A Model for the Optical Absorption in Porous Silicon Quantum Wires

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 © 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 .