Thermo-mechanical theory of a device film-on-foil structure reveals that the layer-to-layer alignment accuracy and the radius of curvature of the structure are both controlled by the mismatch strain between the deposited films and the substrate. Amorphous silicon thin-film transistors fabricated on thin foils of steel or plastic must be grown with tensile built-in stress to make the structure as flat as possible, and for accurate layer-to-layer alignment.