Abstract
For electron devices that make use of innovative materials, a basic step in the development of models and simulation computer aided design (CAD) tools is the determination of the mobility curves for the charge carriers. These can be obtained from experimental data or by directly solving the electron semiclassical Boltzmann equation. Usually the numerical solutions of the transport equation are obtained by Direct Simulation Monte Carlo (DSMC) approaches with the unavoidable stochastic noise due to the statistical fluctuations. Here we derive the mobility curves numerically solving the electron semiclassical Boltzmann equation with a deterministic method based on a discontinuous Galerkin (DG) scheme in the case of monolayer graphene. Comparisons with analytical mobility formulas are presented.
Highlights
Graphene is a gapless semiconductor made of a single layer of carbon atoms arranged into a honeycomb hexagonal lattice [ ]
An important step in the analysis of the electrical features of graphene is the determination of the mobility curves that can be inserted in the simulation computer aided design (CAD) tools already available for several semiconductor materials, e.g. Silicon and GaAs
The direct way to determine the mobility curves is by experiments
Summary
Graphene is a gapless semiconductor made of a single layer of carbon atoms arranged into a honeycomb hexagonal lattice [ ]. In the case of monolayer graphene, we derive the mobility curves numerically solving the electron semiclassical Boltzmann equation with a deterministic DG method [ , ]. In Section the transport equation for charge carriers in graphene is presented along with the derivation of the mobility expressions from the electron distribution functions. In this paper we consider the case of a high value of the Fermi energy, which is equivalent for conventional semiconductors to a n-type doping Under such a condition, electrons belonging to the conduction band do not move to the valence band and vice versa. The mobilities μi are assumed to be functions of the electric field and can parametrically depend on other physical quantities We will investigate their dependence on the Fermi level εF or equivalently on the electron density. If we are able to solve numerically the semiclassical Boltzmann equation, it is possible to get in a rather simple way the numerical values of the mobility as function of the electric field once the lattice temperature and Fermi energy have been assigned
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