There is an empirical equation by Y.P. Varshni, but the science is missing. A formula needs to be developed to define this relationship based on science.
Ravi Chanana.
Dear Ravi,
Perhaps you had in mind the following:
How is the band gap of a semiconductor determined?
It is the width of this energy gap that makes a semiconductor a semiconductor. In this experiment you will use the temperature-voltage curve of a diode under constant current to determine the band gap for the diode material.[1] Safety note In this lab you will be working with a high-temperature mineral-oil bath.
Bandgap in a Semiconductor Diode - CSU, Chico
physics.csuchico.edu/~eayars/publications/bandgap.pdf
How does temperature affect the energy bandgap of a semiconductor?
2.2.5 Temperature dependence of the energy bandgap. The energy bandgap of semiconductors tends to decrease as the temperature is increased. This behavior can be better understood if one considers that the interatomic spacing increases when the amplitude of the atomic vibrations increases due to the increased thermal energy.
2.2.5 Temperature dependence of the energy bandgap
ecee.colorado.edu/~bart/book/eband5.htm
How does band gap affect thermoelectric conductivity?
It is observed that the electric conductivity depends upon the energy Band Gap of the thermoelectric material. As soon as the Band Gap of the thermoelectric material reduces, it automatically increases the thermoelectric performance. It was concluded that the Band Gap of the semiconductor tends to decrease as the temperature increases.
Determination of the Band-Gap of a Semiconductor: Germanium Chip U…
ijsr.net/archive/v5i2/NOV161376.pdf
What is the relationship between band gap energy and temperature?
The relationship between band gap energy and temperature can be described by Varshni 's empirical expression (named after Y. P. Varshni ), {\displaystyle E_ {g} (T)=E_ {g} (0)- {\frac {\alpha T^ {2}} {T+\beta }}} , where Eg (0), α and β are material constants.
Band gap - Wikipedia
en.wikipedia.org/wiki/Band_gap
temperature means the kinetic energy of the electrons
thus the energy of the electrons increases due to heat energy which would lead to a decrease in the energy band gap
https://ecee.colorado.edu/~bart/book/eband5.htm
but other classes of materials the energy bandgap increases
https://www.iue.tuwien.ac.at/phd/mwagner/node64.html
Dear Ravi,
The band gap of a semiconductor decreases with increasing temperature because at higher temperature the crystal lattice expands and the amplitude of interatomic vibrations increase and hence less energy is needed to promote an electron in the conduction band.
Do you know this paper?
https://www.tu-chemnitz.de/physik/RSTP/JAP97-02611.pdf
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