Optical Absorption in Nano-Structures: Classical and Quantum Models

In the last decade, nano-structured materials have gained a significant interest for applications in solar cells and other optical and opto-electronic devices. Due to carrier confinement, the absorption characteristics in these structures are quite different from the absorption in bulk materials and thin films. Optical absorption coefficients of a silicon nano-wire are obtained based on a semi-classical model where the photon-electron interaction is described by the interaction of an electromagnetic wave with the electrons in the valence band of a semiconductor. The absorption characteristics showed enhanced optical absorption but no resonant peaks. In our modified model, we have identified optically active inter band transitions by performing electronic structure calculations on unit cells of nano-dimensions. The absorption spectrum obtained here shows explicit excitonic processes. This absorption is tunable from the visible region to near UV portion of the solar spectrum. In our previous work on thin films (100？nm) of ITO, we have used classical Drude model to describe free electron absorption. Using the imaginary part of the calculated complex dielectric function, we have plotted the absorption coefficient versus wavelength of the photon and compared with the experimental data showing good agreement between theory and experiment. 1. Introduction The efficiency of a solar cell is dependent on the optical absorption of the material used to fabricate the solar cell. In bulk crystalline materials and even in thin films, the bulk absorption coefficient is the most important parameter that determines the optical absorption. Classical models such as Drude model or Drude-Lorentz model describe the optical absorption based on the complex dielectric function [1, 2]. This approach works very well for the absorption of photons by the electrons inside a band, for example, conduction band. However, from band to band excitation of electrons, a detailed understanding of the band structure of the material is essential. To calculate band structure in semiconductors, one has to invoke quantum mechanical models using Schrodinger's wave equation [3, 4]. In this paper, we illustrate the applications of classical and quantum models with examples from our past research on indium tin oxide (ITO) thin films [5, 6], silicon quantum dots [7], and silicon nanowires [8]. In nanostructures, excitons play a dominant role [9, 10]. 2. Classical Models 2.1. Drude Model When the energy of incident radiation is less than the band gap energy of a semiconductor (typically 1？eV), free