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Electrical and optical bistability in [111] GaInAs–GaAs piezo-electric quantum wells
Superlattices and Microstructures, Vol. 21, No. 1, 1997
Electrical and optical bistability in [111] GaInAs–GaAs piezo-electric quantum wells L. R. Wilson, D. J. Mowbray, M. S. Skolnick, D. W. Peggs Department of Physics, University of Sheffield, Sheffield S3 7RH, U.K.
G. J. Rees, J. P. R. David, R. Grey, G. Hill, M. A. Pate Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 4DU, U.K.
(Received 15 July 1996) Optically induced bistability in the electrical and optical characteristics of a (111)B piezoelectric strained In0.15 Ga0.85 As–GaAs single quantum well (SQW) p-i-n structure is reported. We demonstrate that the bistability results from photo-induced charge build-up in the SQW. Charge build-up is enhanced relative to a (100) structure as a consequence of the modified band profile due to the large internal piezo-electric field. A region of hysteresis is observed in the low temperature current–voltage characteristics of the device under illumination. Dependent upon the sweep direction, for a given voltage the device is stable in one of two states, corresponding to either low or high current. Optical measurements demonstrate that the two current states correspond to very different electron densities in the SQW. An electron accumulation of n s ≈ 3.5 × 1011 cm−2 occurs with the sample at 0 V in the low current state. For the high current state there is negligible electron accumulation in the SQW. Using these values we have modelled the band profiles of the structure in the two bistable states. c 1997 Academic Press Limited
There is considerable interest in the physics of charge accumulation in low dimensional systems. Intrinsic bistability resulting from space charge formation in double barrier resonant tunnelling structures has been extensively studied [1]. Other novel non-resonant structures, such as that described by Zrenner et al. [2], have also been shown to exhibit intrinsic bistability due to carrier accumulation in the device. Bistability has also been achieved in a self-electro-optic device (SEED) [3]. The SEED utilizes the electric field induced shift in absorption of a multi-quantum well structure, which arises as a consequence of the quantum confined Stark effect. In this letter we report the observation of both electrical and optical bistability in a strained layer, piezoelectric SQW. The proposed mechanism for this bistability involves the capture of electrons in the SQW when the device is illuminated under low bias. The strain in the quantum well leads to the formation of a large internal piezo-electric field, of a sign which opposes the built-in p-i-n field. This results in an enhancement of the electron capture and accumulation in the SQW, due to the modified band profile, which in turn leads to further enhancement and the observed bistability. .
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The SQW is situated at the centre of the intrinsic region of a p-i-n structure, thus allowing the study of its electrical and optical characteristics as a function of applied voltage. Hysteresis is observed in the current–voltage (I –V ) characteristics under illumination, with photoluminescence (PL) and magneto-PL measurements clearly demonstrating electron accumulation in the SQW with the sample in the low current state. The bistable mechanism we observe is similar to that discussed by Zrenner et al. [2]. However, the high quality of our sample and, in addition, magnetic field measurements allow the accurate determination of both the density and sign of the carriers involved in the bistable process. Thus we can accurately model the band profiles of the structure in both of the bistable states. The sample was fabricated by molecular beam epitaxy and grown on a n + (111)B GaAs substrate misoriented 2◦ toward the (211) axis. In order of growth the layers consist of: 1 µm n + GaAs, 0.610 µm GaAs ˚ In0.15 Ga0.85 As SQW is incorporated centrally and 0.3 µm p + GaAs. Mesa intrinsic region in which the 100 A photodiodes of diameter 400 µm were fabricated allowing optical access through an annular contact on the p + region. ˚ Low temperature I –V characteristics, both with and without optical excitation from a Ti:S laser at 7800 A, are shown in Fig. 1. With no illumination the sample exhibits typical diode-like characteristics with a small reverse bias leakage current and a reverse breakdown voltage of ∼ −20 V, as shown in Fig. 1(a). However, under illumination with light of energy greater than the GaAs bandgap, a region of hysteresis is observed in the I –V characteristics. For applied voltages in this region there are two possible, stable current states; a low current state on the voltage downsweep branch and a high current state on the voltage upsweep branch. For any voltage within this hysteresis region a transition from the low current to the high current state may be induced by a brief interruption of the optical excitation. As the excitation power density is decreased, the range of voltages over