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Tunneling in double quantum well structures: Role of optical phonons
Surface Science 229 ( 1990) North-Holland
189
189-l 9 1
TUNNELING
IN DOUBLE QUANTUM
WELL STRUCTURES:
D.Y. OBERLI,
Jagdeep SHAH, T.C. DAMEN,
J.M. KU0
ROLE OF OPTICAL PHONONS
*, R.F. KOPF * and J.E. HENRY
AT&T Bell Laboratories, Holmdel, NJ 07733. USA Received
11 July 1989; accepted
for publication
14 September
1989
Using subpicosecond time-resolved luminescence spectroscopy, we show that the tunneling rate for electrons in an asymmetric double quantum well structure changes dramatically as the energy separation between the two lowest conduction subbands of the coupled well system is tuned through the optical phonon energy by applying an electric field. These results demonstrate the importance of phononassisted tunneling processes in this structure as well as in the carrier transport of related multiple quantum well structures, and raise a number of interesting questions concerning the nature of phonons and carrier-phonon interactions in these structures.
The investigation of tunneling of electrons and holes through potential barriers in semiconductor heterostructures is an area of active research. In this paper, we present experimental results of a study of optical phonon-assisted tunneling, a problem of current interest [ 1,2 1, using subpicosecond luminescence spectroscopy. We investigated the rate of electron tunneling across a single potential barrier separating two quantum wells of different thicknesses. The use of isolated structures, rather than superlattices, allowed us to investigate the effect of tunneling without interference from any transportrelated effects. The sample studied was grown at 600°C by molecular beam epitaxy on ( 100) n-type GaAs substrate. Eight periods of an asymmetrical double quantum well structure were grown in the intrinsic region of a p-i-n diode structure; a 150 A thick layer of AlO.SsGao.ssAs separated each period. Each unit consists of two GaAs wells of different thicknesses, nominally 70 and 110 A, and a 55 A Alo.JsGao.ssAs barrier. The total width of the intrinsic region is 6080 A. The use of a p-i-n structure allowed us to tune the separation between the two lowest subbands of the coupled system through an optical phonon energy and investigate the role of phonons directly (fig. 1). Tunneling rates of electrons from the wide well to the narrow well were determined by measuring the * AT&T Bell Laboratories, 0039-6028/90/$03.50 (North-Holland)
Murray
Hill, NJ, USA.
0 Elsevier Science Publishers
B.V.
FLAT BAND
--u-r n=2
“=l’
n=,
WITH
ELECTRIC
FIELD
Fig. 1. Schematic diagram of the energy levels in a double quantum well structure for two values of the applied electric field.
decay times of the wide well luminescence [ 3 1. Short optical pulses of 750 fs duration tunable over the range of 7200 to 8000 A are generated at an 82 MHz rate by synchronously pumping a dye-laser
190
D. Y. Oberli et al./Tunnelhg
(Styryl 8) with the compressed and frequency doubled output of a mode-locked CW Nd-YAG laser. Time-resolved luminescence is realized by the energy up-conversion in a LiI03 crystal; photoluminescence is excited at a photon energy of 1.7 1 eV; the area1 carrier density is estimated to be 1.5 x 10” cm-2 per pulse. In fig. 2, we show the time evolution of luminescence intensity of the wide well for three different electric fields. The electric field at a given applied voltage was obtained directly by measuring the shift in the time-integrated luminescence spectrum due to quantum-confined Stark-effect (fig. 3). In fig. 4, we present the decay time of the wide well luminescence as a function of the applied electric field. These data show that for F-c30kV/cm, for which the energy separation between the n =:1 subband in the wide well and the n = 1’ subband in the narrow well is less than an optical phonon energy, the decay time of the luminescence is long and nearly independent of the field. At a field of about 40 kV/cm the decay time is strongly reduced because of the onset of phononassisted tunneling processes. Beyond a field of 60 kVI cm, we observe a continuous increase of the decay time presumably due to (1) the increase in the phonon wavevector of the phonon participating in the tunneling process and (2) the reduced overlap of the electronic wavefunction in adjacent wells. These
in double quantum well structures CALIBRATION OF ELECTRIC IN p-i-n DIODE
FIELD
WIDTH = 5700 r\
0
1 2 REVERSE
3 4 BIAS VOLTAGE
5
6
(V)
Fig. 3. Calibration of electric field in p-i-n diode obtained from quantum confided Stark effect.
results are, we believe, the first experimental evidence of phonon-assisted tunneling between two coupled quantum wells. This problem has been treated theoretically by Weil and Vinter [ 5 ] and Liu et al. 161 have argued that impurity assisted processes dominate in such tunneling. Our results show LO PHONON-ASSISTED TUNNELING IN COUPLED QUANTUM WELL STRUCTURE
TIME-RESOLVED LUMINESCENCE UNDER APPLIED FIELD
0
0
““1’1”” 20
t, , , : 40 ELECTRIC
J
11 0
’
’
’
’
’
’
’
750 TIME DELAY
’
’
1 1500
(ps)
Fig. 2. Decay curves of the luminescence intensity of the wide well (at the spectral peak), for three values of the electric field.
