The present invention provides two-transistor silicon-oxide-nitride-oxide-semiconductor (2-Tr SONOS) non-volatile memory cells with randomly accessible storage locations as well as a design structure including the semiconductor memory devices embodied in a machine readable medium. In one embodiment, a 2-Tr SONOS cell is provided in which the select transistor is located with a trench structure having trench depth from 1 to 2 μm and the memory transistor is located on a surface of a semiconductor substrate adjoining the trench structure. In another embodiment, a 2-Tr SONOS memory cell is provided in which both the select transistor and the memory transistor are located within a trench structure having the depth mentioned above.