The spherical harmonics expansion method for assessing hot carrier degradation

Abstract

An overview of recent developments for solving the Boltzmann transport equation for semiconductors in a deterministic manner using spherical harmonics expansions is given. The method is an attractive alternative to the Monte Carlo method, since it does not suffer from inherent stochastic limitations such as the difficulty of resolving small currents, excessive execution times, or the inability to deal with rare events such as tunneling or low-frequency noise. In particular, the method allows for a resolution of the high-energy tail of the distribution function free from stochastic noise, which makes it very attractive for hot carrier degradation. We review recent improvements to the method and compare results obtained for a 250 nm and a 25 nm MOSFET, demonstrating the importance of electron-electron scattering in scaled-down devices.