A three-dimensional flash memory array incorporates thin film transistors having a charge storage dielectric arranged in series-connected NAND strings to achieve a 4F.sup.2 memory cell layout. The memory array may be programmed and erased using only tunneling currents, and no leakage paths are formed through non-selected memory cells. Each NAND string includes two block select devices for respectively coupling one end of the NAND string to a global bit line, and the other end to a shared bias node. Pairs of NAND strings within a block share the same global bit line. The memory cells are preferably depletion mode SONOS devices, as are the block select devices. The memory cells may be programmed to a near depletion threshold voltage, and the block select devices are maintained in a programmed state having a near depletion mode threshold voltage. NAND strings on more than one layer may be connected to global bit lines on a single layer. By interleaving the NAND strings on each memory level and using two shared bias nodes per block, very little additional overhead is required for the switch devices at each end of the NAND strings. The NAND strings on different memory levels are preferably connected together by way of vertical stacked vias, each preferably connecting to more than one memory level. Each memory level may be produced with less than three masks per level.