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AlGaAs heterostructure
Physica E 13 (2002) 663 – 666
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Study of free GaAs surfaces using a back-gated undoped GaAs=AlGaAs heterostructure A. Kawaharazukaa; b; ∗ , T. Sakua , C.A. Kikuchia , Y. Horikoshib , Y. Hirayamaa; c a NTT
Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan c CREST Core Research for Evolutional Science and Technology, 4-1-8 Honmachi, Kawaguchi-shi, Saitama 331-0012, Japan
Abstract We study the free GaAs surface by using a back-gated undoped AlGaAs=GaAs heterostructure. This structure is suitable for investigating this surface since a two-dimensional electron gas is induced by the back-gate bias in the undoped heterostructure. We compare the channel depth dependence of the transport characteristics with two di/erent models of the free GaAs: the ‘mid-gap pinning model’, which assumes a constant surface Fermi level, and an alternative approach called the ‘frozen surface model’, which assumes a constant surface charge density. The experimental results indicate that the frozen surface model appropriately describes free GaAs surfaces at low temperature in spite of the fact that the characteristics deviate from this model at higher temperature or for a shallow channel. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 73.20.−r; 73.40.−c; 73.61.Ey Keywords: Surface state; AlGaAs=GaAs heterostructure; Frozen surface; Mid-gap pinning
Recently, many types of low-dimensional systems have been fabricated based on AlGaAs=GaAs heterostructures by using a surface Schottky gate and=or surface etching. They have a free semiconductor surface as well as a surface covered with metal. In modeling the electrostatics of these devices, the ‘mid-gap pinning model’ (MPM) [1,2] is widely used to determine the boundary condition for the surfaces and metal=(Al)GaAs interfaces. This model implicitly assumes that charges can be transferred between the surface and bulk and that a system always maintains thermal equilibrium. However, it is not obvious if thermal equilibrium is also achieved for ∗ Corresponding author. Present address: Paul Drude Institut fuer Festkoerperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany. Fax: +49-30-20377-515. E-mail address: [email protected] (A. Kawaharazuka).
free GaAs surfaces at the low temperatures where we usually operate mesoscopic devices so that we may see weak quantum mechanical e/ects. In this situation, the transfer of charges between the surface and bulk seems to be rather diEcult. Therefore, it is very important to study the free surface of (Al)GaAs at low temperature. An alternative surface model called the ‘frozen surface model’ (FSM) [3,4] has been investigated for the free surface of (Al)GaAs. This model assumes a constant surface charge density, namely a surface electric Feld, for the free semiconductor surface. Here, we study the surface state of free GaAs surface by using the back-gated undoped AlGaAs=GaAs heterostructure [5 –7] shown in Fig. 1. The whole device surface is a free GaAs surface since a two-dimensional electron gas (2DEG) is induced only by the back-gate. Therefore, the transport characteristics well reGect the condition of the
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 2 5 3 - 9
664
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
Fig. 1. A schematic cross-section of the undoped AlGaAs=GaAs heterostructure. The whole structure is undoped except for the n-GaAs used as a back-gate. For some devices, the central region is chemically etched to vary the channel depth.
free GaAs surface. We evaluate the channel depth dependence of the transport characteristics by Hall e/ect measurement. We analyze experimental results based on a simple capacitance model, assuming both the MPM and FSM for the free GaAs surface. The thickness of the 2DEG is calculated to be about 10 nm due to a Fnite wave function distribution. However, this extension is much smaller than d1 for most of the devices and the result discussed here is not signiFcantly inGuenced by it. We measure electron densities at various channel depths at 1:5 K as a function of the back-gate bias voltage. For all samples, the electron density (n) is proportional to the back-gate bias voltage (Vb ) as shown in the inset of Fig. 2. The threshold voltages (Vbth ) for deep channels (¿ 100 nm) are almost the same. For the shallow channels (70 nm; 54 nm), the threshold voltage increases with decreasing channel depth. We analyze the operation based on the MPM and FSM [7]. In both models, the electron density (n) is expressed as 2 n= (Vb − Vbth ): (1) d2 e Based on expressed d2 Vbth = d1
the MPM, the threshold voltage (Vbth ) is as 1 1
s ˙ ; (2) 2 d1
where s is the surface Fermi level. The surface Fermi level ( s ) is constant. On the other hand, based on
Fig. 2. Measurement (Flled square) and calculations with the MPM (dashed line) and FSM (solid line) are plotted as a function of channel depth. For a deep channel (¿ 100 nm), the measured data are well explained by the FSM. The inset shows the electron densities as a function of the back-gate bias voltage for various channel depths. The barrier layer is the same in each case (420 nm).
