A large amplitude surface plasma wave (SPW), propagating over a semiconductor-free space interface, is susceptible to filamentation instability. A small perturbation in the amplitude of the SPW across the direction of propagation exerts a ponderomotive force on free electrons and holes, causing spatial modulation in free carrier density and hence the effective permittivity εeff of the semiconductor. The regions with higher εeff attract more power from the nieghborhood, leading to the growth of the perturbation. The growth rate increases with the intensity of the surface wave. It decreases with the frequency of the SPW.