A DRAM array having trench capacitor cells of potentially 4F2 surface area (F being the photolithographic minimum feature width), and a process for fabricating such an array. The array has a cross-point cell layout in which a memory cell is located at the intersection of each bit line and each word line. Each cell in the array has a vertical device such as a transistor, with the source, drain, and channel regions of the transistor being formed from epitaxially grown single crystal silicon. The vertical transistor is formed above the trench capacitor.