Thin film transistor memory cells are stackable, and employ bandgap engineered tunneling layers in a junction free, NAND configuration, that can be arranged in 3D arrays. The memory cells have a channel region in a semiconductor strip formed on an insulating layer, a tunnel dielectric structure disposed above the channel region, the tunnel dielectric structure having a multilayer structure including at least one layer having a hole-tunneling barrier height lower than that at the interface with the channel region, a charge storage layer disposed above the tunnel dielectric structure, an insulating layer disposed above the charge storage layer, and a gate electrode disposed above the insulating layer.