Silicon is a material commonly used for solar cells and can be modified through pulsed laser melting, a hyperdoping method, which in theory can increase the efficiency of silicon solar cells. Hyperdoping is a process that incorporates other elements, such as gold, into the silicon lattice, allowing the material to capture a broader range of light. However, pulsed laser melting results in a dopant pile up near the surface of the material, so we hypothesized that surface etching would create a more effective concentration profile and maximize the material's excited electron survival rate. Using numerical simulation of electron diffusion and recombination, we investigate how the process of surface etching modifications on the concentration profile affects electron survival under both visible and infrared light. We determined that surface etching successfully results in a higher electron survival rate for gold hyperdoped silicon under both types of light. Under visible light, we found the ideal profile was a narrow distribution of gold in silicon, so that the electrons diffused quickly out of the doped area. Conversely, under infrared light, the ideal profile was a wide distribution of gold, which allowed a longer time frame before dopants diffused back into the doped area.