and open squares (samples d-1 and d-2). Solid, dotted and chained lines are the roughness dominated mobilities calculated at 0 K. Dotted line is the impurity dominated mobility calculated at 0 K.
[1] H. Sakaki, in: Proc. Intern. Symp. on the Foundations of Quantum Mechanics, Tokyo, 1983 (Phys. Soc. Japan, Tokyo, 1984) p. 94. [2] L. Goldstein, Y. Horikoshi, S. Tarucha and H. Okamoto, Japan. J. Appl. Phys. 22 (1983) 1489. [31H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. AppI. Phys. 24 (1985) L4i7; T. Fukunaga, K.L.I. Kobayashi and H. Nakashima, Japan. J. Appi. Phys. 24 (1985) L510.
352
T• Noda et a/.
/ Lateral correlation length
of interface roughness in MBE grown GaAs/AlAs
[4] H. Sakaki, T. Noda, K. Hirakawa, M. Tanaka and T. Matsusue, Appl. Phys. Letters Si (1987) 1934. [5]M. Tanaka, H. Sakaki and J. Yoshino, Japan. J. AppI. Phys. 25 (1986) L155; M. Tanaka and H. Sakaki, J. Crystal Growth 81 (i987) 153. [61 J.M. Van Hove and P.1. Cohen, J. Crystal Growth 81 (1987) 13.
[71F.
Q Ws
Briones, D. Golmayo, L. Gonzales and A. Ruiz, J. Crystal Growth 81 (1987) 19. [8] Y. Horikoshi, K. Kawashima and H. Yamaguchi, Japan. J. AppI. Phys. 25 (1986) L868. [9] A. Gold, Z. Physik B74 (1989) 53.
Journal of Crystal Growth 111 (1991) 348—352 North-Holland
Characterization of lateral correlation length of interface roughness in MBE grown GaAs/AlAs quantum wells by mobility measurement T. Noda, M. Tanaka
*
and H. Sakaki
* *
Institute of Industrial Science, University of Tokyo, 7-22-1 Roppong4 Minato-ku Tokyo 106, Japan
The correlation length (A) of interface rougimess in GaAs/AlAs quantum wells (QWs) prepared by molecular beam epitaxy (MBE) was studied by measuring and analyzing the electron concentration dependences of mobilities. When the bottom AlAs barrier of QWs is prepared by alternate beam MSE and/or by the use of superlattice buffer beneath the QW, the mobility of two-dimensional electrons is substantially enhanced. The lateral correlation length A of such samples is found to become as large as 200—300 A. We have found that A of the bottom (GaAs-on-AlAs) interface of the QW is about 70 A when prepared by conventional MBE.
In a variety of quantum heterostructures, most of the electronic and optical properties are determined by the interaction of electrons with heterointerfaces [1]. Hence, the understanding of the atomic structures of interfaces and their controls is extremely important. Key parameters to characterize interface roughness are the amplitude and the lateral correlation length. Interfaces of GaAs/AlAs quantum wells (QWs) grown by conventional molecular beam epitaxy (MBE) have a roughness of monoatomic fluctuation. This results in the broadening of photoluminescence (PL) spectra [2,3] and a substantial decrease in mobility, particularly in the case of thin QWs [4]. From PL studies in GaAs/AlAs QWs, it is established that the GaAs surface or AlAs-on-GaAs (top) interface can be made atomically flat by growth interruption (GI), whereas the roughness on the AlAs surface or GaAs-on-AlAs (bottom) interface has a short correlation length A (<100 A) and is difficult to smooth out at the growth temperature
*
* *
Present address: Department of Electronic Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan. Also at Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153, Japan.
