L−to−Xcrossover in the conduction-band minimum of Ge quantum dots

Screened-pseudopotential calculations of large $(\lesssim 3000$ atoms) surface-passivated Ge quantum dots show that below a critical dot diameter that depends on the passivant, the character of the lowest conduction state changes from an L-derived to an X-derived state. Thus, in this size regime, Ge dots are Si-like. This explains the absence, in a pseudopotential description, of a crossing between the band gaps of Si and Ge dots as a function of size, predicted earlier in single-valley effective-mass calculations. The predicted $\overrightarrow{L}X$ crossing suggests that small Ge dots will have an X-like, red shift of the band gap with applied pressure, as opposed to an L-like blue shift of large dots.