Sharp periodic Ge concentration modulations beyond the conduction band valley wavevector $k_0$ in nuclear spin-free Si quantum wells

Abstract

Periodic Ge modulations within strained Si quantum wells in SiGe heterostructures offer a route to deterministically enhance conduction-band valley splitting in Si, a key requirement for scalable spin-qubit quantum computing. Efficient enhancement requires modulations in the order of the Si valley wavevector $k_0$ (9.7 nm${}^{-1}$), corresponding to a period of 0.64 nm and near-monolayer growth control. Using nuclear-spin-free molecular beam epitaxy with ${}^{28}$Si and ${}^{72}$Ge, we demonstrate Ge-modulated Si quantum wells with periods from 2.00 to 0.49 nm, including modulations at $k_0$ and $2k_0/3$. Synchrotron X-ray techniques and scanning transmission electron microscopy reveal laterally homogeneous Ge modulations over micrometer scales, with amplitudes up to 10 at-% and gradients reaching 20 at-%/nm. Two-bands $\mathbf{k}\cdot \mathbf{p}$ simulations suggest deterministic enhancement of valley splittings in steep trapezoidal $2k_0/3$ heterostructures, while the effect in $k_0$-type quantum wells is much weaker.