- Email: [email protected]
GaAs one-side-modulation-doped quantum well
Solid State Communications,
Vol. 93, No. 7. pp. 647T651, 1995 Elwier Science Ltd Printed in Great Britain. 0038-1098/95 $9.50 + .OO
00.3%1o!M(!94)00737-3
ELECTRONIC
SUBBAND STUDIES OF A STRAINED A10.22Gao,78As/Ino,,sGao,85As/GaAs ONE-SIDE-MODULATION-DOPED QUANTUM WELL T.W. Kim, M. Jung and T.H. Park
Department
of Physics, Kwangwoon University, 447- 1 Wolgye-dong, Nowon-ku, Seoul 139-70 1, Korea and K.H. Yoo Department
of Physics, Kyung Hee University, Seoul 137-701, Korea (Received 12 September 1994 by C.N.R. Rao)
Shubnikov-de Haas and \‘an der Pauw Hall effect measurements on a strained A10.z2G~,78As/In o,,sGa0,85As/GaAs one-side-modulationdoped quantum well grown by molecular beam epitaxy have been carried out to investigate the properties of an electron gas in a single quantum well. Transmission electron microscopy measurements showed that the Ab,22Gao,,8As/Ino.,sGao.ssAs and Ino,,sGao.8sAs/ GaAs interfaces have no misfit dislocations. The results of the Shubnikov-de Haas measurements and the observation of the quantum Hall effect at 1.5 K clearly demonstrated the existence of a two-dimensional electron gas in the quantum well, and the fast Fourier transform results for the S-dH data clearly indicate electron occupation of two subbands in the In0,i5Ga0,s5AS single quantum well. Electronic subband energies and wavefunctions in the In,,15Gao.ssAS quantum well were calculated by a self-consistent method taking into account exchange-correlation effects. Keywords: A: quantum wells, B: transmission electron microscopy, D: electronic states (localized), electronic transport, quantum Hall effect. EXPERIMENTAL measurements and theoretical calculations of the two-dimensional electron gas (2DEG) in various quantum structures have been investigated for many years [l-5]. In recent years, rapid advancements in epitaxial film growth technology, such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition, have made possible the fabrication of several new types of strained quantum wells [6-lo]. Among many strained quantum structures, pseudomorphic quantum well Al,Ga, _ VAs/In,Gai _.As/GaAs structures have been attractive due to the large conduction band discontinuity and due to the increase in the electron saturation velocity in the In,Ga, _,As quantum well compared to those in GaAs quantum wells [ll]. Although the mobility of an Al,Ga, _.As/In,Ga, _,As/GaAs modulationdoped structure is smaller than that of a conventional Al,Ga, _,As/GaAs modulation-doped structure at
low temperatures, its room temperature mobility is higher than that of the Al,Ga, _,As/GaAs structure. In addition, a 2DEG with a density of up to lo’* cm-* can be achieved in an Al,Ga, _.As/ In,Ga, _,As/GaAs system. This high carrier density allows us not only to decrease depletion spreading but also to increase the Fermi energy and the electron mean-free path. Such properties have allowed a variety of device applications, such as high electron mobility transistors [12] and double barrier resonant tunneling structures [13, 141. Although some studies concerning the optical properties in Al,Ga, _ .yAs/ In,,Gai _,As/GaAs modulation-doped quantum well structures have been performed [ 15, 161,to the best of our knowledge, both a clear demonstration of the existence of a 2DEG and an investigation of the electronic subband studies in a strained In,Gai _ ,As quantum well have not been reported yet. Thus, this communication reports transmission
647
648
STUDIES OF A STRAINED
A10,22Gao.~sAs/Ino.,sGao,ssAs/GaAs
