Determining quantum eigenfunctions in three-dimensional nanoscale structures

As semiconductor devices become ever smaller, their behavior is more likely to be determined by quantum mechanics than by classical physics. The starting point for the analysis of most nanoscale devices is the determination of the eigenstates and eigenfunctions of the structure. We present a method to solve the time-dependent Schrodinger equation that is capable of determining the eigenenergies and eigenfunctions of arbitrary three-dimensional nanostructures. The heart of this method is a formulation of the time-dependent Schrodinger equation into the finite-difference time-domain method. No approximations are made except the finite differencing of the derivatives for implementation in a computer.

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