A new treatment of the recombination term in the current continuity equations of semi‐conductor device models

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Abstract
An integral identity is derived by the method of Marchuk for the continuity equation of a carrier current in a semi‐conductor device. The coefficients of this identity are then approximated systematically. The terms involving the discretization of the carrier current turn out to be the same as those in the well known finite difference scheme of Scharfetter and Gummel, while those involving the recombination term are different. It is suggested that this new finite difference scheme will perform significantly better than the Scharfetter‐Gummel scheme especially in regions of the device where the net recombination is sharply peaked.

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