Monte Carlo algorithms for stationary device simulations

The stochastic method used to simulate the stationary transport in semiconductor devices is revised in terms of the numerical Monte Carlo theory. A mathematically based approach has been used to derive the basic simulation algorithms, previously devised from physical considerations. The approach reveals novel properties of the method. It is shown that the method can be interpreted as a regenerative stationary process. The ergodicity of the process is proved and the random variable whose realizations are independent is identified.