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Item type:Publication, Access status: without files , Highly accurate quadrature-based Scharfetter–Gummel schemes for charge transport in degenerate semiconductorsWe introduce a family of two point flux expressions for charge carrier transport described by drift–diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoï finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newton's method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter–Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.Publicationtype: Journal Article230 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Highly accurate discretizations for non-boltzmann charge transport in semiconductors(IEEE, 2018-12-07); ; ; ; We present and analyze a family of highly accurate quadrature-based Scharfetter-Gummel fluxes for charge carrier transport in semiconductors which are particularly useful for non-Boltzmann statistics.Publicationtype: Conference Paper209 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi–Dirac and Gauss–Fermi statistics(2018-02-01); ; ; We compare three thermodynamically consistent Scharfetter–Gummel schemes for different distribution functions for the carrier densities, including the Fermi–Dirac integral of order 1/2 and the Gauss–Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter–Gummel scheme requires the solution of an integral equation. Since one cannot solve this integral equation analytically, several modified Scharfetter–Gummel schemes have been proposed, yielding explicit flux approximations to the implicit generalized flux. The two state-of-the-art modified fluxes used in device simulation software are the diffusion-enhanced flux and the inverse activity coefficient averaging flux. We would like to study which of these two modified schemes approximates the implicit flux better. To achieve this, we propose a new method to solve the integral equation numerically based on Gauss quadrature and Newton’s method. This numerical procedure provides a highly accurate reference flux, enabling us to compare the quality of the two modified Scharfetter–Gummel schemes. We extend previous results (Farrell in J Comput Phys 346:497–513, 2017a) showing that the diffusion-enhanced ansatz leads to considerably lower flux errors for the Blakemore approximation to the physically more relevant Fermi–Dirac and Gauss–Fermi statistics.Publicationtype: Journal Article153