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Lateral tunneling through the controlled barrier between edge channels in a two-dimensional electron gas system
Physica B 272 (1999) 133}135
Lateral tunneling through the controlled barrier between edge channels in a two-dimensional electron gas system A.A. Shashkin!, V.T. Dolgopolov!, E.V. Deviatov!,*, B. Irmer", A.G.C. Haubrich", J.P. Kotthaus", M. Bichler#, W. Wegscheider# !Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia "Ludwig-Maximilians-Universita( t, Geschwister-Scholl-Platz 1, D-80539 Mu( nchen, Germany #Walter Schottky Institut, Technische Universita( t Mu( nchen, D-85748 Garching, Germany
Abstract We study the lateral tunneling through the gate-voltage-controlled barrier, which arises as a result of partial elimination of the donor layer of a heterostructure along a "ne strip using an atomic force microscope, between edge channels at the depletion-induced edges of a gated two-dimensional electron system. For a su$ciently high barrier a typical current}voltage characteristic is found to be strongly asymmetric and includes, apart from a positive tunneling branch, the negative branch that corresponds to the current over#owing the barrier. We establish that the barrier height depends linearly on both gate voltage and magnetic "eld and we describe the data in terms of electron tunneling between the outermost edge channels. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Nanostructures; Quantum Hall e!ect
Recently there has arisen much interest in the lateral tunneling into the edge of a two-dimensional electron system (2DES), which is related not only to the problem of integer and fractional edge states in the 2DES but also to that of resonant tunneling and Coulomb-blockade [1}9]. In contrast to vertical tunneling into the bulk of a 2D electron system at a quantizing magnetic "eld, when the 2D spectrum shows up, in the lateral tunneling electrons can always tunnel into the Landau levels that bend up at the edge to form edge channels where they intersect the Fermi level. As a result, the spectrum
* Corresponding author. Fax: #7-096-576-4111. E-mail address: [email protected] (E.V. Deviatov)
gaps are not directly seen in lateral tunneling and it re#ects, instead, the edge channel structure and density of states. We study the lateral tunneling through the gatevoltage-controlled barrier, which arises as a result of partial elimination of the donor layer of a heterostructure along a "ne strip using an atomic force microscope, between edge channels at the depletion-induced edges of a gated 2DES. The samples are submicron constrictions of the 2D electron layer in a GaAs/AlGaAs heterostructure in which the donor layer is removed along a "ne line across by locally oxidizing the heterostructure using AFM-induced oxidation [10]. This technique allows one to de"ne 140 As wide oxide lines of su$cient depth and oxide quality so as to
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 2 5 6 - 2
134
A.A. Shashkin et al. / Physica B 272 (1999) 133}135
Fig. 1. (a) Change in the onset voltages < and < with < at O T ' B"0 for the constrictions of di!erent widths =; and (b) the "t (dashed lines) of I}< curves (solid lines) by the exponentional dependence with the parameters ¸"0.6 lm (tunneling length), p "38 M)~1 (pre-exponent factor), < "!0.4 mV (thre0 5) shold voltage). In case (a), the data marked by "lled and open triangles are obtained for di!erent cooling of the sample.
