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Effects of residual doping on the quantum confined Stark effect in p-i-n multiple quantum well structures
im*~,
Surface Science 267 (1992) 518-522 North-Holland
surface
science
Effects of residual doping on the quantum confined Stark effect in p - i - n multiple quantum well structures T. Tezuka, A. Kurobe 1, y. Ashizawa Toshiba R&D Center, I Komukai Toshiba-cho, Saiwat-ku, Kawasaki 210, Japan
H. Yoshida and M. N a k a m u r a Optoelectronics Technology Research Corp., 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 210, Japan Received 2 June 1991; accepted for publication 28 June 1991
Photocurrent spectra and time resolved photoluminescence for p - i - n diodes which have multiple quantum well structures in the i-region have been investigated. Anomalous features characterized by a pair of shoulders were observed in the photocurrer~t spectra. Suppression of sequential resonant tunneling was also deduced from a rate equation analysis of the photoluminescence decay tilt e. These indicate that excitonic levels in the multiple quantum well structures are spread by a non-uniform electric field across the i-region caused by residual doping.
I. Introduction The quantum confined Stark effect (QCSE) in p - i - n diodes with multiple quantum well (MQW) structures is widely applied to opto-electronic devices such as optical modulators [1-5]. It has been theoretically pointed out that residual doping in the i-region, where the MQW structure is grown, results in a spread of excitonic energy shifts in different wells because it produces a non-uniform electric field across the i-region as shown in fig. l a. For example, residual doping of 1 x 1016 c m - 3 in the Al0.aGa0.7As (10 nm)/GaAs (10 nm) MQW structure with 10 wells spreads the excitonic energy shifts over half of the average peak shift [6]. Residual doping of the i-region strongly depends on the growth method and conditions as well as the materials of--"-'-'wmu. the i-region consists. In a MOCVD grown AIGaAs/GaAs MQW, residual doping is reported to be relatively high (1015-10~6 cm -3) because of carbon incorporai Present address: Toshiba Cambridge Research Centre, 260 Cambrid,;e Science Park, Milton Road, Cambridge, CB4 4WE, Ukex.
tion during the growth process of AIGaAs barriers [7,8]. Although broadening of the excitonic absorption peak and suppression of he peal: shift, due to the spread of excitonic energy shifts, degrade the devices, to our knowledge, no quanti tative analysis of experiments has been made on the effects of residual doping in p-i(MQW)-r;,
~
I ~-._------'7 ! ~ ' \
WAVELENGTH
[0)
{bl
Fig. 1. Schematic diagram of the effects of residual doping in the i-region. (a) Band bending with increasing residual doping of i-region. (b) Solid lines: photocurrent spectra which originate in each well, located in the strongest,middle and the weakest fields in the MQW. Broken line: expected photocurrent spectrum for MQW.
0039-6028/92/$05.00 'O 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation. All rights reserved
T. Tezuka et aL / Residual doping in p - i - n MQW's
diodes. This paper reports anomalous excitonic features in the photocurrent spectra for the p - i - n diodes with Al0.3Ga0.vAs/GaAs MQW structures. Suppression of sequential resonant tunneling is also discussed. We show that the spread of excitonic energy shifts in the MQW, which originated from residual doping, reasonably explains experimental results.
2. Experiments
Samples grown by low pressure MOCVD consisted of 1.9 /zm thick n+-Alo.3Ga0.vAs cladding layers, 31 nm thick i-Al0.3Ga0.TAS spacer layers, i-Al0.3Ga0.TAS/GaAs MQW's, 63 nm i-Al0.3 Ga0.7As spacer layers, 1.9 /zm thick p+Al0.3Ga0.7As cladding layers and 0.5 /zm thick p +-GaAs cap layers. Three kinds of samples which had 10, 50 and 100 wells were prepared. The barrier and well thicknesses of all samples were 12.5 and 10 nm, respectively. The residual doping of each layer was 1 x 1016 cm -3 (p-type) and 1 x 1014 cm -3 (p-type), respectively, which was determined by Hall measurements on single layers grown in the same conditions just after the growth of the diodes. The A u / C r and AuGe electrodes were deposited onto the cap layers and onto the backs of the n-GaAs substrates, respectively. The A u / C r electrodes and cap layers were removed partially to allow optical access. We have measured photocurrent spectra and time-resolved photoluminescence (PL) to investigate static and dynamic effects of residual doping, respectively. Photocurrent spectra were measured by means of standard lock-in technique employing monochromated light from a halogen lamp as a light source. In the measurements of time-re.~oived PL, samples were illuminated by a syncllronously pumped Styryl 9 dye laser pumped by the second harmonic wave of cw mode-locked YAG laser. The PL were detected by a synchroscan streak camera through a monochromator which was set to the peak wavelength of the l e - l h h exciton luminescence. All measurements were carried out at room temperature.
