Hello, when a semiconductor is heated then the lattice expands and the bandgap shrinks.

Some references to other semiconductor you can find here:

http://www.ioffe.ru/SVA/NSM/Semicond/

under tempearture dependence. For ZnO, the oldest reference I know is this:

http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220640159/pdf

Phenomenologically, the relationship between bandgap and temperature may be described by Varshni's empirical expression,

E g ( T ) = E g ( 0 ) − α T ^2 / (T + β)

{\displaystyle E_{g}(T)=E_{g}(0)-{\frac {\alpha T^{2}}{T+\beta }}} ,

where Eg(0), α and β are constants.

Hello,

Thankx for your interesting comment.

Varshni describe well the variation of bandgap energy. I used it.

Then, I calculate the varaiation of lattice constante (c and a). It's interesting for my study to consist the modification of c and a to the variation of bandgap !!!

Best regards.

Dear Bouzouraa, I agree with the Dr. Thomas, because in the function of temperature, atom of the material will start vibration resulting expenditure of unit cell (including c and a for ZnO hexagonal). This effect will modified the band gap of the material. I think u are confusing in three phenomena temperature, lattice constant and band gap energy, but all are related to each other. The main cause of this confusion is temperature, which will effect to both lattice constant and band gap energy.

Thanks dear Gaurav for your comment.

Me also I agree Dr. Thomas. Just I want confirm by a formulation that the modification of lattice results a shift of bandgap energy.

I research a formulation between the lattice and the bandgap energy. It's concern the ab-initio calculation. I'm not a specilist in it (ab-initio).

Best regards.

Bouzouraa Montassar.