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.