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A new discretization scheme for the semiconductor current continuity equations

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4 Author(s)
Burgler, J.F. ; Inst. fur Integrierte Syst., ETH, Zurich, Switzerland ; Bank, R.E. ; Fichtner, Wolfgang ; Smith, R.K.

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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Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on  (Volume:8 ,  Issue: 5 )