Energy-band-structure calculation by below-band-gap spectrophotometry in thin layers of non-crystalline semiconductors: A case study of unhydrogenated 𝑎-Si

Abstract

We have in depth analyzed the refractive-index behavior and optical absorption of below-band-gap light, in order to calculate the basic parameters of the energy-band structure of thin layers of non-crystalline semiconductors. By carrying out a semi-empirical determination of the influence of the finite (non-zero) width of the valence and conduction electronic bands, we find the dependence of the index of refraction upon the photon energy, 𝑛(𝐸), which goes just one order beyond the Wemple–DiDomenico two-level single-oscillator expression, and we simultaneously obtain the spectral dependence of the absorption coefficient, 𝛼(𝐸). By model fitting the measured normal-incidence transmittance spectrum, we demonstrate that with a highlysensitive double-beam spectrophotometer, it can be accurately determined the energy distance, 𝐸M,Sol, between the corresponding ‘centers of mass’ of the bonding and anti-bonding electronic bands, and also a reasonable estimate of the so-called effective width, 𝛥eff , of both valence and conduction bands. We have used this devised optical approach with a series of uniform and non-uniform thin layers of unhydrogenated fully 𝑎-Si, grown by RF-magnetron-sputtering deposition, onto room-temperature transparent glass substrates. The advantages of our novel approach are mainly due to the additional attention paid to the roles of the weak-absorption Urbach tail and the thickness non-uniformity of the studied 𝑎-Si films. We have also used a universal normalincidence transmission expression reported by the authors in an earlier paper, which can be applied even to strongly-wedge-shaped semiconductor layers. Together with the use of the improved Solomon formula for the normal optical dispersion of the refractive index, the complete approach with all its elements constitutes the main novelty of the present paper, in comparison with other existing works.