Detailed analysis of a 4H-SiC MOSFET has been carried out by numerically solving the steady state semiconductor Drift-Diffusion equations. Mobility models for bulk phonon scattering, surface phonon scattering, surface roughness scattering, Coulomb scattering by interface traps and oxide charges, and high field effects, have been developed and implemented. A first principles Coulomb scattering mobility model has been developed specifically to model the physics of the inversion layer in 4H-SiC MOSFETs. The Coulomb scattering model takes into account, scattering of mobile charges by occupied interface traps and fixed oxide charges, distribution of mobile charges in the inversion layer, and screening. Simulated IV curves have been compared to experimental data. Density of states for the interface traps have been extracted, and seem to be in agreement with experimental measurements. Simulations indicate that occupied interface traps in 4H-SiC MOSFETs are responsible for mobility degradation, low currents and high threshold voltages. Their effect diminishes at high temperatures due to reduction in trap occupancy, and at high gate voltages due to increased screening. At high gate voltages, surface roughness scattering plays the major role in mobility degradation in 4H-SiC MOSFETs.