Optical Properties and Electronic Structure of Amorphous Germanium

Abstract

The optical constants of amorphous Ge are determined for the photon energies from 0.08 to 1.6 eV. From 0.08 to 0.5 eV, the absorption is due to k‐conserving transitions of holes between the valence bands as in p‐type crystals; the spin‐orbit splitting is found to be 0.20 and 0.21 eV in non‐annealed, and annealed samples respectively. The effective masses of the holes in the three bands are 0.49 m (respectively 0.43 m); 0.04 m, and 0.08 m. An absorption band is observed below the main absorption edge (at 300 °K the maximum of this band is at 0.86 eV); the absorption in this band increases with increasing temperature. This band is considered to be due to excitons bound to neutral acceptors, and these are presumably the same ones that play a decisive role in the transport properties and which are considered to be associated with vacancies. The absorption edge has the form: ω2ϵ2∼(hω−Eg)2 (Eg = 0.88 eV at 300 °K). This suggests that the optical transitions conserve energy but not k vector, and that the densities of states near the band extrema have the same energy‐dependence as in crystalline Ge. A simple theory describing this situation is proposed, and comparison of it with the experimental results leads to an estimate of the localization of the conduction‐band wavefunctions.

Rethinking Coal: Thin Films of Solution Processed Natural Carbon Nanoparticles for Electronic Devices

“…To demonstrate the variation of the optical bandgaps across the natural carbon phase space and its modification with thermal processing, optical absorption spectroscopy was performed. Using the method developed by Tauc et al 38 to determine the value of an optical bandgap, a function of the product of the absorbance (α) and the photon energy (E) may be plotted as a function of photon energy and the x-intercept of a fit of the linear region gives the value of the optical band gap (Figure 3f). Because slightly different treatments of the density of states and matrix elements gives rise to different functional forms to be plotted on the ordinate, 39 we have used the square root of the product of the absorbance and the photon energy, (αE) 1/2 , as it is appropriate for the electrical states of a-C and hydrogenated amorphous carbon (a-C:H) 22 and fits the data reported here well.…”

Optical properties and surface characterization of pulsed laser-deposited Cu 2 ZnSnS 4 by spectroscopic ellipsometry

“…The fused silica substrate is fitted in all samples with a Sellmeier model [8]. The optical functions of the film and of the overlayer are both parameterized with a Tauc-Lorentz expression, typical of amorphous materials [9], but they are kept independent from each other. The overlayer is defined as partially depolarizing, with the depolarization fraction being a fitting parameter.…”

Synthesis of Nanoamorphous Germanium and Its Transformation to Nanocrystalline Germanium

“…The bandgap of nc-Ge can be predicted from E(d) = 0.66 + 16.8/d 2 , where the bulk bandgap of nc-Ge is 0.66 eV, 16.8 is all the constants in the expression for nc-Ge, d is the diameter of nc-Ge, and m e and m h are 0.123 and 0.33, [31] respectively; for the na-Ge, E(d) = 1.05 + 10.3/d 2 , where the bulk bandgap of na-Ge, m e , and m h are 1.05 eV, 0.22, and 0.43, [33,34] respectively (see Figure S6). Note also that the nanoparticles selected for size analysis are the largest ones in the solution, which are formed first and therefore they have the absorption at the lowest energy.…”