Direct observation of strain and confinement shaping the hole subbands of Ge quantum wells

Abstract

Germanium-silicon-germanium (Ge/Si$_{x}$Ge$_{1-x}$) heterostructures have emerged as a promising platform for hole-spin quantum technologies and high-mobility electronics, where strain and quantum confinement strongly reshape the Ge valence bands. However, the momentum-resolved valence-band structure of buried strained Ge quantum wells has so far been inferred only indirectly. Here we use soft X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to directly probe the electronic structure of strained Ge quantum wells embedded in SiGe barriers. We resolve strain-split and size-quantized valence subbands, determine their heavy-hole, light-hole and split-off composition, and measure the valence-band offset at the Ge/SiGe heterojunction. Comparison with ab initio calculations shows that an accurate description requires explicit inclusion of the confinement potential imposed by the SiGe barrier, which plays a decisive role in determining the dispersion, ordering and mixing of the hole states. Our results provide the first direct experimental picture of how strain and confinement determine the valence-band structure of Ge quantum wells, establishing a foundation for predictive modelling of hole-spin qubits and high-mobility devices based on group-IV heterostructures.