Solutions to Fokker-Planck Equations for Non-Gaussian White Noise in FET Undergoing Weak Inversion

We study the dynamics of charge transport under weak inversion. In this regime, uncertainties in the charge distribution and propagation are dominant. A couple of assumptions were made for the white noises present during weak inversion which include the probability function following a Markov process and can be represented as having non-Gaussian properties as the charges accumulating at the metal due to the presence of the gate electrons follow a non-Gaussian distribution. The system is be analyzed using the Levy-Khintchine formula which works when the source of perturbation to the system behaves in non-uniform manner. The probabilistic particle fluxes are obtained for this type of white noises in the presence and in the absence of any external influences by analyzing the characteristic function of the noisy source and finding the solutions of the equivalent Fokker-Planck equation.