the FSM Vbth =
d2 e Qs ; 2
(3)
where Qs is the surface charge density determined by the equilibrium before cooling [7]. Note that in the FSM, we assume that the surface charge density is constant. Accordingly, the system is not in a state of thermal equilibrium after application of a back-gate bias. The threshold voltages calculated by Eqs. (2) and (3) are plotted in Fig. 2 as a function of channel depth (d1 ) together with the measured data. We assume that the surface Fermi level is pinned 0:96 eV below the conduction band edge [8]. When we compare the experimental data with the calculated results, the FSM explains the experimental data well. In the MPM, the threshold voltage depends strongly on the channel depth and is much larger than in the FSM. Therefore, the appropriate model for the free GaAs surface at low temperature is the FSM rather than the widely accepted MPM. The increase in the threshold voltage observed in the shallow channels (70 nm; 54 nm) is explained by considering the charge transfer from the 2DEG to the surface since the system is substantially non-equilibrium in the
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
Fig. 3. Measured (open circles) and calculated (lines) mobilities of the samples with a 70-nm channel depth. In the low-electron-density region, the total mobility is dominated by the scattering due to the surface charge. The total mobilities are calculated for surface charge densities estimated from the measured threshold bias (thick line), expected from the MPM (thin line), and corresponding to no surface charges (dashed line). The experimental data agree well with theoretical calculations performed with the measured surface charge density.
FSM. As expected from Eq. (3), the threshold voltage increases as the surface charge density increases. We examine the validity of the measured surface charge density by analyzing the mobility [5]. At low temperature, the mobility is dominated by Coulomb scattering since phonon scattering is negligible. With shallow channels in particular, scattering due to the surface charge becomes signiFcant and dominates the total mobility in the low-electron-density region [6]. Fig. 3 shows measured (open circles) and calculated (lines) mobilities of a sample with a 70-nm-deep channel as a function of electron density. In the calculation we assume background impurity concentration of 1:2 × 1014 cm−3 , which is obtained from the mobility analysis of deep channel devices. In spite of the shallow channel depth, the mobility is still very high and the highest value reaches 2:3×106 cm2 =V s. The thick solid line represents the mobility calculated with the surface charge density (1:55 × 1011 cm−2 ) obtained from the measured threshold bias. This surface charge density is close to the value (1:10 × 1011 cm−2 ) expected from the FSM. The thin solid and dashed lines
665
Fig. 4. Time dependence of the 2DEG density measured at 30 K. The back-gate bias is Fxed at 4:0 V during the measurement. The electrons are transferred from the 2DEG to the surface and the system moves closer to thermal equilibrium.
are calculated with the surface charge density expected from the MPM (9:93 × 1011 cm−2 ) and without surface charge, respectively. The mobility without surface charge is determined solely by the scattering due to the background impurity. The measured mobilities are well explained when we assume the measured surface charge density. The mobility values calculated with the MPM are about one third of the measured ones. Therefore, we conFrm that the surface charge density is much lower than that expected from the MPM because charges cannot be transferred to the surface. We measure the time dependence of the 2DEG density at 30 K to conFrm that the system is non-equilibrium. The channel depth and the barrier layer thickness of the device used in this measurement are 100 and 620 nm, respectively. First, we directly cooled the device to 30 K without applying the back-gate bias. Then, we operate the device by setting the back-gate bias at 4:0 V and maintain this condition while measuring the Hall voltage. Fig. 4 shows the measured time dependence of the 2DEG density. The initial 2DEG density of 3:38×1011 cm−2 is identical to that at 1:5 K. Initially, the 2DEG density decreases rapidly and the decreasing rate becomes lower as time passed. After several hours, the 2DEG density becomes almost constant. This in-
666
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
