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A new type of scanning probe microscope: combination between an electrometer and a THz microscope
Microelectronics Journal 36 (2005) 592–595 www.elsevier.com/locate/mejo
A new type of scanning probe microscope: combination between an electrometer and a THz microscope Y. Kawano*, T. Okamoto Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Available online 14 April 2005
Abstract We present a new application of the quantum Hall effect (QHE): a combined technique of an electrometer and a THz microscope. In this system, we exploit the QHE devices as a voltage sensor and a THz detector. Using this technique, we simultaneously mapped out longitudinal voltage and cyclotron emission in a quantized Hall bar. This measurement enabled us to separately image spatial distributions of intra- and inter-Landau-level scattering in the QHE systems. q 2005 Elsevier Ltd. All rights reserved. Keywords: Quantum Hall effect; Scanning electrometer; THz microscope
1. Introduction When a two-dimensional electron gas (2DEG) formed in semiconductor interfaces or surfaces is subject to a perpendicular magnetic filed, it exhibits dramatic properties known as integer and fractional quantum Hall effects (QHEs) [1,2]. In the QHE regime, the longitudinal resistance vanishes and the Hall resistance is exactly quantized. Since their discovery in 1980s, the QHE has been intensively studied from the standpoint of not only their fundamental aspects, but also practical use in devices. As for device applications of the QHE, resistance standard using the precise quantization of the Hall resistance is well known [3]. Besides, other fascinating devices such as quantum bit [4] and relaxation oscillator [5] have been recently developed. It has been thus recognized that the QHE can be exploited as a useful tool. In this paper, we present a novel technique using advantageous properties of the QHE: a hybrid system combining an electrometer and a THz microscope. In this new type of scanning probe system, we utilize the QHE devices as a highly sensitive voltage sensor and a highly sensitive and tunable THz detector, each of which we previously developed [6,7]. The spacing between key * Corresponding author. Tel.: C81 3 5841 4129; fax: C81 3 5841 4532. E-mail address: [email protected] (Y. Kawano).
0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.02.099
energy levels in low-dimensional semiconductors, such as subband energy levels and Landau-levels, mostly corresponds to the THz region. Therefore, this developed technique works as a unique tool for characterizing local properties of non-equilibrium electrons excited into higher energy levels, together with gaining information of local voltage (electrostatic potential). Though recently THz imaging technique has been intensively developed, most works are done at room temperature. Our THz microscope can be used under liquid He temperature and in the presence of high magnetic filed. Cryogenic scanning electrometers using single electron transistor (SET) [8] and atomic force microscope (AFM) cantilever [9] have been developed in the late 1990s. However, these earlier techniques have the following disadvantages: the operation of the SET electrometer is restricted to be in a 3He–4He dilution refrigerator (below a few hundred milliKelvin). In contrast, since our electrometer makes use of the integer QHE, it is available over a wider range of temperature (up to several Kelvin). The AFM technique requires applying a high electric field between the tip and the sample, leading to disturbance of the real electronic state of the sample. In our system, it is not necessary to apply external voltage between sensor and sample, as described in the subsequent section. In this work, we apply the developed probe system to a QHE sample, and simultaneously observe spatial distributions of longitudinal voltage Vxx and cyclotron emission (CE). Since CE is radiated through inter-Landau-level
Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
593
transitions of electrons, comparing the mapped data of Vxx and the CE intensity VCE allows us to distinguish the contributions of intra- and inter-Landau-level scattering (LLS) to the generation of Vxx. We found that the two LLS distributions are in marked contrast: intra LLS takes place over the whole 2DEG channel while inter LLS is significant around the current contacts, especially the source contact. In Section 4, we discuss (i) the respective scattering processes and (ii) possible improvement of spatial resolutions of the electrometer and the THz microscope.
