What is the difference between compositional superlattice and doping superlattice?
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A compositional superlattice is a periodic layer structure of different materials. These typically have different bandgaps, effective masses, refractive indices etc. There are limitations on which materials can be stacked. They need to have the same crystal structure and lattice constant or at least negligible strain. The model system would be $GaAs$/$AlAs$ or any alloy of $Al_{x}Ga_{1-x}As$, as these gave nearly the same lattice constant. But such structures were also realized with $Si$/$Si_{1-x}Ge_{x}$ alloys or $InAs$/$GaSb$/$AlSb$ heterostructures, just to mention a few.
On the other hand, a doping superlattice is just a periodic structure of layers of the same material, just with different doping levels. This is also called modulation doping. Although, this sometimes also refers to superlattices of different materials, where just one is doped.