electron microscopy (TEM) measurements which were carried out to investigate the structure of Alo.22Gao.~sAs/Ino.rsGao.sSAs/GaAs strained quantum wells and Shubnikov-de Haas (S-dH) and Van der Pauw Hall effect measurements which were performed in order to investigate the existence of the 2DEG in the quantum wells grown by MBE. Furthermore, with these experimental results, the subband energies and wavefunction were determined by a self-consistent numerical method which took into account the exchange-correlation effects. The samples used in this work were grown on semi-insulating (10 0)-oriented GaAs substrates by MBE and consisted of the following structures: a 5OOA Si-doped (2.5 x lo’* cmp3) GaAs capping layer for ohmic contacts, a 4OOA Si-doped (8.0 x 1018cm-3) Ale22Ga0.7gAs modulation layer, a 2OA undoped A10,22Ga0,78Asspace layer, a 150 A undoped Ino,isGao.ssAs quantum well layer, a 4OOOAundoped GaAs layer, a 45OA [Alo,3Gao,~As/GaAs] superlattice buffer layer, and a 10008, GaAs buffer layer. The compositions of the layers were measured by using double-crystal X-ray diffraction, and the thicknesses of the layers were determined from the TEM measurements. Ohmic contacts to the samples were made by diffusing a small amount of indium through several layers at 450°C in a hydrogen atmosphere for approximately 10min. After ohmic contacts were performed, the GaAs cap layer was removed to get rid of parallel conductance for the S-dH and Hall effect measurements. The TEM observations were performed in a JEOL 200CX transmission electron microscope operating at 400 kV. The samples for TEM measurements were prepared by cutting and polishing to approximately 3Opm thickness using a diamond paper, and were then argon-ion milled at liquid-nitrogen temperature to electron transparency. The S-dH and Hall-effect
Fig. 1. A transmission electron microscopy image of an A10.22Gao.~sAs/Ino,isGao,s5As/GaAs quantum well.
Vol. 93, No. 7
Fig. 2. An electron diffraction pattern for transmission electron microscopy of an A10,22Ga,,78A~/ InsisGao,ssAs/GaAs quantum well. measurements were carried out at a temperature of 1.5 K in magnetic fields up to 12 T in an Oxford superconducting magnet system using a Keithley 181 nanovoltmeter. The bright-field TEM image shows that there are no defects due to dislocations or stacking faults, as can be seen in Fig. 1. The electron diffraction pattern from the sample is shown in Fig. 2. Figure 2 shows that there are no misfit dislocations at the Ab.22Gao.7sAs/Ino.lsGao.ssAs and the In~.isG%.ssAs/ GaAs heterointerfaces, resulting from the fully strained ho.lsG~.g5AS layer due to the GaAs and A10.22Ga0,7sAslayers. A high-resolution TEM image of a cross-sectional sample of the Alo.z2Gas7sAs/ Ino.lsGao.ssAs/GaAs structure is presented in Fig. 3. Figure 3 directly shows the lattice structures on both sides of the heteroepitaxial interface. There are no dislocations, staking faults, and twins. These results show a very smooth interface plane on the atomic scale. The results of the S-dH measurements clearly show multiple oscillations as shown in the lower curve of Fig. 4. The oscillation frequency of the subband was obtained by digitizing the data linearly
Vol. 93, No. 7
STUDIES OF A STRAINED
649
~,~~G~.~~As/I~.~~G~.~~As/G~As I
I
A
I=0
v) .t: 5 G (0 Y
111 I
W
100
FREQUENCY
Fig. 3. A high-resolution transmission electron microscopy image of a cross-sectional sample of an Alo.2~Ga~.7sAs/Ino,l~G~,s~As/GaAs quantum well. in terms of l/B and by performing high-pass filtering and a fast Fourier transformation (FFT) by computer. Since the S-dH oscillations are periodic in the inverse of the magnetic field [17, 181, the S-dH data must be digitized linearly with the reciprocal of the magnetic field. After the FFT was performed, the resulting data was expressed as a curve of arbitrary amplitude as a function of frequency. The frequency peaks determined from the S-dH data measured at 1.5 K were observed at 26.06T and 57.1 T as shown in Fig. 5. The oscillation frequencies of 26.06 T and 87.1 T correspond to electron densities of 1.26 x 10” cm-’ and 4.22 x lOi* cm-* for the, first and zeroth subbands, respectively. The total electron density determined from the S-dH m.easurements is (5.48 f 0.3) x lOi cm-*. The Hall-effect
5v
I
r
0
2
I
1
-
J 4
MAGNETIC
6
8
10
FIELD ( T )
Fig. 4. Shubnikov-de Haas and quantum Hall effect results at 1.5 K for an A10,22Ga~,,sAs/I~.,sG~,s~As/ GaAs quantum well.
