A method for making crown-shaped capacitors with uniform capacitance from the center to the edge of the DRAM device is achieved. The uniform capacitance is achieved using a two-step planarization process or a uniformly deposited CVD sacrificial layer. After forming a first conducting layer in openings in an insulator, a sacrificial layer is spin coated on the substrate. The non-uniformity, by virtue of the spin coating, is then partially polished back to form a globally uniform surface followed by a plasma etch-back to leave portions of the sacrificial layer of equal height in the openings. The first conducting layer in the openings is uniformly recessed for making capacitors having uniform values across the DRAM device. In a second approach a relatively thin uniform CVD polymer is deposited requiring only a single polishing step or etch-back to achieve uniform portions of the polymer in the openings.