which the hysteresis is observed decreases, eventually collapsing to a step feature for power densities < 0.1 W cm−2 . No hysteresis is observed if the laser excites electrons and holes directly into ˚ indicating that the bistability requires the photocreation of ˚ > λex > 8200 A), the InGaAs SQW (9500 A carriers in the GaAs barriers and subsequent capture by the SQW. PL spectra recorded for voltages in the hysteresis region enable the bistability to be understood. Fig. 2 shows PL spectra taken at various bistable voltages, with the sample in both the low and high current state for each voltage. The PL spectra with the sample in the high current state have a typical linewidth of 5 meV, probably arising from alloy and well width fluctuations. In contrast, PL spectra with the sample in the low current state are considerably broader with a tail to higher energy, indicative of carrier accumulation in the SQW [4]. In a perfect quantum well containing a large number of electrons but relatively few photoexcited holes, only vertical transitions close to k = 0 are allowed. However, the presence of disorder (e.g. alloy or well width fluctuations) partially lifts the vertical transition selection rule and recombination from all electron states up to the Fermi energy, E F , may be observed. In the present sample this gives rise to the weak, high energy tail in the PL spectra. The relative weakness of this high energy tail is characteristic of a quantum well with a low degree of disorder [4]. The position of the Fermi-edge cut-off E F is marked on the low current spectra. The energy difference between the PL peak and E F provides an estimate for the Fermi energy, which is found to increase from 8.0 meV at an applied voltage of +0.7 V to 13.8 meV at 0 V. Using an electron effective mass m ∗e = 0.07m 0 , this corresponds to an increase in the electron density in the SQW from n s ≈ 2.3 × 1011 cm−2 at +0.7 V to n s ≈ 3.9 × 1011 cm−2 at 0 V. Whilst the above measurements provide evidence for charge build up in the SQW, the sign of the charge carriers is not determined. Magneto-PL measurements confirm the presence of charge accumulation and, in addition, demonstrate that the observed behaviour is due to electron accumulation in the SQW when the sample is in the low current state. A typical magneto-PL spectrum obtained at B = 4.5 T, with the device at 0 V in the low current state, is shown in the inset to Fig. 2. The single, broad zero field PL line is split into a series of Landau level (LL) transitions, labelled (Ne , Nh ), which arise from the recombination of electrons and holes of LL indices Ne and Nh respectively [4]. Recombination between the ground state electron and hole LLs (0,0) gives rise to the dominant transition in the magneto-PL spectrum with a nominally forbidden, non.
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0.15
0.10
0.05 (a)
Current (mA)
0.00
–0.05
–0.10
–0.15
–0.20
–0.25
–0.30 –5
(b)
–4
–3
–2 –1 0 Applied voltage (V)
1
2
Fig. 1. Low temperature current–voltage characteristics, (a) without optical excitation (– – –) (b) with optical excitation from a Ti:S ˚ ——: Downsweep, device illuminated; - - - -: upsweep, device illuminated. laser, power density = 4 W cm−2 , λex = 7800 A.
Landau-number-conserving transition (1,0) observed to higher energy due to the effects of disorder. The (1,1) transition arises because of a small photocreated hole population in the Nh = 1 level. The energy separation between the two lowest energy LL transitions corresponds to a cyclotron energy h¯ ωc = h¯ eB/m ∗ , where m ∗ = 0.07m 0 . This value for the effective mass corresponds to the expected electron effective mass, m ∗e , for In0.15 Ga0.85 As. The smaller separation between the second and third LL transitions is consistent with that expected for the heavy-hole cyclotron energy. These results confirm our identification of the LL transitions. The (1,0) and (1,1) transitions are not observed for magnetic fields greater than 6.75 T, due to the depopulation of the Ne = 1 LL level at this field. Using the LL degeneracy, 2eB/ h, this gives a value for the electron density of (3.4 ± 0.2) × 1011 cm−2 , in good agreement with the value obtained from the linewidth of the zero magnetic field PL spectrum. With the sample in the high current state the PL shows no splitting and exhibits a diamagnetic shift with increasing magnetic field, consistent with excitonic behaviour and indicating negligible carrier accumulation in this state [5]. PL and magneto-PL measurements clearly demonstrate that the two current states involved in the bistability are associated with very different electron densities in the SQW. Using the values for the electron densities obtained from our measurements we can self-consistently model the band profiles of the structure corresponding to the two states. The piezo-electric field of 170 kV cm−1 gives rise to the large change in slope of the band edge profiles at the left and right hand boundaries of the SQW. Figure 3(a) shows the band profile of the structure at 0 V with no charge in the SQW, corresponding to the high current state. Figure 3(b) .
