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AlSb quantum wells
Superlattices
and Microstructures,
363
Vol. 7, No. 4, 1990
OPTICALLY INDUCED VARIABILITY OF THE STRAIN-INDUCED ELECTRIC FIELDS IN (111) GaSb/AlSb QUANTUMWELLS
Naval
B.V. Shanabrook Research Laboratory,
and
D. Gammon Washington DC, USA
and R. Beresford and V.I. Wang Columbia University, New York, USA and
Harry
R.P. Leavitt U.S. Army Laboratory Command Diamond Laboratories,Adelphi, ED, USA and
Boston
D.A. College,
(Received
Broido Boston, 30 July
MS, USA 1990)
Electronic Raman scattering and x-ray diffraction measurements on GaSb/AlSb quantum wells grown on (111) and (100) oriented substrates A kinematic simulation of the x-ray diffraction have been performed. intensity profiles has been used to determine the strain in the layers Using the piezoelectric tensor of GaSb of the multiple quantum wells. and the strain estimated from the x-ray measurements, one expects that should exist in the GaSb layers of the an electric field of -6OkV/cm Intersubband transitions in the conduction band (111) oriented sample. in the (111) and (100) oriented samples exhibit very different energies. A blue shift of the intersubband transition of the (111) oriented sample from that of (100) sample occurs because of the piezoelectricallyThe energy of the intersubband generated electric field in the former. transition of the (111) oriented sample is sensitive to optical excitation density. This sensitivity arises because the electron-hole pairs screen the piezoelectrically generated electric field.
1.
Introduction
Strained layer growth of thin film semiconductors onto lattice mismatched substrates or buffer layers allows the energy band structure of the thin film to be modified significantly. Such examples include, employing biaxial strain in InAsSb to lower the energy gap so that it is suitable as a detector for wavelengths smaller that 12 pm or employing strain so that the highest energy valence band state is light hole like. Another potential consequence of strain in multiple quantum wells has been discussed recently by Smith and Mailhiot.’ In their work, they suggest that the combination of strain and the piezoelectric effect can lead to large built-in electric fields with correspondingly large modifications in the energy band structure
of the quantum wells. Shown in Figure 1 is a comparison of the valence and conduction band edges of a quantum well constructed from III-V compounds and grown along the (100) and (111) crystallographic directions. In this example the barrier and well materials are under biaxial compression and tension, respectively. In the case for growth in the (100) direction, the strain leads to a splitting of the heavy and light hole valence bands where the relative energies of the valence and conduction states are determined by the a and b deformation potentials and the quantum confinement. Furthermore, because the off diagonal elements of the strain tensor are zero and because of the form of the piezoelectric tensor for III-V compounds, electric fields that arise from the piezoelectric effect are zero. For (111) oriented samples,
0 1990 Academic Press Limited
364
Superlattices (100)
Vol. 7, No. 4, 1990
(111)
Figure 1 - Conduction and valence band edges for quantum wells grown along the (100) and (111) The wells and barriers are under directions. biaxial tension and compression, respectively.
the splitting in the valence bands also occurs and the relative energies of the conduction and valence bands are determined by the a and d deformation potentials and the quantum confinement. In addition, the non-zero off diagonal elements of the strain tensor combined with the piezoelectric tensor lead to large built-in electric fields along the growth axis in the well and barrier layers. Because the barriers and wells are under biaxial compression and tension, respectively, the electric fields in the wells and barriers point in opposite directions. Employing typical values of the piezoelectric coefficients and attainable biaxial strains in III-V semiconductors, electric fields as large as -1E5V/cm should be achievable. Studies by Laurich et al.’ and Yoo et a1.a in InGaAs/GaAs have indicated that large electric fields can be produced in strained layer superlattices grown in the (111) direction. Others have shown that the built-in electric fields offer advantages in optoelectronic4 and electronic” devices. we present x-ray diffracIn this paper, tion data and electronic Raman scattering spectra from (100) and (111) multiple quantum wells In addition to showing that large of GaSb/AlSb. electric fields exist in the GaSb layers of the (111) quantum well, we show that the band structure is very sensitive to the optical generation As shown schematiof an electron-hole plasma. cally in Figure 2 (only one valence band is shown for simplicity), these changes in band structure occur because the two-component plasma acts to screen the strain-generated electric field and therefore causes a red shift of the intersubband transitions, EIZ , and a blue shift of the interband energies, El-Vl. 2.
