A two-dimensional array of discrete dielectric template structures is formed over a substrate. A first dielectric spacer matrix may be formed in lower portions of the trenches between the discrete dielectric template structures. A second dielectric spacer matrix layer may be formed in upper portions of the trenches. A pair of a source cavity and a drain cavity may be formed within a volume of each of the discrete dielectric template structures. A source electrode and a drain electrode may be formed in each source cavity and each drain cavity, respectively. The gate electrodes may be formed prior to, or after, formation of the two-dimensional array of discrete dielectric template structures to provide a two-dimensional array of field effect transistors that may be connected to, or may contain, memory elements.