Analytical techniques for the simulation of electron transport in semiconductor systems

This work investigates analytical techniques for the solutions of the coupled system of non-linear Schrodinger-Poisson Model for simulation of electronic states in semiconductor devices. Using techniques from complex analysis, we calculate the electrostatic potential and eigenvalues of the system. In particular, the eigenvalues and eigenfunctions are obtained via Evans function which is a complex analytical function. The results obtained for two and three dimensional systems show improved simulation times.