On the Scharfetter-Gummel Box-Method
For a linear potential function one-dimensional constant current drift-diffusion equations can be integrated in closed form, yielding the Scharfetter-Gummel (SG) discretization. The box-method generalizes the insistence on exact current conservation to higher dimensions by imposing the exact balancing of Scharfetter-Gummel fluxes through box-faces.
It has long been recognized that the one-dimensional SG discretization defines a finite element method that yields the exact solution by employing closed form solutions as an approximant. Finite element analyses of the box-method tend to employ piecewise linear approximating functions and fail to incorporate the exact integration properties of the SG discretization.
Nevertheless, the current conservation validates for the SG box-method an analytical coupling limitation for the differential drift-diffusion equations.
KeywordsPiecewise Linear Current Conservation Linear Interpolant Exact Balance Semiconductor Device Simulation
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