A three-dimensional memory device includes an alternating stack of insulating layers and word lines located over a substrate, memory stack structures extending through the alternating stack and containing a respective vertical semiconductor channel and a respective memory film, drain select gate electrodes located over the alternating stack, extending along a first horizontal direction, and laterally spaced apart along a second horizontal direction, and a dielectric cap layer located between adjacent drain select gate electrodes. An air gap is located between adjacent drain select gate electrodes in the dielectric cap layer.