Yes Dr. Nadir you can use this effect to explain the widening of the energy gap for special material such as TCO transparent conducting oxides (CdO,ZnO, SnO2 , In2O3  and other materials like CdS InSb etc.....) and in the case of highly dopant concentration where the lower states of the conduction band will be occupied by the excess carriers (electrons) from the impurities atoms, therefore the electron need additional energy to promote from valence band to empty state in the conduction band.

The attached papers enhance the B-M effect.

1. page 56 . 

2. page  6 or 38 .

Also the widening of the energy gap ( blue shift of the absorption edge) can be attribuited to several reasons : 

The blue shift in the band gaps observed for the films may be explained by severalmechanisms such as (i) Moss-Burstein effect which originates from the lifting of Fermi level into the conduction band due tothe increase in charge carrier concentration; (ii) the decrease in shallow-level trap concentration near the conduction band resulting from the improved crystallinity, and(iii) reduction of band bending effect at the grain boundaries. In nanocrystalline materials band bending effect takes place atgrain boundaries due to their increased surface to volume ratio. For smaller grains, the band bending effect is large whereasit becomes flatter for larger grains. as in the paper 3 page 5. 

Best regards.

Yes Dr. Nadir you can use this effect to explain the widening of the energy gap for special material such as TCO transparent conducting oxides (CdO,ZnO, SnO2 , In2O3  and other materials like CdS InSb etc.....) and in the case of highly dopant concentration where the lower states of the conduction band will be occupied by the excess carriers (electrons) from the impurities atoms, therefore the electron need additional energy to promote from valence band to empty state in the conduction band.

The attached papers enhance the B-M effect.

1. page 56 . 

2. page  6 or 38 .

Also the widening of the energy gap ( blue shift of the absorption edge) can be attribuited to several reasons : 

The blue shift in the band gaps observed for the films may be explained by severalmechanisms such as (i) Moss-Burstein effect which originates from the lifting of Fermi level into the conduction band due tothe increase in charge carrier concentration; (ii) the decrease in shallow-level trap concentration near the conduction band resulting from the improved crystallinity, and(iii) reduction of band bending effect at the grain boundaries. In nanocrystalline materials band bending effect takes place atgrain boundaries due to their increased surface to volume ratio. For smaller grains, the band bending effect is large whereasit becomes flatter for larger grains. as in the paper 3 page 5. 

Best regards.