Effects of Spatial Reproduction as a Result of the Interference of Electron Waves in Two-Dimensional Semiconductor Nanostructures with Parabolic Quantum Wells

Abstract

Effects of spatial nonuniformity for the probability flux density jx(x, z) or for the density of the quantum-mechanical current ejx(x, z), where e is the elementary charge) are studied. These effects arise in two-dimensional semiconductor nanostructures that consist of thin rectangular and wide parabolic quantum wells that are consecutively arranged in the direction of the electron-wave propagation (the x axis) and are oriented along the dimensional-quantization axis z. A nonuniform distribution of jx(x, z) arises as a result of interference of electron waves that propagate simultaneously in a wide quantum well over different quantum-dimensional subbands. Particular attention is paid to the effects of the spatial reproduction of electron waves in the nanostructures under consideration. It is shown that the transverse distribution jx(0, z) existing at the entry to the wide quantum well is reproduced to a certain accuracy at a distance of X1 from the entry. In addition, the initial distribution jx(0, z) is reproduced periodically in the sections Xq = qX1 (coefficients q are integers). The results of numerical calculations of magnitudes of these effects in the structures that are symmetric with respect to the z axis are reported; a modification of the effects under consideration in asymmetric nanostructures is considered.