a Matrix Iterative Path Variable Solution to the Boltzmann Transport Equation for Simulation of Electron Transport in Gallium Arsenide and Aluminum
Abstract
A path variable solution to the Boltzmann Transport Equation (BTE) is established, with an emphasis on the spatial homogeneous, steady state solution including multiple conduction band valleys. An iterative matrix solution is obtained via a reversal of order of the nested integrals and invoking the Dirac Delta function in the scattering description to obtain the matrix elements. This change of order of integration does not affect the value of the integral, but it affects the value of the integrand under the condition of equal roots in the delta function. This subtlety ensures total equivalence between the Rees's technique and the matrix iterative technique. The Rees's technique keeps track of electron transport in the time domain but the iterative matrix technique performs equivalent tracking in the vec{rm k}space domain. This matrix technique allows the computation of the final electron distribution function (EDF) without an apriori assumption about its shape. It also achieves its stability without including self scattering, and is capable of isolating effects due to different scattering mechanisms. The numerical algorithm is highly vectorizable and suitable for parallel supercomputers. The numerical results on elastic acoustic, nonequivalent intervalley and polar optical scatterings for both GaAs and Al_{rm x}Ga _{rm 1x}As are obtained under different electric fields and temperatures. Simulation results with insufficient vec{rm k} grid density near the equal root condition produces a large void in the EDF near k ~ 0 in the case of elastic acoustic scattering. An alternative approach using a perturbed value for pi gives good approximation to the actual EDF for elastic acoustic scattering as the void is diminished. Application of adaptive mesh techniques to obtain accurate transport parameters is highly recommended. The technique methodology is extended to formulate iterative matrix solutions for handling spatialinhomogenous, timedependent, tunneling junctions, reflecting boundaries, graded heterojunctions and ellipsoidal energy bands. A divergence term is proposed in handling the heterojunction case.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT........81W
 Keywords:

 X)GALLIUM(1 X)ARSENIDE (GALLIUM ARSENIDE;
 ALUMINUM;
 Engineering: Electronics and Electrical; Physics: Condensed Matter; Computer Science