dicates that after the formation of the 2DEG at the interface, electrons are transferred to the surface due to the thermionic emission. They are trapped by the deep levels at the surface because the system is not in a state of thermal equilibrium. The increase in the surface charge density causes an increase in the surface electric Feld. This increases the potential barrier height and reduces the thermionic emission. Through this process, the 2DEG density approaches a constant and the system moves closer to thermal equilibrium. The mobility analysis and the time dependence of the 2DEG density also support the validity of the FSM. In conclusion, we studied the free GaAs surface by using a back-gated undoped AlGaAs=GaAs heterostructure. We measured the channel depth dependence of the transport characteristics. We analyzed experimental results based on the MPM and FSM for a free GaAs surface. We showed that FSM is the appropriate model for a free GaAs surface at low temperature. This is because charges cannot be transferred to the surface at low temperature. The surface charge density is constant, thus contradicting the widely accepted MPM. However, the FSM becomes inappropriate at higher temperature or for a shallow channel where charge transfer from the 2DEG to the surface is signiFcant. We also conFrmed the validity of our conclusions from a mobility analysis and time dependence
measurement of the 2DEG density. This characteristic is promising as regards applying the back-gated undoped AlGaAs=GaAs heterostructure to Fne pattern devices since it means a shallow 2DEG can be formed. This work was partly funded by the Japan Society for the Promotion of Science (‘Research for the Future JSPS-RFTF96P00103), COE Program ‘Molecular Nano-Engineering’ from the Ministry of Education, Science and Culture, Japan, and NEDO program (NTDP-98). References [1] W.E. Spicer, P.W. Chyne, P.R. Skeath, C.Y. Su, I. Lindau, J. Vac. Sci. Technol. 16 (1979) 1422. [2] W.E. Spicer, I. Lindau, P. Skeath, C.Y. Su, P. Chyne, Phys. Rev. Lett. 44 (1980) 420. [3] S.E. Laux, D.J. Frank, F. Stern, Surf. Sci. 196 (1988) 101. [4] J.H. Davies, I.A. Larkin, Phys. Rev. B 49 (1994) 4800. [5] Y. Hirayama, K. Muraki, T. Saku, Appl. Phys. Lett. 72 (1998) 1745. [6] A. Kawaharazuka, T. Saku, Y. Hirayama, Y. Horikoshi, J. Appl. Phys. 87 (2000) 952. [7] A. Kawaharazuka, T. Saku, C.A. Kikuchi, Y. Horikoshi, Y. Hirayama, Phys. Rev. B 63 (2001) 245 309. [8] H. Takahashi, T. Yoshida, M. Moriuchi, T. Sakai, H. Hasegawa, Solid State Electron. 43 (1999) 1561.
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Study of free GaAs surfaces using a back-gated undoped GaAs=AlGaAs heterostructure A. Kawaharazukaa; b; ∗ , T. Sakua , C.A. Kikuchia , Y. Horikoshib , Y. Hirayamaa; c a NTT
Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan c CREST Core Research for Evolutional Science and Technology, 4-1-8 Honmachi, Kawaguchi-shi, Saitama 331-0012, Japan
Abstract We study the free GaAs surface by using a back-gated undoped AlGaAs=GaAs heterostructure. This structure is suitable for investigating this surface since a two-dimensional electron gas is induced by the back-gate bias in the undoped heterostructure. We compare the channel depth dependence of the transport characteristics with two di/erent models of the free GaAs: the ‘mid-gap pinning model’, which assumes a constant surface Fermi level, and an alternative approach called the ‘frozen surface model’, which assumes a constant surface charge density. The experimental results indicate that the frozen surface model appropriately describes free GaAs surfaces at low temperature in spite of the fact that the characteristics deviate from this model at higher temperature or for a shallow channel. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 73.20.−r; 73.40.−c; 73.61.Ey Keywords: Surface state; AlGaAs=GaAs heterostructure; Frozen surface; Mid-gap pinning
Recently, many types of low-dimensional systems have been fabricated based on AlGaAs=GaAs heterostructures by using a surface Schottky gate and=or surface etching. They have a free semiconductor surface as well as a surface covered with metal. In modeling the electrostatics of these devices, the ‘mid-gap pinning model’ (MPM) [1,2] is widely used to determine the boundary condition for the surfaces and metal=(Al)GaAs interfaces. This model implicitly assumes that charges can be transferred between the surface and bulk and that a system always maintains thermal equilibrium. However, it is not obvious if thermal equilibrium is also achieved for ∗ Corresponding author. Present address: Paul Drude Institut fuer Festkoerperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany. Fax: +49-30-20377-515. E-mail address: [email protected] (A. Kawaharazuka).
