Integrated circuit transistor structures are disclosed that include a gate structure that is lattice matched to the underlying channel. In particular, the gate dielectric is lattice matched to the underlying semiconductor channel material, and in some embodiments, so is the gate electrode. In an example embodiment, single crystal semiconductor channel material and single crystal gate dielectric material that are sufficiently lattice matched to each other are epitaxially deposited. In some cases, the gate electrode material may also be a single crystal material that is lattice matched to the semiconductor channel material, thereby allowing the gate electrode to impart strain on the channel via the also lattice matched gate dielectric. A gate dielectric material that is lattice matched to the channel material can be used to reduce interface trap density (Dit). The techniques can be used in both planar and non-planar (e.g., finFET and nanowire) metal oxide semiconductor (MOS) transistor architectures.