The Boltzmann equation for transport in semiconductors is projected onto spherical harmonics in such a way that the resultant balance equations for the coefficients of the distribution function times the generalized density of states can be discretized over energy and real space by box integration. This ensures exact current continuity for the discrete equations. Spurious oscillations of the distribution function are successfully suppressed by stabilization based on a maximum entropy dissipation principle avoiding the H-transformation. The derived formulation can be used on arbitrary grids as long as box integration is possible. The new approach works not only with analytical bands but also with full-band structures in the case of holes. Results are presented for holes in bulk silicon based on a full band structure and electrons in a Si NPN BJT. For the first time the convergence of the spherical harmonics expansion is shown for a device and it is found that the quasiballistic transport in nanoscale devices requires an expansion of considerably higher order than the usual first one. The stability of the discretization is demonstrated for a range of grid spacings in the real space and bias points which produce huge gradients in the electron density and electric field. It is shown that the resultant large linear system of equations can be solved memory efficiently by the numerically robust package ILUPACK.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks. Product Liability: The publisher can give no guarantee for the information contained in this book. This also refers to that on drug dosage and application thereof. In each individual case the respective user must check the accuracy of the information given by consulting other pharmaceutical literature.The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.