partly remove the donor layer and, therefore, locally decrease the original electron density. The sample is covered with a metallic gate to tune the carrier density: when depleting the 2D layer the oxidized regions get depopulated "rst, resulting in the creation of tunnel barriers. Current}voltage (I}<) characteristics of the tunnel barriers are investigated at a temperature of about 30 mK at di!erent gate voltages and magnetic "elds. For the "rst time we "nd in the well-developed tunneling regime a typical current}voltage characteristic that is strongly asymmetric and includes, apart from a tunneling branch, the branch that corresponds to the current over#owing the barrier. The tunneling branch is much smaller and saturates rapidly in zero B with increasing bias voltage. The obvious reason for the asymmetry is the gate screening of in-plane electric "elds in the wide tunnel barrier as compared to the distance between the
Fig. 2. (a) Behaviour of the onset voltages < and < with O T magnetic "eld; and (b) the "t (dashed lines) of I}< curves (solid lines) by the calculated dependence at < "0 with the para' meters ¸"0.6 lm, p "1.3 M)~1, < "!1.4 mV. 0 5)
gate and the 2D electron layer. Another consequence of the gate screening is that the 2D band bottom in the barrier region should follow the gate potential, thereby giving an opportunity to control the barrier height. The onset voltages < and O < for these branches are de"ned in a standard way T by extrapolation of I}< branches to zero conductance. For the case of small tunneling probabilities the behaviour of the tunneling branch of I}< curves is easily calculated and has an exponential form. The expected dependence of the tunneling onset voltage < on gate voltage < is given by < J T ' T (!*< )3@2. The over#owing onset voltage < de' O termines the barrier height and thus should be proportional to the gate voltage. As seen from Fig. 1(a), the expected behaviour of both < and O < with changing < is indeed the case; the slope of T ' the former is very close to one. Fitting the set of I}< characteristics at di!erent < by the theoret' ical dependence is depicted in Fig. 1(b). One can see from the "gure that our model is con"rmed by the experiment at zero magnetic "eld.
A.A. Shashkin et al. / Physica B 272 (1999) 133}135
Switching a normal magnetic "eld gives rise to emerging tunnel barrier in a similar way to gate depletion, since electrons now have to tunnel through the magnetic parabola. As seen from Fig. 2(a), the change in the barrier height !e< with O B is very close to +u /2, which points to a shift of # the 2D band bottom by half of the cyclotron energy. For describing the tunneling branch of I}< characteristics we calculate the tunneling probability in the presence of a magnetic "eld if only the lowest Landau level is taken into account, i.e., the tunneling occurs substantially between the outermost edge channels. From our analysis it follows that at su$ciently strong magnetic "elds the tunneling onset voltage < is related to the barrier T height as < lJ+u /2!e*< , which is consistent T # ' with the experiment (Fig. 2(a)). Fig. 2(b) displays the "t of I}< characteristics at di!erent magnetic "elds by the calculated dependence. The calculation describes well the experimental I}< curves with the same barrier width as at zero magnetic "eld.
Acknowledgements This work was supported in part by the Russian Foundation for Basic Research under Grants
135
No. 97-02-16829 and No. 98-02-16632, the Programme`Nanostructuresa from the Russian Ministry of Sciences under Grant No. 97-1024, and Volkswagen-Stiftung under Grant No. I/68769.
References [1] A. Palevski, M. Heiblum, C.P. Umbach, C.M. Knoedler, A.N. Broers, R.H. Koch, Phys. Rev. Lett. 62 (1989) 1776. [2] K. Ismail, D.A. Antoniadis, H.I. Smith, Appl. Phys. Lett. 55 (1989) 589. [3] S.J. Manion, L.D. Bell, W.J. Kaiser, P.D. Maker, R.E. Muller, Appl. Phys. Lett. 59 (1991) 213. [4] A.J. Peck, S.J. Bending, J. Weis, R.J. Haug, K. von Klitzing, K. Ploog, Phys. Rev. B 51 (1995) 4711. [5] A.M. Chang, L.N. Pfei!er, K.W. West, Phys. Rev. Lett. 77 (1996) 2538. [6] M. Grayson, D.C. Tsui, L.N. Pfei!er, K.W. West, A.M. Chang, Phys. Rev. Lett. 80 (1998) 1062. [7] T. Bever, A.D. Wieck, K. von Klitzing, K. Ploog, Phys. Rev. B 44 (1991) 3424. [8] T. Bever, A.D. Wieck, K. von Klitzing, K. Ploog, P. Wyder, Phys. Rev. B 44 (1991) 6507. [9] T. Heinzel, D.A. Wharam, J.P. Kotthaus, G. BoK hm, W. Klein, G. TraK nkle, G. Weimann, Phys. Rev. B 50 (1994) 15. [10] B. Irmer, M. Kehrle, H. Lorenz, J.P. Kotthaus, Appl. Phys. Lett. 71 (1997) 1733.