519
3. Photocurrent spectra
Fig. 2 shows the photocurrent spectra for the nw = 50 (n w is the number of wells) sample at several reverse biases. The single peak around 850 nm which originated from the l e - l h h exciton was broadened as the reverse bias was increased. Above 4.5 V, the anomalous feature, which was characterized by two shoulders at longer and shorter wavelengths, appeared in the spectra. The shoulder at shorter wavelength did not shift up to 5.5 V and began to shift towards the longer wavelength side above 6 V. On the other hand, the shoulder at longer wavelength monotonically shifted to the longer wavelength side. As a result, the separation between the two shoulders increased monotonically as the reverse bias increased. These anomalous features can be ascribed to the spread of the excitonic energy shifts in the MQW. Here, we neglect the effects of well-width fluctuations because the spread induced by the fluctuations, estimated from the PL spectrum at 5.5 K, was less than a quarter of the energy separation between the two shoulders. Fig. lb schematically shows the spectrum which is ex-
55 V
GoAs/A~o.3Gao.r As nw - 5 0
5V .5V z
::)
4V
m n,.
I
Iz
LIJ CE CE :D (J
-lr" n
840
860
880
WAVE LENGTI-I (nm)
Fig. 2. Photocurrent spectra for the sample with 50 wells at various reverse bias. I" Peaks or shoulders whose wavelength are plotted in fig. 3.
T. Tezuka et al. / Residual doping in p-i-n MQW's
520
GaAs p-i-n MQW 860
. -
nw-50
F-
PC peak 84
,
,
,
REVERSE
Pres=4xlOtsern'a ,
=t
,
BIAS
,
,
,
(V)
Fig. 3. ,x, o: Peaks and shoulders for the sample with 50 wells. Solid lines: upper and lower limits for the spread of excitonic levels in MQW calculated variationally.
pected when the spread is much larger than the absorption peak width of each well. In this case, shorter and longer wavelength shoulders nearly correspond to the absorption peaks of the wells to which the weakest and the strongest field is applied, respectively. The observed shoulders and peaks are plotted in fig. 3 with the calculated spread of excitonic energy shifts in the MQW. The calculation was based on the variational method assuming uniform doping concentration of the i-region ('°re,) as a unique fitting parameter[6]. The built-in potential used in the calculation was 1. ~ V, which was determined experimentally as the forward bias where no photocurrent was observed. The upper curve and lower curve indicate the excitonic levels of the wells to which the strongest and the weakest field is applied, resp~.ctiwly. A good agreement between theory and experiment was obtained when Pres = 4 × 10 ]5 cm -3. This value is comparable to the estimated average residual doping concentration of the i-region. The l e - l h h excitonic peak in the spectra for n w = lO and !00 samples revealed nn anomalous features, except for small peak shifts. By increasing the reverse bias, ,'he broadening of the peak in the spectra for the n w = 100 sample became so much larger than the peak shift that an accurate quantitative treatment was beyond the framework of this theory. Qualitatively, however, relatively large thickness of the i-region is considered to be
the origin of the small shift and large broadening of the peak because the ratio of the field dispersion to the average field in the i-region becomes larger as the thickness of the i-region becomes larger. In fact, when Pres = 4 × 1015 cm -3, the calculated excitonic energy level for the well located in the center of the MQW reveals a good agreement with the observed peak. On the other hand, the peak shifts in the spectra for the nw = 10 sample could be fitted to the excitonic energy shift for the well to which the weakest field was applied when Pres = 1.5 × 1016 cm -3. This relatively high carrier concentration is supposed to be explained by the small thickness of the MQW structure, which is comparable to the total thickness of A10.3Ga0.7As spacer layers, a n d / o r Zn diffusion from the cladding layer. Since the calculated largest field in the MQW, even at a reverse bias of 0 V, is 0.9 × 10 5 V / c m , longer wavelength side shoulders are expected to be smeared out because of the short exciton lifetime [1]. This is consistent with the observed spectra without longer wavelength side shoulders.
