A three-dimensional memory device includes alternating stacks of insulating strips and electrically conductive strips located over a substrate, generally extending along a first horizontal direction, and laterally spaced apart from each other along a second horizontal direction by width-modulated line trenches, memory films located on a respective sidewall of the alternating stacks, the memory films containing a charge storage layer and blocking dielectric which generally extend along the first horizontal direction and laterally undulate along the second horizontal direction, and a plurality of discrete vertical semiconductor channels located on a sidewall of a respective one of the memory films.