Lateral tunneling through the controlled barrier between edge channels in a two-dimensional electron gas system A.A. Shashkin!, V.T. Dolgopolov!, E.V. Deviatov!,*, B. Irmer", A.G.C. Haubrich", J.P. Kotthaus", M. Bichler#, W. Wegscheider# !Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia "Ludwig-Maximilians-Universita( t, Geschwister-Scholl-Platz 1, D-80539 Mu( nchen, Germany #Walter Schottky Institut, Technische Universita( t Mu( nchen, D-85748 Garching, Germany
Abstract We study the lateral tunneling through the gate-voltage-controlled barrier, which arises as a result of partial elimination of the donor layer of a heterostructure along a "ne strip using an atomic force microscope, between edge channels at the depletion-induced edges of a gated two-dimensional electron system. For a su$ciently high barrier a typical current}voltage characteristic is found to be strongly asymmetric and includes, apart from a positive tunneling branch, the negative branch that corresponds to the current over#owing the barrier. We establish that the barrier height depends linearly on both gate voltage and magnetic "eld and we describe the data in terms of electron tunneling between the outermost edge channels. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Nanostructures; Quantum Hall e!ect
Recently there has arisen much interest in the lateral tunneling into the edge of a two-dimensional electron system (2DES), which is related not only to the problem of integer and fractional edge states in the 2DES but also to that of resonant tunneling and Coulomb-blockade [1}9]. In contrast to vertical tunneling into the bulk of a 2D electron system at a quantizing magnetic "eld, when the 2D spectrum shows up, in the lateral tunneling electrons can always tunnel into the Landau levels that bend up at the edge to form edge channels where they intersect the Fermi level. As a result, the spectrum
* Corresponding author. Fax: #7-096-576-4111. E-mail address: [email protected] (E.V. Deviatov)
gaps are not directly seen in lateral tunneling and it re#ects, instead, the edge channel structure and density of states. We study the lateral tunneling through the gatevoltage-controlled barrier, which arises as a result of partial elimination of the donor layer of a heterostructure along a "ne strip using an atomic force microscope, between edge channels at the depletion-induced edges of a gated 2DES. The samples are submicron constrictions of the 2D electron layer in a GaAs/AlGaAs heterostructure in which the donor layer is removed along a "ne line across by locally oxidizing the heterostructure using AFM-induced oxidation [10]. This technique allows one to de"ne 140 As wide oxide lines of su$cient depth and oxide quality so as to
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 2 5 6 - 2
134
A.A. Shashkin et al. / Physica B 272 (1999) 133}135
Fig. 1. (a) Change in the onset voltages < and < with < at O T ' B"0 for the constrictions of di!erent widths =; and (b) the "t (dashed lines) of I}< curves (solid lines) by the exponentional dependence with the parameters ¸"0.6 lm (tunneling length), p "38 M)~1 (pre-exponent factor), < "!0.4 mV (thre0 5) shold voltage). In case (a), the data marked by "lled and open triangles are obtained for di!erent cooling of the sample.
