Abstract
Macroscopic transport models based on the first six moments of Boltzmann's equation (Grasser et al., 2001) are a natural extension to the well known drift-diffusion (DD) model (two moments) and the various hydrodynamic and energy-transport models (three or four moments) (Grasser et al., 2003). In addition to the solution variables of the energy-transport (ET) model, which are the carrier concentration n = <1> and the average energy w/sub 1/ = <E>, the six moments (SM) model provides w/sub 2/ = <E/sup 2/>. The quantity /spl beta/ = (3/5)w/sub 2//w/sub 1//sup 2/ is the kurtosis of the distribution function and indicates the deviation from a heated Maxwellian distribution for which /spl beta/ = 1 holds (for parabolic bands). Here we present results of numerical solutions of consistent DD, ET, and SM models and compare them to self-consistent analytic-band (Jacoboni and Lugli, 1989) and full-band (Jungemann and Meinerzhagen, 2003) Monte Carlo (MC) simulation results.
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