Determination of space-dependent electron distribution function by combined use of energy and Boltzmann transport equations: improvement, evaluation, and explanation

An improved extrapolation technique for obtaining space-dependent electron energy distribution functions by combining energy transport simulations with solutions to the homogeneous-field Boltzmann equation is presented. The accuracy of the method depends on two criteria. First, the validity of this method relies strongly on the accurate average energy, which is used as a vehicle for extrapolation and is ascertained by solving the energy balance equation. Second, the method should be applicable when the spatial variations of average energy are not appreciable over the distance of a mean free path. In light of the importance of the average energy, the details of application of the energy balance equation and their impact on the modeling of the distribution function are examined by comparison with the Monte Carlo calculations. An explanation for the success of the technique is presented. In addition to being efficient enough for daily use in device design, the method incorporates many of the physical details required for accurate analysis