Figure 1

(a) The three-particle AR process in direct-gap bulk semiconductors. (b) Phonon-assisted four-particle AR process in indirect-gap bulk semiconductors. (c) AR in NCs. Relaxation of momentum conservation requirements in NCs diminishes the difference between direct- and indirect-gap materials with regard to AR.Reuse & Permissions

Figure 2

(a) Linear absorption spectra of Ge NCs indicate an absorption onset, which is blueshifted in comparison to bulk Ge [19]. Insets: Examples of large-area (upper left corner) and high-resolution (lower right corner) transmission electron micrographs of Ge NCs indicating good size monodispersity and a high degree of crystallinity. (b) Pump-intensity-dependent TA dynamics of 1.85 nm radius Ge NCs for average initial exciton occupancies from 0.016 to 8.3. Inset: Pump-intensity dependence of early- and late-time TA signals. (c) Pump-intensity dependence of TA signals shortly after excitation for Ge NCs with radii of 1.85, 2.75, and 5.0 nm (symbols) fit to a linear dependence (line). (d) Long-time TA signals ($t\gg {\tau }_2$) as a function of $⟨N_0⟩$ fit to the Poissonian distribution describing the total number of photoexcited NCs. Inset: Absorption cross sections (symbols) derived from fits to experimental data in the main panel in comparison to calculations based on the $R^3$ scaling (line; the shaded region is the range of uncertainty due to the distribution in NC sizes).Reuse & Permissions

Figure 3

(a) Biexcitonic decay component in Ge NCs as a function of NC size. Symbols are color-coded according to NC size, while different shapes correspond to different initial occupancies. (b) Biexciton lifetimes in Ge NCs (symbols) fit to the $R^3$ dependence (line). Stirred (squares) and unstirred (circles) samples produce essentially identical results, indicating that ionization and photodegradation processes do not affect our measurements. (c) Auger constants of bulk (solid square) and NC (open square) Ge as a function of $E_g$. (d) $C_A$ in bulk (solid symbols) and NC (open symbols) forms of direct-gap semiconductors PbSe (squares), InAs (triangles), and CdSe (circles) as a function of $E_g$. Lines are projected values of $C_A$ based on bulklike exponential dependences of Auger constants on $E_g$.Reuse & Permissions

Figure 4

Universal size dependence of AR constants in semiconductor NCs. When plotted as a function of NC radius, $C_A$ values for NCs of both direct- and indirect-gap semiconductors show a similar size dependence described by $C_A=\gamma R^3$ (corresponds to the direction of the shaded stripe).Reuse & Permissions