This paper investigates n-type doping of point-defect compensated high purity semi-insulating (HPSI) 4H-SiC using a pulsed laser (10 ns FWHM @ 260 nm) for the introduction of nitrogen to shallow depths. A thermal model is presented using COMSOL Multiphysics featuring nonlinear temperature dependent material properties and a volumetric heat source term that takes into account the laser absorption depth for common ultraviolet irradiating wavelengths. The temperature distribution in the material and the amount of time that the surface and near-surface regions are at high temperature determines how many laser pulses are required to dope to the desired depth, and simulation results are presented and fit to measured data. The simulations and measured data show that for shallow doping a short wavelength ultraviolet laser should be used to localize the heat at the surface so the dopant can't diffuse deep into the material. The laser enhanced diffusion process has been used to incorporate nitrogen into HPSI 4H-SiC with a measured surface concentration greater than 1020 cm-3 and a nonlinear thermal model was built.