2. Experimental setup Fig. 1 illustrates our experimental setup. A small Hall bar (electrometer) and a hyper-hemisphere lens made of pure silicon crystal are in contact with the front and back surfaces of the sample, respectively. A THz detector is mounted at the bottom of the system. The electrometer, the sample, and the THz detector are fabricated on GaAs/AlGaAs heterostructure wafers, in which the 2DEG layers are located 0.1 mm beneath the crystal surfaces. In imaging experiments, the sample alone is moved by an X–Y translation stage, while the electrometer and the optical system are spatially fixed. The whole system is directly immersed into liquid 4He and is subject to a perpendicular magnetic field B. Let us explain each component of the system, viz. the electrometer and the THz microscope. In Fig. 2(a), we show an equivalent circuit of the electrometer system. The important point is that since the distance between the two 2DEG layers is very short, they are capacitively coupled. Therefore, when a current IS is passed through the sample, excess charges DQ are induced into the 2DEGs, accordingly to CV(x,y)ZDQ. Here, V(x,y) is a local voltage in the sample right below the electrometer, and C is the capacitance between the two 2DEG layers. The generation of DQ results in the change, DRE, in the longitudinal resistance of the electrometer. By translating the electrometer over the surface of the sample and measuring
Fig. 1. Sketch of the scanning probe system combining the electrometer and the THz microscope.
Fig. 2. Schematic of the sensing mechanism of (a) the electrometer and (b) the THz detector.
DRE!IE, we can obtain images of V(x,y) in the sample (IE is the bias current for the electrometer). The electrometer is processed into a Hall bar geometry from a GaAs/AlGaAs heterostructure with an electron mobility mHZ18 m2/Vs and a sheet electron density nsZ2.2!1015 mK2 at 4.2 K. The device has a main channel with a length LZ200 mm and a width WZ1.5 mm, and the two voltage probes with the interval of 2.3 mm. Spatial resolution of this system is about 2 mm, which is determined by the sensing 2DEG area of the electrometer, defined by the channel width and the interval between the two voltage probes. The maximum sensitivity in the present system reaches about 2 mV/Hz1/2. Imaging of THz emission (CE) is carried out by scanning the lens across the sample back surface. In this optical system, the focal point of the lens with a 2.8-mm diameter and a 1.48-mm thickness is on the 2DEG layer of the sample. The CE from the focal point is collimated via the lens and is guided through a metallic light pipe to the highly sensitive and wavelength-selective THz detector. We obtain a resolution of about 50mm at 120 mm, the wavelength of CE in vacuum. As shown in Fig. 2(b), mechanism of the THz detection is based on the change, DRD, in longitudinal resistance induced by cyclotron resonance. In order to obtain large resistance change, the detector has a long-zigzag 2DEG channel with LZ167 mm and WZ50 mm (L/WZ3.3!103). The detector sensitivity is NEPw1!10-15 W/Hz1/2 with a voltage responsivity w109 V/W. The sample studied is a standard Hall bar with LZ2.8 and WZ1 mm, which is fabricated from a GaAs/AlGaAs heterostructure with mHZ53 m2/Vs and nsZ2.4!1015 mK2 at 4.2 K. In spatially resolved measurements, V(x,y) and VCE(x,y) are simultaneously measured with two lock-in amplifiers, where a 30 Hz rectangular-wave current
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Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
alternating between zero and a given finite value IS is passed through the sample. All measurements are performed at 4.2 K.
3. Experimental results Fig. 3 shows longitudinal resistances RD and the detected signal Vsig(ZDRD!ID), of the THz detector, as a function of B at the detector current IDZ4 mA. In this measurement, we fix the sample at a certain position and transmit the current, ISZ140 mA, for the sample. The strong photoresponse appears only in the vicinity of the QHE plateau with a two-peaked structure. Our previous work [7] showed that this feature can be reasonably interpreted to be due to electron heating effect caused by cyclotron absorption. Fig. 4 displays imaging plots of Vxx and VCE at ISZ 140 mA and BZ5.75 T (Landau-level filling factor, nZ 1.74, of the sample). We obtain the Vxx(x,y) data by differating V(x,y) over a distance of 50 mm in the direction of the length of the sample: Vxx(x,y)ZV(xCDx,y)KV(x,y) with DxZ50 mm [10]. The images obtained show that Vxx appears over the entire 2DEG channel, whereas CE is present only in a localized region. This means that Vxx observed in most part except in the area covered by CE originates from intra LLS. It is also found that a large Vxx shows up around the source contact and at one corner on the side of the drain contact. Comparing with the VCE data reveals that a strong CE appears in the similar region, indicating that Vxx observed in this localized area mainly arises from inter LLS. The above results show that spatial distributions of intra- and inter-LLS are markedly different.