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Superlattices and Microstructures, Vol. 21, No. 1, 1997 (0,0)
(1,0) (1,1)
B = 4.5 T ×10 1.33
1.35
1.37
1.39
PL intensity (arb. units)
High current Low current EF 0.0 V
EF +0.4 V
EF +0.7 V 1.32
1.33
1.34
1.35 1.36 Energy (eV)
1.37
Fig. 2. PL spectra at 4.2 K for various bistable voltages. In the low current state a broad PL band, arising from recombination of electrons in states E = 0 up to E F , is observed. The inset shows a typical magneto-PL spectrum obtained in the low current state where the zero field spectrum has split into Landau level transitions.
shows the calculated, self-consistent band profile at 0 V with the sample in the low current state and with the experimentally determined SQW electron density of 3.4 × 1011 cm−2 . As shown in the expanded boxes of Fig. 3, electron capture is considerably enhanced in the piezo-electric SQW, relative to a conventional (100) grown sample. This is a consequence of the larger potential barrier to the right hand side of the SQW, resulting from the internal piezo-electric field which is in the opposite sense to the built in p-i-n field. Light incident on the sample via the p + contact region predominantly creates electrons. These electrons diffuse through the intrinsic region and, as the voltage is swept from +1.5 V to 0 V, become trapped in the SQW, giving rise to the band profile of Fig. 3(b) which corresponds to the low current branch of the I –V characteristics. The current is reduced in this state because now only those carriers photocreated in the region to the right of the SQW are swept out to the contacts by the remaining electric field. No further electron accumulation occurs beyond the band profile of Fig. 3(b) as the intrinsic region to the left of the SQW is almost flat. The small number of electrons which continue to be captured replenish those that are lost from the SQW by tunnelling or
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N
Energy (eV)
cb
(a) High current state
vb
cb
(b) Low current state vb –3000
0 Distance (Å)
3000
Fig. 3. (a) Calculated band profile of the structure at 0 V. (b) Self-consistent band profile of the structure at 0 V in the low current state. The experimentally determined value for the electron density in the SQW of 3.4 × 1011 cm−2 is used in the calculation.
recombination. With increasing reverse bias the electric field in the region to the right of the SQW increases, leading to a decrease in the effective width of the potential barrier on the right hand side of the well. Eventually significant electron tunnelling out of the well can occur, the well rapidly empties, and the device switches to the high current state. When the bias is swept from negative to positive the band profile is of a form similar to that shown in Fig. 3(a), which does not permit significant charge build up and the device remains in the high current, zero accumulation state. Our band profile modelling demonstrates that two distinct states exist for all applied voltages throughout the region of hysteresis, consistent with the observation of bistability. In conclusion, we have studied a simple piezo-electric SQW p-i-n structure that exhibits both electrical and optical bistability under illumination. The large internal piezo-electric field results in a band profile which enhances electron capture and accumulation by the SQW resulting in the observed bistability. Optical measurements provide conclusive evidence for the presence of a two-dimensional electron gas in one of the states, and allow the electron density to be determined. Using the experimentally determined electron densities, the band profiles of the structure have been modelled self-consistently.
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Acknowledgements—We wish to acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC), U.K. Grant GR/H45773. One of us (DJM) acknowledges the receipt of an EPSRC Advanced Fellowship.
References .
[1] }V. J. Goldman, D. C. Tsui and J. E. Cunningham, Phys. Rev. B 35, 9387 (1987). } Zrenner, J. M. Worlock, L. T. Florez, J. P. Harbison and S. A. Lyon, Appl. Phys. Lett. 56, 18 (1990). [2] A. } A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood and C. A. Burrus, [3] D. Appl. Phys. Lett. 45, 13 (1984). } S. Skolnick, K. J. Nash, M. K. Saker, S. J. Bass, P. A. Claxton and J. S. Roberts, Appl. Phys. Lett. 50, [4] M. 26 (1987). } C. Rogers, J. Singleton, R. J. Nicholas, C. T. Foxon and K. Woodbridge, Phys. Rev. B 34, 4002 (1986). [5] D. .
