  We consider Schr\"odinger operators on $L^2(R^d)$ with a random potential
concentrated near the surface $R^{d_1}\times\{0\}\subset R^d $. We prove that
the integrated density of states of such operators exhibits Lifshits tails near
the bottom of the spectrum. From this and the multiscale analysis by Boutet de
Monvel and Stollmann [Arch. Math. 80 (2003) 87] we infer Anderson localization
(pure point spectrum and dynamical localization) for low energies. Our proof of
Lifshits tail relies on spectral properties of Schr\"odinger operators with
partially periodic potentials. In particular, we show that the lowest energy
band of such operators is parabolic.
