text: The electron-phonon coupling is responsible for electron generation in the pV cell. In this phenomenon, the phonon leads to ion motion which perturbs the highest occupied valence state (HOS). This state begins to overlap with the lowest unoccupied conduction state (LUS), and the electron can switch states if energy and momentum are conserved. If it does, an electron-hole pair is generated.
  Using a taylor expansion of the change in electron potential, , due to the ionic displacement of a phonon provides a matrix element for use in Fermi's golden rule, and the derivation of a generation rate. This Taylor expansion gives the following matrix element 
  where  is the average atomic mass,  and  are the frequency and atomic displacement due to a phonon with polarization  and momentum , and  is the electron wavefunction for an electron with momentum  in band i. From Fermi's golden rule
  where  is the energy of an electron in band i and momentum ,  is the corresponding electron occupation, and  is the phonon occupancy.