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**Analysis of a discretization algorithm for stationary continuity equations in semiconductor device models.**
*(English)*
Zbl 0619.65116

An explanation is given for the apparent accuracy of the most commonly used method for discretization of the stationary continuity equations in semiconductor device models. The accuracy of this method does not depend on relatively small changes in the electrostatic potential or the quasi- Fermi potentials between neighboring mesh points, or on the flow of current essentially along the mesh lines as has been previously suggested. It is obtained because implicit in this procedure is a consistent, and fairly accurate, discretization of the associated systems for the stream functions and recombination potential.

Our analysis indicates suitable choices for various parameters appearing in the discrete system, and conditions on the construction and refinement of a mesh so as to obtain reasonable or optimal accuracy. In addition, it is determined that given the electrostatic potential distribution, the values of the device terminal currents (but not the point values of the carrier densities or the local current densities) can be computed with an accuracy independent of some of the bias voltages by this procedure.

Our analysis indicates suitable choices for various parameters appearing in the discrete system, and conditions on the construction and refinement of a mesh so as to obtain reasonable or optimal accuracy. In addition, it is determined that given the electrostatic potential distribution, the values of the device terminal currents (but not the point values of the carrier densities or the local current densities) can be computed with an accuracy independent of some of the bias voltages by this procedure.

### MSC:

65Z05 | Applications to the sciences |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |

78A35 | Motion of charged particles |

35J65 | Nonlinear boundary value problems for linear elliptic equations |

### Keywords:

mesh refinement; mesh generation; stationary continuity equations; semiconductor device models; electrostatic potential; quasi-Fermi potentials### References:

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