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Fabrication and transport characterization of GaAs quantum dots connected with quantum wires fabricated by selective area metalorganic vapor phase epitaxy
Physica E 2 (1998) 809—814
Fabrication and transport characterization of GaAs quantum dots connected with quantum wires fabricated by selective area metalorganic vapor phase epitaxy K. Kumakura*, J. Motohisa, T. Fukui Research Center for Interface Quantum Electronics (RCIQE), Hokkaido University, North 13 West 8, Sapporo 060, Japan
Abstract GaAs wire transistors and single electron transistors (SETs) were successfully fabricated using GaAs/AlGaAs modulation doped structures grown by selective area metalorganic vapor phase epitaxy (SA-MOVPE) on (0 0 1) masked GaAs substrates. The results of magnetoresistance of wire transistors applying the negative gate bias show the one-dimensional transport. In SETs, near the pinch-off voltage, Coulomb blockade type conductance oscillations were observed up to 65 K. Coulomb gap and total capacitance CR were estimated to be 12 mV and 13 aF, respectively. Fabrication process and transport properties of the devices were described. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Selective area MOVPE; Quantum dot; Quantum wire transistor; Single electron transistor; Coulomb blockade
1. Introduction Semiconductor quantum wires (QWRs) and quantum dots (QDs) have attracted much attention for new optical device applications, such as quantum dot lasers. Many researchers have reported GaAs and In(Ga)As QD structures fabricated using selective area metalorganic vapor phase epitaxy (SA-MOVPE) [1—4] and self-organized growth [5—7]. High density In(Ga)As QDs were automati* Corresponding author. Fax: #81 11 716 6004; e-mail: [email protected].
cally formed on GaAs substrate by the strain effects, and QD lasers were reported using this selforganized growth mode [5,6]. On the other hand, new quantum functional devices which are consisting of such QWRs and QDs have attracted much attention. In particular, for the fabrication of single electron transistors (SETs) and electron wave interference devices (EWIDs), it is important to connect these QWRs and QDs with tunneling barriers, and to form the periodic modulated potential energy. SA-MOVPE is one of the useful techniques for the fabrication of these quantum nano-structures
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 1 6 5 - 9
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K. Kumakura et al. / Physica E 2 (1998) 809—814
[1], and has been applied to the fabrication of optical integrated circuits [8]. Using this selective growth, uniform QD structures can be formed by adjusting the growth conditions as well as substrate orientation and mask pattern, e.g., GaAs (0 0 1) [2—4] and GaAs (1 1 1)B [1] substrates. A QDnetwork, which is QDs connected with QWRs, was also reported in our previous study [9]. Thus, SAMOVPE is the promising formation method for future optical devices and opto-electronic integrated circuits (OEIC). The application of QDs to electron transport devices, especially single electron devices is also a very important research field for future electron devices. For the fabrication of these devices, these well-arranged QDs have to be connected to each other. To realize the SET structure, it has been attempted to fabricate quantum dot—tunnel barrier systems by molecular beam epitaxy on patterned substrates [10]. The purpose of this paper is to fabricate GaAs SETs using GaAs/AlGaAs modulation doped structures grown on the masked substrates by SAMOVPE, and clarify the transport properties. Firstly, GaAs wire transistors showed Shubnikov—de Haas (SdH) oscillations in applying the gate voltage, one-dimensional transport and controllability of effective channel width by the gate voltage. Next, SETs showed Coulomb blockade type conductance oscillation near the pinch-off voltage up to 65 K. Coulomb gap and total capacitance CR was estimated to be 12 mV and 13 aF, respectively.
