Energy Gap-Refractive Index Relations in Semiconductors - An Overview

Abstract

The refractive index and energy gap of semiconductors represent two fundamental physical aspects that characterize their optical and electronic properties. The applications of semiconductors as electronic, optical and optoelectronic devices are very much determined by the nature and magnitude of these two elementary material properties. These properties also aid in the performance assessment of band gap engineered structures for continuous and optimal absorption of broad band spectral sources. In addition, devices such as photonic crystals, wave guides, solar cells and detectors require a pre-knowledge of the refractive index and energy gap. Application specific coating technologies (ASPECTTM) [1] including antireflection coatings and optical filters [2] rely on the spectral properties of materials. The energy gap determines the threshold for absorption of photons in semiconductors. The refractive index in the semiconductor is a measure of its transparency to incident spectral radiation. A correlation between these two fundamental properties has significant bearing on the band structure of semiconductors. In 1950, Moss [3] proposed a basic relationship between these two properties using the general theory of photoconductivity which was based on the photo effect studies of Mott and Gurney [4], Smekal [5], Zwicky [6], Gudden and Pohl [7] and Pearson and Bardeen [8]. According to this theory, the absorption of an optical quantum will raise an electron in alkali halides to an excited state rather than freeing it from the center. Thermal energy then moves this electron to the conduction band from the lattice. Such a photo effect takes place in imperfections at certain lattice points, and thus, the electron behaves similar to an electron in an isolated atom with a dielectric constant of the bulk material. As a result of this effective dielectric constant, eEff, the energy levels of the electron are scaled down by a factor of 1=e2 Eff which approximately corresponds to the square of the refractive index, n. This factor, thus, should be proportional to the energy required to raise an electron in the lattice to an excited state as given by the Bohr formula for the ionization energy, E, of the hydrogen atom, E = 2p2 m*e 4 /e 2 h2 , where, m* is the electron effective mass, e is the electronic charge, e is the relative permittivity and h is the Plank constant. This minimum energy determines the threshold wavelength, ke, which then varies as the fourth power of the refractive index. Experimental data on different photoconductive compounds show that the values of n4 /ke were close to 77 throughout a range of refractive indices.