125
1 150
(T )
Fig. 5. Fast Fourier analyses of Shubnikov-de Haas data for an Al~.~~Gao.~8As/Ino,lsGao,ssAs/GaAs quantum well. measurements at 300, 77, 4.2, and 1.5 K in a magnetic field of 2T showed that the mobilities and carrier concentrations were 2.72 x 103, 1.35 x 104, 1.62 x 104, and 1.61 x 104cm-*Vs-‘, and 1.09 x 1013 5.56 x lo’* 5.43 x lOi* and 5.31 x lO’*cn-*. The’magnitude of mobility is almost comparable with that obtained from the Ino.IsAlo,ssAs/Ino,,7Gao,ssAs strained quantum well [19], the mobility for low temperatures saturated at a value due to increased remote ionized impurity scattering. The increase in the carrier density with the increase of the temperature is attributed to the thermal generation of carriers in the Al,-,22Ga0.7sAsbarrier. Even though there are several uncertainties resulting from the non-ideal geometry of the contacts, the agreement of the carrier density determined from the S-dH and Hall effect measurements at 1.5 K is reasonable. In addition to the S-dH measurements, quantum Hall effect measurements were performed on the same samples. The upper curve of Fig. 4 shows a recording of the Hall resistivity. This indicates that the Hall resistance becomes constant over a finite range of magnetic field magnitudes around the regions where the magnetoresistance approaches a local minimum in the lower curve of Fig. 4. Klitzing et al. [20] first showed that the Hall resistivity is given by the very accurate relation pX,,= h/e*i, where i is the number of completely filled Landau levels. This allows very accurate measurements of the fine structure constant [20, 211. The quantum Hall plateaus observed in the Al,,22G%.7sA~/ InslSGassSAs/GaAs system are extended over a wide region of the magnetic field. This is due to the presence of higher-order Landau potential fluctuations, which lead to the localization states in the Landau level tails [22].
650
STUDIES OF A STRAINED
GaAS
:
. .._
“
A10.22Gao,,sAs/Ino,,sGao,sSAs/GaAs
two subband in the Ino,,sGao.ssAs quantum well. Self-consistent numerical calculations show the subband energy structures in this potential well. Although more detailed studies on basic physical properties, including optical measurements, remain to be carried out, the present observations can help improve our understanding of these strained quantum-well structures.
EC
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...
‘-,,.... ‘.
,’ ._
.,
Acknowledgement - This work was supported by the
_’
I
I
I
-20
Eo
~
:
‘.
I
-10
0
DISTANCE
Vol. 93, No. 7
IO
20
1993 Faculty University.
Research
Grant
of
Kyung
Hee
30
REFERENCES
( nm )
Fig. 6. A subband energy structure of an Alo,22Gao.7sAs/Ino.,sGao.ssAs/GaAs quantum well. To determine the subband energies, the experimental results and a self-consistent numerical calculation taking into account the exchange-correlation effects were used [19]. The results of the numerical calculation for the subbands in an A10.22Ga0,78As/ Ino,isGa,,ssAs/GaAs single quantum well are shown in Fig. 6. The dielectric constant of 13.5 is assumed to be the same in both the barriers and the well [23], while the conduction band edges and the electron effective masses were assumed to change abruptly at the heterointerface. The conduction band offsets at the Alo.22Gao.7sAs/Ino.,sGao.ssAs and In,,,sGaO,sSAs/GaAs heterointerfaces were taken to be 322meV and 141 meV, respectively [8, 241. The values of the A10.22Ga0.7sAs,Ino.isGao.ssAs, and GaAs electron effective masses were assumed to be 0.079 mp and 0.058 m,, 0.067 m,, respectively [25]. Because deep impurity states can have a substantial effect on the electron density, the value determined from S-dH measurements was used. For the given electron density the subband energies and subband wavefunctions could be calculated in a self-consistent manner. In this case, the calculated magnitudes of the two eigenenergies for the potential bottom in the well were 100.8 and 160.2meV corresponding to the zeroth and first electron subbands, respectively. The energy eigenfunctions are indicated by the dashed line in Fig. 6. In summary, TEM measurements showed that an Als.22Gae.7sAs/In o.,sGa0.s5As/GaAs quantum well with high quality interfaces was grown on a GaAs substrate. The results of the S-dH measurements and the observation of quantum Hall effects at 1.5 K demonstrated clearly the existence of a 2DEG in the Ino,,sGao.ssAs quantum well grown by MBE. The FFT results for the data show two oscillation frequencies, indicating the electron occupation of
1. 2. 3.