4. Discussion In this section, we first discuss the contrasting situation of intra- and inter-LLS distributions, presented in Fig. 4, and secondly suggest possible improvement of spatial resolutions of the present scanning probe microscope.
Fig. 3. B dependence of RD (thin line) and Vsig (thick line) at ISZ140 and IDZ4 mA.
Fig. 4. Imaging plots of Vxx and VCE at IEZ0.3, ISZ140, and IDZ4 mA, and BZ5.75 T. The white broken lines denote the 2DEG boundaries of the sample.
Earlier works reported that inter-LLS is a relatively slow process (10–100 ns) [11] and accordingly the equilibrium length of excited electrons reaches a very long scale (100–300 mm) [12]. On the other hand, although there is no clear experimental information about intra-LLS, one can imagine that the scattering rate will be much higher because the scattering does not require much energy. If we assume that the main mechanism of intra LLS is impurity scattering originating from ionized donors in the AlGaAs layer, the characteristic length of intra LLS can be taken as period of the ionized impurities, 0.05–0.3 mm [13]. Based on this, the significant difference between intra- and inter-LLS distributions can be reasonably understood as arsing from that of the scattering process and the characteristic length scale. Finally, we would like to discuss spatial resolutions of the present system. The spatial resolution, 2 mm, of the electrometer system is determined by the size of the sensing area. Therefore, the resolution can be improved by using an electrometer with a reduced size 2DEG as sensing area. We envisage that further improvement would be achieved by implementing a metallic probe with a tip diameter of w100 nm between the electrometer and the sample. In this system, since the voltage sensing is made through capacitive coupling between the probe tip and the sample, a resolution is mainly determined by the tip diameter. As for the THz microscope, as long as we use the optics based on the lens system, the resolution is restricted by the diffraction limit of the microscope. In order to overcome this restriction, we will scan a small
Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
bow-tie antenna over the front surface of the sample. We expect that collecting THz radiation at a tip of the antenna would lead to a resolution of several mms.
5. Conclusion We have constructed a new type of scanning probe microscope using the QHE, where an electrometer and a THz microscope are combined. With this system, we have imaged spatial distributions of Vxx and VCE in the QHE Hall bar sample. The resulting data reveal that intra- and interLLS distributions are strikingly different, indicating similar difference of the scattering processes and their characteristic lengths.
Acknowledgements This work was supported by the Grant-in-Aid for Young Scientists (A) (16684007) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
595
References [1] K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45 (1980) 494. [2] D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48 (1982) 1559. [3] Forexample, see F. Delahaye, et al., Metrologia 22 (1986) 103. [4] T. Machida, T. Yamazaki, K. Ikushima, S. Komiyama, Appl. Phys. Lett. 82 (2003) 409. [5] G. Nachtwei, N.G. Kalugin, B.E. Saol, Ch. Stellmachv, G. Hein, Appl. Phys. Lett. 82 (2003) 2068. [6] Y. Kawano, T. Okamoto, Appl. Phys. Lett. 84 (2004) 1111. [7] Y. Kawano, Y. Hisanaga, H. Takenouchi, S. Komiyama, J. Appl. Phys. 89 (2001) 4037. [8] M.J. Yoo, et al., Science 276 (1999) 579; A. Yacoby, et al., Solid State Commun. 111 (1999) 1. [9] K.L. McCormick, et al., Phys. Rev. B 59 (1999) 4654. [10] Very sharp changes of Hall voltage VH occur in the junction regions between the current contacts and the 2DEG. In order to exclusively obtain the Vxx image, the data points associated with these sharp changes of VH are excluded from the final images. [11] S. Komiyama, T. Takamasu, S. Hiyamizu, S. Sasa, Solid State Commun. 54 (1985) 497; B.R.A. Neves, et al., Phys. Rev. B 52 (1995) 4666. [12] S. Komiyama, Y. Kawaguchi, T. Osada, Y. Shiraki, Phys. Rev. Lett. 77 (1996) 558; I.I. Kaya, et al., Europhys. Lett. 46 (1999) 62. [13] S.H. Tessmer, P.I. Glicofridis, R.C. Ashoori, L.S. Levitov, M.R. Melloch, Nature (London) 392 (1998) 51.
