Scaling of the Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) towards shorter channel lengths, has lead to an increasing importance of quantum effects on the device performance. Until now, a semi-classical model based on Monte Carlo method for instance, has been sufficient to address these issues in silicon, and arrive at a reasonably good fit to experimental mobility data. But as the semiconductor world moves towards 10nm technology, many of the basic assumptions in this method, namely the very fundamental Fermi’s golden rule come into question. The derivation of the Fermi’s golden rule assumes that the scattering is infrequent (therefore the long time limit) and the collision duration time is zero. This thesis overcomes some of the limitations of the above approach by successfully developing a quantum mechanical simulator that can model the low-field inversion layer mobility in silicon MOS capacitors and other inversion layers as well. It solves for the scattering induced collisional broadening of the states by accounting for the various scattering mechanisms present in silicon through the non-equilibrium based near-equilibrium Green’s Functions approach, which shall be referred to as near-equilibrium Green’s Function (nEGF) in this work. It adopts a two-loop approach, where the outer loop solves for the self-consistency between the potential and the subband sheet charge density by solving the Poisson and the Schrödinger equations self-consistently. The inner loop solves for the nEGF (renormalization of the spectrum and the broadening of the states), self-consistently using the self-consistent Born approximation, which is then used to compute the mobility using the Green-Kubo Formalism.