4. Time-resolved photoluminescence The PL decay time for the nw= 100 and 50 samples ranged from 15 to 30 ns, and decreased gradually with increasing reverse bias. The PL decay time for the n w = 100 sample was always longer than that for the n w = 50 sample because of the self-absorption effect [9] and the smaller average field. The decay time for the nw = 10 sample could not be measured because the PL from the GaAs substrate was too strong to extract the PL from the MQW. The PL decay time of n w = 50 slightly decreased around 3.5 V, with a 3 V width, whereas that of n w = 100 showed no ~l~c,h n dip. The tunneling time r t for photoexcited electrons from one well to the next was deduced tram the measured PL decay time by means of a rate equation analysis proposed by Tarucha and Ploog [10]. ~'t is shown in fig. 4. In the analysis, we assumed uniform field in the i-region, and the field-independent recombination time r c was a
T. Tezuka et al. / Residual doping in p-i-n MQW's
fitting parameter. The tunneling process is assumed to be dominated by sequential tunneling, because the barrier is thick enough to suppress tunneling out of the MQW without relaxation to the ground level of each well [10], within the reverse bias used here. When residual doping in the i-region is not negligible, the tunneling time through a barrier depends on the position of the barrier. So we have interpreted the tunneling time deduced from this analysis as the effective tunneling time which was averaged over MQW structure. To separate the resonant tunneling effect from the whole tunneling process, we introduce a resonant tunneling time Trt as Tt- 1 _ T r -t l +q.nrt - 1,
where 1"nrt is the nonresonant tunneling time through a barrier calculated by the WKB approximation [11]. rn, was fitted to "/'t above 5 V where resonance effects were supposed to be negligible (solid line in fig. 4). Enhancement of tunneling was clearly shown as a dip. We ascribed this enhancement to the resonant tunneling between the le level in one quantum well and the 2e level in the next well, since the reverse bias at the center of the dip agreed with the resonant bias. But the dip was shallower and broader than that
GaAs p-i-n MQW nw = 5 0
I
0
•
GoAs p-i-n MQW
nw -50
"7
2-
% m |
!-, I -
O
fJ I I °1~ l 0 2 4 6 8 R E V E R S E BIAS (V)
i0
Fig. 5. Dependence of resonant tunnelingrate defined in the text on applied reverse bias. The solid line is a guide to the eye.
reported elsewhere [10,12,13]. Especially, the tunneling time at 3.5 V was about two orders of magnitude larger than 16 ps, which is the estimated resonant tunneling time through a barrier [10]. This is because resonant tunneling occurs in a limited portion of the MQW due to a nonuniform field. The resonant tunneling rate ~'~ is plotted in fig. 5. rrt rapidly increases at about 1 V and goes back to zero at about 6 V with increasing reverse bias. When Pre~ = 4 × 10 ~5 cm -3, tt',e calculation revealed that the resonance region, where resonant tunneling occurs, first appears at a reverse bias of 0.5 V in the region nearest to the i - n junction, moves toward the i - p junction through the MQW and disappears at 6.5 V. This resonance behavior accounts for the dependence of ~.ffl on reverse bias very well.
5. Conclusions
o o o ~pR~o~.o..~
O
521
I
I
I
1
I
I
2
4
6
8
iO
12
REVERSE BIAS (V) Fig.4. o: Tunneling time deduced from rate equation analysis of measured PL decay time when % = 2 7 ns. Solid line: nonresonant tunneling time calculated using WKB approximation.
