New Theoretical Model to Describe Carrier Multiplication in Semiconductors: Explanation of Disparate Efficiency in MoTe₂ versus PbS and PbSe

We present a theoretical model to compute the efficiency of the generation of two or more electron-hole pairs in a semiconductor by the absorption of one photon via the process of carrier multiplication (CM). The photogeneration quantum yield of electron-hole pairs is calculated from the number of possible CM decay pathways of the electron and the hole. We apply our model to investigate the underlying cause of the high efficiency of CM in bulk 2H-MoTe₂, as compared to bulk PbS and PbSe. Electronic band structures were calculated with density functional theory, from which the number of possible CM decay pathways was calculated for all initial electron and hole states that can be produced at a given photon energy. The variation of the number of CM pathways with photon energy reflects the dependence of experimental CM quantum yields on the photon energy and material composition. We quantitatively reproduce experimental CM quantum yields for MoTe₂, PbS, and PbSe from the calculated number of CM pathways and one adjustable fit parameter. This parameter is related to the ratio of Coulomb coupling matrix elements and the cooling rate of the electrons and holes. Large variations of this fit parameter result in small changes in the modeled quantum yield for MoTe₂, which confirms that its high CM efficiency can be mainly attributed to its extraordinary large number of CM pathways. The methodology of this work can be applied to analyze or predict the CM efficiency of other materials.