2. Fabrication process and device structure Selective area (SA-) MOVPE growth was carried out using a low-pressure horizontal, RF-heated, quartz reactor system. The working pressure of 76 Torr was automatically controlled. Purified hydrogen (H ) was used as a carrier gas. The source 2 materials were trimethylgallium (TMGa), trimethylaluminum (TMAl) and 20% arsine (AsH ) in H . 3 2 The partial pressures of TMGa and TMAl were kept constant at 3.8]10~6 and 6.3]10~7 atm, respectively. The partial pressure of AsH was 3 1.3]10~4 atm for GaAs buffer layer, and
6.7]10~4 atm for Al Ga As layer to achieve 0.3 0.7 better quality, respectively. Growth rates of GaAs and Al Ga As were 0.93 and 1.5 lm/h for 0.3 0.7 planar substrates, respectively. SA-MOVPE was carried out on the masked substrates at the growth temperature of 700°C. The layer sequences are as follows; a 400 nm GaAs buffer layer, a 50 nm Al Ga As layer, a 15 nm 0.3 0.7 GaAs well layer, a 10 nm undoped Al Ga As 0.3 0.7 layer, a 50 nm n-doped Al Ga As layer, and 0.3 0.7 a 10 nm n-doped GaAs capping layer. The mobility and sheet electron concentration of two dimensional electron gas (2DEG) grown on a planar substrate were 62 000 cm2/(V s), 1.2]1012 cm~2 at 77 K, respectively. Schematic illustration of the mask pattern for SET structure (device A, S) is shown in Fig. 1a. The pattern is formed on semi-insulating (0 0 1) GaAs coated with 40 nm thick SiN layer by electron x beam lithography and wet chemical etching. The wire-like opening with three prominences aligned in the [1 1 0] direction corresponds to the channel region of SET. Fig. 1b shows SEM image after the selective growth and Fig. 1c, the schematic illustration of the device structure. The wire region consists of M1 1 1NB facet sidewalls, and M1 1 0N facet sidewalls are formed near the prominences. A (0 0 1) plane appeared on the top portion of the whole structure. Due to three prominences on the wire, the quasi one dimensional electron gas (Q-1DEG) channel has periodic variation in its width. This leads to the formation of a quantum dot near the central prominence and two tunneling barriers beside a dot which are connected to the quantum wires. For reference, the quantum wire was also grown on masked substrate without prominences (device R). The channel width of the present Q-1DEG is 400 nm by SEM observation. After the growth of these structures, source and drain Ge/Au/Ni ohmic electrodes were formed on the wide 2DEG regions (see Fig. 1b) by a lift-off process followed by alloying at 350°C for 5 min in N atmosphere. In the next step, a Schottky gate 2 consisting of an Al electrode was formed by a lift-off process on the three prominences region. Since no growth occurs on the M1 1 1NB facets, both edges of the Q-1DEG channel are exposed to air. Therefore,
K. Kumakura et al. / Physica E 2 (1998) 809—814
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3. Transport properties of GaAs Q-1DEG structure In order to investigate the transport properties of GaAs Q-1DEG structure under gate bias » , magG netoresistance was measured at 3.4 K in a device R which has no prominences. Both at » "0 V G and » "!1.25 V, the device showed clear magG netoresistance (MR) oscillations, as shown in Fig. 2. From these MR, Landau index N was L plotted as a function of the reciprocal magnetic field 1/B which gives MR maxima, and the results are shown in the inset in Fig. 2. A deviation from the straight line was observed when » " G !1.25 V and !1.30 V. By fitting the data to a theory based on the parabolic potential approximation [11], the carrier density and the effective channel width can be estimated as summarized in Table 1. These results indicate that the channel width as well as carrier density can be changed by controlling the gate voltage via expansion of depletion layer from both edges of Q-1DEG. Fig. 3 shows drain current I —gate voltage D » characteristics measured at constant sourceG drain bias condition » "200 lV at 3.4 K. DS
Fig. 1. (a) Schematic illustration of SiNx masked substrate for selective area MOVPE, (b) SEM image after the selective growth on the masked substrate and (c) schematic illustration of the device structure.
the Schottky gate has direct contact at the edges of the Q-1DEG, and controls the electric field perpendicular to the edges. The gate length of devices A and R is 5 lm, and that of device S is 2 lm.
