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A simplified two-dimensional numerical analysis program has been developed for MOS devices. The calculation speed of this program is an order of magnitude faster than that of the finite-difference or finite-element methods due to the reduced number of analysis node points. The method solves only a one-dimensional current-continuity equation along the channel. Poisson's equation in two dimensions is replaced by an initial solution and a boundary-value problem formulation for the incremental potential and charge. In this method, the nodes are allocated only along the boundaries and the channel; therefore, it has a much smaller number of nodes than that required for other methods. MOS characteristics are simulated and compared with results from the finite-difference program [2], [9]. The agreement is satisfactory within 10 percent over a wide range of the substrate doping concentrations and channel lengths.
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Oh et al. (1980) studied this question.
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