The structure includes transistors in rows and columns and each having an electric field-based programmable threshold voltage at either a first threshold voltage (VT) or a second VT. The structure further includes first and second signal lines for the rows and columns, respectively. Each first signal line is connected to transistors in a row and each second signal line is connected to transistors in a column. When operated in a switch mode, the transistors may or may not become conductive depending upon their respective VTs. Conductive transistors form connected pairs of first and second signal lines and, thus, create signal paths. The structure can also include mode control circuitry to selectively operate the transistors in either a program mode to set a first VT or an erase mode to set a second VT and to concurrently operate the transistors in the switch mode.