A model for optical gain in colloidal nanoplatelets

Cadmium chalcogenide nanoplatelets (NPLs) and their heterostructures have been reported to have low gain thresholds and large gain coefficients, showing great potential for lasing applications. However, the further improvement of the optical gain properties of NPLs is hindered by a lack of models that can account for their optical gain characteristics and predict their dependence on the properties (such as lateral size, concentration, and/or optical density). Herein, we report a systematic study of optical gain (OG) in 4-monolayer thick CdSe NPLs by both transient absorption spectroscopy study of colloidal solutions and amplified spontaneous emission (ASE) measurement of thin films. We showed that comparing samples with the same optical density at the excitation, the OG threshold is not dependent of the NPL lateral area, while the saturation gain amplitude is dependent on the NPL lateral area when comparing samples with the same optical density at the excitation wavelength. Both the OG and ASE thresholds increase with the optical density at the excitation wavelength for samples of the same NPL thickness and lateral area. We proposed an OG model for NPLs that can successfully account for the observed lateral area and optical density dependences. The model reveals that OG originates from stimulated emission from the bi-exciton states and the OG threshold is reached when the average number of excitons per NPL is about half the occupation of the band-edge exciton states. The model can also rationalize the much lower OG thresholds in the NPLs compared to QDs. This work provides a microscopic understanding of the dependence of the OG properties on the morphology of the colloidal nanocrystals and important guidance for the rational optimization of the lasing performance of NPLs and other 1- and 2-dimensional nanocrystals.