and Microstructures,
Results
and Discussion
The samples examined in this study were grown by MBE on (100) and (lllb) GaAs substrates They conmounted on the same molybdenum block. sisted of a 1.2 urn buffer layer of AlSb and then a 20 period superlattice of GaSb/AlSb. All
High Densky
Plasma
Figure 2 - Schematic representation of the changes that occur in the band structure of a piezoelectric superlattice with increasing twocomponent plasma density.
(111) GoSb/AISb
SUPERLATTICE
2
.~~ a?1 ::;.,-, m=-2
Experiment
4
Theory
m=-1
-t
c m 6
m=+2
to -d
m=+l
m=+3
m=O
m=-3
m=+4
‘_
,...,’
x
80.8
81.2
al.6 FTHETA
82.0
82.4
82.8
15.2
(degrees)
Figure 3 - X-ray power diffraction spectrum, obtained using Cu Ka radiation, of the (333) reflection of the (111) oriented GaSb/AlSb strained-layer superlattice discussed in the The Kal satellite peaks are labeled by text. The weaker Kaz peaks of order m the index m. are nearly coincident with the Kal peaks of order m+l. layers are unintentionally doped in the -101Jcm-3 range. X-ray diffraction measurements were performed on a powder diffractometer with the reflections from the (400) and (333) planes of The the (100) and (111) samples, respectively. results from these measurements were compared with those from a kinematic simulation of the xA non-linear leastray diffraction process. squares fitting algorithm was used to determine
Superlattices
and Microstructures,
365
Vol. 7, No. 4, 1990
Table l-Values for the diffraction measurements layer superlattices.
layer for
thicknesses the (100)
and
and strains obtained from (111) oriented GaSb/AlSb
the x-ray strained-
the individual layer thicknesses and perpendicular lattice constants of the GaSb and The in-plane lattice constants of AlSb layers. the GaSb and AlSb layers of the multiple quantum Shown in Figure 3 well were taken to be equal. are the measured and fitted diffraction patterns from the (333) reflections of the (111) sample. The strains and layer thicknesses obtained from The AlSb this procedure are shown in Table 1. and CaSb layer thicknesses of the (100) and (111) samples were the same to within experimenThe relationship between strain and tal error. the piexoelectrically generated electric field for the (111) oriented sample is given by,
but rather arises because conduction band mass, the (111) sample has a large electric field in the GaSb layers that arises from the piezoelecIn order to test this hypothesis, tric ef feet. we have employed an effective mass quantum well model with the current conserving boundary conditions using the band offsets and electron masses determined by Menendez et a1.g for this material systemlo,*l. For the (100) sample, the calculated transition energy of 33.5 meV is in good agreement with the measured value. Employing the band structure model shown in Figure 1. a constant electric field of 61000V/cm is required to fit the 58 meV EIZ transltion energy This value of electric of the (111) sample. field is in good agreement with that estimated from the strain in the layers and the piezoelectric coefficient of GaSb.
