Transistor structures with a deposited channel semiconductor material may have a vertical structure that includes a gate dielectric material that is localized to a sidewall of a gate electrode material layer. With localized gate dielectric material threshold voltage variation across a plurality of vertical transistor structures, such as a NAND flash memory string, may be reduced. A via may be formed through a material stack, exposing a sidewall of the gate electrode material layer and sidewalls of the dielectric material layers. A sidewall of the gate electrode material layer may be recessed selectively from the sidewalls of the dielectric material layers. A gate dielectric material, such as a ferroelectric material, may be selectively deposited upon the recessed gate electrode material layer, for example at least partially backfilling the recess. A semiconductor material may be deposited on sidewalls of the dielectric material layers and on the localized gate dielectric material.