Ion bombardment induced surface roughening in submicron-scale is modelled. The effect of ion beam on the evolution of the surface is described as a Lévy stable shot noise. Height fluctuations are assumed to be smoothed out only by surface tension or diffusion, which is driven by height gradient. The resulting noise driven diffusion equation leads to the development of self-affine surfaces, where the roughness exponent α depends on the distribution of noise amplitude. High values of α ≈ 0.5 recently observed in experiments are shown to result from a shot noise proportional to the typical recoil displacements in cascades created by low energy, heavy ion bombardment.