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To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.

A combination of finite difference and finite element methods is applied to deal with the differential operators in the Boltzmann transport equation. By taking advantage of a piecewise polynomial approximation of the electron distribution function, the collision operator can be treated without further simplifications. The finite difference method is formulated as a third order WENO approach for non‐uniform grids.

Comparisons with other methods for a well‐investigated test case reveal that the new method allows faster simulations of devices without losing physical information. It is shown that the presented model provides a better convergence behaviour with respect to the applied grid size than the Minmod scheme of the same order.

The presented direct solution methods provide an easily extensible base for other simulations in 1D or 2D. By modifying the boundary conditions, the simulation of metal‐semiconductor junctions becomes possible. By applying a dimension by dimension approximation models for two‐dimensional devices can be obtained.

The new model is an efficient tool to acquire transport coefficients or current‐voltage characteristics of 1D semiconductor devices due to short computation times.

New grounds have been broken by directly solving the Boltzmann equation based on a combination of finite difference and finite elements methods. This approach allows us to equip the model with the advantages of both methods. The finite element method assures macroscopic balance equations, while the WENO approximation is well‐suited to deal with steep gradients due to the doping profiles. Consequently, the presented model is a good choice for the fast and accurate simulation of one‐dimensional semiconductor devices.

The purpose of this paper is to present a new deterministic solution method to the coupled Boltzmann‐Poisson system for simulating semiconductor devices.

A non‐parabolic six‐valley model allows for the investigation of anisotropy effects. The solution method is based on a discontinuous piecewise polynomial approximation of the carrier distribution function. Integrating the Boltzmann equation over tiny cells of the phase space leads to a system of ordinary differential equations. The Poisson equation is selfconsistently solved by applying a finite element Galerkin approach.

Good agreement with shock‐capturing “WENO solutions” is obtained for n⁺‐n‐n⁺ silicon diodes. The anisotropy due to the six‐valley model affects considerably macroscopic quantities at the beginning of the transients. The method is also applicable to spatially two‐dimensional problems.

The presented method is extendable by including full band structure data, although the method is much easier applicable when analytical band structure models can be used.

The new model is an efficient tool to acquire transport coefficients for device simulations or to directly simulate one‐ or two‐dimensional submicron devices on a kinetic level.

New grounds are broken by introducing a fast finite volume method for solving the Boltzmann equation in the spirit of finding a weak solution. The presented model is a good choice for the simulation of anisotropy effects in silicon semiconductor devices.

Using full-potential density functional calculations we have investigated the structural and electronic properties of graphene and some of its structural analogues, viz., monolayer (ML) of SiC, GeC, BN, AlN, GaN, ZnO, ZnS and ZnSe. While our calculations corroborate some of the reported results based on different methods, our results on ZnSe, the two dimensional bulk modulus of ML-GeC, ML-AlN, ML-GaN, ML-ZnO and ML-ZnS and the effective masses of the charge carriers in these binary mono-layers are something new. With the current progress in synthesis techniques, some of these new materials may be synthesized in near future for applications in nano-devices.