We studied the intrinsic alignment of liquid crystals (LCs) together with the distorted electric potential (DEP) effect on a substrate with one dimensional surface geometric grating (SGG). It was found that in the presence of such SGG, a periodic array of micro-domain structures arises naturally from the DEP effect. The formation of the regular micro-domains in a twisted nematic structure is explored. The micro-domain structure was found to significantly improve the gray scale stability of a LC display.