Germanium quantum wells on silicon-germanium

If the SiGe cap (ε_r = 15) between the Ge QW and the gate oxide is d = 20 nm thick, and the Ge content of the SiGe layer causes a band offset of ΔE_v = 0.3 eV, what maximum sheet density would you expect to be able to achieve in the QW before charge would start to accumulate at the oxide interface?

c. 1.2×10¹² cm^-2
 

For a valence band offset of ΔE_v = 0.3 eV and a cap thickness of d = 20 nm, we can estimate the maximum electric field in the cap which will be related to the charge density σ = ne in the QW by

[(ΔE_V/d)≃(ne/ε_rε₀)].So