IInfluence of Electron Interference Effects on Tunneling in 2D Semiconductor Nanostructures

V.A. Petrov, A.V. Nikitin
Institute of Radio Engineering and Electronics, Russian Academy of Sciences,
Russian Federation

Keywords: electron interference effects, 2D semiconductor nanostructures, probability current density


Influence of electron interference effects on the electron’s tunneling in a geometrically inhomogeneous semiconductor 2D nanostructure with a rectangular potential barrier is theoretically investigated. This 2D nanostructure is represented by sequentially located in the direction of wave’s propagation (axis x being a symmetry axis of a structure) narrow and wide in transverse direction (axis z being a dimensional quantization axis) quantum wells (QWs) of rectangular profile that are separated in their articulation point by tunneling barrier V in height. It has been supposed that the structure consists of three regions: reg. 1 (х < 0) а wide, reg. 2 represented by potential barrier А (0 < х < b) wide and reg. 3 (х > b) that is also А wide. The presence of geometrical irregularity of the structure leads to the scattering of electron wave on it, and, as a result of entanglement of wave functions of different regions due to their nonorthogonality, and to the possibility of propagation of waves along various dimensional subbands of the structure. We considered the situation when the fall of an electron wave of unit amplitude with longitudinal energy Ex< V occurs in the lower subband in reg.1.The most interesting one is the case when undamped wave reflection in reg. 1 at х → - ∞ is possible simultaneously on two subbands spaced by energies, its passing in reg. 3 at х → ∞ being possible in two or more subbands with real quasi-momenta. Interference of such waves in such situation leads to the occurrence of spatial dependence of probability current density jх (x, z) in such nanostructure. As a result of calculations it has been shown that transverse distribution jх (b, z), that exists on the entrance of reg.3 in the wide QW, is reproduced with certain accuracy at distance Х1 from the entrance (i.e., reproduction) and is periodically reproduced in cross-sections Хp = pХ1 (р being integer). And in the middle of every repetitive section of length Х1 it is split by z-symmetric nanostructure into 2 identical peaks with half as great intensity (i.e., multiplication). Inhomogeneous distribution jх (x, z) also occurs in reg. 1. Thus, for example, at b = 50 Å it includes periodically the following along negative direction of axis x peaks (regions) jх (x, z) that are accompanied by satellites with lesser amplitude in which the current density is directed in positive direction of axis x. At b = 150 Å, when the barrier reflection is high, besides the peaks (regions) with positive direction jх (x, z) there are regions in region 1 where jх (x, z) has an opposite direction. Besides that under the barrier on the boundary of regions 1 and 2 there is a region consisting of three parts, i.e., the central one in which jх (x, z) is directed in axis x positive direction and two side regions in which jх (x,z) is oppositely directed. Such distribution jх (x,z) exponentially subsides under the barrier. Parameters of structure based on GaAs are as following: a = 160Å ; A = 300Å.