A new type of scanning probe microscope: combination between an electrometer and a THz microscope Y. Kawano*, T. Okamoto Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Available online 14 April 2005
Abstract We present a new application of the quantum Hall effect (QHE): a combined technique of an electrometer and a THz microscope. In this system, we exploit the QHE devices as a voltage sensor and a THz detector. Using this technique, we simultaneously mapped out longitudinal voltage and cyclotron emission in a quantized Hall bar. This measurement enabled us to separately image spatial distributions of intra- and inter-Landau-level scattering in the QHE systems. q 2005 Elsevier Ltd. All rights reserved. Keywords: Quantum Hall effect; Scanning electrometer; THz microscope
1. Introduction When a two-dimensional electron gas (2DEG) formed in semiconductor interfaces or surfaces is subject to a perpendicular magnetic filed, it exhibits dramatic properties known as integer and fractional quantum Hall effects (QHEs) [1,2]. In the QHE regime, the longitudinal resistance vanishes and the Hall resistance is exactly quantized. Since their discovery in 1980s, the QHE has been intensively studied from the standpoint of not only their fundamental aspects, but also practical use in devices. As for device applications of the QHE, resistance standard using the precise quantization of the Hall resistance is well known [3]. Besides, other fascinating devices such as quantum bit [4] and relaxation oscillator [5] have been recently developed. It has been thus recognized that the QHE can be exploited as a useful tool. In this paper, we present a novel technique using advantageous properties of the QHE: a hybrid system combining an electrometer and a THz microscope. In this new type of scanning probe system, we utilize the QHE devices as a highly sensitive voltage sensor and a highly sensitive and tunable THz detector, each of which we previously developed [6,7]. The spacing between key * Corresponding author. Tel.: C81 3 5841 4129; fax: C81 3 5841 4532. E-mail address: [email protected] (Y. Kawano).
0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.02.099
energy levels in low-dimensional semiconductors, such as subband energy levels and Landau-levels, mostly corresponds to the THz region. Therefore, this developed technique works as a unique tool for characterizing local properties of non-equilibrium electrons excited into higher energy levels, together with gaining information of local voltage (electrostatic potential). Though recently THz imaging technique has been intensively developed, most works are done at room temperature. Our THz microscope can be used under liquid He temperature and in the presence of high magnetic filed. Cryogenic scanning electrometers using single electron transistor (SET) [8] and atomic force microscope (AFM) cantilever [9] have been developed in the late 1990s. However, these earlier techniques have the following disadvantages: the operation of the SET electrometer is restricted to be in a 3He–4He dilution refrigerator (below a few hundred milliKelvin). In contrast, since our electrometer makes use of the integer QHE, it is available over a wider range of temperature (up to several Kelvin). The AFM technique requires applying a high electric field between the tip and the sample, leading to disturbance of the real electronic state of the sample. In our system, it is not necessary to apply external voltage between sensor and sample, as described in the subsequent section. In this work, we apply the developed probe system to a QHE sample, and simultaneously observe spatial distributions of longitudinal voltage Vxx and cyclotron emission (CE). Since CE is radiated through inter-Landau-level
Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
593
transitions of electrons, comparing the mapped data of Vxx and the CE intensity VCE allows us to distinguish the contributions of intra- and inter-Landau-level scattering (LLS) to the generation of Vxx. We found that the two LLS distributions are in marked contrast: intra LLS takes place over the whole 2DEG channel while inter LLS is significant around the current contacts, especially the source contact. In Section 4, we discuss (i) the respective scattering processes and (ii) possible improvement of spatial resolutions of the electrometer and the THz microscope.
