Abstract
Until now, no analytical relationships have been derived for the temperature dependence of the Urbach energy in non-crystalline semiconductors. Consequently, the problem associated with the theoretical study of the temperature dependence of this energy has not been solved. This paper presents the results of theoretical calculations and attempts to establish the temperature dependence of the Urbach energy in non-crystalline semiconductors. A linear increase in the Urbach energy with increasing temperature is shown.
Highlights
Exponential frequency dependence of the light absorption coefficient in noncrystalline semiconductors near the optical absorption edge, i.e. in the frequency range ћω < Eg has the form [1]: α (= ћω ) const ⋅ exp ћω EU (1)where EU is the Urbach energy, which for noncrystalline semiconductors can take on a value of 30 - 100 meV
This paper presents the results of theoretical calculations and attempts to establish the temperature dependence of the Urbach energy in non-crystalline semiconductors
When calculating the Urbach energy for the slope of the exponential tails of the valence and conduction bands, the following values were chosen β1 = 14 eV−1 and β2 = 25 eV−1, β1 = 19 eV−1 and β2 = 25 eV−1. It can be seen from the figure that the calculated values of the Urbach energy obtained from formula (16) increase linearly with increasing temperature
Summary
Exponential frequency dependence of the light absorption coefficient in noncrystalline semiconductors near the optical absorption edge, i.e. in the frequency range ћω < Eg has the form [1]:. Let us calculate the Urbach energy for the spectra of the coefficient of optical transitions with the participation of localized electronic states at the exponential tails of the allowed bands. Calculations of expressions for determining the exponential absorption spectra were carried out in the cases of constant, parabolic, and linear distributions of the densities of electronic states at the boundaries of the allowed bands. An insignificant difference in the values of the spectral absorption coefficients of optical transitions with the participation of the above states was shown Based on these considerations, in order to simplify the analytical form of the expressions for these spectra, we consider the case of constant nonlocalized electronic states.
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