I am not really sure about it because I have been working with TiO2 nanoparticles supported in porous silicas tha last times and not with thin films. What semiconductor you are using?

But I think you case use the Effective Mass Approximation Model for electron/holes to estimate the grain size from the band gap values. Above are two papers that describe it:

Brus, L. J. Chem. Phys. (1984), 80, 4403.

Brus, L. J. Phys. Chem. (1986), 90, 2555.

For TiO2 recently we have used in our lab the Phonons Confinament Model to estimate the grain size, and we are getting great results from it. You can read these two work from our groups to understand how we applied it.

M. Strauss, C. M. Maroneze, J. M. de Souza e Silva, F. A. Sigoli, Y. Gushikem, I. O. Mazali. Materials Chemistry and Physics 126 (2011),188-194.

Mazali, I. O., Alves, O. L. J. Phys. Chem. Solids (2005), 66, 37.

Mazali, I.O., Viana, B.C., Alves, O.L., Mendes Filho, J., Souza Filho, A.G. J. Phys. Chem. Solids (2007), 68, 622.

If grains in thin films are fully crystalline, the dependence of the bandgap on the grain size, in principle, no. This relationship holds for nanocrystals as a result of quantum size effect. However, if the grains is not completely crystalline (amorphous present on the surface), then such a relationship can be. I recommend you read a work that is attached.

Dear Gnatenko, 

Thanks you for giving useful information. But I can not reach the pdf in the attachment. Could you please provide it again?