  We fabricate an undoped Ge quantum well under 30 nm Ge0.8Si0.2 shallow
barrier with reverse grading technology. The under barrier is deposited by
Ge0.8Si0.2 followed by Ge0.9Si0.1 so that the variation of Ge content forms a
sharp interface which can suppress the threading dislocation density
penetrating into undoped Ge quantum well. And the Ge0.8Si0.2 barrier introduces
enough in-plane parallel strain -0.41% in the Ge quantum well. The
heterostructure field-effect transistors with a shallow buried channel get a
high two-dimensional hole gas (2DHG) mobility over 2E6 cm2/Vs at a low
percolation density of 2.51 E-11 cm2. We also discover a tunable fractional
quantum Hall effect at high densities and high magnetic fields. This approach
defines strained germanium as providing the material basis for tuning the
spin-orbit coupling strength for fast and coherent quantum computation.