where e14 is the piezoelectric coefficient of the material,rlI is the magnitude of the offdiagonal element of the strain tensor, to is the permittivity of vacuum and c is the dielectric Using the piezoelectric coefficients6 constant. of GaSb and AlSb and strains given in Table 1, the electric fields in the (111) sample due to the piezoelectric effect are 56000V!ca and 30000V/cm for the GaSb and AlSb layers, respectively. Electronic Raman scattering has proven to be very valuable in determining the energy separations of the subbands and electron concentrations in quantum wells. In these measurements one determines the energies of the spin density and charge density waves by measuring the scattering in the depolarized and polarized scattering geometries, respectively.’ Because of the small effective electron mass of electrons in GaSb I.O41mo), the energy of the spin density wave is very close to the intersubband the charge density wave ocenergy, EIZ, while curs at higher energy because of the depolarization shift.8 The energy difference between the spin density and charge density waves allows one to estimate the electron density.8 We have performed resonant electronic Raman scattering measurements near the E, + & gap of GaSb for the (111) and (1001 samples. At low pump powers, the plasma densities are -1010cm-2 and the EIZ transitions for the (111) and (100) samples occur at 58 meV and 37 WV, respectively. This large difference in intersubband energy cannot arise from differences in quantum well widths or from anisotropies in the
If one employs higher lasel powers and generates an electron-hole plasma, the behavior of the intersubband transitions of the (100) similar sample is to that observed in CaAs/AlGaAs quantum wells.lz Specifically, EI 2 remains constant in energy and the charge density wave moves to higher energy. This occurs because the electron and hole envelope functions exhibit similar spatial forms and give rise to a self-consistent Hartree potential that does not significantly alter the forlr ,>f the square well potential. The charge density wave shifts to higher energy because of the increasing electron concentration. In contrast, and as shown in Figure 4. the EL. transition of the (111) sample exhibits large shifts to lower energy as the excitation power density’” and, therefore, plasma density is increased. The vertical arrow in the figure marks the energy of the Eltransition obtained from the (100) sample. Shown in Figure 5 are the result:; ilf a calculation for the energy of the spin density intersubband transitions as a function of plasma density. In this calculation, the rlectron and hole wave functions have been calculated selfconsistently by the simultaneous solution of the Schrodinger and Poisson equations’4. Ye have approximated the form of the txchangecorrelation electron-electron interactions via the local density approximation assuming that the electrons and hcles form indepsnd?nt plasmas _ The energy of the spin density intersubband transition exhibits large shifts to lower energy as the plasma density increases because the electrons and holes Ire separated in
366
Superlattices
2000
Gi t1500 5 z Fi 000 z E z
500
n “25
30
35
40
45 50 55 60 ENERGY (meV)
65
70
Figure 4 - Intersubband transitions observed in the depolarized Raman scattering geometry with the indicated laser power densities from the The arrow indicates the energy of (111) sample. the intersubband transition observed in the (100) sample.
ts 5 45 -
??
Spin Density
??
Charge Density
-
Calculation
40 -
between the measured and Figure 5 - Comparison calculated energies of the intersubband transitions from the (111) sample.
real space and give rise to an electric field that partially cancels or screens the piezoelecUsing the measured trically generated field. energy difference between spin density and the the density of the opticharge density waves, cally created plasma has been estimated for each The measured laser excitation density.’
and Microstructures,
Vol. 7, No. 4, 1990
energies of the spin and charge density waves as a function of plasma density are also shown in The agreement between this model and Figure 5. the experimental energies for the spin density waves substantiates our conclusion that optically generated carriers screen the large electric fields that exist in strained (111) superPreliminary calculations result in lattices. better agreement between experiment and theory for both the (100) and (111) samples if the effective mass of the electrons is reduced from 0.041mo (the value for bulk GaSb) to 0.036m0. This reduction in electron mass is physically reasonable because of the reduction in energy gap that occurs because of biaxial strain. When one performs an optical measurement to determine the built-in electric field in piezoelectric superlattices, it is not necessary for the piezoelectrically generated electric field to be equal to the measured built-in electric field. The magnitudes of these fields can differ because of rearrangement of positive and negative charges in the sample. The rearrangement can arise from a number of different mechanisms. For example, the d2pletion charge density that exists because of surface pinning phenomena gives rise to an electric field that can modify the magnitude of the total electric field in the quantum well. For our samples, the small background doping concentration implies that this is a small correction to the piezoelectrically generated electric field. Larger corrections would be expected to occur from a second effect in our samples. Specif itally, employing the piezoelectric coefficients of GaSb and AlSb, their corresponding layer thicknesses and biaxial strains, we calculate that there is a net change of potential of 0.07leV across the 480 A period and 1.42eV across the 20 periods of the structure. Because the net change in potential across the structure cannot be larger than the band gap of GaSb (- .8eV), there should be a screening of the built-in field by charge redistribution in the The good agreement between the superlattice. electric field calculated from the Raman measurements and that estimated from the piezoelectric effect and the strain in the GaSb Howlayers suggest that this zffect is small. ever, because the penetration depth of th2 light employed in the Raman measurement is small, we can only comment on the magnitude of the electric field in the GaSb layers near the surface of the sample. 3. Conclusions We have performed x-ray diffraction measurem2nts and Raman scattering mfasurements on (100) and (111) GaSb/AlSb supzrlattices. These measurements indicate that large electric fi2lds exist in th2 GaSb layfrs of the (111) superlattice and that the magnitud2 of the 212ctric field can be reduced through screening of the piezoelectrically generated field by th2 opThe tical production of electron-hole pairs.
