Magnetotransport in p-type Ge quantum well narrow wire arrays

We report magnetotransport measurements of a SiGe heterostructure containing a 20 nm p-Ge quantum well with a mobility of 800 000 cm² V^-1 s^-1. By dry etching arrays of wires with widths between 1.0 μm and 3.0 μm, we were able to measure the lateral depletion thickness, built-in potential, and the phase coherence length of the quantum well. Fourier analysis does not show any Rashba related spin-splitting despite clearly defined Shubnikov-de Haas oscillations being observed up to a filling factor of ν = 22. Exchange-enhanced spin-splitting is observed for filling factors below ν = 9. An analysis of boundary scattering effects indicates lateral depletion of the hole gas by 0.5 ± 0.1 μm from the etched germanium surface. The built-in potential is found to be 0.25 ± 0.04 V, presenting an energy barrier for lateral transport greater than the hole confinement energy. A large phase coherence length of 3.5 ± 0.5 μm is obtained in these wires at 1.7 K.