Yes Fermi Level of Metal Nanoparticles changes with its size.

Thanks much Saurav Kumar!, could you explain the reason or suggest me a good source which I can read to get more information about that

Yes, size has an important effect on the electronic structure of nanoparticles. Unlike bulk material, nanoparticles have discrete energy levels due to the confinement of the electron wavefunction resulting from their limited physical dimensions. Changing NP size causes shifts in the band structure that do not occur in the bulk material, which results in changing the position of the Fermi level.

The band structure shifts can be explained by considering that, at small enough sizes, NPs possess coordinatively unsaturated sites (not preset in the bulk material) that create distinct, localized electronic structures that result in a gap between the valence and conduction bands. The gap size is determined by the number of valence electrons in the nanomaterial, and the position of the Fermi level is related to band and gap positions.

Here are some good sources:

Article Nanocatalysis: Mature Science Revisited or Something Really New?

Dissertation of Robert M. Rioux (2006): https://digital.library.unt.edu/ark:/67531/metadc889196/

Hope that helps!

Thanks a lot Clare Davis-Wheeler Chin

You're very welcome! I did a lot of research for my dissertation on the electronic structure and plasmonic response of small noble metal nanoparticles, so please let me know if there is anything else I can do to help.

Great! Thank you so much!, Sure I will ask!

what about the fermi energy?that too changes.please clarify.