Superlattices
and Microstructures,
367
Vol. 7, No. 4, 1990
latter observation suggests that these superlattices could act as optically-activated optithis modulation, Furthermore, cal modulators. if induced by the creation of virtual excitons, could occur in the time regime of hundreds of femtoseconds.15 Acknowledgements--We wish to acknowledge the financial support of the U.S. Office of Naval Research under Contracts No. NOG014-86-K-0694 (R.B and W.I.W.) and No. N00014-90-AF-00002 This research is supported (B.V.S. and D.G.). by the Columbia Center for Telecommunications of Martin Research. We thank J. W. Little Marietta Laboratories for his assistance with the x-ray diffraction measurements.
8. 9.
10.
11.
12. 13.
References Smith and C. Mailhiot, Phys. Rev. 1. D.L. 58 1264 (1987) and C. Mailhiot and Lett. D.L. Smith, Phys. Rev. Bl?. 10415 (1988) and references therein. B.K. Laurich, K. Elcess, C.G. Fonstad, J.G. 2. C. Mailhiot and D.L. Smith, Phys. Berry, Rev. Lett. 62 649 (1989). B. S. Yoo, X. C. Liu, A. Petrou, J-P Cheng, 3. A.A. Reeder and B.D. McCombe, Superlattices and Microstructures 5, 363 (1989). E.A. Caridi, T.Y. Chang, K.W. Goossen and 4. Eastman, Appl. Phys. Lett. 56 659 L.F. (1990) and Appl. Phys. Lett. 56 715 (1990). Shanabrook and D. Gammon, 5. E.S. Snow, B.V. Appl. Phys. Lett. 56 758 (1990). 6. Sadao Adachi, J. Appl. Phys. u 8775 (1982). 7. G. Abstreiter, M. Cardona and A. Pinczuk, in Light Scattering in Solids IV, edited by n. Cardona (Springer, and G. Guntherodt Berlin, 1984), p. 5.
14.
15.
D. Gammon, B.V. Shanabrook, J.C. Ryan and D.S. Katzer, Phys. Rev EI~ 12311 (1990). J. Menendez, A. Pinczuk, D.J. Werder, J.P. Valladares, T.H. Chiu and W.T. Tsang, Solid State Commun. 6.1 703 (1987). n. Maaref, F.F. Charfi, M. Zouaghi, C. Benoit a la Guillaume and A. Joullie, Phys. REV. Bg 8650 (1986). Electron nonparabolicity was ignored in the calculation. An electron mass of 0.041m09 and 0.14 mot0 for the GaSb and AlSb have been assumed and a 62-389 split of the conduction and valence band offsets of GaSb and AlSb I bands was employed. A. Pinczuk, J. Shah, A.C. Gossard and X. Yiegmann, Phys. Rev. Lett. 46 1307 (1981). The relative intensity of the Stokes and anti-Stokes scattering from the LO phonons out of resonance indicates that at the highest power densities (6KW/cmzi the sample temperature is near 100K. This increase in temperature will cause small changes in the effective mass of the electrons but does not cause a measureable shift in the SDE energies of the (100) sample. We have employed values of Luttinger parameters and deformation potentials given in Landolt-Bornstein, New Series 1982 Group III Vol. 17a (Berlin:Springer). Specif itally, the Luttinger parameters are 71 (GaSb)=11.8, r2 (GaSb)=4.03, 13 (GaSb)=5.26, rI (AlSb)=4.15, rz (AlSb)=l.Ol and 73 (AlSbj11.75. The deformation potentials are a = -8.3eV and d = -4.6eV for GaSb. D.S. Chemla, D.A.B. Miller and S. SchmittRink, Phys. Rev. Lett. 59 1018 (1987) and M. Yamanishi, Phys. Rev. Lett. 59 1014 (1987).
