Density of quantum states in quasi-1D layers

Recently, new quantum effects have been studied in thin nanograting layers. Nanograting on the surface imposes additional boundary conditions on the electron wave function and reduces the density of states (DOS). When the nanograting dimensions are close to the de Broglie wavelength, the DOS reduction is considerable and leads to changes in the layer properties. DOS calculations are challenging to perform and are related to the quantum billiard problem. Performing such calculations requires finding the solutions for the time-independent Schrödinger equation with Dirichlet boundary conditions. Here, we use a numerical method, namely the Method of Auxiliary Sources, which offers significant computational cost reduction relative to other numerical methods. We found the first five eigenfunctions for the nanograting layer and compared them with the corresponding eigenfunctions for a plain layer by calculating the correlation coefficients. Furthermore, the numerical data were used to analyze the DOS reduction. The nanograting is shown to reduce the probability of occupation of a particular quantum state, reducing the integrated DOS by as much as 4.1-fold. This reduction in the DOS leads to considerable changes in the electronic properties.