Spatially Inhomogeneous Distribution of the Quantum Mechanical Current Density at the Sub-Barrier Reflection of the Electron Wave from the Potential Step in the 2D Nanostructure

In this paper, the influence of the interference of electron waves during their reflection from a rectangular semi-infinite potential barrier to the spatial distribution of quantum mechanical current density еjx(x, z) (e is the electron charge and jx(x, z) is the flow of probability density) in a semiconductor 2D nanostructure is theoretically studied. The structure consists of narrow and wide rectangular quantum wells (QWs) arranged successively along the direction of electron wave propagation. It is assumed that the wave falls from narrow QW1 on a potential barrier of height V0 in wide QW2. It is shown that when a wave with energy less than V0 falls on the barrier, then, in certain conditions, spatially inhomogeneous distribution $$ej_{x}^{{\left( 1 \right)}}(x,z)$$ oscillating in a complicated way exists in QW1. An exponential attenuation and coordinate dependent leakage $$ej_{x}^{{\left( 2 \right)}}(x,z)$$ under the barrier may occur in QW2. It is shown that this behavior of $$ej_{x}^{{\left( 1 \right)}}(x,z)$$ and $$ej_{x}^{{\left( 2 \right)}}(x,z)$$ is caused by the interference of electron waves propagating through different quantum-dimensional subbands in the considered nanostructure.