Anomalous features in the photocurrent spectra and small enhancement of tunneling, even at the resonant bias, in a p - i ( M Q W ) - n diode were observed. These are explained consistently taking into account the spread of excitonic shifts in MQW, which originates from residual doping of the i-region. It was confirmed experimentally that residual dopin( affects the dynamic properties of
522
T. Tezuka et al. / Residual doping in p-i-n MQW's
devices based on QCSE, as well as the static properties.
[61 D.J. Newson and A. Kurobe, Electron. Lett. 23 (1987) 439.
[7] T.F. Kuech, E. Veuhoff, T.S. Kuan, V. Deline ",nd R. Potemski, J. Cryst. Growth 77 (1986) 257.
[81 T.F. Kuech, E. Veuhoff, D.J. Wolford and J.A. Bradley, References [1] D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood and C.A. Burrus, Phys. Rev. B 32 (1985) 1043. [2] D.A.B. Miller, Surf. Sci. 174 (1986) 221. [31 P.J. Bradley, M. Whitehead, G. Parry, P. Mistry and J.S. Roberts, Appi. Opt. 28 (1989) 1560. [4] P.J. Bradley, G. Parry and J.S. Roberts, Electron. Lett. 25 (1989) 1349. [5] Li Chen, K.C. P,ajkumar and A. Madhukar, Appl. Phys. Lett. 57 (1990) 2478.
Inst. Phys. Conf. Ser. No. 74, ch. 3 (1984) 181.
[91 P. Asbeck, J. Appl. Phys. 48 (1977) 820. [10] S. Tarucha and K. Ploog, Phys. Rev. B 39 (1989) 5353. [111 T.B. Norris, X.J. Song, W.J. Schaff, L.F. Eastman, G. Wicks and G.A. Mcurou, Apoi. Phys. Lett. 54 (1989) 60.
[121 G. Livescu, A.M. Fox, D.A.B. Miller, T. Sizer, W.H. Knox, A.C. Gossard and J.H. English, Phys. Rev. Lett. 63 (1989) 438. [131 H. Schneider, H.T. Grahn ar.d K. yon Klitzing, Surf. Sci. 228 (1990) 362.
Surface Science 267 (1992) 518-522 North-Holland
surface
science
Effects of residual doping on the quantum confined Stark effect in p - i - n multiple quantum well structures T. Tezuka, A. Kurobe 1, y. Ashizawa Toshiba R&D Center, I Komukai Toshiba-cho, Saiwat-ku, Kawasaki 210, Japan
H. Yoshida and M. N a k a m u r a Optoelectronics Technology Research Corp., 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 210, Japan Received 2 June 1991; accepted for publication 28 June 1991
Photocurrent spectra and time resolved photoluminescence for p - i - n diodes which have multiple quantum well structures in the i-region have been investigated. Anomalous features characterized by a pair of shoulders were observed in the photocurrer~t spectra. Suppression of sequential resonant tunneling was also deduced from a rate equation analysis of the photoluminescence decay tilt e. These indicate that excitonic levels in the multiple quantum well structures are spread by a non-uniform electric field across the i-region caused by residual doping.
I. Introduction The quantum confined Stark effect (QCSE) in p - i - n diodes with multiple quantum well (MQW) structures is widely applied to opto-electronic devices such as optical modulators [1-5]. It has been theoretically pointed out that residual doping in the i-region, where the MQW structure is grown, results in a spread of excitonic energy shifts in different wells because it produces a non-uniform electric field across the i-region as shown in fig. l a. For example, residual doping of 1 x 1016 c m - 3 in the Al0.aGa0.7As (10 nm)/GaAs (10 nm) MQW structure with 10 wells spreads the excitonic energy shifts over half of the average peak shift [6]. Residual doping of the i-region strongly depends on the growth method and conditions as well as the materials of--"-'-'wmu. the i-region consists. In a MOCVD grown AIGaAs/GaAs MQW, residual doping is reported to be relatively high (1015-10~6 cm -3) because of carbon incorporai Present address: Toshiba Cambridge Research Centre, 260 Cambrid,;e Science Park, Milton Road, Cambridge, CB4 4WE, Ukex.