T. Ando, A.B. Fowler & F. Stern, Rev. Mod. Phys. 54, 437 (1982). F. Capasso, Physics of Quantum Devices. Springer, Heidelberg (1990).
Electron
T.W. Kim, Y.H. Chang, Y.D. Zheng, A.A. Reeder, B.D. McCombe, R.F.C. Farrow, T. Temofonte, F.A. Shirland & A. Noreika, J. Vat. Sci. Technol. B5, 980 (1987). G. Ihm, S.K. Noh, J.I. Lee, J-S. Hwang & T.W. Kim, Phys. Rev. B44, 6266 (1991).
T. W. Kim, J.I. Lee, K.N. Kang, K-S. Lee & KH. Yoo, Phys. Rev. B44, 12891 (1991). L.Q. Qian & B.W. Wessels, Appl. Phys. Lett. 63, 628 (1993).
B.K. Meyer, M. Drechsler, C. Wetzel, V. Harle, F. Scolz, H. Linke, P. Omling & P. Sobkowicz, Appl. Phys. Lett. 63, 657 (1993).
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M.T. Emeny, M.S. Skolnick, C.R. Whitehouse, D.G. Hayes, P.D.J. Calcott & A.W. Higgs,
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J.M. Fernandez, Jianhui Chen & H.H. Wieder, J. Vat. Sci. Technol. All, 889 (1993). C.A. Hoffman, J.R. Meyer, F.T. Bartoli & W.I. Wang, Phys. Rev. B48, 1959 (1993). N. Moll, M.R. Hueschen & A. Fisher-Colbrie, IEEE Trans. Electron Devices Ed-35,879 (1988). T. Henderson, J. Klem, C.K. Peng, J.S. Gedymin, W. Koop & H. Morkoc, Appl.
Appl. Phys. Lett. 63, 824 (1993).
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H. Riechert, D. Bernklass, J.P. Reithmaier & R.D. Schnell, Electron. Lett. 26, 341 (1990). R. Kapre, A. Madhukar, K. Kariami, S. Guha & K.C. Rajkumar, Appl. Phys. Lett. 56, 922
(1990). Y. Yin, H. Qiang, F.H. Pollak, D.C. Streit & M. Wojtowicz, Appl. Phys. Lett. 61, 1579 (1992).
A. Dimoulas, K. Zekentes, M. Androulidaki, N. Kornelios, C. Michelakis & Z. Hatzopoulos, Appl. Phys. Lett. 63, 1417 (1993).
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R.J. Justice, D.G. Seiler, W. Zawadzki, R.J. Koestner, M.W. Goodwin & M.A. Kinch, .J.
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D.G. Seiler, G.B. Ward, R.J. Justice, R.J. Koestner, M.W. Goodwin, M.A. Kinch & J.R. Meyer, J. Appl. Phys. 66, 303 (1989).
Vat. Sci. Technol. A6, 2779 (1988).
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A10.*2Gao.~sAs/Ino,1sGao,sSAs/GaAs
F. Stern & S.D. Sarma, Phys. Rev. B30,840 (1984). K. Von Klitzing, G. Dorda & M. Pepper, Phys. Rev. Lett. 45, 494 (1980). D.C. Tsui & A.C. Gossard, A@. Phys. Lett. 38, 550 (1981). R.J. Nicholas, R.A. Stradling & R.J. Tidey, Solid State Commun. 23, 55 (1977).
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G. Ji, U.K. Reddy, D. Haung, T.S. Henderson & H. Morkoc, Superlattices and Microstruct. 3, 539 (1987). S. Niki, C.L. Lin, W.S.C. Chang & H.H. Wieder, Appl. Phys. L&t. 55, 1339 (1989). W. Chen, M. Fritze, W. Walecki, A.V. Nurmikko, D. Ackley, J.M. Hong & L.L. Chang, Phys. Rev. B45, 8464 (1992).