0022-0248/91/$03.50 © 1991
—
of 600°C[5].Our earlier mobility study has clarified that A of roughness at the bottom interface is typically 50—70 A [4]. We present in the first part of this paper our continuing effort to determine the correlation length by measuring and analyzing the mobility as a function of electron concentration. In the second part, we study the possibility of the enhancement of surface migration of adatoms by modification of MBEs. In particular, we evaluate the influence of the periodic reduction of arsenic pressure [6,7], referred to as alternate beam MBE or migration enhanced epitaxy [8] and the use of superlattice (SL) buffer. We show that these modifications are effective in enhancing A of the bottom interface to 200—300 A or more. In addition, we also discuss the dependence of the mobility on in-plane crystallographic orientation. Samples used are selectively doped GaAs/AlAs QWs with the well width L~ ranging from 17 monolayers (ML) to 30 ML. We prepared three sample groups (I, II, and III) on (001) Cr-doped semi-insulating GaAs at 590—600°C. Groups I and II were prepared by growing successively 8000 A-thick undoped GaAs, an SL buffer consisting of 21 periods of undoped AIAs(14 ML)/ GaAs(14 ML) with GI of 60 s prior to form the top interfaces, a 21-ML-thick undoped AlAs spacer, an
Elsevier Science Publishers B.V. (North-Holland)
T. Noda et al.
/ Lateral correlation
length of interface roughness in MBE grown GaAs/A/As QWs
undoped GaAs QW with various L~, a 21-MLthick undoped AlAs spacer, a 800-A-thick Si-
P’r =
doped 7Al03Ga07As with aa donor density ND of cm~3,and finally 100-A-thick undoped 7 x iO’capping layer. For group III, the structure is GaAs
where V
the same as for groups I and II except that the buffer layers are 5000 A GaAs and 3. 2000 A Al0The 3Ga07As, and ND 1 x 1018 AlAs layer justisbelow the cm~ GaAs well was prepared by alternate beam MBE for group I, and by conventional MBE for groups II and III. In alternate beam MBE, the Al flux corresponding to 1 ML coverage and the As 4 flux for 5 s are alternately supplied with no for interval. The 2s~ Al and 8 Xbeam iO’4 flux is s~’ 1.4 for X 1014 cm~2 As cm~ 4. When the As4 cell shutter is closed, the beam equivalent pressure of As4 is reduced from 1 X 10~~ to 6 X iO—~Torr, or the 2 s1. In As4 about 5 X iO’~cm~ thesebeam thin flux QWs,of the roughness at the bottom interface plays a dominant role in the scattering process because the top interface prepared with Glof6osisexpectedtohavea Aofmorethan 1000 A and contributes little to the scattering [5]. The reduction of mobility due to possible contamination of growth surfaces during GI is negligibly small since the mobility of selectively doped single heterostructures with GI of 60 s exceeds i05 cm2/V s at 4.2 K. Typical growth rates in usual MBE growth are 0.55, 0.23 and 0.79 ~tm/h for GaAs, AlAs and Al 03Ga07As, respectively. It has been clarified [4,9] that interface roughness (IFR) scattering can be theoretically evaluated as long as the roughness is characterized by the height ~ and the lateral correlation length A of the Gaussian fluctuation. Since the fluctuation of the well width L~leads to the spatial fluctuation of the ground level E0,scattenng the potential fluctuation ~V responsible for the is given by
L~ const-~-g(A, N~,T)
349
(when V0
=
oo), (ib)
0 is the barrier height, and g is a function of A, the electron concentration and the ternperature Eq. ~1 (ib) indicates the dependence of 11r onT. L and N~is that separable and not interlinked. In particular, the N~dependence of ~tr is determined primarily by A, and independent of z~as long as T is constant. This is because the change of ~ with N~results mainly from the ~,
Fermi wavelength dependence of the scattering probability. We plot 4.2 K mobilities (it) of three sample groups, measured as a function of L~,in fig. 1. Closed circles are the data for group I, the closed triangle forsets group and closed for group III. These of II, mobility data squares are strongly dependent on L~, approximately proportional to L~,indicating that the mobilities are dominated ________________
io5
-
-
I
>~)4 -
A~250A
/ -
-
‘?i=70A
/ /
/ / 3 10
i0
I 20 40 70100 200 WELL WIDTH Lw (A)
Fig. 1. Calculated and measured mobilities at 4.2 K as a
L~V=(aE 0(L~,V0)/0L~) L~. Then, theexpressed roughness retically aslimited [4,9]. mobility I OE P~r=
I
) /
(j.& r)
is theo-
2
g(A, N~,T),
(la)
function of the well width L~.Closed circles are the data for group I, the closed triangle for group II and closed 2 squares for is shown in the following form N~(L~). For group I:10” 4.0(30 ML), 2.0(21 group III. N~ of each sample in the unit of cm ML), 2.7(19 ML), 1.6(17 ML). For group II: 4.2(17 ML). For group III: 4.3(23 ML), 1.9(21 ML), 3.2(19 ML), 3.1(17 ML). Solid and broken lines are the roughness dominated mobilities calculated for V 2. 0 = cc and V0 =1.2 eV, respectively, at N~= 2x 1011 cm
