Three-dimensional spectral solution of Schrodinger equation with arbitrary bands

The goal of this work is to obtain a numerical solution of the three-dimensional Schrodinger equation using arbitrary bands, for the calculation of confined states in conditions where the usual parabolic approximation is inadequate. A Fast Fourier Transform (FFT) algorithm was used for the numerical implementation. Two simple 3-D silicon structures were solved, a quantum capacitor and a quantum cavity, using an ellipsoidal multi-valley non-parabolic model of the band structure.