  We address the properties of surface solitons supported by optical lattices
imprinted in photorefractive media with asymmetric diffusion nonlinearity. Such
solitons exist only in finite gaps of lattice spectrum. In contrast to
latticeless geometries, where surface waves exist only when nonlinearity
deflects light towards the material surface, the surface lattice solitons exist
in settings where diffusion would cause beam bending against the surface.