and Microstructures,
363
Vol. 7, No. 4, 1990
OPTICALLY INDUCED VARIABILITY OF THE STRAIN-INDUCED ELECTRIC FIELDS IN (111) GaSb/AlSb QUANTUMWELLS
Naval
B.V. Shanabrook Research Laboratory,
and
D. Gammon Washington DC, USA
and R. Beresford and V.I. Wang Columbia University, New York, USA and
Harry
R.P. Leavitt U.S. Army Laboratory Command Diamond Laboratories,Adelphi, ED, USA and
Boston
D.A. College,
(Received
Broido Boston, 30 July
MS, USA 1990)
Electronic Raman scattering and x-ray diffraction measurements on GaSb/AlSb quantum wells grown on (111) and (100) oriented substrates A kinematic simulation of the x-ray diffraction have been performed. intensity profiles has been used to determine the strain in the layers Using the piezoelectric tensor of GaSb of the multiple quantum wells. and the strain estimated from the x-ray measurements, one expects that should exist in the GaSb layers of the an electric field of -6OkV/cm Intersubband transitions in the conduction band (111) oriented sample. in the (111) and (100) oriented samples exhibit very different energies. A blue shift of the intersubband transition of the (111) oriented sample from that of (100) sample occurs because of the piezoelectricallyThe energy of the intersubband generated electric field in the former. transition of the (111) oriented sample is sensitive to optical excitation density. This sensitivity arises because the electron-hole pairs screen the piezoelectrically generated electric field.
1.
Introduction
Strained layer growth of thin film semiconductors onto lattice mismatched substrates or buffer layers allows the energy band structure of the thin film to be modified significantly. Such examples include, employing biaxial strain in InAsSb to lower the energy gap so that it is suitable as a detector for wavelengths smaller that 12 pm or employing strain so that the highest energy valence band state is light hole like. Another potential consequence of strain in multiple quantum wells has been discussed recently by Smith and Mailhiot.’ In their work, they suggest that the combination of strain and the piezoelectric effect can lead to large built-in electric fields with correspondingly large modifications in the energy band structure
of the quantum wells. Shown in Figure 1 is a comparison of the valence and conduction band edges of a quantum well constructed from III-V compounds and grown along the (100) and (111) crystallographic directions. In this example the barrier and well materials are under biaxial compression and tension, respectively. In the case for growth in the (100) direction, the strain leads to a splitting of the heavy and light hole valence bands where the relative energies of the valence and conduction states are determined by the a and b deformation potentials and the quantum confinement. Furthermore, because the off diagonal elements of the strain tensor are zero and because of the form of the piezoelectric tensor for III-V compounds, electric fields that arise from the piezoelectric effect are zero. For (111) oriented samples,
0 1990 Academic Press Limited
364
Superlattices (100)
Vol. 7, No. 4, 1990
(111)
Figure 1 - Conduction and valence band edges for quantum wells grown along the (100) and (111) The wells and barriers are under directions. biaxial tension and compression, respectively.
the splitting in the valence bands also occurs and the relative energies of the conduction and valence bands are determined by the a and d deformation potentials and the quantum confinement. In addition, the non-zero off diagonal elements of the strain tensor combined with the piezoelectric tensor lead to large built-in electric fields along the growth axis in the well and barrier layers. Because the barriers and wells are under biaxial compression and tension, respectively, the electric fields in the wells and barriers point in opposite directions. Employing typical values of the piezoelectric coefficients and attainable biaxial strains in III-V semiconductors, electric fields as large as -1E5V/cm should be achievable. Studies by Laurich et al.’ and Yoo et a1.a in InGaAs/GaAs have indicated that large electric fields can be produced in strained layer superlattices grown in the (111) direction. Others have shown that the built-in electric fields offer advantages in optoelectronic4 and electronic” devices. we present x-ray diffracIn this paper, tion data and electronic Raman scattering spectra from (100) and (111) multiple quantum wells In addition to showing that large of GaSb/AlSb. electric fields exist in the GaSb layers of the (111) quantum well, we show that the band structure is very sensitive to the optical generation As shown schematiof an electron-hole plasma. cally in Figure 2 (only one valence band is shown for simplicity), these changes in band structure occur because the two-component plasma acts to screen the strain-generated electric field and therefore causes a red shift of the intersubband transitions, EIZ , and a blue shift of the interband energies, El-Vl. 2.