350
T. Noda et al.
/ Lateral correlation
length of interface roughness in MBE grown GaAs/AlAs QWs
by IFR scattering at the bottom interface and all other scattering mechanisms are far less important. Mobilities of group I are higher than those of group III, indicating that alternate beam MBE and/or the use of an SL buffer suppresses IFR scattering to some extent. When L~= 17 ML, p. of group II has an intermediate value, between those of groups I and III. This suggests that the use of an SL buffer alone enhances the
fig. 1, one cannot determine A and 4 separately only from the L~dependence of .t. The best way to determine A is to study the N~dependence of p. because it is determined by A, as indicated in eq. (1). As examples, we show by solid lines in fig. 2 the N~dependence of p.~for a QW with L~= 21 ML for various correlation lengths A. Note that the N~dependence of !.tr is primarily determined by A, and does not depend on V0 or 4. We also
mobility in thin QWs. For comparison, theoretical mobilities for inT=0 andtheN2 correlation = 2 X 1011 2 are (p.r) plotted fig. 1K for cm lengths A of 250 and 70 A; solid lines are for = ~ and 4 = 2.83 A, and broken lines for = 1.2 eV and 4 = 3.7 A. Note that the slope of p. versus L~at other values of N~is almost the same as that for N, = 2 x 1011 cm2 because 12r has a stronger dependence on L~than on N~(see fig. 2). Although the data have some spread, primarily due to the difference of N~in different sampies, the L~ dependence of p. is close to the theoretical prediction. Although a good agreement can be found in
show, by a broken line in fig. 2, p.~for a QW with L~ 23 of ML, V0 = 1.2 eV and 4we= plot 3.4 A. show the =role impurity scattering, by To a dotted line the mobility for a QW with L~= 21 ML dominated by ionized donors in A1GaAs. Now we plot in fig. 2 the measured p. at 4.2 K as a function of /~for three samples (a, b-i and b-2) of group III. Closed squares are for a QW (sample a) with L~= 21 ML and N~was changed by using the persistent photoconductivity (PPC) effect. The current is along the (110) direction. Closed and open circles are the mobilities measured for QWs (samples b-i and b-2) with L~= 23 ML and N~was changed by a gate electric field in a FET configuration. The current directions are along the (110) direction for sample b-i and along (110) for sample b-2. We first discuss p. of sample a (shown by closed squares), which is almost constant when /sç <4 x 1011 crn2 and gradually increases with increase of N,. This N~dependence of ~A agrees very well with a theoretical prediction of IFR scattering only when we assume A = 70 A. To achieve the corn-
10~
‘/
‘
// I~N/
/
/
/
/
/‘‘
,A:300A ~200 A
N100A
/
/
// ~70A
plete fit in A since V the absolute magnitude, we find 4 4.2 0 = 1.2 eV. These values of 4 and A are consistent with our previous results obtained from the p.—T characteristic [4]. To avoid ambiguities due to the PPC effect, we also examine p. of
• Sample a • Sample b-i
sample b (closed and open circles). The measured p. of this sample is a little more strongly depen-
,~
/
/“
-
/
—50 A
O&
0
Sample b-2
2)
1012
Ns (cm Fig. 2. The 1V~dependences of mobilities of group III. Measured data are plotted by closed squares for a QW (sample a) with L~= 21 ML, closed and open circles for QWs (samples b-i and b-2) with L = 23• ML. Solid, .•• broken and chained lines are the roughness dominated mobilities calculated at 0 K. Dotted line is the impurity dominated mobility calculated at 0 K.
dent on N,. By adopting the same process, we find that 4A isis 3.4 100A A for for(110) bothchannel samples. orientation We find also and 4 = 3.8 A for (110) channel orientation. These values are close to those of sample a. The reason for finding a larger value of A and a smaller value of 4 is probably due to small changes in the growth condition, such as the As 4 flux or the substrate temperature. We find from these results
T Noda er al.
