I wonder if dielectrics exist in your physics once you call these wide-bandgap dielectrics "semiconductors". They are not! This statement is also reflected in the fact that both involved materials are not much prone to the effects of quantum confinement, which means that their bandgaps do not significantly change with descreasing particle size unless you really approach 1 nm or go below it. I mean, I cannot help you with an idea of experimental setup but maybe you could reconsider whether or not you need such an experiment at all. I would suggest that good XRD would be enough to show that you have the two well crystallized phases and say that the bandgaps must match those of the bulk materials.

Thanks Roman for your answer. I can understood you, people even say them insulators. That's fine. My question was not about just finding band gap alone. I was interested to locate the respective band position (i.e.like finding respective position of homo lumo in QD) of core-shell nanoparticles with respect to each other or valence band and conduction band position as a single core-shell nanoparticle. If there is any experimental method you can suggest, let me know.

For my understanding, bringing the two insulating materials in contact with each other does not change the positions of the edges of their valence and conduction bands due to lacking free charge carriers in insulators. I suggest you perform something like UV photoelectron spectroscopy on your oxides separately, not as a core-shell system, and assume that the electron affinity, work function and positions of the deeper bands with respect to vacuum are the same as when these phases are mixed with each other at the nanoscale. If you are lucky, you could also come across some useful relevant literature data. In any case, you still need to prove that the components are well crystallized

Hi Roman,

Thank you for your comments and suggestions. I found one interesting paper related to my question, here is the link.  http://pubs.acs.org/doi/full/10.1021/am505861c