60
)
,
,
,
,
,
,
80
,
,
,
100
I
I
,I] 120
FIELD (kV/cm)
Fig. 4. Dependence of the luminescence decay times on electric field. The large decrease of decay time in the wide well occurs at the onset of optical phonon-assisted tunneling (calculated value of field at which resonance is expected for a 37 meV phonon is indicated by an arrow).
D. Y. Oberli et al./TunneNing in double quantum well structures
that phonon-assisted tunneling dominates over impurity assisted processes in our samples. This study raises a number of important questions concerning the nature of phonons that participate in the tunneling process. For a phonon-assisted tunneling process, the optical phonons are likely to be emitted from the barrier layer since the overlap of the electronic wavefunctions is strongest there. Because AlGaAs exhibits a two-mode behavior, the scattering of a longitudinal optical phonon will occur at two distinct frequencies: approximately 35 and 47 meV for 35% aluminum content [ 71. The onset of optical phonon-assisted tunneling has, however, not been resolved separately for these two phonon modes because the electric field may not be uniform across the eight periods of the double quantum well structure or because of interaction with broad interface modes, as discussed below. Some insight with regard to these questions was gained from resonant Raman scattering studies of interface and confined optical phonon modes in GaAs-AlAs superlattices [ 8,9]. These modes should be of importance for intersubband inelastic scattering of an electron in a coupled quantum well system. A calculation of the dispersion relation of interface modes performed by Fuchs and Kliewer for ionic slabs [ lo] and by Lassnig for double heterostructures [ 111, shows that the phonon frequencies of these modes span a range between the optical phonon energies corresponding to the longitudinal and transverse modes, thereby contributing to the broadening of the phonon threshold of our data. From all these observations, we conclude that a direct comparison of the phonon-assisted tunneling scattering rates with theoretical estimates should take into account the complexities of the interface and confined phonon modes and their dispersion relations.
191
In conclusion, we have performed a time-resolved luminescence study of electron tunneling in coupled asymmetric quantum wells. These results demonstrate the existence of strong phonon-assisted tunneling in this system when the energy separation of the two lowest energy subbands exceeds some optical phonon energy. Beyond this threshold, the tunneling rate decreases again, presumably due to a reduction in the wavefunction overlap and the Frohlich matrix elements. This study has raised a number of questions concerning the nature of phonon modes and their coupling to carries; it will be interesting to investigate these aspects in detail. We would like to thank stimulating discussions.
D.A.B. Miller for many
References [ I] V.J. Goldman, D.C. Tsui and J.E. Cunningham, Phys. Rev. B 36 (1987) 7635. [2] N.S. Wingreen, K.W. Jacobsen and J.W. Wilkens, Phys. Rev. Lett. 61 (1988) 1396. [3] D.Y. Oberli, Jagdeep Shah, T.C. Damen, C.W. Tu, T.Y. Chang, D.A.B. Miller, J.E. Henry, R.F. Kopf, N. Sauer and A.E. DiGiovanni, Phys. Rev. B 40 (1989) 3028. [4 ] J. Shah, IEEE J. Quantum Electron. QE-24 (1988) 276. [ 51T. Weil and B. Vinter, J. Appl. Phys. 60 (1986) 3227. [6] H.W. Liu et al., Appl. Phys. Lett. 54 ( 1989) 2082. [ 7 ] R. Tsu, H. Kawamura and L. E&i, in: Proc. 11 th Int. Conf. on the Physics of Semiconductors, Warsaw, 1972, Ed. M. Miasek, p. 1135. [ 81 A.K. Sood, J. Menendez, M. Cardona and K. Ploog, Phys. Rev.Lett. 54 (1985) 2115. [9] B. Jusserand, D. Paquet and A. Regreny, Phys. Rev. B 30 (1984) 6245. [lo] R. Fuchs and K.L. Kliewer, Phys. Rev. A 140( 1965) 2076. [ 111 R. Lassnig, Phys. Rev. B 30 ( 1984) 7 132.
