Carrier Multiplication in Semiconductor Nanocrystals: Theoretical Screening of Candidate Materials Based on Band-Structure Effects

Direct carrier multiplication (DCM) occurs when a highly excited electron-hole pair decays by transferring its excess energy to the electrons rather than to the lattice, possibly exciting additional electron-hole pairs. Atomistic electronic structure calculations have shown that DCM can be induced by electron-hole Coulomb interactions, in an impact-ionization-like process whose rate is proportional to the density of biexciton states rho(XX). Here we introduce a DCM "figure of merit" R-2(E) which is proportional to the ratio between the biexciton density of states rho(XX) and the single-exciton density of states rho(X), restricted to single-exciton and biexciton states that are coupled by Coulomb interactions. Using R2(E), we consider GaAs, InAs, InP, GaSb, InSb, CdSe, Ge, Si, and PbSe nanocrystals of different sizes, Although DCM can be affected by both quantum-confinement effects (reflecting the underly electronic structure of the confined dot-interior states) and surface effects, here we are interested to isolate the former. To this end the nanocrystal energy levels are obtained from the corresponding bulk band structure via the truncated crystal approximation. We find that PbSe, Si, GaAs, CdSe, and InP nanocrystals have larger DCM figure of merit than the other nanocrystals. Our calculations suggest that high DCM efficiency requires high degeneracy of the corresponding bulk band-edge states. Interestingly, by considering band structure effects we find that as the dot size increases the DCM critical energy E-0 (the energy at which R-2(E) becomes >= 1) is reduced, suggesting improved DCM. However, whether the normalized E-0/epsilon(g) increases or decreases as the dot size increases depends on dot material.