Journal Article10.1109/43.24876
A new discretization scheme for the semiconductor current continuity equations
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TL;DR: A hybrid finite-element method to discretize the continuity equation in semiconductor device simulation is given, finding that the method works in any dimension and for (d-dimensional) simplexes as well as for quadrilaterals, bricks, prisms, and so on, although the authors have no proof that it will not break down in particular cases.
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Abstract: A hybrid finite-element method to discretize the continuity equation in semiconductor device simulation is given. Within each element of a finite element discretization, the current is uniquely determined by nodal values of the density and the potential. The authors use the integrability condition for a system of partial differential equations to obtain the equations that determine the current within the element. They then satisfy the continuity in the current flow across interelement boundaries in a weak sense. They have found that the method works in any dimension and for (d-dimensional) simplexes as well as for quadrilaterals, bricks, prisms, and so on, although they have no proof that it will not break down in particular cases. >
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