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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.

The purpose of this paper is to simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities.

The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well.

The importance of the inter-band scatterings is accurately evaluated for several values of the Fermi energy, addressing the issue related to the validity of neglecting the generation-recombination terms. It is found out that the inclusion of the inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy.

The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper.

As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort.