Available online at http://www.idealibrary.com on doi:10.1006/spmi.2001.1013 Superlattices and Microstructures, Vol. 31, No. 5, 2002 An explicit model for a quantum channel in 2DEG V ALERI A. F EDIRKO † ,MEI -HSIN CHEN,CHIUNG-CHUAN CHIU,S HI -F ONG CHEN, KAUNG-HSIUNG WU,J ENH-YIH J UANG,TZENG-MING UEN ,YI -S HUN GOU Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China (Received 22 November 2001) A two-parametric model for a channel in a two-dimensional electron gas (2DEG) is pro- posed which allows for the explicit analytical solution for the problem of quantum electron transport through the constriction. Conductance step smearing appears naturally and a sim- ple criterion for the step occurrence in terms of channel parameters is given. c  2002 Elsevier Science Ltd. All rights reserved. Key words: quantum electron transport, quantum constriction, conductance quantization, two-dimensional electron gas. 1. Introduction An interest has persistently been growing in micro- and nano-structures in which an electron can move ballistically through some active region [1]. Quantization of the conductance of a narrow ballistic channel in a two-dimensional electron gas (2DEG) by G 0 = 2e 2 / h , first discovered by van Wees et al. [2] and Wharam et al. [3], is, perhaps, one of the most exciting phenomena which can be realized in such structures. Moreover, the differential conductance may also be quantized in such structures as a function of applied bias [4, 5]. Though the principal physical reason for the quantization effects has been clear since the earliest works [2–5], various theoretical approaches have been exploited for treating the problem (see, e.g. [6–23]). Smooth [6–9, 17, 18] and abruptly [10–15] changing channel boundaries were assumed and some channel wall roughness [20, 21] was taken into account. The differential conductance quantization and other effects of non-zero bias [4, 5, 19, 22, 23] were described. The so-called ‘adiabatic’ approximation based on the Born–Oppenheimer approach [23] for a hard-wall smooth channel [6–9] is, perhaps, one of the most developed and widely used. Nevertheless no explicit model of a constricting quantum channel has yet been analysed which allows for an exact analytical adia- batic solution for electron quantum transmission. Such a model however, though not a general one in itself, could permit a good physical insight and provide physical criteria for experimental observation of quan- tization effects in terms of model structure parameters. 1 It is useful for experimental structure evaluation and for experimental data analysis and can be easily generalized. In this paper we propose and analyse a two-parametric model of that kind. † Permanent address: Moscow State University of Technology “Stankin”, Moscow 101472, Russia. 1 Actually, an attempt of that kind was undertaken in [17] but a parabolic potential used there can hardly be brought into correspondence to some real structure and is in fact only an approximation near the bottleneck. 0749–6036/02/050207 + 11 $35.00/0 c  2002 Elsevier Science Ltd. All rights reserved.