Role of Quantum Confinement in Luminescence Efficiency of Group IV Nanostructures

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 $Dapprox$ 6.2 nm: $E_{G}sim D^{-1}$ due to a changing effective mass (EM), while below $Dapprox$ 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 $D$.