Nonparabolic macroscopic transport models for device simulation based on bulk Monte Carlo data Available to Purchase

We derive higher-order macroscopic transport models for semiconductor device simulation from Boltzmann’s transport equation using the method of moments. To obtain a tractable equation set suitable for numerical implementation the validity of the diffusion limit will be assumed which removes the convective terms from the equation system. The infinite hierarchy of equations is then truncated at the orders two (drift-diffusion model), four (energy-transport model), and six. Nonparabolicity correction factors are included in the streaming terms. Closure relations for the highest-order moments are obtained from a cold Maxwell distribution (drift-diffusion) and a heated Maxwell distribution (energy-transport). For the six moments model this issue is more complicated. In particular, this closure relation is identified to be crucial both in terms of accuracy and in terms of numerical stability. Various possible closure relations are discussed and compared. In addition to the closure of the highest-order moment, various transport parameters such as mobilities and relaxation times appear in the models and need to be accurately modeled. Particularly for higher-order transport models this is a complicated issue and since the analytical models used in our previous attempts did not deliver satisfactory results we extract all these parameters using homogeneous Monte Carlo simulations. Since all macroscopic transport models are based on rather stringent assumptions a practical evaluation is mandatory. Therefore, the proposed six moments model, a corresponding energy-transport model, and the drift-diffusion model are carefully compared to self-consistent Monte Carlo simulations.