We present numerical simulations for the design of gated few-electron quantum dot structures in the Si/SiO2 material system. Because of the vicinity of the quantum dots to the exposed surface, we take special care in treating the boundary conditions at the oxide/vacuum interfaces. In our simulations, the confining potential is obtained from the Poisson equation with a Thomas-Fermi charge model. We find that the dot occupancy can be effectively controlled in the few-electron regime.