Internal electronic structure and fine structure of multiexcitons in semiconductor quantum dots

Abstract

We perform a detailed theoretical study of the characteristic internal electronic structure of various multiexcitons $({N}_{h},{N}_{e})$, where ${N}_{h}$ is number of holes and ${N}_{e}$ is the number of electrons in the self-assembled semiconductor quantum dots (QDs). For each of the leading $({N}_{h},{N}_{e})$ excitonic complexes we start from the single-particle configuration (e.g., a specific occupation pattern of $S$ and $P$ electron and hole levels by a few carriers) and then show the many-particle multiplet levels for the initial state of emission $({N}_{h},{N}_{e})$ and the final state of emission $({N}_{h}\ensuremath{-}1,\text{ }{N}_{e}\ensuremath{-}1)$. We denote which states are dark and which are bright; the order and multiplicity, the leading single-particle character of each multiplet state, and the fine-structure splittings. These are of general utility. We also show explicit numerical values for distances between various transitions for four specific QDs. Here the presented information is important and potentially useful for a few reasons: (i) the information serves as a guide for spectroscopic interpretation; (ii) the information reveals non-Aufbau cases, where the dot does not have Aufbau occupation of carriers' levels; (iii) the information shows which transitions are sensitive to random-alloy fluctuations (if the dot is alloyed) and importance of this effect. We show that because of such alloy information, distances between peaks cannot be used to gauge structural information.