Quasi-Fermi-level splitting in ideal silicon nanocrystal superlattices

Abstract

Silicon quantum dots open up the possibility for solar cells with a higher voltage than in the Si bulk but still based on crystalline Si. An upper limit of a solar cell's open circuit voltage is the splitting of the quasi-Fermi-levels under illumination. To determine this splitting, the band structure and the density of states of a superlattice of cubic silicon quantum dots is calculated. Furthermore, the absorption and the minority charge-carrier lifetime of size-controlled Si NCs in a silicon dioxide matrix are measured. From these data the excess carrier density under illumination with the AM1.5G solar spectrum is estimated to be about 10${}^{16}$ cm${}^{\ensuremath{-}3}$. Based on the density of states and the carrier concentration, the quasi-Fermi-levels are calculated. Superlattices of silicon nanocrystals in SiO${}_{2}$, Si${}_{3}$N${}_{4}$, and SiC are compared. It is found that under AM1.5G illumination the integrated density of states in the first miniband is always much higher than the excess carrier density and the splitting of the quasi-Fermi-levels follows the calculated band gap with an offset of about 0.36 eV.