Vol. 93, No. 7. pp. 647T651, 1995 Elwier Science Ltd Printed in Great Britain. 0038-1098/95 $9.50 + .OO
00.3%1o!M(!94)00737-3
ELECTRONIC
SUBBAND STUDIES OF A STRAINED A10.22Gao,78As/Ino,,sGao,85As/GaAs ONE-SIDE-MODULATION-DOPED QUANTUM WELL T.W. Kim, M. Jung and T.H. Park
Department
of Physics, Kwangwoon University, 447- 1 Wolgye-dong, Nowon-ku, Seoul 139-70 1, Korea and K.H. Yoo Department
of Physics, Kyung Hee University, Seoul 137-701, Korea (Received 12 September 1994 by C.N.R. Rao)
Shubnikov-de Haas and \‘an der Pauw Hall effect measurements on a strained A10.z2G~,78As/In o,,sGa0,85As/GaAs one-side-modulationdoped quantum well grown by molecular beam epitaxy have been carried out to investigate the properties of an electron gas in a single quantum well. Transmission electron microscopy measurements showed that the Ab,22Gao,,8As/Ino.,sGao.ssAs and Ino,,sGao.8sAs/ GaAs interfaces have no misfit dislocations. The results of the Shubnikov-de Haas measurements and the observation of the quantum Hall effect at 1.5 K clearly demonstrated the existence of a two-dimensional electron gas in the quantum well, and the fast Fourier transform results for the S-dH data clearly indicate electron occupation of two subbands in the In0,i5Ga0,s5AS single quantum well. Electronic subband energies and wavefunctions in the In,,15Gao.ssAS quantum well were calculated by a self-consistent method taking into account exchange-correlation effects. Keywords: A: quantum wells, B: transmission electron microscopy, D: electronic states (localized), electronic transport, quantum Hall effect. EXPERIMENTAL measurements and theoretical calculations of the two-dimensional electron gas (2DEG) in various quantum structures have been investigated for many years [l-5]. In recent years, rapid advancements in epitaxial film growth technology, such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition, have made possible the fabrication of several new types of strained quantum wells [6-lo]. Among many strained quantum structures, pseudomorphic quantum well Al,Ga, _ VAs/In,Gai _.As/GaAs structures have been attractive due to the large conduction band discontinuity and due to the increase in the electron saturation velocity in the In,Ga, _,As quantum well compared to those in GaAs quantum wells [ll]. Although the mobility of an Al,Ga, _.As/In,Ga, _,As/GaAs modulationdoped structure is smaller than that of a conventional Al,Ga, _,As/GaAs modulation-doped structure at
low temperatures, its room temperature mobility is higher than that of the Al,Ga, _,As/GaAs structure. In addition, a 2DEG with a density of up to lo’* cm-* can be achieved in an Al,Ga, _.As/ In,Ga, _,As/GaAs system. This high carrier density allows us not only to decrease depletion spreading but also to increase the Fermi energy and the electron mean-free path. Such properties have allowed a variety of device applications, such as high electron mobility transistors [12] and double barrier resonant tunneling structures [13, 141. Although some studies concerning the optical properties in Al,Ga, _ .yAs/ In,,Gai _,As/GaAs modulation-doped quantum well structures have been performed [ 15, 161,to the best of our knowledge, both a clear demonstration of the existence of a 2DEG and an investigation of the electronic subband studies in a strained In,Gai _ ,As quantum well have not been reported yet. Thus, this communication reports transmission
647
648
STUDIES OF A STRAINED
A10,22Gao.~sAs/Ino.,sGao,ssAs/GaAs
electron microscopy (TEM) measurements which were carried out to investigate the structure of Alo.22Gao.~sAs/Ino.rsGao.sSAs/GaAs strained quantum wells and Shubnikov-de Haas (S-dH) and Van der Pauw Hall effect measurements which were performed in order to investigate the existence of the 2DEG in the quantum wells grown by MBE. Furthermore, with these experimental results, the subband energies and wavefunction were determined by a self-consistent numerical method which took into account the exchange-correlation effects. The samples used in this work were grown on semi-insulating (10 0)-oriented GaAs substrates by MBE and consisted of the following structures: a 5OOA Si-doped (2.5 x lo’* cmp3) GaAs capping layer for ohmic contacts, a 4OOA Si-doped (8.0 x 1018cm-3) Ale22Ga0.7gAs modulation layer, a 2OA undoped A10,22Ga0,78Asspace layer, a 150 A undoped Ino,isGao.ssAs quantum well layer, a 4OOOAundoped GaAs layer, a 45OA [Alo,3Gao,~As/GaAs] superlattice buffer layer, and a 10008, GaAs buffer layer. The compositions of the layers were measured by using double-crystal X-ray diffraction, and the thicknesses of the layers were determined from the TEM measurements. Ohmic contacts to the samples were made by diffusing a small amount of indium through several layers at 450°C in a hydrogen atmosphere for approximately 10min. After ohmic contacts were performed, the GaAs cap layer was removed to get rid of parallel conductance for the S-dH and Hall effect measurements. The TEM observations were performed in a JEOL 200CX transmission electron microscope operating at 400 kV. The samples for TEM measurements were prepared by cutting and polishing to approximately 3Opm thickness using a diamond paper, and were then argon-ion milled at liquid-nitrogen temperature to electron transparency. The S-dH and Hall-effect
Fig. 1. A transmission electron microscopy image of an A10.22Gao.~sAs/Ino,isGao,s5As/GaAs quantum well.
