Effects of electron transport dominate semiconductor device behavior. The main objective of the proposed research is to develop a comprehensive, physically accurate transport model, which is suitable for efficient numerical evaluation. The model will integrate two approaches for characterizing electron transport: the Legendre polynomial technique, and the energy transport method. In addition to determining current densities and electric potentials, when fully realized, the model will allow for rapid calculation of the electron distribution function throughout a device. Initial studies will focus on numerically solving the homogeneous Boltzmann transport equation, using Legendre polynomials, while incorporating the effects of phonon scattering, one non-parabolic conduction band, and impact ionization. The model will then be used to calculate currents generated by ionization in MOSFETs. Next, the effect of several conduction bands will be introduced. Finally, the effect of nonlinear electron-electron scattering will be accounted for by using Fokker Plank formulation. Spatial dependence will be obtained by evaluating the energy balance equation to determine the space-dependent average electron energy. The space-dependent distribution function will then be determined by simultaneous solutions of the energy balance equation and the homogeneous Boltzmann equation. This study will facilitate a better understanding of the physical phenomena which affect submicron device operation, and is well suited for applications in CAD.
