Statistical fluctuations for the noise current from random telegraph signals in semiconductor devices: Monte Carlo computer simulations and best fits

Random Telegraph Signals (RTS) has become a major source of variability in the electrical behavior of modern transistors. The major contribution of this work is a new model based on a Monte Carlo algorithm for the mechanisms leading to RTS noise in semiconductor devices. To describe the statistical sample noise current produced by Monte Carlo simulations we experiment with many possible fits using different functions. In order to perform this fitting we follow two distinct approaches: (a) by calculating the sampling moments and by direct substitution in assumed distributions and (b) by performing a non-linear fit using the Levenberg Marquardt algorithm. Our results show a breaking of gaussianity for the nanometer dimensions of deeply scaled technologies, and we show that the ECS peak function is the most appropriate distribution to fit suitably the data for these dimensions. Another relevant contribution is the study of how ballistic effects can change the current distribution. The results indicate an enlargement of the average and variance of the total current when ballistic effects are considered, which are analytically expressed as a function of relevant physical parameters of the semiconductor device.