Size-dependent bandgap and particle size distribution of colloidal semiconductor nanocrystals

Abstract

A new analytical expression for the size-dependent bandgap of colloidal semiconductor nanocrystals is proposed within the framework of the finite-depth square-well effective mass approximation in order to provide a quantitative description of the quantum confinement effect. This allows one to convert optical spectroscopic data (photoluminescence spectrum and absorbance edge) into accurate estimates for the particle size distributions of colloidal systems even if the traditional effective mass model is expected to fail, which occurs typically for very small particles belonging to the so-called strong confinement limit. By applying the reported theoretical methodologies to CdTe nanocrystals synthesized through wet chemical routes, size distributions are inferred and compared directly to those obtained from atomic force microscopy and transmission electron microscopy. This analysis can be used as a complementary tool for the characterization of nanocrystal samples of many other systems such as the II-VI and III-V semiconductor materials.

Photocatalytic performance of Fe‐substituted ZnAl2O4 powders under sunlight irradiation on degradation of industrial dyes

“…The direct bandgap for the prepared ZnAl 2 O 4 where x = 0 was 5.60 eV, reflecting a small improvement over the gained value of 5.1 eV when urea was used as a fuel 20 . This optical band gap change can occur as a consequence of the various particle sizes and distributions contributing to a failure of uniformity in the expansion of the optical spectra 64 . The results indicate substantial reductions in bandgap quantities for all replacement zinc‐aluminum samples as a result of Fe 3+ ions, which were observed in comparison to pure samples.…”

“…20 This optical band gap change can occur as a consequence of the various particle sizes and distributions contributing to a failure of uniformity in the expansion of the optical spectra. 64 The results indicate substantial reductions in bandgap quantities for all replacement zinc-aluminum samples as a result of Fe 3+ ions, which were observed in comparison to pure samples. These findings are summarized in Table 4.…”

Synthesis and characterization of magnetic recyclable Fe-substituted zinc aluminate photocatalysts with enhanced sunlight-driven degradation of industrial dyes

“…The direct bandgap for the prepared ZnAl2O4 where x = 0 was 5.60 eV, reflecting a small improvement over the gained value of 5.1 eV when urea was used as a fuel [20]. This optical band gap change can occur as a consequence of the various particle sizes and distributions contributing to a failure of uniformity in the expansion of the optical spectra [55].…”

Size-dependent electron chemical potential in nanostructures derived from statistical configuration

“…where m ef f is the reduced mass and ε is the dielectric constant of the nanoparticles. Using a finite-depth square-well effective mass approximation to provide a quantitative description of the quantum confinement effect, Ferreira et al obtained a new analytical expression for the size dependence of colloidal semiconductor nanocrystals as [47]…”

“…At a certain size, there is an optimum temperature where the power factor is maximum. The optimum temperature can be derived from Equation (47). In this equation, the temperature occurs in η c , given by Equation (42).…”