Model plasma dispersion functions for SO phonon scattering in Monte Carlo simulations of high-κ dielectric MOSFETS

Abstract

We have developed an accurate Padé approximant for the plasma dispersion function that is valid for degenerate semiconductors that occur in ultra-small MOSFETs. The new approximant is based on a two pole model that enables a simple evaluation of the Lindhard dielectric function for the full dynamic response of electrons of any degeneracy. The importance of this result is that it enables a fast numerical algorithm for determining the energies and scattering strengths of coupled plasmon-phonon modes in silicon MOSFET devices with high-κ gate stacks. Moreover, the formalism allows the systematic inclusion of Landau damping and other processes such as collisional damping that damp out some of the modes at particular ranges of wave vector. The new model is a non-trivially scaled model of a previous approximant derived for Boltzmann statistics. The new model reduces to the classical result in the appropriate limit. Results are presented that compare the exact numerically computed complex plasma dispersion function with the new Padé approximant model. Comparison is also made between exact numerical calculations and the Padé approximant model for static screening. A brief outline is made of the potential application to high-κ gate stack devices where the formalism should provide a significantly large reduction in complexity that will enable efficient Monte Carlo simulation of SO phonon and plasmon scattering.