tion during the growth process of AIGaAs barriers [7,8]. Although broadening of the excitonic absorption peak and suppression of he peal: shift, due to the spread of excitonic energy shifts, degrade the devices, to our knowledge, no quanti tative analysis of experiments has been made on the effects of residual doping in p-i(MQW)-r;,
~
I ~-._------'7 ! ~ ' \
WAVELENGTH
[0)
{bl
Fig. 1. Schematic diagram of the effects of residual doping in the i-region. (a) Band bending with increasing residual doping of i-region. (b) Solid lines: photocurrent spectra which originate in each well, located in the strongest,middle and the weakest fields in the MQW. Broken line: expected photocurrent spectrum for MQW.
0039-6028/92/$05.00 'O 1992 - Elsevier Science Publishers B.V. and Yamada Science Foundation. All rights reserved
T. Tezuka et aL / Residual doping in p - i - n MQW's
diodes. This paper reports anomalous excitonic features in the photocurrent spectra for the p - i - n diodes with Al0.3Ga0.vAs/GaAs MQW structures. Suppression of sequential resonant tunneling is also discussed. We show that the spread of excitonic energy shifts in the MQW, which originated from residual doping, reasonably explains experimental results.
2. Experiments
Samples grown by low pressure MOCVD consisted of 1.9 /zm thick n+-Alo.3Ga0.vAs cladding layers, 31 nm thick i-Al0.3Ga0.TAS spacer layers, i-Al0.3Ga0.TAS/GaAs MQW's, 63 nm i-Al0.3 Ga0.7As spacer layers, 1.9 /zm thick p+Al0.3Ga0.7As cladding layers and 0.5 /zm thick p +-GaAs cap layers. Three kinds of samples which had 10, 50 and 100 wells were prepared. The barrier and well thicknesses of all samples were 12.5 and 10 nm, respectively. The residual doping of each layer was 1 x 1016 cm -3 (p-type) and 1 x 1014 cm -3 (p-type), respectively, which was determined by Hall measurements on single layers grown in the same conditions just after the growth of the diodes. The A u / C r and AuGe electrodes were deposited onto the cap layers and onto the backs of the n-GaAs substrates, respectively. The A u / C r electrodes and cap layers were removed partially to allow optical access. We have measured photocurrent spectra and time-resolved photoluminescence (PL) to investigate static and dynamic effects of residual doping, respectively. Photocurrent spectra were measured by means of standard lock-in technique employing monochromated light from a halogen lamp as a light source. In the measurements of time-re.~oived PL, samples were illuminated by a syncllronously pumped Styryl 9 dye laser pumped by the second harmonic wave of cw mode-locked YAG laser. The PL were detected by a synchroscan streak camera through a monochromator which was set to the peak wavelength of the l e - l h h exciton luminescence. All measurements were carried out at room temperature.
519
3. Photocurrent spectra
Fig. 2 shows the photocurrent spectra for the nw = 50 (n w is the number of wells) sample at several reverse biases. The single peak around 850 nm which originated from the l e - l h h exciton was broadened as the reverse bias was increased. Above 4.5 V, the anomalous feature, which was characterized by two shoulders at longer and shorter wavelengths, appeared in the spectra. The shoulder at shorter wavelength did not shift up to 5.5 V and began to shift towards the longer wavelength side above 6 V. On the other hand, the shoulder at longer wavelength monotonically shifted to the longer wavelength side. As a result, the separation between the two shoulders increased monotonically as the reverse bias increased. These anomalous features can be ascribed to the spread of the excitonic energy shifts in the MQW. Here, we neglect the effects of well-width fluctuations because the spread induced by the fluctuations, estimated from the PL spectrum at 5.5 K, was less than a quarter of the energy separation between the two shoulders. Fig. lb schematically shows the spectrum which is ex-
55 V
GoAs/A~o.3Gao.r As nw - 5 0
5V .5V z
::)
4V
m n,.
I
Iz
LIJ CE CE :D (J
-lr" n
840
860
880
WAVE LENGTI-I (nm)
Fig. 2. Photocurrent spectra for the sample with 50 wells at various reverse bias. I" Peaks or shoulders whose wavelength are plotted in fig. 3.