Vol. 93, No. 7
Fig. 2. An electron diffraction pattern for transmission electron microscopy of an A10,22Ga,,78A~/ InsisGao,ssAs/GaAs quantum well. measurements were carried out at a temperature of 1.5 K in magnetic fields up to 12 T in an Oxford superconducting magnet system using a Keithley 181 nanovoltmeter. The bright-field TEM image shows that there are no defects due to dislocations or stacking faults, as can be seen in Fig. 1. The electron diffraction pattern from the sample is shown in Fig. 2. Figure 2 shows that there are no misfit dislocations at the Ab.22Gao.7sAs/Ino.lsGao.ssAs and the In~.isG%.ssAs/ GaAs heterointerfaces, resulting from the fully strained ho.lsG~.g5AS layer due to the GaAs and A10.22Ga0,7sAslayers. A high-resolution TEM image of a cross-sectional sample of the Alo.z2Gas7sAs/ Ino.lsGao.ssAs/GaAs structure is presented in Fig. 3. Figure 3 directly shows the lattice structures on both sides of the heteroepitaxial interface. There are no dislocations, staking faults, and twins. These results show a very smooth interface plane on the atomic scale. The results of the S-dH measurements clearly show multiple oscillations as shown in the lower curve of Fig. 4. The oscillation frequency of the subband was obtained by digitizing the data linearly
Vol. 93, No. 7
STUDIES OF A STRAINED
649
~,~~G~.~~As/I~.~~G~.~~As/G~As I
I
A
I=0
v) .t: 5 G (0 Y
111 I
W
100
FREQUENCY
Fig. 3. A high-resolution transmission electron microscopy image of a cross-sectional sample of an Alo.2~Ga~.7sAs/Ino,l~G~,s~As/GaAs quantum well. in terms of l/B and by performing high-pass filtering and a fast Fourier transformation (FFT) by computer. Since the S-dH oscillations are periodic in the inverse of the magnetic field [17, 181, the S-dH data must be digitized linearly with the reciprocal of the magnetic field. After the FFT was performed, the resulting data was expressed as a curve of arbitrary amplitude as a function of frequency. The frequency peaks determined from the S-dH data measured at 1.5 K were observed at 26.06T and 57.1 T as shown in Fig. 5. The oscillation frequencies of 26.06 T and 87.1 T correspond to electron densities of 1.26 x 10” cm-’ and 4.22 x lOi* cm-* for the, first and zeroth subbands, respectively. The total electron density determined from the S-dH m.easurements is (5.48 f 0.3) x lOi cm-*. The Hall-effect
5v
I
r
0
2
I
1
-
J 4
MAGNETIC
6
8
10
FIELD ( T )
Fig. 4. Shubnikov-de Haas and quantum Hall effect results at 1.5 K for an A10,22Ga~,,sAs/I~.,sG~,s~As/ GaAs quantum well.
