Memory cells comprising thin film transistor, stacked arrays, employing bandgap engineered tunneling layers in a junction free, NAND configuration. The cells comprise 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 comprising 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 Arrays and methods of operation are described.