T. Tezuka et al. / Residual doping in p-i-n MQW's
520
GaAs p-i-n MQW 860
. -
nw-50
F-
PC peak 84
,
,
,
REVERSE
Pres=4xlOtsern'a ,
=t
,
BIAS
,
,
,
(V)
Fig. 3. ,x, o: Peaks and shoulders for the sample with 50 wells. Solid lines: upper and lower limits for the spread of excitonic levels in MQW calculated variationally.
pected when the spread is much larger than the absorption peak width of each well. In this case, shorter and longer wavelength shoulders nearly correspond to the absorption peaks of the wells to which the weakest and the strongest field is applied, respectively. The observed shoulders and peaks are plotted in fig. 3 with the calculated spread of excitonic energy shifts in the MQW. The calculation was based on the variational method assuming uniform doping concentration of the i-region ('°re,) as a unique fitting parameter[6]. The built-in potential used in the calculation was 1. ~ V, which was determined experimentally as the forward bias where no photocurrent was observed. The upper curve and lower curve indicate the excitonic levels of the wells to which the strongest and the weakest field is applied, resp~.ctiwly. A good agreement between theory and experiment was obtained when Pres = 4 × 10 ]5 cm -3. This value is comparable to the estimated average residual doping concentration of the i-region. The l e - l h h excitonic peak in the spectra for n w = lO and !00 samples revealed nn anomalous features, except for small peak shifts. By increasing the reverse bias, ,'he broadening of the peak in the spectra for the n w = 100 sample became so much larger than the peak shift that an accurate quantitative treatment was beyond the framework of this theory. Qualitatively, however, relatively large thickness of the i-region is considered to be
the origin of the small shift and large broadening of the peak because the ratio of the field dispersion to the average field in the i-region becomes larger as the thickness of the i-region becomes larger. In fact, when Pres = 4 × 1015 cm -3, the calculated excitonic energy level for the well located in the center of the MQW reveals a good agreement with the observed peak. On the other hand, the peak shifts in the spectra for the nw = 10 sample could be fitted to the excitonic energy shift for the well to which the weakest field was applied when Pres = 1.5 × 1016 cm -3. This relatively high carrier concentration is supposed to be explained by the small thickness of the MQW structure, which is comparable to the total thickness of A10.3Ga0.7As spacer layers, a n d / o r Zn diffusion from the cladding layer. Since the calculated largest field in the MQW, even at a reverse bias of 0 V, is 0.9 × 10 5 V / c m , longer wavelength side shoulders are expected to be smeared out because of the short exciton lifetime [1]. This is consistent with the observed spectra without longer wavelength side shoulders.
4. Time-resolved photoluminescence The PL decay time for the nw= 100 and 50 samples ranged from 15 to 30 ns, and decreased gradually with increasing reverse bias. The PL decay time for the n w = 100 sample was always longer than that for the n w = 50 sample because of the self-absorption effect [9] and the smaller average field. The decay time for the nw = 10 sample could not be measured because the PL from the GaAs substrate was too strong to extract the PL from the MQW. The PL decay time of n w = 50 slightly decreased around 3.5 V, with a 3 V width, whereas that of n w = 100 showed no ~l~c,h n dip. The tunneling time r t for photoexcited electrons from one well to the next was deduced tram the measured PL decay time by means of a rate equation analysis proposed by Tarucha and Ploog [10]. ~'t is shown in fig. 4. In the analysis, we assumed uniform field in the i-region, and the field-independent recombination time r c was a
T. Tezuka et al. / Residual doping in p-i-n MQW's
fitting parameter. The tunneling process is assumed to be dominated by sequential tunneling, because the barrier is thick enough to suppress tunneling out of the MQW without relaxation to the ground level of each well [10], within the reverse bias used here. When residual doping in the i-region is not negligible, the tunneling time through a barrier depends on the position of the barrier. So we have interpreted the tunneling time deduced from this analysis as the effective tunneling time which was averaged over MQW structure. To separate the resonant tunneling effect from the whole tunneling process, we introduce a resonant tunneling time Trt as Tt- 1 _ T r -t l +q.nrt - 1,
where 1"nrt is the nonresonant tunneling time through a barrier calculated by the WKB approximation [11]. rn, was fitted to "/'t above 5 V where resonance effects were supposed to be negligible (solid line in fig. 4). Enhancement of tunneling was clearly shown as a dip. We ascribed this enhancement to the resonant tunneling between the le level in one quantum well and the 2e level in the next well, since the reverse bias at the center of the dip agreed with the resonant bias. But the dip was shallower and broader than that
GaAs p-i-n MQW nw = 5 0
I
0
•
GoAs p-i-n MQW
nw -50
"7
2-
% m |
!-, I -
O
fJ I I °1~ l 0 2 4 6 8 R E V E R S E BIAS (V)
i0
Fig. 5. Dependence of resonant tunnelingrate defined in the text on applied reverse bias. The solid line is a guide to the eye.