/ Lateral correlation length
of interface roughness in MBE grown GaAs/AlAs
that the roughness at the bottom interface of group III has a typical correlation length A of 70—100 A and a effective height 4 of 1—1.5 ML. Next, we study whether or not A is enhanced by alternate beam MBE and/or the use of SL buffer. Mobilities of three samples (c, d-i and d-2) of group I are plotted in fig. 3. Closed circles are measured p. for a QW (sample c) with L~= 21 ML with current flowing along (110) direction. Closed and open squares are measured p. for QWs (samples d-1 and d-2) with L~= 21 ML with current flowing along (110) for sample d-1 and (110) for sample d-2. In samples d-1 and d-2, not only the bottom AlAs but also the central GaAs well layer is prepared by alternate beam MBE. However, the main feature of bottom interfaces is the same as sample c because the top interface contributes little to the scattering process. Note in these samples (c, d-i and d-2) that p. is strongly dependent on N~,suggesting that the nature of bottom interfaces has changed as compared with those of group III. Although the ionized impurity
I
//
oN//
.
~
/,~$ /
c~io~
351
(ION) scattering plays some role, particularly at high N~,the mobility is still mostly affected by IFR scattering. This indicates that a steep p.—N~ characteristic of samples c, d-1 and d-2 originates from the interface with A larger than that of group III. By analyzing the data, A is estimated to be 200 A or longer. Note that the N, dependence of p. is no longer sensitive to A when A exceeds 200 A and the exact determination of A gets difficult. Hence, one may conclude that A is 250— 300 A if we assume 4 = 4.2 A (broken lines), and A is about 200 A if 4 = 2.83 A (chained lines). A similar conclusion is obtained for group I with L~= 19 ML. This implies that A of bottom interfaces prepared by modified MBE with alternate supply of beams and SL buffer becomes about three times larger than those prepared by the usual MBE. Further study is necessary to clarify which of the two modifications has a major contribution. In conclusion, we have determined the correlation length A of roughness at the bottom interface by measuring and analyzing the p.—N~characteristics. It is shown that A of the bottom interface is short (70—100 A when prepared with conventional MBE but A can be enhanced to 200—300 A by the use of alternate beam MBE and/or SL buffer layer. In addition, we have clanfied the depen-
________________ .•
/
Q Ws
iooA
-
dence of the mobility on intraplane orientation. This work is supported by a Grant in Aid from the Ministry of Education and by the Research ~ the
5qA
70A References
• Sample c • Sample d-i a Sample d-2 I
10
Ns (cmz)
101
Fig. 3. The N~dependences of mobilities of group I with L~= 21 ML. Measured data are plotted by closed circles (sample c), and closed and open squares (samples d-1 and d-2). Solid, dotted and chained lines are the roughness dominated mobilities calculated at 0 K. Dotted line is the impurity dominated mobility calculated at 0 K.
[1] H. Sakaki, in: Proc. Intern. Symp. on the Foundations of Quantum Mechanics, Tokyo, 1983 (Phys. Soc. Japan, Tokyo, 1984) p. 94. [2] L. Goldstein, Y. Horikoshi, S. Tarucha and H. Okamoto, Japan. J. Appl. Phys. 22 (1983) 1489. [31H. Sakaki, M. Tanaka and J. Yoshino, Japan. J. AppI. Phys. 24 (1985) L4i7; T. Fukunaga, K.L.I. Kobayashi and H. Nakashima, Japan. J. Appi. Phys. 24 (1985) L510.
352
T• Noda et a/.
/ Lateral correlation length
of interface roughness in MBE grown GaAs/AlAs
[4] H. Sakaki, T. Noda, K. Hirakawa, M. Tanaka and T. Matsusue, Appl. Phys. Letters Si (1987) 1934. [5]M. Tanaka, H. Sakaki and J. Yoshino, Japan. J. AppI. Phys. 25 (1986) L155; M. Tanaka and H. Sakaki, J. Crystal Growth 81 (i987) 153. [61 J.M. Van Hove and P.1. Cohen, J. Crystal Growth 81 (1987) 13.
[71F.
Q Ws
Briones, D. Golmayo, L. Gonzales and A. Ruiz, J. Crystal Growth 81 (1987) 19. [8] Y. Horikoshi, K. Kawashima and H. Yamaguchi, Japan. J. AppI. Phys. 25 (1986) L868. [9] A. Gold, Z. Physik B74 (1989) 53.