I am synthesizing semiconducting Nanoparticles as Antibacterial agents. Is there any relation between its band-gap and surface charge. Or can we co-relate these two properties.
The reduction of the size of the material leads to the socalled quantum confinement. It is so that the energy gap of the bulk material will be modified by the size reduction according to the theory of quantum confinement of the bulk material.
It is so that the increases in the energy gap will be equal to first allowed level of the quantum dot dE, Then Eg= Egb+ 2dE,
dE can be expressed as in the link: https://arxiv.org/ftp/arxiv/papers/1212/1212.2318.pdf
I would like to say that the surface charge and BandGap is different for semiconducting materials as the surface of a material is exposed to the environment which tends to change its properties by the simultaneous reaction happening between the atmosphere of the Material and the surface molecules. This tends to increase or decrease the band energy at the surface of the material when compared to that of the whole material. This is very well proved by the experimentations of Surface Photovoltage in thin film solar cells which gives a clear explanation and experimental proof towards this phenomena.
I aint totally sure about the same phenomenon taking place with semiconductor nanoparticles but I suppose something like this should occur until and unless the surface of a material is completely inert towards the atmosphere.
My first answer went in other direction which do not agree with the question.
The surface charges causes what is called band bending and does not affect the bandgap of the material.Only when the surface charges cause a high charge accumulation at the surface the high carrier concentration causes reduction of the bandgap of the material. I would like that you refer to my paper about the charge carrier concentration on the bandgap: Article A New and Simple Model for Plasma and Doping induced Band Ga...