reported elsewhere [10,12,13]. Especially, the tunneling time at 3.5 V was about two orders of magnitude larger than 16 ps, which is the estimated resonant tunneling time through a barrier [10]. This is because resonant tunneling occurs in a limited portion of the MQW due to a nonuniform field. The resonant tunneling rate ~'~ is plotted in fig. 5. rrt rapidly increases at about 1 V and goes back to zero at about 6 V with increasing reverse bias. When Pre~ = 4 × 10 ~5 cm -3, tt',e calculation revealed that the resonance region, where resonant tunneling occurs, first appears at a reverse bias of 0.5 V in the region nearest to the i - n junction, moves toward the i - p junction through the MQW and disappears at 6.5 V. This resonance behavior accounts for the dependence of ~.ffl on reverse bias very well.
5. Conclusions
o o o ~pR~o~.o..~
O
521
I
I
I
1
I
I
2
4
6
8
iO
12
REVERSE BIAS (V) Fig.4. o: Tunneling time deduced from rate equation analysis of measured PL decay time when % = 2 7 ns. Solid line: nonresonant tunneling time calculated using WKB approximation.
Anomalous features in the photocurrent spectra and small enhancement of tunneling, even at the resonant bias, in a p - i ( M Q W ) - n diode were observed. These are explained consistently taking into account the spread of excitonic shifts in MQW, which originates from residual doping of the i-region. It was confirmed experimentally that residual dopin( affects the dynamic properties of
522
T. Tezuka et al. / Residual doping in p-i-n MQW's
devices based on QCSE, as well as the static properties.
[61 D.J. Newson and A. Kurobe, Electron. Lett. 23 (1987) 439.
[7] T.F. Kuech, E. Veuhoff, T.S. Kuan, V. Deline ",nd R. Potemski, J. Cryst. Growth 77 (1986) 257.
[81 T.F. Kuech, E. Veuhoff, D.J. Wolford and J.A. Bradley, References [1] D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood and C.A. Burrus, Phys. Rev. B 32 (1985) 1043. [2] D.A.B. Miller, Surf. Sci. 174 (1986) 221. [31 P.J. Bradley, M. Whitehead, G. Parry, P. Mistry and J.S. Roberts, Appi. Opt. 28 (1989) 1560. [4] P.J. Bradley, G. Parry and J.S. Roberts, Electron. Lett. 25 (1989) 1349. [5] Li Chen, K.C. P,ajkumar and A. Madhukar, Appl. Phys. Lett. 57 (1990) 2478.
Inst. Phys. Conf. Ser. No. 74, ch. 3 (1984) 181.
[91 P. Asbeck, J. Appl. Phys. 48 (1977) 820. [10] S. Tarucha and K. Ploog, Phys. Rev. B 39 (1989) 5353. [111 T.B. Norris, X.J. Song, W.J. Schaff, L.F. Eastman, G. Wicks and G.A. Mcurou, Apoi. Phys. Lett. 54 (1989) 60.
[121 G. Livescu, A.M. Fox, D.A.B. Miller, T. Sizer, W.H. Knox, A.C. Gossard and J.H. English, Phys. Rev. Lett. 63 (1989) 438. [131 H. Schneider, H.T. Grahn ar.d K. yon Klitzing, Surf. Sci. 228 (1990) 362.