Fig. 2. Magnetoresistance oscillation at 3.5 K in a device R, Landau plots for various gate voltages shown in inset.
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K. Kumakura et al. / Physica E 2 (1998) 809—814
Table 1 Calculated carrier densities, effective widths of Q-1DEG channel and hu , where u is a characteristic frequency defining the 0 0 strength of the confinement Gate voltage (V)
Carrier density
Effective width (nm)
+u 0 (meV)
0 !1.25 !1.30
1.12]1012 cm~2 (N2D) % 1.07]107 cm~1 (N1D) % 6.72]106 cm~1 (N1D) %
— 105 66
— 3.6 5.8
Fig. 4. Temperature dependence of I —» characteristics in D G a device A.
Fig. 3. I —» characteristics at 3.4 K in a device R. D G
Conductance oscillations were observed near the pinch-off voltage. This conductance oscillation is thought to be the results from random interference due to impurity scattering or the fluctuations in the width of Q-1DEG channel. With decreasing the gate voltage near the pinch-off, potential modulation was formed due to the partially narrowed Q-1DEG channel.
4. Transport properties of GaAs single electron transistor structure In Fig. 4, I —» characteristics of the quantum D G dot structure connected with quantum wires (device A) with constant source—drain bias condition
(» "200 lV) for various temperatures is shown. DS Clear conductance oscillations were observed near the pinch-off, and oscillations were observed up to 65 K. Similar I —» characteristics can be obD G served as shown in Fig. 5 in another device (device S). The pinch-off gate voltages are slightly different in each device due to run-to-run fluctuation of the doping carrier density for the MOVPE growth. Note that the conductance oscillations of these devices are more clear. These results suggest that three prominences in the channel region play an important role for the large oscillations. I —» characteristics of device S measured at D DS 2.1 K show clear Coulomb blockade effect as shown in Fig. 6. Coulomb gaps and their modulation by gate voltage were seen near the pinch-off voltage. The maximum Coulomb gap D is about 12 mV, which corresponds to a thermal energy k¹ of 140 K. Following a simple model of Coulomb blockade, the total capacitance CR of the dot can be estimated to be about 13 aF from D"e/CR, and the radius R of the dot is estimated to be about 14 nm, using the formula CR"8ee R. 0 Each SET structure showed clear conductance oscillation near the pinch-off gate voltage. The possible mechanism for the formation of a small dot
K. Kumakura et al. / Physica E 2 (1998) 809—814
813
sult of electron wave interference, similar to Si quantum dot [12]. Near the pinch-off voltage, the difference of the width of depletion layer from the edges of Q-1DEG due to three prominences leads to the formation of a small dot and wires with tunneling barriers. Therefore, Coulomb blockade type conductance oscillation was observed near the pinch-off gate voltage.
5. Conclusions
Fig. 5. I —» characteristics at 1.8 K in a device S. D G
We have demonstrated the fabrication of GaAs quantum dots connected with GaAs quantum wires by SA-MOVPE, and applied these structures to GaAs wire transistors and SETs. Their transport properties were investigated at low temperature. The results of magnetoresistance measurements of wire transistors show the one-dimensional transport on applying the gate voltage, and the effective wire width can be controlled by the gate voltage. In SETs, near the pinch-off voltage, Coulomb blockade type conductance oscillations were observed up to 65 K. Coulomb gap and total capacitance CR were estimated to be 12 mV and 13 aF, respectively.