125
1 150
(T )
Fig. 5. Fast Fourier analyses of Shubnikov-de Haas data for an Al~.~~Gao.~8As/Ino,lsGao,ssAs/GaAs quantum well. measurements at 300, 77, 4.2, and 1.5 K in a magnetic field of 2T showed that the mobilities and carrier concentrations were 2.72 x 103, 1.35 x 104, 1.62 x 104, and 1.61 x 104cm-*Vs-‘, and 1.09 x 1013 5.56 x lo’* 5.43 x lOi* and 5.31 x lO’*cn-*. The’magnitude of mobility is almost comparable with that obtained from the Ino.IsAlo,ssAs/Ino,,7Gao,ssAs strained quantum well [19], the mobility for low temperatures saturated at a value due to increased remote ionized impurity scattering. The increase in the carrier density with the increase of the temperature is attributed to the thermal generation of carriers in the Al,-,22Ga0.7sAsbarrier. Even though there are several uncertainties resulting from the non-ideal geometry of the contacts, the agreement of the carrier density determined from the S-dH and Hall effect measurements at 1.5 K is reasonable. In addition to the S-dH measurements, quantum Hall effect measurements were performed on the same samples. The upper curve of Fig. 4 shows a recording of the Hall resistivity. This indicates that the Hall resistance becomes constant over a finite range of magnetic field magnitudes around the regions where the magnetoresistance approaches a local minimum in the lower curve of Fig. 4. Klitzing et al. [20] first showed that the Hall resistivity is given by the very accurate relation pX,,= h/e*i, where i is the number of completely filled Landau levels. This allows very accurate measurements of the fine structure constant [20, 211. The quantum Hall plateaus observed in the Al,,22G%.7sA~/ InslSGassSAs/GaAs system are extended over a wide region of the magnetic field. This is due to the presence of higher-order Landau potential fluctuations, which lead to the localization states in the Landau level tails [22].
650
STUDIES OF A STRAINED
GaAS
:
. .._
“
A10.22Gao,,sAs/Ino,,sGao,sSAs/GaAs
two subband in the Ino,,sGao.ssAs quantum well. Self-consistent numerical calculations show the subband energy structures in this potential well. Although more detailed studies on basic physical properties, including optical measurements, remain to be carried out, the present observations can help improve our understanding of these strained quantum-well structures.
EC
E,
...
‘-,,.... ‘.
,’ ._
.,
Acknowledgement - This work was supported by the
_’
I
I
I
-20
Eo
~
:
‘.
I
-10
0
DISTANCE
Vol. 93, No. 7
IO
20
1993 Faculty University.
Research
Grant
of
Kyung
Hee
30
REFERENCES
( nm )
Fig. 6. A subband energy structure of an Alo,22Gao.7sAs/Ino.,sGao.ssAs/GaAs quantum well. To determine the subband energies, the experimental results and a self-consistent numerical calculation taking into account the exchange-correlation effects were used [19]. The results of the numerical calculation for the subbands in an A10.22Ga0,78As/ Ino,isGa,,ssAs/GaAs single quantum well are shown in Fig. 6. The dielectric constant of 13.5 is assumed to be the same in both the barriers and the well [23], while the conduction band edges and the electron effective masses were assumed to change abruptly at the heterointerface. The conduction band offsets at the Alo.22Gao.7sAs/Ino.,sGao.ssAs and In,,,sGaO,sSAs/GaAs heterointerfaces were taken to be 322meV and 141 meV, respectively [8, 241. The values of the A10.22Ga0.7sAs,Ino.isGao.ssAs, and GaAs electron effective masses were assumed to be 0.079 mp and 0.058 m,, 0.067 m,, respectively [25]. Because deep impurity states can have a substantial effect on the electron density, the value determined from S-dH measurements was used. For the given electron density the subband energies and subband wavefunctions could be calculated in a self-consistent manner. In this case, the calculated magnitudes of the two eigenenergies for the potential bottom in the well were 100.8 and 160.2meV corresponding to the zeroth and first electron subbands, respectively. The energy eigenfunctions are indicated by the dashed line in Fig. 6. In summary, TEM measurements showed that an Als.22Gae.7sAs/In o.,sGa0.s5As/GaAs quantum well with high quality interfaces was grown on a GaAs substrate. The results of the S-dH measurements and the observation of quantum Hall effects at 1.5 K demonstrated clearly the existence of a 2DEG in the Ino,,sGao.ssAs quantum well grown by MBE. The FFT results for the data show two oscillation frequencies, indicating the electron occupation of
1. 2. 3.
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Electron
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