Abstract
A time-dependent and multi-dimensional numerical modeling for semiconductor device operation is proposed, in which the quasi-Fermi potentials for electrons and holes rather than the carrier densities are directly analyzed. Fundamental equations for the quasi-Fermi potential are reduced to a diffusion equation that includes a drift term. Boundary conditions are straightforwardly derived from the device physics and are shown in a mathematically simple manner, independent of device structure complexities. From the viewpoint of numerical procedure, a combination of an implicit time integral and upwind difference scheme is adopted. The quasi-Fermi potential is a gradually changing value between the maximum and minimum external applied voltages, and the present method is suitable for numerical modeling. A time dependent and two dimensional analysis program has been developed. The advantages of the present modeling are demonstrated through the carrying out of sample calculations of, for example, MOSFET switching characteristics. Quick and stable convergence in the numerical scheme has been obtained over the range of practically used operation voltages.
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