The distribution function of hot carriers in state-of-the-art devices is insufficiently described using just the electric field or the average carrier energy as parameters. Still, the standard models to describe carrier transport in semiconductor devices, namely the drift-diffusion model and the energy-transport model rely on these assumptions. In this article we summarize our work on six moments transport models which allow an accurate characterization of the distribution function. Within this framework it is possible to selfconsistently model the scattering integral without resorting to the relaxation time approximation. In addition, hot electron processes such as impact ionization, which are difficult to model in lower order transport models, can be described accurately.

1 Introduction

Accurate modeling of hot carrier effects in modern semiconductor devices has become a crucial ingredient to successful device simulation. In the traditional drift-diffusion model the carrier gas is assumed to be in equilibrium with the electric field ^[1]. This assumption has been shown to be invalid as the distribution function lags behind the electric field, for both rising and falling fields. In order to obtain information about this non-local behavior of the distribution function, various hydrodynamic and energy-transport models have been proposed ^[2], ^[3], ^[4]