Acknowledgements The authors wish to thank Professor H. Hasegawa for fruitful discussions and encouragement, and greatly acknowledge S. Hara, T. Umeda, Y. Oda for technical assistance in MOVPE growth, and Dr. S. Kasai, H. Okada, M. Akabori for helpful discussions. One of the authors (K.K.) would like to thank the Japan Society for the Promotion of Science for the partial financial support. Fig. 6. I —» characteristics at 2.1 K in a device S. D DS
and tunneling barriers is as follows: When the depletion layer from the surface and both edges of Q-1DEG is expanded by applying the negative gate voltage, potential energy modulation was formed due to variation of effective channel width. The conductance oscillation was thought to be the re-
References [1] T. Fukui, S. Ando, Y. Tokura, T. Toriyama, Appl. Phys. Lett. 58 (1991) 2018. [2] Y. Nagamune, S. Tsukamoto, M. Nishioka, Y. Arakawa, J. Crystal Growth 126 (1993) 707. [3] K. Kumakura, K. Nakakoshi, J. Motohisa, T. Fukui, H. Hasegawa, Jpn. J. Appl. Phys. 34 (1995) 4387. [4] J.A. Lebens, C.S. Tsai, K.J. Vahala, T.F. Kuech, Appl. Phys. Lett. 56 (1990) 2642.
814
K. Kumakura et al. / Physica E 2 (1998) 809—814
[5] J. Temmyo, E. Kuramochi, M. Sugo, T. Nishiya, R. No¨tzel, T. Tamamura, Electron. Lett. 31 (1995) 209. [6] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Yu. Egorov, A.E. Zhukov, P.S. Kopev, Zh.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Jpn. J. Appl. Phys. 35 (1996) 1311. [7] D. Leonard, M. Krishnamurthy, C.M. Reaves, S.P. Denbaars, P.M. Petroff, Appl. Phys. Lett. 63 (1993) 3203.
[8] M. Aoki, H. Sano, M. Suzuki, M. Takahashi, K. Uomi, A. Takai, Electron. Lett. 27 (1991) 2138. [9] K. Kumakura, J. Motohisa, T. Fukui, J. Crystal Growth 170 (1997) 700. [10] M. Dilger, R.J. Haug, K. Eberl, A. Kurtenbach, Y. Kershaw, K.V. Klitzing, Appl. Phys. Lett. 68 (1996) 3132. [11] K.-F. Berggren, G. Roos, H. van Houten, Phys. Rev. B. 37 (1988) 10118. [12] E. Leobandung, L. Guo, Y. Wang, S.Y. Chou, Appl. Phys. Lett. 67 (1995) 938.
Fabrication and transport characterization of GaAs quantum dots connected with quantum wires fabricated by selective area metalorganic vapor phase epitaxy K. Kumakura*, J. Motohisa, T. Fukui Research Center for Interface Quantum Electronics (RCIQE), Hokkaido University, North 13 West 8, Sapporo 060, Japan
Abstract GaAs wire transistors and single electron transistors (SETs) were successfully fabricated using GaAs/AlGaAs modulation doped structures grown by selective area metalorganic vapor phase epitaxy (SA-MOVPE) on (0 0 1) masked GaAs substrates. The results of magnetoresistance of wire transistors applying the negative gate bias show the one-dimensional transport. In SETs, near the pinch-off voltage, Coulomb blockade type conductance oscillations were observed up to 65 K. Coulomb gap and total capacitance CR were estimated to be 12 mV and 13 aF, respectively. Fabrication process and transport properties of the devices were described. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Selective area MOVPE; Quantum dot; Quantum wire transistor; Single electron transistor; Coulomb blockade
1. Introduction Semiconductor quantum wires (QWRs) and quantum dots (QDs) have attracted much attention for new optical device applications, such as quantum dot lasers. Many researchers have reported GaAs and In(Ga)As QD structures fabricated using selective area metalorganic vapor phase epitaxy (SA-MOVPE) [1—4] and self-organized growth [5—7]. High density In(Ga)As QDs were automati* Corresponding author. Fax: #81 11 716 6004; e-mail: [email protected].