and Microstructures,
Results
and Discussion
The samples examined in this study were grown by MBE on (100) and (lllb) GaAs substrates They conmounted on the same molybdenum block. sisted of a 1.2 urn buffer layer of AlSb and then a 20 period superlattice of GaSb/AlSb. All
High Densky
Plasma
Figure 2 - Schematic representation of the changes that occur in the band structure of a piezoelectric superlattice with increasing twocomponent plasma density.
(111) GoSb/AISb
SUPERLATTICE
2
.~~ a?1 ::;.,-, m=-2
Experiment
4
Theory
m=-1
-t
c m 6
m=+2
to -d
m=+l
m=+3
m=O
m=-3
m=+4
‘_
,...,’
x
80.8
81.2
al.6 FTHETA
82.0
82.4
82.8
15.2
(degrees)
Figure 3 - X-ray power diffraction spectrum, obtained using Cu Ka radiation, of the (333) reflection of the (111) oriented GaSb/AlSb strained-layer superlattice discussed in the The Kal satellite peaks are labeled by text. The weaker Kaz peaks of order m the index m. are nearly coincident with the Kal peaks of order m+l. layers are unintentionally doped in the -101Jcm-3 range. X-ray diffraction measurements were performed on a powder diffractometer with the reflections from the (400) and (333) planes of The the (100) and (111) samples, respectively. results from these measurements were compared with those from a kinematic simulation of the xA non-linear leastray diffraction process. squares fitting algorithm was used to determine
Superlattices
and Microstructures,
365
Vol. 7, No. 4, 1990
Table l-Values for the diffraction measurements layer superlattices.
layer for
thicknesses the (100)
and
and strains obtained from (111) oriented GaSb/AlSb
the x-ray strained-
the individual layer thicknesses and perpendicular lattice constants of the GaSb and The in-plane lattice constants of AlSb layers. the GaSb and AlSb layers of the multiple quantum Shown in Figure 3 well were taken to be equal. are the measured and fitted diffraction patterns from the (333) reflections of the (111) sample. The strains and layer thicknesses obtained from The AlSb this procedure are shown in Table 1. and CaSb layer thicknesses of the (100) and (111) samples were the same to within experimenThe relationship between strain and tal error. the piexoelectrically generated electric field for the (111) oriented sample is given by,
but rather arises because conduction band mass, the (111) sample has a large electric field in the GaSb layers that arises from the piezoelecIn order to test this hypothesis, tric ef feet. we have employed an effective mass quantum well model with the current conserving boundary conditions using the band offsets and electron masses determined by Menendez et a1.g for this material systemlo,*l. For the (100) sample, the calculated transition energy of 33.5 meV is in good agreement with the measured value. Employing the band structure model shown in Figure 1. a constant electric field of 61000V/cm is required to fit the 58 meV EIZ transltion energy This value of electric of the (111) sample. field is in good agreement with that estimated from the strain in the layers and the piezoelectric coefficient of GaSb.