free GaAs surfaces at the low temperatures where we usually operate mesoscopic devices so that we may see weak quantum mechanical e/ects. In this situation, the transfer of charges between the surface and bulk seems to be rather diEcult. Therefore, it is very important to study the free surface of (Al)GaAs at low temperature. An alternative surface model called the ‘frozen surface model’ (FSM) [3,4] has been investigated for the free surface of (Al)GaAs. This model assumes a constant surface charge density, namely a surface electric Feld, for the free semiconductor surface. Here, we study the surface state of free GaAs surface by using the back-gated undoped AlGaAs=GaAs heterostructure [5 –7] shown in Fig. 1. The whole device surface is a free GaAs surface since a two-dimensional electron gas (2DEG) is induced only by the back-gate. Therefore, the transport characteristics well reGect the condition of the
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 2 5 3 - 9
664
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
Fig. 1. A schematic cross-section of the undoped AlGaAs=GaAs heterostructure. The whole structure is undoped except for the n-GaAs used as a back-gate. For some devices, the central region is chemically etched to vary the channel depth.
free GaAs surface. We evaluate the channel depth dependence of the transport characteristics by Hall e/ect measurement. We analyze experimental results based on a simple capacitance model, assuming both the MPM and FSM for the free GaAs surface. The thickness of the 2DEG is calculated to be about 10 nm due to a Fnite wave function distribution. However, this extension is much smaller than d1 for most of the devices and the result discussed here is not signiFcantly inGuenced by it. We measure electron densities at various channel depths at 1:5 K as a function of the back-gate bias voltage. For all samples, the electron density (n) is proportional to the back-gate bias voltage (Vb ) as shown in the inset of Fig. 2. The threshold voltages (Vbth ) for deep channels (¿ 100 nm) are almost the same. For the shallow channels (70 nm; 54 nm), the threshold voltage increases with decreasing channel depth. We analyze the operation based on the MPM and FSM [7]. In both models, the electron density (n) is expressed as 2 n= (Vb − Vbth ): (1) d2 e Based on expressed d2 Vbth = d1
the MPM, the threshold voltage (Vbth ) is as 1 1
s ˙ ; (2) 2 d1
where s is the surface Fermi level. The surface Fermi level ( s ) is constant. On the other hand, based on
Fig. 2. Measurement (Flled square) and calculations with the MPM (dashed line) and FSM (solid line) are plotted as a function of channel depth. For a deep channel (¿ 100 nm), the measured data are well explained by the FSM. The inset shows the electron densities as a function of the back-gate bias voltage for various channel depths. The barrier layer is the same in each case (420 nm).
the FSM Vbth =
d2 e Qs ; 2
(3)
where Qs is the surface charge density determined by the equilibrium before cooling [7]. Note that in the FSM, we assume that the surface charge density is constant. Accordingly, the system is not in a state of thermal equilibrium after application of a back-gate bias. The threshold voltages calculated by Eqs. (2) and (3) are plotted in Fig. 2 as a function of channel depth (d1 ) together with the measured data. We assume that the surface Fermi level is pinned 0:96 eV below the conduction band edge [8]. When we compare the experimental data with the calculated results, the FSM explains the experimental data well. In the MPM, the threshold voltage depends strongly on the channel depth and is much larger than in the FSM. Therefore, the appropriate model for the free GaAs surface at low temperature is the FSM rather than the widely accepted MPM. The increase in the threshold voltage observed in the shallow channels (70 nm; 54 nm) is explained by considering the charge transfer from the 2DEG to the surface since the system is substantially non-equilibrium in the
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
Fig. 3. Measured (open circles) and calculated (lines) mobilities of the samples with a 70-nm channel depth. In the low-electron-density region, the total mobility is dominated by the scattering due to the surface charge. The total mobilities are calculated for surface charge densities estimated from the measured threshold bias (thick line), expected from the MPM (thin line), and corresponding to no surface charges (dashed line). The experimental data agree well with theoretical calculations performed with the measured surface charge density.
FSM. As expected from Eq. (3), the threshold voltage increases as the surface charge density increases. We examine the validity of the measured surface charge density by analyzing the mobility [5]. At low temperature, the mobility is dominated by Coulomb scattering since phonon scattering is negligible. With shallow channels in particular, scattering due to the surface charge becomes signiFcant and dominates the total mobility in the low-electron-density region [6]. Fig. 3 shows measured (open circles) and calculated (lines) mobilities of a sample with a 70-nm-deep channel as a function of electron density. In the calculation we assume background impurity concentration of 1:2 × 1014 cm−3 , which is obtained from the mobility analysis of deep channel devices. In spite of the shallow channel depth, the mobility is still very high and the highest value reaches 2:3×106 cm2 =V s. The thick solid line represents the mobility calculated with the surface charge density (1:55 × 1011 cm−2 ) obtained from the measured threshold bias. This surface charge density is close to the value (1:10 × 1011 cm−2 ) expected from the FSM. The thin solid and dashed lines
665
Fig. 4. Time dependence of the 2DEG density measured at 30 K. The back-gate bias is Fxed at 4:0 V during the measurement. The electrons are transferred from the 2DEG to the surface and the system moves closer to thermal equilibrium.