2. Experimental setup Fig. 1 illustrates our experimental setup. A small Hall bar (electrometer) and a hyper-hemisphere lens made of pure silicon crystal are in contact with the front and back surfaces of the sample, respectively. A THz detector is mounted at the bottom of the system. The electrometer, the sample, and the THz detector are fabricated on GaAs/AlGaAs heterostructure wafers, in which the 2DEG layers are located 0.1 mm beneath the crystal surfaces. In imaging experiments, the sample alone is moved by an X–Y translation stage, while the electrometer and the optical system are spatially fixed. The whole system is directly immersed into liquid 4He and is subject to a perpendicular magnetic field B. Let us explain each component of the system, viz. the electrometer and the THz microscope. In Fig. 2(a), we show an equivalent circuit of the electrometer system. The important point is that since the distance between the two 2DEG layers is very short, they are capacitively coupled. Therefore, when a current IS is passed through the sample, excess charges DQ are induced into the 2DEGs, accordingly to CV(x,y)ZDQ. Here, V(x,y) is a local voltage in the sample right below the electrometer, and C is the capacitance between the two 2DEG layers. The generation of DQ results in the change, DRE, in the longitudinal resistance of the electrometer. By translating the electrometer over the surface of the sample and measuring
Fig. 1. Sketch of the scanning probe system combining the electrometer and the THz microscope.
Fig. 2. Schematic of the sensing mechanism of (a) the electrometer and (b) the THz detector.
DRE!IE, we can obtain images of V(x,y) in the sample (IE is the bias current for the electrometer). The electrometer is processed into a Hall bar geometry from a GaAs/AlGaAs heterostructure with an electron mobility mHZ18 m2/Vs and a sheet electron density nsZ2.2!1015 mK2 at 4.2 K. The device has a main channel with a length LZ200 mm and a width WZ1.5 mm, and the two voltage probes with the interval of 2.3 mm. Spatial resolution of this system is about 2 mm, which is determined by the sensing 2DEG area of the electrometer, defined by the channel width and the interval between the two voltage probes. The maximum sensitivity in the present system reaches about 2 mV/Hz1/2. Imaging of THz emission (CE) is carried out by scanning the lens across the sample back surface. In this optical system, the focal point of the lens with a 2.8-mm diameter and a 1.48-mm thickness is on the 2DEG layer of the sample. The CE from the focal point is collimated via the lens and is guided through a metallic light pipe to the highly sensitive and wavelength-selective THz detector. We obtain a resolution of about 50mm at 120 mm, the wavelength of CE in vacuum. As shown in Fig. 2(b), mechanism of the THz detection is based on the change, DRD, in longitudinal resistance induced by cyclotron resonance. In order to obtain large resistance change, the detector has a long-zigzag 2DEG channel with LZ167 mm and WZ50 mm (L/WZ3.3!103). The detector sensitivity is NEPw1!10-15 W/Hz1/2 with a voltage responsivity w109 V/W. The sample studied is a standard Hall bar with LZ2.8 and WZ1 mm, which is fabricated from a GaAs/AlGaAs heterostructure with mHZ53 m2/Vs and nsZ2.4!1015 mK2 at 4.2 K. In spatially resolved measurements, V(x,y) and VCE(x,y) are simultaneously measured with two lock-in amplifiers, where a 30 Hz rectangular-wave current
594
Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
alternating between zero and a given finite value IS is passed through the sample. All measurements are performed at 4.2 K.
3. Experimental results Fig. 3 shows longitudinal resistances RD and the detected signal Vsig(ZDRD!ID), of the THz detector, as a function of B at the detector current IDZ4 mA. In this measurement, we fix the sample at a certain position and transmit the current, ISZ140 mA, for the sample. The strong photoresponse appears only in the vicinity of the QHE plateau with a two-peaked structure. Our previous work [7] showed that this feature can be reasonably interpreted to be due to electron heating effect caused by cyclotron absorption. Fig. 4 displays imaging plots of Vxx and VCE at ISZ 140 mA and BZ5.75 T (Landau-level filling factor, nZ 1.74, of the sample). We obtain the Vxx(x,y) data by differating V(x,y) over a distance of 50 mm in the direction of the length of the sample: Vxx(x,y)ZV(xCDx,y)KV(x,y) with DxZ50 mm [10]. The images obtained show that Vxx appears over the entire 2DEG channel, whereas CE is present only in a localized region. This means that Vxx observed in most part except in the area covered by CE originates from intra LLS. It is also found that a large Vxx shows up around the source contact and at one corner on the side of the drain contact. Comparing with the VCE data reveals that a strong CE appears in the similar region, indicating that Vxx observed in this localized area mainly arises from inter LLS. The above results show that spatial distributions of intra- and inter-LLS are markedly different.
