Numerical simulation of electron transport in mesoscopic structures with weak dissipation

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Abstract
A numerical method for simulating transient through steady-state electron transport in multidimensional mesoscopic structures in the presence of weak electron-phonon interactions is presented. This method allows both visualization and quantitative analysis of such electron-phonon coupling processes in these structures. To allow simulation of quantum interference effects within multidimensional structures, a previously developed method for simulating dissipationless transport based on the time-dependent Schrödinger equation is used as a starting point. Then, to allow simulation of the effects of electron-phonon coupling yet retain numerical tractability, a limited number of discretized harmonic oscillator degrees of freedom are added to those of the electron. Coupling between the electron and oscillator degrees of freedom is via Monte Carlo sampled potential functions that are obtained from the true electron-phonon coupling potentials. The method is exact to first order in the coupling and models some higher order coupling processes as well. Example simulations are performed for both real emission of polar-optical phonons and self-energy processes in prototypical mesoscopic structures.