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Electrical and optical bistability in [111] GaInAs–GaAs piezo-electric quantum wells L. R. Wilson, D. J. Mowbray, M. S. Skolnick, D. W. Peggs Department of Physics, University of Sheffield, Sheffield S3 7RH, U.K.
G. J. Rees, J. P. R. David, R. Grey, G. Hill, M. A. Pate Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 4DU, U.K.
(Received 15 July 1996) Optically induced bistability in the electrical and optical characteristics of a (111)B piezoelectric strained In0.15 Ga0.85 As–GaAs single quantum well (SQW) p-i-n structure is reported. We demonstrate that the bistability results from photo-induced charge build-up in the SQW. Charge build-up is enhanced relative to a (100) structure as a consequence of the modified band profile due to the large internal piezo-electric field. A region of hysteresis is observed in the low temperature current–voltage characteristics of the device under illumination. Dependent upon the sweep direction, for a given voltage the device is stable in one of two states, corresponding to either low or high current. Optical measurements demonstrate that the two current states correspond to very different electron densities in the SQW. An electron accumulation of n s ≈ 3.5 × 1011 cm−2 occurs with the sample at 0 V in the low current state. For the high current state there is negligible electron accumulation in the SQW. Using these values we have modelled the band profiles of the structure in the two bistable states. c 1997 Academic Press Limited
There is considerable interest in the physics of charge accumulation in low dimensional systems. Intrinsic bistability resulting from space charge formation in double barrier resonant tunnelling structures has been extensively studied [1]. Other novel non-resonant structures, such as that described by Zrenner et al. [2], have also been shown to exhibit intrinsic bistability due to carrier accumulation in the device. Bistability has also been achieved in a self-electro-optic device (SEED) [3]. The SEED utilizes the electric field induced shift in absorption of a multi-quantum well structure, which arises as a consequence of the quantum confined Stark effect. In this letter we report the observation of both electrical and optical bistability in a strained layer, piezoelectric SQW. The proposed mechanism for this bistability involves the capture of electrons in the SQW when the device is illuminated under low bias. The strain in the quantum well leads to the formation of a large internal piezo-electric field, of a sign which opposes the built-in p-i-n field. This results in an enhancement of the electron capture and accumulation in the SQW, due to the modified band profile, which in turn leads to further enhancement and the observed bistability. .
.
.
.
.
.
0749–6036/97/010113 + 06 $25.00/0
SM960180
c 1997 Academic Press Limited
114
Superlattices and Microstructures, Vol. 21, No. 1, 1997
The SQW is situated at the centre of the intrinsic region of a p-i-n structure, thus allowing the study of its electrical and optical characteristics as a function of applied voltage. Hysteresis is observed in the current–voltage (I –V ) characteristics under illumination, with photoluminescence (PL) and magneto-PL measurements clearly demonstrating electron accumulation in the SQW with the sample in the low current state. The bistable mechanism we observe is similar to that discussed by Zrenner et al. [2]. However, the high quality of our sample and, in addition, magnetic field measurements allow the accurate determination of both the density and sign of the carriers involved in the bistable process. Thus we can accurately model the band profiles of the structure in both of the bistable states. The sample was fabricated by molecular beam epitaxy and grown on a n + (111)B GaAs substrate misoriented 2◦ toward the (211) axis. In order of growth the layers consist of: 1 µm n + GaAs, 0.610 µm GaAs ˚ In0.15 Ga0.85 As SQW is incorporated centrally and 0.3 µm p + GaAs. Mesa intrinsic region in which the 100 A photodiodes of diameter 400 µm were fabricated allowing optical access through an annular contact on the p + region. ˚ Low temperature I –V characteristics, both with and without optical excitation from a Ti:S laser at 7800 A, are shown in Fig. 1. With no illumination the sample exhibits typical diode-like characteristics with a small reverse bias leakage current and a reverse breakdown voltage of ∼ −20 V, as shown in Fig. 1(a). However, under illumination with light of energy greater than the GaAs bandgap, a region of hysteresis is observed in the I –V characteristics. For applied voltages in this region there are two possible, stable current states; a low current state on the voltage downsweep branch and a high current state on the voltage upsweep branch. For any voltage within this hysteresis region a transition from the low current to the high current state may be induced by a brief interruption of the optical excitation. As the excitation power density is decreased, the range of voltages over which the hysteresis is observed decreases, eventually