  Experimental results obtained previously for the photoluminescence efficiency
(PL$_{eff}$) of Ge quantum dots (QDs) are theoretically studied. A
$\log$-$\log$ plot of PL$_{eff}$ versus QD diameter ($D$) resulted in an
identical slope for each Ge QD sample only when $E_{G}\sim (D^2+D)^{-1}$. We
identified that above $D\approx$ 6.2 nm: $E_{G}\sim D^{-1}$ due to a changing
effective mass (EM), while below $D\approx$ 4.6 nm: $E_{G}\sim D^{-2}$ due to
electron/ hole confinement. We propose that as the QD size is initially
reduced, the EM is reduced, which increases the Bohr radius and interface
scattering until eventually pure quantum confinement effects dominate at small
$D$.
