A two-dimensional numerical simulation model of interface states in scanning capacitance microscopy (SCM) measurements of p-n junctions is presented. In the model, amphoteric interface states with two transition energies in the Si band gap are represented as fixed charges to account for their behavior in SCM measurements. The interface states are shown to cause a stretch-out and a parallel shift of the capacitance-voltage characteristics in the depletion and neutral regions of p-n junctions, respectively. This explains the discrepancy between the SCM measurement and simulation near p-n junctions, and thus modeling interface states is crucial for SCM dopant profiling of p-n junctions.