where e14 is the piezoelectric coefficient of the material,rlI is the magnitude of the offdiagonal element of the strain tensor, to is the permittivity of vacuum and c is the dielectric Using the piezoelectric coefficients6 constant. of GaSb and AlSb and strains given in Table 1, the electric fields in the (111) sample due to the piezoelectric effect are 56000V!ca and 30000V/cm for the GaSb and AlSb layers, respectively. Electronic Raman scattering has proven to be very valuable in determining the energy separations of the subbands and electron concentrations in quantum wells. In these measurements one determines the energies of the spin density and charge density waves by measuring the scattering in the depolarized and polarized scattering geometries, respectively.’ Because of the small effective electron mass of electrons in GaSb I.O41mo), the energy of the spin density wave is very close to the intersubband the charge density wave ocenergy, EIZ, while curs at higher energy because of the depolarization shift.8 The energy difference between the spin density and charge density waves allows one to estimate the electron density.8 We have performed resonant electronic Raman scattering measurements near the E, + & gap of GaSb for the (111) and (1001 samples. At low pump powers, the plasma densities are -1010cm-2 and the EIZ transitions for the (111) and (100) samples occur at 58 meV and 37 WV, respectively. This large difference in intersubband energy cannot arise from differences in quantum well widths or from anisotropies in the
If one employs higher lasel powers and generates an electron-hole plasma, the behavior of the intersubband transitions of the (100) similar sample is to that observed in CaAs/AlGaAs quantum wells.lz Specifically, EI 2 remains constant in energy and the charge density wave moves to higher energy. This occurs because the electron and hole envelope functions exhibit similar spatial forms and give rise to a self-consistent Hartree potential that does not significantly alter the forlr ,>f the square well potential. The charge density wave shifts to higher energy because of the increasing electron concentration. In contrast, and as shown in Figure 4. the EL. transition of the (111) sample exhibits large shifts to lower energy as the excitation power density’” and, therefore, plasma density is increased. The vertical arrow in the figure marks the energy of the Eltransition obtained from the (100) sample. Shown in Figure 5 are the result:; ilf a calculation for the energy of the spin density intersubband transitions as a function of plasma density. In this calculation, the rlectron and hole wave functions have been calculated selfconsistently by the simultaneous solution of the Schrodinger and Poisson equations’4. Ye have approximated the form of the txchangecorrelation electron-electron interactions via the local density approximation assuming that the electrons and hcles form indepsnd?nt plasmas _ The energy of the spin density intersubband transition exhibits large shifts to lower energy as the plasma density increases because the electrons and holes Ire separated in
366
Superlattices
2000
Gi t1500 5 z Fi 000 z E z
500
n “25
30
35
40
45 50 55 60 ENERGY (meV)
65
70
Figure 4 - Intersubband transitions observed in the depolarized Raman scattering geometry with the indicated laser power densities from the The arrow indicates the energy of (111) sample. the intersubband transition observed in the (100) sample.
ts 5 45 -
??
Spin Density
??
Charge Density
-
Calculation
40 -
between the measured and Figure 5 - Comparison calculated energies of the intersubband transitions from the (111) sample.
real space and give rise to an electric field that partially cancels or screens the piezoelecUsing the measured trically generated field. energy difference between spin density and the the density of the opticharge density waves, cally created plasma has been estimated for each The measured laser excitation density.’
and Microstructures,
Vol. 7, No. 4, 1990
energies of the spin and charge density waves as a function of plasma density are also shown in The agreement between this model and Figure 5. the experimental energies for the spin density waves substantiates our conclusion that optically generated carriers screen the large electric fields that exist in strained (111) superPreliminary calculations result in lattices. better agreement between experiment and theory for both the (100) and (111) samples if the effective mass of the electrons is reduced from 0.041mo (the value for bulk GaSb) to 0.036m0. This reduction in electron mass is physically reasonable because of the reduction in energy gap that occurs because of biaxial strain. When one performs an optical measurement to determine the built-in electric field in piezoelectric superlattices, it is not necessary for the piezoelectrically generated electric field to be equal to the measured built-in electric field. The magnitudes of these fields can differ because of rearrangement of positive and negative charges in the sample. The rearrangement can arise from a number of different mechanisms. For example, the d2pletion charge density that exists because of surface pinning phenomena gives rise to an electric field that can modify the magnitude of the total electric field in the quantum well. For our samples, the small background doping concentration implies that this is a small correction to the piezoelectrically generated electric field. Larger corrections would be expected to occur from a second effect in our samples. Specif itally, employing the piezoelectric coefficients of GaSb and AlSb, their corresponding layer thicknesses and biaxial strains, we calculate that there is a net change of potential of 0.07leV across the 480 A period and 1.42eV across the 20 periods of the structure. Because the net change in potential across the structure cannot be larger than the band gap of GaSb (- .8eV), there should be a screening of the built-in field by charge redistribution in the The good agreement between the superlattice. electric field calculated from the Raman measurements and that estimated from the piezoelectric effect and the strain in the GaSb Howlayers suggest that this zffect is small. ever, because the penetration depth of th2 light employed in the Raman measurement is small, we can only comment on the magnitude of the electric field in the GaSb layers near the surface of the sample. 3. Conclusions We have performed x-ray diffraction measurem2nts and Raman scattering mfasurements on (100) and (111) GaSb/AlSb supzrlattices. These measurements indicate that large electric fi2lds exist in th2 GaSb layfrs of the (111) superlattice and that the magnitud2 of the 212ctric field can be reduced through screening of the piezoelectrically generated field by th2 opThe tical production of electron-hole pairs.