collapsing to a step feature for power densities < 0.1 W cm−2 . No hysteresis is observed if the laser excites electrons and holes directly into ˚ indicating that the bistability requires the photocreation of ˚ > λex > 8200 A), the InGaAs SQW (9500 A carriers in the GaAs barriers and subsequent capture by the SQW. PL spectra recorded for voltages in the hysteresis region enable the bistability to be understood. Fig. 2 shows PL spectra taken at various bistable voltages, with the sample in both the low and high current state for each voltage. The PL spectra with the sample in the high current state have a typical linewidth of 5 meV, probably arising from alloy and well width fluctuations. In contrast, PL spectra with the sample in the low current state are considerably broader with a tail to higher energy, indicative of carrier accumulation in the SQW [4]. In a perfect quantum well containing a large number of electrons but relatively few photoexcited holes, only vertical transitions close to k = 0 are allowed. However, the presence of disorder (e.g. alloy or well width fluctuations) partially lifts the vertical transition selection rule and recombination from all electron states up to the Fermi energy, E F , may be observed. In the present sample this gives rise to the weak, high energy tail in the PL spectra. The relative weakness of this high energy tail is characteristic of a quantum well with a low degree of disorder [4]. The position of the Fermi-edge cut-off E F is marked on the low current spectra. The energy difference between the PL peak and E F provides an estimate for the Fermi energy, which is found to increase from 8.0 meV at an applied voltage of +0.7 V to 13.8 meV at 0 V. Using an electron effective mass m ∗e = 0.07m 0 , this corresponds to an increase in the electron density in the SQW from n s ≈ 2.3 × 1011 cm−2 at +0.7 V to n s ≈ 3.9 × 1011 cm−2 at 0 V. Whilst the above measurements provide evidence for charge build up in the SQW, the sign of the charge carriers is not determined. Magneto-PL measurements confirm the presence of charge accumulation and, in addition, demonstrate that the observed behaviour is due to electron accumulation in the SQW when the sample is in the low current state. A typical magneto-PL spectrum obtained at B = 4.5 T, with the device at 0 V in the low current state, is shown in the inset to Fig. 2. The single, broad zero field PL line is split into a series of Landau level (LL) transitions, labelled (Ne , Nh ), which arise from the recombination of electrons and holes of LL indices Ne and Nh respectively [4]. Recombination between the ground state electron and hole LLs (0,0) gives rise to the dominant transition in the magneto-PL spectrum with a nominally forbidden, non.
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Superlattices and Microstructures, Vol. 21, No. 1, 1997
115
0.15
0.10
0.05 (a)
Current (mA)
0.00
–0.05
–0.10
–0.15
–0.20
–0.25
–0.30 –5
(b)
–4
–3
–2 –1 0 Applied voltage (V)
1
2
Fig. 1. Low temperature current–voltage characteristics, (a) without optical excitation (– – –) (b) with optical excitation from a Ti:S ˚ ——: Downsweep, device illuminated; - - - -: upsweep, device illuminated. laser, power density = 4 W cm−2 , λex = 7800 A.
Landau-number-conserving transition (1,0) observed to higher energy due to the effects of disorder. The (1,1) transition arises because of a small photocreated hole population in the Nh = 1 level. The energy separation between the two lowest energy LL transitions corresponds to a cyclotron energy h¯ ωc = h¯ eB/m ∗ , where m ∗ = 0.07m 0 . This value for the effective mass corresponds to the expected electron effective mass, m ∗e , for In0.15 Ga0.85 As. The smaller separation between the second and third LL transitions is consistent with that expected for the heavy-hole cyclotron energy. These results confirm our identification of the LL transitions. The (1,0) and (1,1) transitions are not observed for magnetic fields greater than 6.75 T, due to the depopulation of the Ne = 1 LL level at this field. Using the LL degeneracy, 2eB/ h, this gives a value for the electron density of (3.4 ± 0.2) × 1011 cm−2 , in good agreement with the value obtained from the linewidth of the zero magnetic field PL spectrum. With the sample in the high current state the PL shows no splitting and exhibits a diamagnetic shift with increasing magnetic field, consistent with excitonic behaviour and indicating negligible carrier accumulation in this state [5]. PL and magneto-PL measurements clearly demonstrate that the two current states involved in the bistability are associated with very different electron densities in the SQW. Using the values for the electron densities obtained from our measurements we can self-consistently model the band profiles of the structure corresponding to the two states. The piezo-electric field of 170 kV cm−1 gives rise to the large change in slope of the band edge profiles at the left and right hand boundaries of the SQW. Figure 3(a) shows the band profile of the structure at 0 V with no charge in the SQW, corresponding to the high current state. Figure 3(b) .
