General Expression for the Size-Dependent Optical Properties of Quantum Dots

Abstract

While initial theories on quantum confinement in colloidal quantum dots (QDs) led to analytical band gap/size relations or sizing functions, numerical methods describe size quantization more accurately. However, because of the lack of reliable sizing functions, researchers fit experimental band gap/size data sets using models with redundant, physically meaningless parameters that break down upon extrapolation. Here, we propose a new sizing function based on a proportional correction for nonparabolic bands. Using known bulk parameters, we predict size quantization for groups IV, III−V, II−VI, and IV−VI and metal−halide perovskite semiconductors, including straightforward adaptations for negativegap semiconductors and nonspherical QDs. Refinement with respect to experimental data is possible using the Bohr diameter as a fitting parameter, by which we show a statistically relevant difference in the band gap/size relation for wurtzite and zinc blende CdSe. The general sizing function proposed here unifies the QD size calibration and enables researchers to assess bulk semiconductor parameters and predict the size quantization in unexplored materials.

Experimental Determination of the Molar Absorption Coefficient of Cesium Lead Halide Perovskite Quantum Dots

“…The sizes obtained for CsPbX 3 (X = Cl or I) in this work range from far below their respective Bohr diameters such as 3.1−14.3 nm in cesium lead iodides (Bohr diameter of ∼12 nm) to 1.9−13.6 nm for cesium lead chlorides (Bohr diameter of ∼5 nm). However, unlike the rich literature about II−VI and eq S1 (Auber et al 33 ) and eq S2 (Maes et al 9 ). Empty circles denote the literature data points.…”

“…Size-dependent absorption spectra of (a) CsPbCl 3 , (b) CsPbBr 3 , and (c) CsPbI 3 NCs dispersed in n-hexane. (d−f) Experimental data points (solid circles) as obtained from UV−vis absorbance spectroscopy and TEM images.The solid lines represent the best fit obtained from 1 and eq S1 (Auber et al33 ) and eq S2 (Maes et al9 ). Empty circles denote the literature data points.…”

“…The fits cover most of the data points for all of the perovskite halides, though there is a deviation from a few data points. However, the fitting for the sizing curve using a single-parameter fitting equation from Aubert et al 33 and a fitting equation from Maes et al 9 also can be useful in predicting the sizing curve in the larger size range, although they do not fit well in the lower size range, specifically for a size range of <5 nm as shown in Figure 3e. Thus, eq 1 is more suitable for sizing curves for all of the available literature values.…”

Synthesis of Weakly Confined, Cube-Shaped, and Monodisperse Cadmium Chalcogenide Nanocrystals with Unexpected Photophysical Properties

“…Consequently, the band gap as well as optical properties of the semiconductor nanocrystals would become strongly size-dependent, and the nanocrystals in this small size regime are commonly known as quantum dots . For instance, with the band gap being 1.66 eV and the exciton Bohr diameter being ∼10 nm in the bulk phase, − the emission color of the mostly studied spheroidal CdSe nanocrystals can be tuned from blue to red by varying their sizes from 2 to 8 nm. , Precisely tunable yet color pure emitters are of great demand in major industrial sectors. For instance, CdSe-based quantum dots offer otherwise-not-available color quality for liquid-crystal-display, which is rapidly becoming a mainstream technology in display industry .…”

Comment on “Size Dependent Optical Properties and Structure of ZnS Nanocrystals Prepared from a Library of Thioureas”

“…Although this type of function may fit well experimental data and provide reliable size calibration within the limits of the fitted data range, we recently pointed out the limitations of this approach, which often makes use of several adjustable parameters without physical meaning . To address this shortcoming, we proposed a general expression to describe size quantization in semiconductor nanocrystals, in an effort to standardize nanocrystal size determination based on optical band gap measurements .…”