I would propose that the grain size of the crystallites in the film will decrease as the thickness decreases. By reducing the size of the grains to nanometer size, the energy gap will increase because of the quantum mechanical confinement.
This question is answered and discussed many time on the ResearchGate.
It is recommend, as a 1st priority, to find out, some related hints from, a more simple/direct relationship, e.g. how the lattice constant(s) is(are) affected by the thickness[1] (nanoscale?) of your semiconductor film/(crystalline) substrate(?).
Also, what is the nominal energy gap of your bulk semiconductor (crystal) ?