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Implementation of Separable Scattering Mechanisms in Three-Dimensional Quantum Mechanical Simulations of a Silicon Quantum Wire

M.J. Gilbert, R. Akis and D.K. Ferry
Arizona State University, US

scattering, quantum wire, simulation, self-consistent

In order to understand the operation of any type of semiconductor device, one must consider the effects of scattering. For many years, Monte Carlo has been the workhorse that has yielded great insight into the operation of a wide variety of semiconductor devices. The Monte Carlo technique handles scattering in a very natural way where quantum mechanical rates are derived from Fermi’s Golden Rule and then applied to a distribution of electrons. However, Monte Carlo cannot account for the quantum effects that are seen in future devices. Therefore, other device simulation techniques, such as Green’s functions and scattering matrices have been proposed which can account for the quantum mechanical effects in these devices in three-dimensions. Nevertheless, the implementations of scattering in these Green’s function techniques are rather problematic, at best. We have developed a recursive scattering matrix approach to treat ballistic transport in small semiconductor devices. In a manner similar to Green’s function approaches, but more amenable to the site representation used in these methods, scattering can be computed on a mode basis and then transformed to the site basis. Here, we present results of the first implementation of separable phonon scattering rates in a three-dimensional, fully quantum mechanical, self-consistent device simulation.

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