189
189-l 9 1
TUNNELING
IN DOUBLE QUANTUM
WELL STRUCTURES:
D.Y. OBERLI,
Jagdeep SHAH, T.C. DAMEN,
J.M. KU0
ROLE OF OPTICAL PHONONS
*, R.F. KOPF * and J.E. HENRY
AT&T Bell Laboratories, Holmdel, NJ 07733. USA Received
11 July 1989; accepted
for publication
14 September
1989
Using subpicosecond time-resolved luminescence spectroscopy, we show that the tunneling rate for electrons in an asymmetric double quantum well structure changes dramatically as the energy separation between the two lowest conduction subbands of the coupled well system is tuned through the optical phonon energy by applying an electric field. These results demonstrate the importance of phononassisted tunneling processes in this structure as well as in the carrier transport of related multiple quantum well structures, and raise a number of interesting questions concerning the nature of phonons and carrier-phonon interactions in these structures.
The investigation of tunneling of electrons and holes through potential barriers in semiconductor heterostructures is an area of active research. In this paper, we present experimental results of a study of optical phonon-assisted tunneling, a problem of current interest [ 1,2 1, using subpicosecond luminescence spectroscopy. We investigated the rate of electron tunneling across a single potential barrier separating two quantum wells of different thicknesses. The use of isolated structures, rather than superlattices, allowed us to investigate the effect of tunneling without interference from any transportrelated effects. The sample studied was grown at 600°C by molecular beam epitaxy on ( 100) n-type GaAs substrate. Eight periods of an asymmetrical double quantum well structure were grown in the intrinsic region of a p-i-n diode structure; a 150 A thick layer of AlO.SsGao.ssAs separated each period. Each unit consists of two GaAs wells of different thicknesses, nominally 70 and 110 A, and a 55 A Alo.JsGao.ssAs barrier. The total width of the intrinsic region is 6080 A. The use of a p-i-n structure allowed us to tune the separation between the two lowest subbands of the coupled system through an optical phonon energy and investigate the role of phonons directly (fig. 1). Tunneling rates of electrons from the wide well to the narrow well were determined by measuring the * AT&T Bell Laboratories, 0039-6028/90/$03.50 (North-Holland)
Murray
Hill, NJ, USA.
0 Elsevier Science Publishers
B.V.
FLAT BAND
--u-r n=2
“=l’
n=,
WITH
ELECTRIC
FIELD
Fig. 1. Schematic diagram of the energy levels in a double quantum well structure for two values of the applied electric field.
decay times of the wide well luminescence [ 3 1. Short optical pulses of 750 fs duration tunable over the range of 7200 to 8000 A are generated at an 82 MHz rate by synchronously pumping a dye-laser
190
D. Y. Oberli et al./Tunnelhg
(Styryl 8) with the compressed and frequency doubled output of a mode-locked CW Nd-YAG laser. Time-resolved luminescence is realized by the energy up-conversion in a LiI03 crystal; photoluminescence is excited at a photon energy of 1.7 1 eV; the area1 carrier density is estimated to be 1.5 x 10” cm-2 per pulse. In fig. 2, we show the time evolution of luminescence intensity of the wide well for three different electric fields. The electric field at a given applied voltage was obtained directly by measuring the shift in the time-integrated luminescence spectrum due to quantum-confined Stark-effect (fig. 3). In fig. 4, we present the decay time of the wide well luminescence as a function of the applied electric field. These data show that for F-c30kV/cm, for which the energy separation between the n =:1 subband in the wide well and the n = 1’ subband in the narrow well is less than an optical phonon energy, the decay time of the luminescence is long and nearly independent of the field. At a field of about 40 kV/cm the decay time is strongly reduced because of the onset of phononassisted tunneling processes. Beyond a field of 60 kVI cm, we observe a continuous increase of the decay time presumably due to (1) the increase in the phonon wavevector of the phonon participating in the tunneling process and (2) the reduced overlap of the electronic wavefunction in adjacent wells. These
in double quantum well structures CALIBRATION OF ELECTRIC IN p-i-n DIODE
FIELD
WIDTH = 5700 r\
0
1 2 REVERSE
3 4 BIAS VOLTAGE
5
6
(V)
Fig. 3. Calibration of electric field in p-i-n diode obtained from quantum confided Stark effect.
results are, we believe, the first experimental evidence of phonon-assisted tunneling between two coupled quantum wells. This problem has been treated theoretically by Weil and Vinter [ 5 ] and Liu et al. 161 have argued that impurity assisted processes dominate in such tunneling. Our results show LO PHONON-ASSISTED TUNNELING IN COUPLED QUANTUM WELL STRUCTURE
TIME-RESOLVED LUMINESCENCE UNDER APPLIED FIELD
0
0
““1’1”” 20
t, , , : 40 ELECTRIC
J
11 0
’
’
’
’
’
’
’
750 TIME DELAY
’
’
1 1500
(ps)
Fig. 2. Decay curves of the luminescence intensity of the wide well (at the spectral peak), for three values of the electric field.
