Methods for removing a material layer from a base substrate utilizing spalling in which mode III stress, i.e., the stress that is perpendicular to the fracture front created in the base substrate, during spalling is reduced. The substantial reduction of the mode III stress during spalling results in a spalling process in which the spalled material has less surface roughness at one of its' edges as compared to prior art spalling processes in which the mode III stress is present and competes with spalling.