In this work we report on the simulation of electrically pumped vertical external cavity surface emitting lasers (EP-VECSELs). We simulate an etched mesa structure (substrate emission) with the substrate acting as the current spreading layer. The effect of contact misalignment on the carrier distribution within the active element is explored and confirms the validity of the model in describing the carrier distribution. We go on to discuss the effects of the substrate thickness and trench depth on the intensity profile. Simulation results show that a thicker substrate and a trench partially etched into the substrate may improve the intensity profile in future devices.