60
)
,
,
,
,
,
,
80
,
,
,
100
I
I
,I] 120
FIELD (kV/cm)
Fig. 4. Dependence of the luminescence decay times on electric field. The large decrease of decay time in the wide well occurs at the onset of optical phonon-assisted tunneling (calculated value of field at which resonance is expected for a 37 meV phonon is indicated by an arrow).
D. Y. Oberli et al./TunneNing in double quantum well structures
that phonon-assisted tunneling dominates over impurity assisted processes in our samples. This study raises a number of important questions concerning the nature of phonons that participate in the tunneling process. For a phonon-assisted tunneling process, the optical phonons are likely to be emitted from the barrier layer since the overlap of the electronic wavefunctions is strongest there. Because AlGaAs exhibits a two-mode behavior, the scattering of a longitudinal optical phonon will occur at two distinct frequencies: approximately 35 and 47 meV for 35% aluminum content [ 71. The onset of optical phonon-assisted tunneling has, however, not been resolved separately for these two phonon modes because the electric field may not be uniform across the eight periods of the double quantum well structure or because of interaction with broad interface modes, as discussed below. Some insight with regard to these questions was gained from resonant Raman scattering studies of interface and confined optical phonon modes in GaAs-AlAs superlattices [ 8,9]. These modes should be of importance for intersubband inelastic scattering of an electron in a coupled quantum well system. A calculation of the dispersion relation of interface modes performed by Fuchs and Kliewer for ionic slabs [ lo] and by Lassnig for double heterostructures [ 111, shows that the phonon frequencies of these modes span a range between the optical phonon energies corresponding to the longitudinal and transverse modes, thereby contributing to the broadening of the phonon threshold of our data. From all these observations, we conclude that a direct comparison of the phonon-assisted tunneling scattering rates with theoretical estimates should take into account the complexities of the interface and confined phonon modes and their dispersion relations.
191
In conclusion, we have performed a time-resolved luminescence study of electron tunneling in coupled asymmetric quantum wells. These results demonstrate the existence of strong phonon-assisted tunneling in this system when the energy separation of the two lowest energy subbands exceeds some optical phonon energy. Beyond this threshold, the tunneling rate decreases again, presumably due to a reduction in the wavefunction overlap and the Frohlich matrix elements. This study has raised a number of questions concerning the nature of phonon modes and their coupling to carries; it will be interesting to investigate these aspects in detail. We would like to thank stimulating discussions.
D.A.B. Miller for many
References [ I] V.J. Goldman, D.C. Tsui and J.E. Cunningham, Phys. Rev. B 36 (1987) 7635. [2] N.S. Wingreen, K.W. Jacobsen and J.W. Wilkens, Phys. Rev. Lett. 61 (1988) 1396. [3] D.Y. Oberli, Jagdeep Shah, T.C. Damen, C.W. Tu, T.Y. Chang, D.A.B. Miller, J.E. Henry, R.F. Kopf, N. Sauer and A.E. DiGiovanni, Phys. Rev. B 40 (1989) 3028. [4 ] J. Shah, IEEE J. Quantum Electron. QE-24 (1988) 276. [ 51T. Weil and B. Vinter, J. Appl. Phys. 60 (1986) 3227. [6] H.W. Liu et al., Appl. Phys. Lett. 54 ( 1989) 2082. [ 7 ] R. Tsu, H. Kawamura and L. E&i, in: Proc. 11 th Int. Conf. on the Physics of Semiconductors, Warsaw, 1972, Ed. M. Miasek, p. 1135. [ 81 A.K. Sood, J. Menendez, M. Cardona and K. Ploog, Phys. Rev.Lett. 54 (1985) 2115. [9] B. Jusserand, D. Paquet and A. Regreny, Phys. Rev. B 30 (1984) 6245. [lo] R. Fuchs and K.L. Kliewer, Phys. Rev. A 140( 1965) 2076. [ 111 R. Lassnig, Phys. Rev. B 30 ( 1984) 7 132.