partly remove the donor layer and, therefore, locally decrease the original electron density. The sample is covered with a metallic gate to tune the carrier density: when depleting the 2D layer the oxidized regions get depopulated "rst, resulting in the creation of tunnel barriers. Current}voltage (I}<) characteristics of the tunnel barriers are investigated at a temperature of about 30 mK at di!erent gate voltages and magnetic "elds. For the "rst time we "nd in the well-developed tunneling regime a typical current}voltage characteristic that is strongly asymmetric and includes, apart from a tunneling branch, the branch that corresponds to the current over#owing the barrier. The tunneling branch is much smaller and saturates rapidly in zero B with increasing bias voltage. The obvious reason for the asymmetry is the gate screening of in-plane electric "elds in the wide tunnel barrier as compared to the distance between the
Fig. 2. (a) Behaviour of the onset voltages < and < with O T magnetic "eld; and (b) the "t (dashed lines) of I}< curves (solid lines) by the calculated dependence at < "0 with the para' meters ¸"0.6 lm, p "1.3 M)~1, < "!1.4 mV. 0 5)
gate and the 2D electron layer. Another consequence of the gate screening is that the 2D band bottom in the barrier region should follow the gate potential, thereby giving an opportunity to control the barrier height. The onset voltages < and O < for these branches are de"ned in a standard way T by extrapolation of I}< branches to zero conductance. For the case of small tunneling probabilities the behaviour of the tunneling branch of I}< curves is easily calculated and has an exponential form. The expected dependence of the tunneling onset voltage < on gate voltage < is given by < J T ' T (!*< )3@2. The over#owing onset voltage < de' O termines the barrier height and thus should be proportional to the gate voltage. As seen from Fig. 1(a), the expected behaviour of both < and O < with changing < is indeed the case; the slope of T ' the former is very close to one. Fitting the set of I}< characteristics at di!erent < by the theoret' ical dependence is depicted in Fig. 1(b). One can see from the "gure that our model is con"rmed by the experiment at zero magnetic "eld.
A.A. Shashkin et al. / Physica B 272 (1999) 133}135
Switching a normal magnetic "eld gives rise to emerging tunnel barrier in a similar way to gate depletion, since electrons now have to tunnel through the magnetic parabola. As seen from Fig. 2(a), the change in the barrier height !e< with O B is very close to +u /2, which points to a shift of # the 2D band bottom by half of the cyclotron energy. For describing the tunneling branch of I}< characteristics we calculate the tunneling probability in the presence of a magnetic "eld if only the lowest Landau level is taken into account, i.e., the tunneling occurs substantially between the outermost edge channels. From our analysis it follows that at su$ciently strong magnetic "elds the tunneling onset voltage < is related to the barrier T height as < lJ+u /2!e*< , which is consistent T # ' with the experiment (Fig. 2(a)). Fig. 2(b) displays the "t of I}< characteristics at di!erent magnetic "elds by the calculated dependence. The calculation describes well the experimental I}< curves with the same barrier width as at zero magnetic "eld.
Acknowledgements This work was supported in part by the Russian Foundation for Basic Research under Grants
135
No. 97-02-16829 and No. 98-02-16632, the Programme`Nanostructuresa from the Russian Ministry of Sciences under Grant No. 97-1024, and Volkswagen-Stiftung under Grant No. I/68769.
References [1] A. Palevski, M. Heiblum, C.P. Umbach, C.M. Knoedler, A.N. Broers, R.H. Koch, Phys. Rev. Lett. 62 (1989) 1776. [2] K. Ismail, D.A. Antoniadis, H.I. Smith, Appl. Phys. Lett. 55 (1989) 589. [3] S.J. Manion, L.D. Bell, W.J. Kaiser, P.D. Maker, R.E. Muller, Appl. Phys. Lett. 59 (1991) 213. [4] A.J. Peck, S.J. Bending, J. Weis, R.J. Haug, K. von Klitzing, K. Ploog, Phys. Rev. B 51 (1995) 4711. [5] A.M. Chang, L.N. Pfei!er, K.W. West, Phys. Rev. Lett. 77 (1996) 2538. [6] M. Grayson, D.C. Tsui, L.N. Pfei!er, K.W. West, A.M. Chang, Phys. Rev. Lett. 80 (1998) 1062. [7] T. Bever, A.D. Wieck, K. von Klitzing, K. Ploog, Phys. Rev. B 44 (1991) 3424. [8] T. Bever, A.D. Wieck, K. von Klitzing, K. Ploog, P. Wyder, Phys. Rev. B 44 (1991) 6507. [9] T. Heinzel, D.A. Wharam, J.P. Kotthaus, G. BoK hm, W. Klein, G. TraK nkle, G. Weimann, Phys. Rev. B 50 (1994) 15. [10] B. Irmer, M. Kehrle, H. Lorenz, J.P. Kotthaus, Appl. Phys. Lett. 71 (1997) 1733.