A transistor structure is formed to include a substrate and, overlying the substrate, a source; a drain; and a channel disposed vertically between the source and the drain. The channel is coupled to a gate conductor that surrounds the channel via a layer of gate dielectric material that surrounds the channel. The gate conductor is composed of a first electrically conductive material having a first work function that surrounds a first portion of a length of the channel and a second electrically conductive material having a second work function that surrounds a second portion of the length of the channel. A method to fabricate the transistor structure is also disclosed. The transistor structure can be characterized as being a vertical field effect transistor having an asymmetric gate.