4. Discussion In this section, we first discuss the contrasting situation of intra- and inter-LLS distributions, presented in Fig. 4, and secondly suggest possible improvement of spatial resolutions of the present scanning probe microscope.
Fig. 3. B dependence of RD (thin line) and Vsig (thick line) at ISZ140 and IDZ4 mA.
Fig. 4. Imaging plots of Vxx and VCE at IEZ0.3, ISZ140, and IDZ4 mA, and BZ5.75 T. The white broken lines denote the 2DEG boundaries of the sample.
Earlier works reported that inter-LLS is a relatively slow process (10–100 ns) [11] and accordingly the equilibrium length of excited electrons reaches a very long scale (100–300 mm) [12]. On the other hand, although there is no clear experimental information about intra-LLS, one can imagine that the scattering rate will be much higher because the scattering does not require much energy. If we assume that the main mechanism of intra LLS is impurity scattering originating from ionized donors in the AlGaAs layer, the characteristic length of intra LLS can be taken as period of the ionized impurities, 0.05–0.3 mm [13]. Based on this, the significant difference between intra- and inter-LLS distributions can be reasonably understood as arsing from that of the scattering process and the characteristic length scale. Finally, we would like to discuss spatial resolutions of the present system. The spatial resolution, 2 mm, of the electrometer system is determined by the size of the sensing area. Therefore, the resolution can be improved by using an electrometer with a reduced size 2DEG as sensing area. We envisage that further improvement would be achieved by implementing a metallic probe with a tip diameter of w100 nm between the electrometer and the sample. In this system, since the voltage sensing is made through capacitive coupling between the probe tip and the sample, a resolution is mainly determined by the tip diameter. As for the THz microscope, as long as we use the optics based on the lens system, the resolution is restricted by the diffraction limit of the microscope. In order to overcome this restriction, we will scan a small
Y. Kawano, T. Okamoto / Microelectronics Journal 36 (2005) 592–595
bow-tie antenna over the front surface of the sample. We expect that collecting THz radiation at a tip of the antenna would lead to a resolution of several mms.
5. Conclusion We have constructed a new type of scanning probe microscope using the QHE, where an electrometer and a THz microscope are combined. With this system, we have imaged spatial distributions of Vxx and VCE in the QHE Hall bar sample. The resulting data reveal that intra- and interLLS distributions are strikingly different, indicating similar difference of the scattering processes and their characteristic lengths.
Acknowledgements This work was supported by the Grant-in-Aid for Young Scientists (A) (16684007) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
595
References [1] K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45 (1980) 494. [2] D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48 (1982) 1559. [3] Forexample, see F. Delahaye, et al., Metrologia 22 (1986) 103. [4] T. Machida, T. Yamazaki, K. Ikushima, S. Komiyama, Appl. Phys. Lett. 82 (2003) 409. [5] G. Nachtwei, N.G. Kalugin, B.E. Saol, Ch. Stellmachv, G. Hein, Appl. Phys. Lett. 82 (2003) 2068. [6] Y. Kawano, T. Okamoto, Appl. Phys. Lett. 84 (2004) 1111. [7] Y. Kawano, Y. Hisanaga, H. Takenouchi, S. Komiyama, J. Appl. Phys. 89 (2001) 4037. [8] M.J. Yoo, et al., Science 276 (1999) 579; A. Yacoby, et al., Solid State Commun. 111 (1999) 1. [9] K.L. McCormick, et al., Phys. Rev. B 59 (1999) 4654. [10] Very sharp changes of Hall voltage VH occur in the junction regions between the current contacts and the 2DEG. In order to exclusively obtain the Vxx image, the data points associated with these sharp changes of VH are excluded from the final images. [11] S. Komiyama, T. Takamasu, S. Hiyamizu, S. Sasa, Solid State Commun. 54 (1985) 497; B.R.A. Neves, et al., Phys. Rev. B 52 (1995) 4666. [12] S. Komiyama, Y. Kawaguchi, T. Osada, Y. Shiraki, Phys. Rev. Lett. 77 (1996) 558; I.I. Kaya, et al., Europhys. Lett. 46 (1999) 62. [13] S.H. Tessmer, P.I. Glicofridis, R.C. Ashoori, L.S. Levitov, M.R. Melloch, Nature (London) 392 (1998) 51.