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Superlattices and Microstructures, Vol. 21, No. 1, 1997 (0,0)
(1,0) (1,1)
B = 4.5 T ×10 1.33
1.35
1.37
1.39
PL intensity (arb. units)
High current Low current EF 0.0 V
EF +0.4 V
EF +0.7 V 1.32
1.33
1.34
1.35 1.36 Energy (eV)
1.37
Fig. 2. PL spectra at 4.2 K for various bistable voltages. In the low current state a broad PL band, arising from recombination of electrons in states E = 0 up to E F , is observed. The inset shows a typical magneto-PL spectrum obtained in the low current state where the zero field spectrum has split into Landau level transitions.
shows the calculated, self-consistent band profile at 0 V with the sample in the low current state and with the experimentally determined SQW electron density of 3.4 × 1011 cm−2 . As shown in the expanded boxes of Fig. 3, electron capture is considerably enhanced in the piezo-electric SQW, relative to a conventional (100) grown sample. This is a consequence of the larger potential barrier to the right hand side of the SQW, resulting from the internal piezo-electric field which is in the opposite sense to the built in p-i-n field. Light incident on the sample via the p + contact region predominantly creates electrons. These electrons diffuse through the intrinsic region and, as the voltage is swept from +1.5 V to 0 V, become trapped in the SQW, giving rise to the band profile of Fig. 3(b) which corresponds to the low current branch of the I –V characteristics. The current is reduced in this state because now only those carriers photocreated in the region to the right of the SQW are swept out to the contacts by the remaining electric field. No further electron accumulation occurs beyond the band profile of Fig. 3(b) as the intrinsic region to the left of the SQW is almost flat. The small number of electrons which continue to be captured replenish those that are lost from the SQW by tunnelling or
Superlattices and Microstructures, Vol. 21, No. 1, 1997 P
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N
Energy (eV)
cb
(a) High current state
vb
cb
(b) Low current state vb –3000
0 Distance (Å)
3000
Fig. 3. (a) Calculated band profile of the structure at 0 V. (b) Self-consistent band profile of the structure at 0 V in the low current state. The experimentally determined value for the electron density in the SQW of 3.4 × 1011 cm−2 is used in the calculation.
recombination. With increasing reverse bias the electric field in the region to the right of the SQW increases, leading to a decrease in the effective width of the potential barrier on the right hand side of the well. Eventually significant electron tunnelling out of the well can occur, the well rapidly empties, and the device switches to the high current state. When the bias is swept from negative to positive the band profile is of a form similar to that shown in Fig. 3(a), which does not permit significant charge build up and the device remains in the high current, zero accumulation state. Our band profile modelling demonstrates that two distinct states exist for all applied voltages throughout the region of hysteresis, consistent with the observation of bistability. In conclusion, we have studied a simple piezo-electric SQW p-i-n structure that exhibits both electrical and optical bistability under illumination. The large internal piezo-electric field results in a band profile which enhances electron capture and accumulation by the SQW resulting in the observed bistability. Optical measurements provide conclusive evidence for the presence of a two-dimensional electron gas in one of the states, and allow the electron density to be determined. Using the experimentally determined electron densities, the band profiles of the structure have been modelled self-consistently.
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Acknowledgements—We wish to acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC), U.K. Grant GR/H45773. One of us (DJM) acknowledges the receipt of an EPSRC Advanced Fellowship.
References .
[1] }V. J. Goldman, D. C. Tsui and J. E. Cunningham, Phys. Rev. B 35, 9387 (1987). } Zrenner, J. M. Worlock, L. T. Florez, J. P. Harbison and S. A. Lyon, Appl. Phys. Lett. 56, 18 (1990). [2] A. } A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood and C. A. Burrus, [3] D. Appl. Phys. Lett. 45, 13 (1984). } S. Skolnick, K. J. Nash, M. K. Saker, S. J. Bass, P. A. Claxton and J. S. Roberts, Appl. Phys. Lett. 50, [4] M. 26 (1987). } C. Rogers, J. Singleton, R. J. Nicholas, C. T. Foxon and K. Woodbridge, Phys. Rev. B 34, 4002 (1986). [5] D. .
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