cally formed on GaAs substrate by the strain effects, and QD lasers were reported using this selforganized growth mode [5,6]. On the other hand, new quantum functional devices which are consisting of such QWRs and QDs have attracted much attention. In particular, for the fabrication of single electron transistors (SETs) and electron wave interference devices (EWIDs), it is important to connect these QWRs and QDs with tunneling barriers, and to form the periodic modulated potential energy. SA-MOVPE is one of the useful techniques for the fabrication of these quantum nano-structures
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 1 6 5 - 9
810
K. Kumakura et al. / Physica E 2 (1998) 809—814
[1], and has been applied to the fabrication of optical integrated circuits [8]. Using this selective growth, uniform QD structures can be formed by adjusting the growth conditions as well as substrate orientation and mask pattern, e.g., GaAs (0 0 1) [2—4] and GaAs (1 1 1)B [1] substrates. A QDnetwork, which is QDs connected with QWRs, was also reported in our previous study [9]. Thus, SAMOVPE is the promising formation method for future optical devices and opto-electronic integrated circuits (OEIC). The application of QDs to electron transport devices, especially single electron devices is also a very important research field for future electron devices. For the fabrication of these devices, these well-arranged QDs have to be connected to each other. To realize the SET structure, it has been attempted to fabricate quantum dot—tunnel barrier systems by molecular beam epitaxy on patterned substrates [10]. The purpose of this paper is to fabricate GaAs SETs using GaAs/AlGaAs modulation doped structures grown on the masked substrates by SAMOVPE, and clarify the transport properties. Firstly, GaAs wire transistors showed Shubnikov—de Haas (SdH) oscillations in applying the gate voltage, one-dimensional transport and controllability of effective channel width by the gate voltage. Next, SETs showed Coulomb blockade type conductance oscillation near the pinch-off voltage up to 65 K. Coulomb gap and total capacitance CR was estimated to be 12 mV and 13 aF, respectively.
2. Fabrication process and device structure Selective area (SA-) MOVPE growth was carried out using a low-pressure horizontal, RF-heated, quartz reactor system. The working pressure of 76 Torr was automatically controlled. Purified hydrogen (H ) was used as a carrier gas. The source 2 materials were trimethylgallium (TMGa), trimethylaluminum (TMAl) and 20% arsine (AsH ) in H . 3 2 The partial pressures of TMGa and TMAl were kept constant at 3.8]10~6 and 6.3]10~7 atm, respectively. The partial pressure of AsH was 3 1.3]10~4 atm for GaAs buffer layer, and
6.7]10~4 atm for Al Ga As layer to achieve 0.3 0.7 better quality, respectively. Growth rates of GaAs and Al Ga As were 0.93 and 1.5 lm/h for 0.3 0.7 planar substrates, respectively. SA-MOVPE was carried out on the masked substrates at the growth temperature of 700°C. The layer sequences are as follows; a 400 nm GaAs buffer layer, a 50 nm Al Ga As layer, a 15 nm 0.3 0.7 GaAs well layer, a 10 nm undoped Al Ga As 0.3 0.7 layer, a 50 nm n-doped Al Ga As layer, and 0.3 0.7 a 10 nm n-doped GaAs capping layer. The mobility and sheet electron concentration of two dimensional electron gas (2DEG) grown on a planar substrate were 62 000 cm2/(V s), 1.2]1012 cm~2 at 77 K, respectively. Schematic illustration of the mask pattern for SET structure (device A, S) is shown in Fig. 1a. The pattern is formed on semi-insulating (0 0 1) GaAs coated with 40 nm thick SiN layer by electron x beam lithography and wet chemical etching. The wire-like opening with three prominences aligned in the [1 1 0] direction corresponds to the channel region of SET. Fig. 1b shows SEM image after the selective growth and Fig. 1c, the schematic illustration of the device structure. The wire region consists of M1 1 1NB facet sidewalls, and M1 1 0N facet sidewalls are formed near the prominences. A (0 0 1) plane appeared on the top portion of the whole structure. Due to three prominences on the wire, the quasi one dimensional electron gas (Q-1DEG) channel has periodic variation in its width. This leads to the formation of a quantum dot near the central prominence and two tunneling barriers beside a dot which are connected to the quantum wires. For reference, the quantum wire was also grown on masked substrate without prominences (device R). The channel width of the present Q-1DEG is 400 nm by SEM observation. After the growth of these structures, source and drain Ge/Au/Ni ohmic electrodes were formed on the wide 2DEG regions (see Fig. 1b) by a lift-off process followed by alloying at 350°C for 5 min in N atmosphere. In the next step, a Schottky gate 2 consisting of an Al electrode was formed by a lift-off process on the three prominences region. Since no growth occurs on the M1 1 1NB facets, both edges of the Q-1DEG channel are exposed to air. Therefore,
