Having access to the colloidal quantum dot (QD) concentration is of great importance to avoid lengthy trial-and-error procedures in fundamental studies and practical applications of QDs. An efficient way to determine the QD concentration is based on the Beer-Lambert law (A= εcl). If the molar extinction coefficients (ε) of those QDs were known, the concentration (c) of suspended QDs can be readily determined by means of absorption spectrometry analysis. To date, the size dependent extinction coefficient properties have been focusing on binaries (Cd-, Pb- and Ag-chalcogenides, InP and InAs), while less attention has been paid to ternary QDs.
In this work, we quantitatively investigate the size dependence of the band gap, of the extinction coefficients, and of the absorption cross-section of ternary CuInS2 QDs over a wide size range (2.7–6.8 nm). We adopt partial cation exchange synthesis protocol to produce nearly stoichiometric and spherical CuInS2 QDs (polydispersity less than 10%) that are comparable in size, size distribution, shape and composition. The size dependence of the band gap allows us to construct a sizing curve valid from 2.7 to 6.8 nm. The extinction coefficients and absorption cross-section per CuInS2 formula unit both at high energies (3.1 eV) and at energies around the band gap are analyzed. The results demonstrate that the extinction coefficients of CIS QDs scale with their volume at high energies and the extinction coefficients at first excitonic transition energies follow a power law with a factor of 2.45. We notice that the absorption cross-section per formula unit at high energies (i.e., far above the band edge) is constant, suggesting that the use of extinction coefficients at high energies is better suited for analytical purposes.