are calculated with the surface charge density expected from the MPM (9:93 × 1011 cm−2 ) and without surface charge, respectively. The mobility without surface charge is determined solely by the scattering due to the background impurity. The measured mobilities are well explained when we assume the measured surface charge density. The mobility values calculated with the MPM are about one third of the measured ones. Therefore, we conFrm that the surface charge density is much lower than that expected from the MPM because charges cannot be transferred to the surface. We measure the time dependence of the 2DEG density at 30 K to conFrm that the system is non-equilibrium. The channel depth and the barrier layer thickness of the device used in this measurement are 100 and 620 nm, respectively. First, we directly cooled the device to 30 K without applying the back-gate bias. Then, we operate the device by setting the back-gate bias at 4:0 V and maintain this condition while measuring the Hall voltage. Fig. 4 shows the measured time dependence of the 2DEG density. The initial 2DEG density of 3:38×1011 cm−2 is identical to that at 1:5 K. Initially, the 2DEG density decreases rapidly and the decreasing rate becomes lower as time passed. After several hours, the 2DEG density becomes almost constant. This in-
666
A. Kawaharazuka et al. / Physica E 13 (2002) 663 – 666
dicates that after the formation of the 2DEG at the interface, electrons are transferred to the surface due to the thermionic emission. They are trapped by the deep levels at the surface because the system is not in a state of thermal equilibrium. The increase in the surface charge density causes an increase in the surface electric Feld. This increases the potential barrier height and reduces the thermionic emission. Through this process, the 2DEG density approaches a constant and the system moves closer to thermal equilibrium. The mobility analysis and the time dependence of the 2DEG density also support the validity of the FSM. In conclusion, we studied the free GaAs surface by using a back-gated undoped AlGaAs=GaAs heterostructure. We measured the channel depth dependence of the transport characteristics. We analyzed experimental results based on the MPM and FSM for a free GaAs surface. We showed that FSM is the appropriate model for a free GaAs surface at low temperature. This is because charges cannot be transferred to the surface at low temperature. The surface charge density is constant, thus contradicting the widely accepted MPM. However, the FSM becomes inappropriate at higher temperature or for a shallow channel where charge transfer from the 2DEG to the surface is signiFcant. We also conFrmed the validity of our conclusions from a mobility analysis and time dependence
measurement of the 2DEG density. This characteristic is promising as regards applying the back-gated undoped AlGaAs=GaAs heterostructure to Fne pattern devices since it means a shallow 2DEG can be formed. This work was partly funded by the Japan Society for the Promotion of Science (‘Research for the Future JSPS-RFTF96P00103), COE Program ‘Molecular Nano-Engineering’ from the Ministry of Education, Science and Culture, Japan, and NEDO program (NTDP-98). References [1] W.E. Spicer, P.W. Chyne, P.R. Skeath, C.Y. Su, I. Lindau, J. Vac. Sci. Technol. 16 (1979) 1422. [2] W.E. Spicer, I. Lindau, P. Skeath, C.Y. Su, P. Chyne, Phys. Rev. Lett. 44 (1980) 420. [3] S.E. Laux, D.J. Frank, F. Stern, Surf. Sci. 196 (1988) 101. [4] J.H. Davies, I.A. Larkin, Phys. Rev. B 49 (1994) 4800. [5] Y. Hirayama, K. Muraki, T. Saku, Appl. Phys. Lett. 72 (1998) 1745. [6] A. Kawaharazuka, T. Saku, Y. Hirayama, Y. Horikoshi, J. Appl. Phys. 87 (2000) 952. [7] A. Kawaharazuka, T. Saku, C.A. Kikuchi, Y. Horikoshi, Y. Hirayama, Phys. Rev. B 63 (2001) 245 309. [8] H. Takahashi, T. Yoshida, M. Moriuchi, T. Sakai, H. Hasegawa, Solid State Electron. 43 (1999) 1561.