K. Kumakura et al. / Physica E 2 (1998) 809—814
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3. Transport properties of GaAs Q-1DEG structure In order to investigate the transport properties of GaAs Q-1DEG structure under gate bias » , magG netoresistance was measured at 3.4 K in a device R which has no prominences. Both at » "0 V G and » "!1.25 V, the device showed clear magG netoresistance (MR) oscillations, as shown in Fig. 2. From these MR, Landau index N was L plotted as a function of the reciprocal magnetic field 1/B which gives MR maxima, and the results are shown in the inset in Fig. 2. A deviation from the straight line was observed when » " G !1.25 V and !1.30 V. By fitting the data to a theory based on the parabolic potential approximation [11], the carrier density and the effective channel width can be estimated as summarized in Table 1. These results indicate that the channel width as well as carrier density can be changed by controlling the gate voltage via expansion of depletion layer from both edges of Q-1DEG. Fig. 3 shows drain current I —gate voltage D » characteristics measured at constant sourceG drain bias condition » "200 lV at 3.4 K. DS
Fig. 1. (a) Schematic illustration of SiNx masked substrate for selective area MOVPE, (b) SEM image after the selective growth on the masked substrate and (c) schematic illustration of the device structure.
the Schottky gate has direct contact at the edges of the Q-1DEG, and controls the electric field perpendicular to the edges. The gate length of devices A and R is 5 lm, and that of device S is 2 lm.
Fig. 2. Magnetoresistance oscillation at 3.5 K in a device R, Landau plots for various gate voltages shown in inset.
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K. Kumakura et al. / Physica E 2 (1998) 809—814
Table 1 Calculated carrier densities, effective widths of Q-1DEG channel and hu , where u is a characteristic frequency defining the 0 0 strength of the confinement Gate voltage (V)
Carrier density
Effective width (nm)
+u 0 (meV)
0 !1.25 !1.30
1.12]1012 cm~2 (N2D) % 1.07]107 cm~1 (N1D) % 6.72]106 cm~1 (N1D) %
— 105 66
— 3.6 5.8
Fig. 4. Temperature dependence of I —» characteristics in D G a device A.
Fig. 3. I —» characteristics at 3.4 K in a device R. D G
Conductance oscillations were observed near the pinch-off voltage. This conductance oscillation is thought to be the results from random interference due to impurity scattering or the fluctuations in the width of Q-1DEG channel. With decreasing the gate voltage near the pinch-off, potential modulation was formed due to the partially narrowed Q-1DEG channel.
4. Transport properties of GaAs single electron transistor structure In Fig. 4, I —» characteristics of the quantum D G dot structure connected with quantum wires (device A) with constant source—drain bias condition
(» "200 lV) for various temperatures is shown. DS Clear conductance oscillations were observed near the pinch-off, and oscillations were observed up to 65 K. Similar I —» characteristics can be obD G served as shown in Fig. 5 in another device (device S). The pinch-off gate voltages are slightly different in each device due to run-to-run fluctuation of the doping carrier density for the MOVPE growth. Note that the conductance oscillations of these devices are more clear. These results suggest that three prominences in the channel region play an important role for the large oscillations. I —» characteristics of device S measured at D DS 2.1 K show clear Coulomb blockade effect as shown in Fig. 6. Coulomb gaps and their modulation by gate voltage were seen near the pinch-off voltage. The maximum Coulomb gap D is about 12 mV, which corresponds to a thermal energy k¹ of 140 K. Following a simple model of Coulomb blockade, the total capacitance CR of the dot can be estimated to be about 13 aF from D"e/CR, and the radius R of the dot is estimated to be about 14 nm, using the formula CR"8ee R. 0 Each SET structure showed clear conductance oscillation near the pinch-off gate voltage. The possible mechanism for the formation of a small dot
K. Kumakura et al. / Physica E 2 (1998) 809—814
813
sult of electron wave interference, similar to Si quantum dot [12]. Near the pinch-off voltage, the difference of the width of depletion layer from the edges of Q-1DEG due to three prominences leads to the formation of a small dot and wires with tunneling barriers. Therefore, Coulomb blockade type conductance oscillation was observed near the pinch-off gate voltage.
