Interest in oxide electronics increased significantly after the discovery of a two-dimensional electron gas (2DEG) at the interface between the insulating complex oxides SrTiO3 (STO) and LaAlO3 (LAO). Despite rapid progress in the growth and characterization of these systems, the underlying mechanisms that determine the density of electrons in the 2DEG remains an area of active debate. In addition, experiments have recently shown that the dielectric constant of STO is highly field dependent, which could play a crucial role at the STO/LAO interface. This project investigates the effects of LAO layer thickness on the 2DEG density in the STO/LAO heterostructure. In order to address the dielectric constant, we are implementing a field-dependent dielectric constant, which is highly location dependent. The simulations were performed using nextnano3, a self-consistent Schrödinger-Poisson solver, using material parameters calculated from first principles. The simulations were performed on four different heterostructures to incorporate the effect of different interface and surface terminations. It was found that the carrier density increases with thickness of the LAO with saturation at 3.3*1014 cm-2 as predicted by theory. The strong field dependency of the dielectric constant tends to decrease the spreading of the electron gas into the STO layer, further localizing the 2DEG at the interface. The values determined from theory are in agreement with experiments.