A Novel Approach to Spherical Harmonics Expansion for Electron Transport in Semiconductors
نویسنده
چکیده
Abstract. A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic band approximation are treated in detail. In these cases, the set of equations is equivalent to those obtained in the spherical-harmonics expansion. Stationary and homogeneous solutions are explicitly treated. In order to solve numerically the equations, a cut in the energy range is introduced. The modified model maintains the physical characteristics of the original equations. The solution of an asymptotic equation is found and compared to the numerical solutions.
منابع مشابه
Spherical Harmonics Expansion of the Vlasov-Poisson initial boundary value problem
We derive and analyze the ‘SHE’ (Spherical Harmonics Expansion) type system of equations coupled in energy. We also show that diffusive behavior occurs on long time and distance scales and we determine the diffusion tensor. The analysis is based on the governing kinetic equations arising in electron transport in semiconductors.
متن کاملInstitute for Mathematical Physics High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors
We present an asymptotic analysis (with the scaled mean free path as small parameter) of the spherical-harmonics expansion (SHE-) model for semiconductors in the case of a large electric eld. The Hilbert and Chapman-Enskog expansions are performed and the dependence of macro-scopic parameter-functions such as the mobility and the diiusivity on the details of the considered elastic and inelastic...
متن کاملThe Spherical Harmonics Expansion Method for Assessing Hot Carrier Degradation
An overview of recent developments for solving the Boltzmann transport equation for semiconductors in a deterministic manner using spherical harmonics expansions is given. The method is an attractive alternative to the Monte Carlo method, since it does not suffer from inherent stochastic limitations such as the difficulty of resolving small currents, excessive execution times, or the inability ...
متن کاملElectron Transport in Semiconductor Superlattices
In this paper, we rigorously derive a diffusion model for semiconductor superlattices, starting from a kinetic description of electron transport at the microscopic scale. Electron transport in the superlattice is modelled by a collisionless Boltzmann equation subject to a periodic array of localized scatters modeling the periodic heterogeneities of the material. The limit of a large number of p...
متن کاملHigh Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors
We present an asymptotic analysis (with the scaled mean free path as small parameter) of the spherical-harmonics expansion (SHE-) model for semiconductors in the case of a large electric field. The Hilbert and Chapman-Enskog expansions are performed and the dependence of macroscopic parameter-functions such as the mobility and the diffusivity on the details of the considered elastic and inelast...
متن کامل