Macroscopic Transport Models for Classical Device Simulation

Abstract

We review macroscopic transport models as used in classical device simulation such as drift-diffusion, hydrodynamic, and energy transport models. Using a systematic approach, these transport models are derived from the semiclassical Boltzmann equation by applying the method of moments. The drift-diffusion model is based on the first two moments of the Boltzmann equation, while hydrodynamic and energy transport models consider three or four moments. Within the framework of the diffusion approximation, the convective terms in the hydrodynamic models can be neglected, resulting in the much simpler diffusive energy transport models. A discussion of the physical assumptions needed for the validity of these models is given.

In cases where the energy distribution is insufficiently described by a heated Maxwellian distribution, energy transport models give poor results. Based on the diffusion approximation, a six-moment model generalizing the energy transport model is presented. All model parameters can be extracted from fullband bulk Monte Carlo simulations. The six-moment model is applied for the simulation of devices with channel length in the deca-nanometer regime. Short-channel and hot-carrier effects for which the heated Maxwellian assumption introduces particularly large errors are studied. Comparing all models, it is demonstrated that the six-moment model can improve on the drift-diffusion and energy transport models.