The increase of bandgap energy is due to quantum confinement. (For more about what is quantum confinement check the links at end)
At small dimensions when the energy levels are quantified, the band overlap present in metals disappears and transformed into a bandgap. This also explains why some metals becomes semiconductor as their size decreased.
https://www.researchgate.net/post/What_is_Quantum_confinement_effect
https://en.wikipedia.org/wiki/Potential_well
https://www.researchgate.net/post/What_is_quantum_confinement
Let's start with a single molecule. It does not have any energy band but single HOMO-LUMO. As more of molecules come together, the HOMO-LUMO energy level will split and form discrete energy levels around the previous HOMO-LUMO levels (some above and some below). Further increasing the number of molecules in the aggregate will end up with the conventional bulk materials with a huge amount of energy levels, which naturally forming continuous (sort of) energy bands (conduction and valence). The lowest level around LUMO becomes further lower, and the highest level around HOMO further higher. Therefore, the band gap in between becomes narrowed. Hope it helps.
Also, Figure 1 in the article Chem. Commun., 2014, 50, 12815--12823 will enhance your understanding. Thanks.
The increase of bandgap energy is due to quantum confinement. (For more about what is quantum confinement check the links at end)
At small dimensions when the energy levels are quantified, the band overlap present in metals disappears and transformed into a bandgap. This also explains why some metals becomes semiconductor as their size decreased.
https://www.researchgate.net/post/What_is_Quantum_confinement_effect
https://en.wikipedia.org/wiki/Potential_well
https://www.researchgate.net/post/What_is_quantum_confinement
Dear sh. A. kakil
the increase of Eg du to nanoscale size reduction can be explained according to the bond length, in this scale valence electrons bonding to lattice ions increases which consecuntly increase the energy gap, for mor details discuse the case with me in my time
Mustafa
thank you so much Dear Dr Omar M S
I understand according to your paper ( Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials) the bond length changes in nano size .
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