Recombination Kinetics of Excitonic Molecules and Free Excitons in Intrinsic Silicon

Abstract

Time-resolved spectra and luminescence decay-time measurements prove that at 1.8\ifmmode^\circ\else\textdegree\fi{}K the excitonic-molecule (EM) and free-exciton (FE) densities decay at different rates in pure silicon. The decay profile of the EM shows a postexcitation increase in luminesence followed by an approximately exponential decay with a decay time of 143 nsec. The FE decay consists of an initial transient followed by a longer nonexponential decay. These observations can be explained in detail by a pair of coupled differential equations governing the time decay of the EM and FE densities. The equations are based on the model used by Haynes to explain the EM recombination spectrum. Comparison of the theoretical and experimental decays shows that the EM decay time is 59 nsec, and the cross section at 1.8\ifmmode^\circ\else\textdegree\fi{}K for the formation of an EM from two FE's is about 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$. Based on these data, arguments are presented to show that the EM's decay primarily by a nonradiative Auger mechanism, which accounts for the low radiative efficiency. Thermal dissociation effects at higher temperatures can be semiquantitatively accounted for.