Extension of the Rees basis function technique to simulate nonstationary transport

Shrinking device geometries have caused considerable interest in accurately modeling nonstationary transport in semiconductors using computationally efficient techniques. In this paper we describe an extension to a basis function technique first proposed by Rees (1973), to model nonstationary effects of electron transport in semiconductors. While the central focus of this paper is to demonstrate and analyze a novel technique to compute a good basis set (based on the “local-effect” and “flux” operations first described by Rees), the Rees technique itself is described in some detail here to serve as the foundation for subsequent arguments. Basis functions computed in this way are not restricted for use in the Rees technique alone-they are also useful in any approach that solves the semi-classical Boltzmann transport equation (BTE) spectrally. However, use of such functions in the Rees spectral technique allows the minimum simulation time-step of the precomputed “transport matrices” to be significantly reduced. Simulation results are presented to demonstrate this improvement in a limited field range