Extinction Coefficients of CdSe, CdS, and CdTe Nanoplatelets in Solution: A Practical Tool for Concentration Determination

TL;DR

The paper addresses the challenge that nanoplatelet absorption spectra reveal thickness but not lateral size or concentration. It develops a theoretical framework for the frequency-dependent extinction coefficient of randomly oriented CdSe, CdS, and CdTe NPLs, showing that the integrated absorption coefficient universally scales with NPL surface area and thickness via $\overline\alpha$ and can be used to extract concentration from absorption measurements combined with TEM-derived lateral area. The approach is validated against CdSe NPL data, incorporating phonon decoherence through a temperature factor $f_T$, and yields practical guidelines for determining concentration using $N=\overline{A}/(b\overline{E})$, with $\overline{E}$ proportional to $S_{\rm NPL}$ and thickness. This framework bridges the characterization gap between quantum dots and NPLs, enabling rapid, non-destructive concentration determination and potentially generalizing to 2.5–7.5 ML CdSe/CdS/CdTe NPLs.

Abstract

Semiconductor nanoplatelets possess exceptional optical properties that make them promising candidates for next-generation optoelectronic applications. However, unlike quantum dots where absorption spectroscopy alone can determine both size and concentration, nanoplatelets present a significant characterization challenge: the absorption peak position reveals only thickness, providing no information about lateral dimensions or concentration. This limitation forces researchers to rely on time-consuming and costly elemental analysis techniques for complete sample characterization. Here, we present an experimentally verified theoretical framework that predicts the frequency-dependent absorption coefficient of randomly oriented CdSe, CdS, and CdTe nanoplatelets, enabling concentration determination from absorption measurements and lateral size estimates. Our model shows that the integrated absorption coefficient depends universally on nanoplatelet surface area and thickness, yielding a practical tool to extract concentrations without laborious elemental analysis. This approach bridges the characterization gap between quantum dots and nanoplatelets, offering a streamlined method for rapid sample analysis that could accelerate nanoplatelet research and applications.

Figures (6)

• Figure 1: Experimental absorption spectra (orange) with cubic spline interpolation (blue) for CdSe NPLs of varying thickness and lateral size. The integrated absorption coefficient $\overline{E}$ is calculated from the area under the first exciton peak (blue shaded region). The linewidth parameter $\Delta$, shown as a black horizontal line, is determined by doubling the left half-width at half-maximum. 4.5 ML samples are labeled A-C, and 5.5 ML samples are labeled A-F.
• Figure 2: Integrated extinction coefficient $\overline{E}$ (top) and peak extinction coefficient $E_\text{max}$ (bottom) as a function of lateral area in CdSe NPLs with thickness 4.5 ML (left) and 5.5 ML (right). Blue dots show experimental data. Orange lines fit Eq. (\ref{['eq:overline_E']}) to the $\overline{E}$ data, with the fitted $\gamma_\text{ph}$ shown in orange on the top panels. The slopes of the orange lines are $\overline{E}/S_\text{NPL} = 4524 \frac{\text{eV}}{\text{M cm nm}^2}$ for 4.5 ML NPLs and $2350 \frac{\text{eV}}{\text{M cm nm}^2}$ for 5.5 ML NPLs. The green line fits Eq. (\ref{['eq:Emax']}) to the $E_\text{max}$ data, with the fitted $\gamma_\text{ph}$ shown in green on the bottom panels.
• Figure 3: Integrated extinction coefficient, $\overline{E}$, plotted as a function of temperature in CdSe, CdS, and CdTe NPLs with thickness 2.5 through 7.5 ML as shown on the legends. Phonon coupling factor $\gamma_\text{ph} = 0.79$ is assumed.
• Figure S1: Exciton parameters in CdSe, CdS, and CdTe as a function of the NPL thickness $d$. (a) Exciton emission energy (eq. \ref{['eq:hbar_omega']}) (b) Electron effective mass (ref. shornikova_addressing_2018 for CdSe, Eq. \ref{['eq:me_kdotp']} for CdS and CdTe). (c) $\mathcal{Q}$ from Eq. \ref{['eq:Q']}. (d) 2D excitons' radius $a_{\rm 2D}$ and (e) Exciton binding energy $E_\text{b}$ as determined variationally using the ansatz Eq. \ref{['eq:wf']}.
• Figure S2: TEM images of 4.5 ML thick CdSe NPLs.