It's related to the quantum size effect. If you consider a simple 1D quantum well, the quantized energy gap reduces as the thickness of the quantum well increases. As the material heats up, you can think of the quantum well thickness increasing, and hence the quantization energy reducing. In a more detailed picture, the band gap can be related to the lattice constant of the material, which increases as temperature is increased. More details can be found in this paper, for example: http://www.public.asu.edu/~gbadams/spr13/ApplPhysLett_58_2924.pdf

Thx for your response Indrasen Bhattacharya.

It's an interesting paper.

Cordially.

You're welcome..

On second thoughts, a better way of thinking about it might be in terms of what happens when you bring two atoms close together to form a covalent bond. There are two energy levels produced from the splitting of the original electron energy in each atom. The lower energy level is the bonding orbital and the higher level is the antibonding level. The energy difference between these two orbitals is analogous to a band gap. This energy difference increases as the wavefunction overlap between the atoms increases i.e. as the distance gets smaller. I think a tight binding calculation of band structure follows this kind of approach.

It is related to free carriers and band gap with thermal energy KT. The raise of temperature ;  

I agree with Indrasen Bhattacharya, it's mainly related to the structural order of your system (material) that is changing when increasing the temperature. Note that all semiconductors behave like metals at very high temperature (in the liquid state, there is no more bandgap).

Since you're from the University of Lorraine, i fully recommend that you meet Prof Jean-Georges Gasser an expert in the electronic properties of metal and semiconductors (both in solid and liquid phase ;). 

Thanks Ben Moussa.

Thanks for your interesting response.

Bouzourâa M.-B.

Hello everybody,

I am very interested in this discussion about the evolution of the gap of semiconductors as a function of temperature. In fact, In my TiO2 samples prepared by sol gel, I note an increase in the value of the gap as a function of the annealing temperature!

I think, we are going to interpret this observation in relation to the increase of oxygenes vacancies linked to the desorption of oxygen at increasing annealing temperature values. Can you help me to better interpret this observation ?

Thanks for your help 

Lolwa SAMET

I don't know the impact of O2, but it could also be related to the "better" material quality after annealing at higher temperature (TBC). Usually annealing contributes to reduce stress in the material film, and help also the diffusion of defects resulting in a better structural order. This can be a possible explanation. 

What is the Eg(max) value reported ? is it coherent with the literature ? 

Did you notice any change in the structural properties of your material after annealing (e.g., raman, X-ray diffraction, TEM, ...) ? 

Thank you for your reply,

Both the direct and indirect gap for the TiO2 samples annealed at 600 ° C are higher than those annealed at 400 ° C (the difference is may be insignificant) :

* TiO2 at 400 ° C indirect Eg = 3 and TiO2 at 600 ° C indirect Eg = 3.03).

* TiO2 at 400 ° C direct = 3.3 and TiO2 at 600 ° C indirect = 3.47)

The DRX spectra show that at 400 ° C. only one anatase phase is present but at 600 ° C anatase and 20% rutile are observed. The size of the crystallites at 600 ° C is much greater than those at 400 ° C.

Thanks

Lolwa SAMET

Energy materials are chosen for applications based on its binding energy,Eb and band gap, Eg to relation with Voc marginal difference. The Eg varies with temperature because the due to thermal diffusion current increases or carrier generation in opposite to the built in field thus reduces the effective gap.

In crystallize materials, the energy gap decreases as the temperature increases. There is a quantum mechanical explanation where as the temperature increases the inter atomic distance increases rendering the the electrons less bound. Less space confinement means lower energy levels.

There is a semi classical explanation: By definition the energy gap is the smallest energy to beak a covalent bond. As the temperature increases the neighboring atoms gets away from each other which weaken the bonding force of the valence electrons to their parent atoms. Weaken the bond leads to less energy to free the electron from the bond inside the crystal.

Best wishes

Thanks for your response.

Best regards.