In this article, we describe a framework for selecting the materials for phase shift masks (PSMs) in x-ray lithography to yield the optimal exposure latitude. Traditional design of PSMs involves choosing the thickness of the material to produce a pi phase shift, as in the case of clear phase shifting masks, or to produce the sufficient contrast needed for imaging with a requisite phase shift to improve linewidth control, as in the cases of attenuated phase shifting masks and half-tone phase shifting masks. We instead find the optical constants of a theoretical material that yield optimal exposure latitude, and try to find combinations or alloys of various materials that have the requisite optical constants.