DOI: 10.5061/dryad.2547d7x1z
title: Third-order photon correlations to extract single nanocrystal multiexciton properties in solution

description: Colloidal semiconductor nanocrystals are considered promising materials
 for high-flux optical applications including lasing,
 light-emitting diodes, biological imaging, and quantum optics.
 In high-flux applications, multiexcitons can significantly
 contribute to emission, influencing its brightness, spectral
 purity, and kinetics. As a result, understanding and controlling
 multiexciton emission in colloidal nanocrystal materials is of
 the utmost importance. In the past, singlenanocrystal photon correlation
 methods have been applied to understand biexciton and triexciton
 efficiencies, lifetimes, and spectra. While powerful, such methods suffer
 from user selection bias and require stable emission from single
 nanocrystals. To compensate for this shortcoming, second-order
 correlation methods were developed to extract
 sample-averaged biexciton properties from a solution of
 nanocrystals. Until now, however, the analogous thirdorder solution photon
 correlation methods remained unexplored. In this work, we present a
 pair of third-order photon correlation techniques to obtain the
 sample-averaged single nanocrystal triexciton quantum yield and
 lifetime in a solution-phase experiment. These techniques
 derive from the relationship between the Poisson probability of
 nanocrystal photon absorption and the intrinsic probability of
 nanocrystal photon emission. We validate the theoretical background
 of these techniques by creating a numerical model to simulate the
 diffusion and emission of many nanocrystals in solution. Our
 simulations confirm that the average triexciton quantum yield
 and triexciton lifetime can be extracted from a solution of
 nanocrystals. These techniques will enable researchers to gain a
 better understanding of the fundamental multiexciton properties
 of colloidal nanocrystals.
description: # Third-order photon correlations to extract single nanocrystal
 multiexciton properties in solution
 [https://doi.org/10.5061/dryad.2547d7x1z](https://doi.org/10.5061/dryad.2547d7x1z) ## Description of the data and file structure Files are stored in matlab (.mat) format ### Folder/File Naming There are two naming structures: One for the solution triexciton quantum yield data and the other for the solution triexciton lifetime data. #### Solution Triexciton Quantum Yield Data For the solution triexciton quantum yield data, the data is stored in folders with the naming convention 'Photons_jBX_iTX' where j and i correspond to the simulated biexciton and triexciton quantum yield, respectively.  Within each folder, the photon stream is split up into a series of photon stream batches which are named 'Photons_1', 'Photons_2','Photons_3',etc. #### Solution Triexciton Lifetime Data For the solution triexciton lifetime data, the data is stored in folders with the naming convention 'Photons_7p5BX_iTX' where i corresponds to the simulated triexciton lifetime. Within each folder, the photon is split up by each individual nanocrystal photon stream which are named 'qd_1', 'qd_2',' qd_3', etc. ### File Content #### Solution Triexciton Quantum Yield Data Each 'Photons_i' file contains three one-dimensional matlab arrays corresponding to the Channel A, Channel B, and Channel C photon streams to be correlated. The photon stream data is in units of picoseconds. We recommend that the third-order cross-correlations are performed on each photon stream batch individually, and then sum the third-order cross-correlations of each batch at the end. #### Solution Triexciton Lifetime Data Each 'qd_i' file contains one two-dimensional matlab array. The first column corresponds to the detection time of the event (in seconds) and the second column corresponds to the detector the event occurred at (0 = excitation time, 1 = Channel A, 2 = Channel B, 3 = Channel C, 4 = Channel D'). We recommend each 'qd_i' file is combined into one large photon stream to perform the Photon Number Resolved Analysis. Below is a sample code that concatenates all the NC photon streams: ``` function [chT] = ConcatenatePhotonStream(folderName) % determine number of files in the folder numNC = length(dir([[folderName], '/*.mat'])); % initialize the concatenated photon stream array chT = []; for ii = 1:numNC % load in the single NC photon stream photons = load([folderName '/qd_' num2str(ii) '.mat']).photons; % add the NC photon stream to the end of the total photon stream array chT = [chT;photons]; disp([num2str(ii) ' out of ' num2str(num_particles)]) end % sort the photon stream in time order chT = sortrows(chT); % convert the photon stream time from seconds to picoseconds chT(:,1) = chT(:,1)*1e12; end ``` ## **Update #1 (04/08/2025):** Third-order cross-correlation data was re-uploaded upon discovering a minor error in the third-order cross-correlation analysis algorithm that introduced a scaling factor to the data. ## **Update #2 (07/08/2025):** Updated the manuscript link now that the manuscript is accepted.