The Fine-Structure Constant as a Ruler for the Band-Edge Light Absorption Strength of Bulk and Quantum-Confined Semiconductors

Abstract

Low-dimensional semiconductors have found numerous applications in optoelectronics. However, a quantitative comparison of the absorption strength of lowdimensional versus bulk semiconductors has remained elusive. Here, we report generality in the band-edge light absorptance of semiconductors, independent of their dimensions. First, we provide atomistic tight-binding calculations that show that the absorptance of semiconductor quantum wells equals mπα (m = 1 or 2 with α as the fine-structure constant), in agreement with reported experimental results. Then, we show experimentally that a monolayer (superlattice) of quantum dots has similar absorptance, suggesting an absorptance quantum of mπα per (confined) exciton diameter. Extending this idea to bulk semiconductors, we experimentally demonstrate that an absorptance quantum equal to mπα per exciton Bohr diameter explains their widely varying absorption coefficients. We thus provided compelling evidence that the absorptance quantum πα per exciton diameter rules the band-edge absorption of all direct semiconductors, regardless of their dimension.

Dielectric and optical properties of superlattices of epitaxially connected nanocrystals

“…2(c)]. We conclude that the amount of absorbed light per layer is the same in bilayer superlattices than in single layer ones, in agreement with experimental observations [15].…”

“…We also present tight-binding calculations of the optical absorptance of square lattices of PbSe (CdSe) NCs and propose a simple analytic model for the lowest-energy absorption peak. By comparison with measured data [15], we show that lattices of epitaxially connected NCs are characterized by approximately the same oscillator strengths as dispersed NCs but have considerably higher local-field factors. We also evaluate the excitonic effects in the particular case of NC dimers.…”

“…where the first term F 2 r = 4/(n s + 1) 2 accounts for the reflection of the light by the substrate [15,18]. F is here the local-field factor defined with respect to the external field composed of the incident and reflected fields.…”

“…Absorptance spectra of superlattices were measured in Ref. [15]. Those for square lattices of epitaxially connected PbSe and CdSe NCs are reproduced in Figs.…”

“…We conclude that atomically coherent superlattices of NCs are promising materials for cost-effective photodetectors, [39] not only for their tunable energy spectrum and their improved transport properties compared to assemblies of disconnected NCs [16] but also for their high absorptance, relatively close to the upper limit corresponding to the perfectly crystalline thin film (nanowire) in 2D (1D) systems, thanks to a reduced screening of the electric component of the external electromagnetic field. The present study of the permeation of the electromagnetic field in low-dimensional semiconductors is inspired by the recent findings [15] that this upper limit for band-edge absorptance in 2D systems such as graphene [17], semiconductor quantum wells [18,19] and atomically coherent superlattices of NCs have a universal character directly related to the absorptance quantum πα, where α is the fine structure constant.…”