I have seen that in the case of many materials band gap decreases in nano regime.
Could you share a source?
To my knowledge this happens if a spatial indirect transition in combination with bend bending from charges (space charge, piezoelectric or interface charges,...) is present. This however does not imply that the bandgap really is decreased.
In a simple picture, bandgaps originate from continuum solutions (bulk) of a crystal. If you have a nano crystal, there is no such continuum.
Kind regards,
Arne
The bandgap of TiO2 decreased from 3.3 eV for microscale to about 1.0 eV for nanoscale. I think that you find some information about your question in the article.
https://www.researchgate.net/publication/258768290_25th_Anniversary_Article_Metal_Oxide_Particles_in_Materials_Science_Addressing_All_Length_Scales
Article 25th Anniversary Article: Metal Oxide Particles in Materials...
...the article Hatice has included above does not show a bandgap shrinkage; it shows that the introduction of disorder and specific defects in TiO2 core-shell nano particles introduces VB tail states and levels within the bandgap through which electronic transitions may proceed. This is not the same as band gap narrowing...(although the choice of text in the article intro does give that impression...)
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