Superlattices
and Microstructures,
367
Vol. 7, No. 4, 1990
latter observation suggests that these superlattices could act as optically-activated optithis modulation, Furthermore, cal modulators. if induced by the creation of virtual excitons, could occur in the time regime of hundreds of femtoseconds.15 Acknowledgements--We wish to acknowledge the financial support of the U.S. Office of Naval Research under Contracts No. NOG014-86-K-0694 (R.B and W.I.W.) and No. N00014-90-AF-00002 This research is supported (B.V.S. and D.G.). by the Columbia Center for Telecommunications of Martin Research. We thank J. W. Little Marietta Laboratories for his assistance with the x-ray diffraction measurements.
8. 9.
10.
11.
12. 13.
References Smith and C. Mailhiot, Phys. Rev. 1. D.L. 58 1264 (1987) and C. Mailhiot and Lett. D.L. Smith, Phys. Rev. Bl?. 10415 (1988) and references therein. B.K. Laurich, K. Elcess, C.G. Fonstad, J.G. 2. C. Mailhiot and D.L. Smith, Phys. Berry, Rev. Lett. 62 649 (1989). B. S. Yoo, X. C. Liu, A. Petrou, J-P Cheng, 3. A.A. Reeder and B.D. McCombe, Superlattices and Microstructures 5, 363 (1989). E.A. Caridi, T.Y. Chang, K.W. Goossen and 4. Eastman, Appl. Phys. Lett. 56 659 L.F. (1990) and Appl. Phys. Lett. 56 715 (1990). Shanabrook and D. Gammon, 5. E.S. Snow, B.V. Appl. Phys. Lett. 56 758 (1990). 6. Sadao Adachi, J. Appl. Phys. u 8775 (1982). 7. G. Abstreiter, M. Cardona and A. Pinczuk, in Light Scattering in Solids IV, edited by n. Cardona (Springer, and G. Guntherodt Berlin, 1984), p. 5.
14.
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D. Gammon, B.V. Shanabrook, J.C. Ryan and D.S. Katzer, Phys. Rev EI~ 12311 (1990). J. Menendez, A. Pinczuk, D.J. Werder, J.P. Valladares, T.H. Chiu and W.T. Tsang, Solid State Commun. 6.1 703 (1987). n. Maaref, F.F. Charfi, M. Zouaghi, C. Benoit a la Guillaume and A. Joullie, Phys. REV. Bg 8650 (1986). Electron nonparabolicity was ignored in the calculation. An electron mass of 0.041m09 and 0.14 mot0 for the GaSb and AlSb have been assumed and a 62-389 split of the conduction and valence band offsets of GaSb and AlSb I bands was employed. A. Pinczuk, J. Shah, A.C. Gossard and X. Yiegmann, Phys. Rev. Lett. 46 1307 (1981). The relative intensity of the Stokes and anti-Stokes scattering from the LO phonons out of resonance indicates that at the highest power densities (6KW/cmzi the sample temperature is near 100K. This increase in temperature will cause small changes in the effective mass of the electrons but does not cause a measureable shift in the SDE energies of the (100) sample. We have employed values of Luttinger parameters and deformation potentials given in Landolt-Bornstein, New Series 1982 Group III Vol. 17a (Berlin:Springer). Specif itally, the Luttinger parameters are 71 (GaSb)=11.8, r2 (GaSb)=4.03, 13 (GaSb)=5.26, rI (AlSb)=4.15, rz (AlSb)=l.Ol and 73 (AlSbj11.75. The deformation potentials are a = -8.3eV and d = -4.6eV for GaSb. D.S. Chemla, D.A.B. Miller and S. SchmittRink, Phys. Rev. Lett. 59 1018 (1987) and M. Yamanishi, Phys. Rev. Lett. 59 1014 (1987).