Calculation of hot electron distributions in silicon by means of an evolutionary algorithm

A new approach to simulate electronic transport at high energies in silicon is introduced, which is based on a mixture of evolutionary optimization algorithms and the Monte Carlo technique. The optimization technique of the evolutionary algorithm is used to find electron distributions which are in agreement with a given physical quantity, for example, a measured substrate current. In this way, the evolutionary algorithm can calculate backward the electron distributions from results of measurements. A mutation operator, which is based on the Monte Carlo technique, is used to direct the optimization of the evolutionary algorithm toward physically correct distributions. A comparison of the results of this new approach with electron distributions calculated by a full band Monte Carlo program demonstrates both the backward calculation ability of the evolutionary algorithm and the correctness of the physical model in the Monte Carlo-like mutation operator. It becomes obvious that the electron distribution in silicon is mainly determined by the scattering rates. By suppressing the optimization of the evolutionary algorithm the Monte Carlo-like mutation operator alone was found 10 provide a powerful new type of Monte Carlo technique. While these methods are not as precise as a full band Monte Carlo approach, they are shown to be numerically efficient and give also a good fit to reliability related bol electron effects.