Semi-conductor wafers with thin and thicker regions at controlled locations may be for Photovoltaics. The interior may be less than 180 microns or thinner, to 50 microns, with a thicker portion, at 180-250 microns. Thin wafers have higher efficiency. A thicker perimeter provides handling strength. Thicker stripes, landings and islands are for metallization coupling. Wafers may be made directly from a melt upon a template with regions of different heat extraction propensity arranged to correspond to locations of relative thicknesses. Interstitial oxygen is less than 6×1017 atoms/cc, preferably less than 2×1017, total oxygen less than 8.75×1017 atoms/cc, preferably less than 5.25×1017. Thicker regions form adjacent template regions having relatively higher heat extraction propensity; thinner regions adjacent regions with lesser extraction propensity. Thicker template regions have higher extraction propensity. Functional materials upon the template also have differing extraction propensities.