A 2D-non-parabolic six moments model

The most accurate way to describe carrier transport is to solve the Boltzmann transport equation (BTE), for instance with the very time consuming Monte-Carlo (MC) technique. On an engineering level however macroscopic transport models are more efficient. Multiplication of the BTE with weight functions, approximation of the scattering integral with a macroscopic relaxation time and integration over k-space yields, for instance, the drift-diffusion model, the energy transport model, and the six moments model. The challenge is to model higher-order transport parameters like the energy relaxation time tau₁, the second-order relaxation time tau₂, the energy mobility mu₁ and the second-order mobility mu₂ with as few simplifying assumptions as possible. A good choice is the use of tabulated, data extracted from MC simulations. So far, bulk data has been used to examine higher-order parameters in a device. However, important effects like surface roughness scattering or the quantization in inversion layers are not included in bulk MC-data.