5. Conclusions
Fig. 5. I —» characteristics at 1.8 K in a device S. D G
We have demonstrated the fabrication of GaAs quantum dots connected with GaAs quantum wires by SA-MOVPE, and applied these structures to GaAs wire transistors and SETs. Their transport properties were investigated at low temperature. The results of magnetoresistance measurements of wire transistors show the one-dimensional transport on applying the gate voltage, and the effective wire width can be controlled by the gate voltage. In SETs, near the pinch-off voltage, Coulomb blockade type conductance oscillations were observed up to 65 K. Coulomb gap and total capacitance CR were estimated to be 12 mV and 13 aF, respectively.
Acknowledgements The authors wish to thank Professor H. Hasegawa for fruitful discussions and encouragement, and greatly acknowledge S. Hara, T. Umeda, Y. Oda for technical assistance in MOVPE growth, and Dr. S. Kasai, H. Okada, M. Akabori for helpful discussions. One of the authors (K.K.) would like to thank the Japan Society for the Promotion of Science for the partial financial support. Fig. 6. I —» characteristics at 2.1 K in a device S. D DS
and tunneling barriers is as follows: When the depletion layer from the surface and both edges of Q-1DEG is expanded by applying the negative gate voltage, potential energy modulation was formed due to variation of effective channel width. The conductance oscillation was thought to be the re-
References [1] T. Fukui, S. Ando, Y. Tokura, T. Toriyama, Appl. Phys. Lett. 58 (1991) 2018. [2] Y. Nagamune, S. Tsukamoto, M. Nishioka, Y. Arakawa, J. Crystal Growth 126 (1993) 707. [3] K. Kumakura, K. Nakakoshi, J. Motohisa, T. Fukui, H. Hasegawa, Jpn. J. Appl. Phys. 34 (1995) 4387. [4] J.A. Lebens, C.S. Tsai, K.J. Vahala, T.F. Kuech, Appl. Phys. Lett. 56 (1990) 2642.
814
K. Kumakura et al. / Physica E 2 (1998) 809—814
[5] J. Temmyo, E. Kuramochi, M. Sugo, T. Nishiya, R. No¨tzel, T. Tamamura, Electron. Lett. 31 (1995) 209. [6] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Yu. Egorov, A.E. Zhukov, P.S. Kopev, Zh.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Jpn. J. Appl. Phys. 35 (1996) 1311. [7] D. Leonard, M. Krishnamurthy, C.M. Reaves, S.P. Denbaars, P.M. Petroff, Appl. Phys. Lett. 63 (1993) 3203.
[8] M. Aoki, H. Sano, M. Suzuki, M. Takahashi, K. Uomi, A. Takai, Electron. Lett. 27 (1991) 2138. [9] K. Kumakura, J. Motohisa, T. Fukui, J. Crystal Growth 170 (1997) 700. [10] M. Dilger, R.J. Haug, K. Eberl, A. Kurtenbach, Y. Kershaw, K.V. Klitzing, Appl. Phys. Lett. 68 (1996) 3132. [11] K.-F. Berggren, G. Roos, H. van Houten, Phys. Rev. B. 37 (1988) 10118. [12] E. Leobandung, L. Guo, Y. Wang, S.Y. Chou, Appl. Phys. Lett. 67 (1995) 938.