# Temperature Effect on Band gap in solid state calculation

I am new in solid-state calculation field.

There has been pretty well-known to use DFT or DFT+U method to calculate the electronic properties such as the band gap for metal, and semiconductors.

When I read the papers, I can always see that people say their band gap calculation is close to the experimental data. From what I know, band gap values are related to temperature, and the experimental condition is about the room temperature, but the calculation from DFT is at 0K! Can we compare the band gap at totally different temperatures? Also how about pressure?

I really appreciate any comments on this. Thank you.

You are absolute right: the electronic band gap depends on the temperature and pressure of the system.

One of the "problems" of DFT is that it fails calculating the band gap for several semiconductors materials. Even using DFT+U, the values may be far from experimental ones (sometime it is better just to use a scissor operator).

When comparing calculated with experimental values, it is only to have an idea of the band gap value, compare with previous publications and to check if the material does not change its conduction type (from semiconductor to semimetal/metal, for example).

The figure below show the calculated band gap temperature dependence for $$\ce{GaAs}$$ following the work of Blakemore [1]. The value for $$0\,K$$ is $$1.5\,eV$$ and for $$300\,K$$ is $$1.43\,eV$$ which are very close.

Recently, I came across with a publication that uses deep neural networks together with DFT to do calculations at finite temperatures [2]. Their workflow if available from GitHub [3].

Dependence with pressure is easier to consider as in most of the DFT software, you can set the pressure under the calculation will run.

References:
[1] J.S. Blakemore. Semiconducting and other major properties of gallium arsenide. J. Appl. Phys. 53, R123 (1982); DOI: 10.1063/1.331665
[2] J.A. Ellis, L. Fiedler, G.A. Popoola, N.A. Modine, J.A. Stephens, A.P. Thompson, A. Cangi, and S. Rajamanickam, Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks. Phys. Rev. B 104, 035120 (2021); DOI: 10.1103/PhysRevB.104.035120 (OpenAcess)
[3] Github: https://github.com/mala-project/mala

I think you can use yambo-code to calculate the temperature dependent correction to the electronic states from your ground state DFT calculation and in turn get the quasi-particle band structure and band gap at a finite temperature.

Take a look at their wiki page for electron-phonon coupling: https://www.yambo-code.eu/wiki/index.php/Electron_Phonon_Coupling