In the quantum mechanical framework, this scattering is most noticeable in confined systems, in which the energies for charge carriers are determined by the locations of interfaces.  An example of such a system is a quantum well, which may be constructed from a sandwich of different layers of semiconductor.  Variations in the thickness of these layers therefore causes the energy of particles to be dependent on their in-plane location in the layer.  Classification of the roughness at a given position, , is complex, but as in the classical models, it has been modeled as a Gaussian distribution by some researchers  
This assumption may be formulated in terms of the ensemble average for some given characteristic height, , and correlation length, , such that