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It is invited statistical explanation of the frequency and temperature dependence of the absorption coefficients of semiconductors on the long-wave edge of the fundamental absorption. With the help of mathematical modeling, it shows that the thermal broadening of the energy states of the conduction band and the discrete states in the band gap can cause long-wave decline according to the Urbach rule.

In [

Changing in the thermodynamic density of states with temperature leads to the temperature dependence of the absorption coefficient. The light absorption coefficient is particularly sensitive to external influences at frequencies near the fundamental absorption edge. The light absorption coefficient on the long edge of the fundamental absorption is often described by the Urbach rule [

where

One of the main assumptions used in the analysis of experimental data is that the combined density of states determines the light absorption coefficient of the band gap of the semiconductor [

where

Temperature dependence must also occur in the absorption coefficient of light in the band gap of the semiconductor. Every model is used to explain the exponential absorption edge in semiconductors should explain and its temperature dependence.

The aim of this work is to study the influence of the temperature dependence of the thermodynamic density of states by a factor of light absorption (Urbach rule) on the long edge of the fundamental absorption.

Here we will use the results of this work and the final expression of the thermodynamic density of states at GN- functions [

The degree of empting discrete levels is determined by the statistics of Shockley-Read-Hall. When the time of ionization state with energy

GN-function takes the following form:

GN―a derivative of the ionization probability of the energy states in the energy and characterizes the thermal broadening of the energy state with energy

For direct transitions chosen in the following form

Here

Analyze the temperature dependence by means of numerical experiments.

With increasing temperature, the thermodynamic density of states of the conduction band are beginning to blur, and the intervals between the edge of the conduction band and the discrete levels begin to fill the new states of these levels. Just show how at a temperature T = 77 K. The solid density of states of the conduction band and the state of the discrete levels in the forbidden band merge (3 - 4). The total number of levels after the thermal smearing of states of the conduction band and the discrete levels remain constant. With further increase in temperature the fraction of states that have come from the conduction band, a much stronger increase in comparison with the share of the states due to the expansion of the discrete levels. In this case, the discrete levels and smeared across the band gap, and mixed with the states, will come from the conduction band. With increasing temperature, the contribution of the discrete states and the thermodynamic density of states are becomes noticeable and the thermodynamic density of states below the bottom of the conduction band is completely determined by the distribution of the density of states in the conduction band.

As a result, the total thermodynamic density of states is determined mainly levels received from the conduction band (line 5, 6). At a temperature T = 300 K, the relative share of localized states, and in the empty, is less than 1%. It follows that the density of states in the band gap below the bottom of the conduction band is completely determined by the states will come from the conduction band. This will be due to the broadening of the huge number of levels allowed zone.

Next, we consider the exponential dependence of (1) and the dependence of the thermodynamic density of states (2) in the band gap below the bottom of the conduction bands.

The results obtained are compared with experimental data [

Based on these studies, we can conclude that the thermodynamic state density at elevated temperatures penetrates into the band gap of the semiconductor. This gives an additional contribution to the tail states at the bottom of the conduction band, which falls into the band gap. Temperature dependence of the thermodynamic density of states with a common position may explain the long-wavelength edge of the fundamental absorption in semiconductors. The temperature dependence of the Urbach rule may be due to the thermal broadening of the energy states of the conduction band and the valence band of semiconductors. Approach and the mechanism proposed in this paper can simultaneously coexist with other mechanisms proposed in the literature as Urbach rule and encourage the most complete explanation of the experimental results.