A Model for the Optical Absorption in Porous Silicon Quantum Wires

TL;DR

This paper presents a new model for optical absorption in porous silicon quantum wires, emphasizing the limitations of traditional band gap extraction methods and highlighting the importance of size-dependent effects and band gap distribution.

Contribution

It introduces a pseudo 1D absorption model accounting for size-dependent oscillator strength and band gap distribution, challenging conventional Tauc plot analysis for nanostructures.

Findings

Traditional Tauc plots are inadequate for porous silicon.

Absorption depends on size-dependent oscillator strength.

Porosity can be non-destructively estimated from transmission data.

Abstract

In this paper, we analyse the optical absorption in porous silicon . This is the first attempt to explicitly demonstrate that it is not possible to extract the band gap of such low dimensional nanostructures like porous silicon from a Tauc plot of Square Root(alpha h nu) vs (h nu) . These objections are also valid for other reduced dimensional systems like quantum wires and quantum dots etc. So we model the absorption process assuming that porous silicon is a pseudo 1D material system having a distribution of band gaps. We show that in order to explain the absorption we specifically need to invoke - (a) k is not conserved in optical transitions,(b) the oscillator strength of these transitions depends on the size of the nanostructure in which the absorption takes place and (c) the distribution of band gaps significantly influences the optical absorption. A natural explanation of the temperature dependence of absorption in porous silicon also follows from our model . We have also shown that porosity can be inferred non-destructively from transmission measurements in the region of low absorption. One can easily generalize our equations and use them to analyse the absorption process of other low dimensional materials too .