Solving the Poisson's and Schrodinger's equations to calculate the electron states in quantum nanostructures using the finite element method

Abstract

In recent years, the sizes of semiconductor nanostructures have become so small that we have to take into account quantum effects. Simultaneously the real geometry of the device is important. In this paper, the two dimensional electron wave functions and the quantized states energies are calculated from the Schrodinger's equation coupled with Poisson's equation using a finite element method. The system of equations is solved iteratively to a sell consistent solution. We have simulated two devices with different carriers confinement. We obtain the carriers density and energy, conduction band and potential in these structures.