Here I am talking about the conductivity of any semiconductor material like Bismuth telluride or lead telluride. Can anyone give the mathematical relationship. Thanks in advance.
For metals exist an easy relationship between thermal and electrical conductivities given by Wiedemann-Fran law. In general the ratio between thermal and electrical conductivities is linear in metals.
In metals the things are quite easy because the thermal conductivity is mainly due to the density of electrons and the phonons are almost negligible. But when you have semiconductors, allows or other interesting structures, the issue is much more complex and it is difficult to obtain a general dependence of the conductivities with the temperature.
I hope that this can helps.
As said above thermal conductivity of metals is contributed by conducting electrons and phonons. However, the contribution of phonons is smaller than electrons because electrons being light particles move relatively much faster than phonon group velocities. Hence electron motion carries thermal energy at a much faster rate than phonons. The Unklapp process responsible for back scattering naturally limits the conductvity contribution. However, for semiconductors the thermal conductivity contribution from phonons is not negligible and it depends on various factors. For example concentration defects and impurities is normally expected reduce thermal conductivity.
Dear Dr. Shubham Dewangan
Have a nice times and good day
The relationship between the thermal and electrical conductivities in case of semiconducting materials is very complicated and is different from material to another. This relationship is still under study till now. Many researchers have tried to get a common formula correlates between the two types of conductivities.
Good luck
Dear S. Dewangan,
After a hecgtic research, i got this formula which u may find useful. KIndly go thorugh the attached links:-
http://www.phy.pku.edu.cn/fsc//admin/fileadmin/upfile/Pat/1417399725624.pdf
https://arxiv.org/ftp/arxiv/papers/1011/1011.3864.pdf
Yes there is.The dependence is related to the material and it's dimension .
http://www.ajer.org/papers/v6(12)/A06120107.pdf
https://arxiv.org/pdf/1606.09287.pdf
https://www.nature.com/articles/srep10718
https://www.doitpoms.ac.uk/tlplib/thermal_electrical/printall.php
https://www.quora.com/What-is-the-difference-between-electrical-conductivity-and-thermal-conductivity
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