An explicit method of numerical integration for the complete set of semiconductor device equations

A method is developed for solving the complete set of semiconductor device equations, based on the explicit method of integration with the characteristic features that time derivatives and spatially dependent intervals for the integration in time are introduced. Determination of the time intervals, which are of decisive importance for the method to converge, is made theoretically on the basis of the Gerschgorin circle theorem. Two categories of equation, with and without the second term on the right-hand side of each continuity equation, have been proposed, with the result that mixed use of these two categories exhibits improved characteristics in achieving convergence. Computations results for two bipolar transistor samples confirm the validity of the method. Comparison with a standard device simulator, TONADDE2, shows that the method requires 5 to 10 times more CPU time than the implicit method. However, it is hoped the explicit method will benefit more than the implicit method through the introduction of parallel processors