A physics based device simulator for detailed numerical analysis of 4H-SiC MOSFETs with an advanced mobility model that accounts for the effects of bulk and surface phonons, surface roughness and Coulomb scattering by occupied interface traps and fixed oxide charges, has been developed. A first principles quasi-2D Coulomb scattering mobility model specifically for SiC MOSFETs has been formulated. Using this, we have been able to extract the interface trap density of states profile for 4H-SiC MOSFETs and have shown that at room temperature, Coulomb scattering controls the total mobility close to the interface. High temperature, low field simulations and experiments show that the current increases with increase in temperature. The effect of Coulomb scattering decreases with increase in temperature causing an increase in the total mobility near the interface at low gate voltages.