Bandgap Expansion Photon Emission and Absorption

The Eg of a semiconductor is proportional to the first Fourier series coefficient of the interatomic potential. 

Skin-resolved bond contraction and entrapment perturb that the Hamiltonian originates and the increased fraction of undercoordinated atoms expands the Eg-Energies of photon emission and photon absorption are superposition of the interatomic binding energy and the electron-phonon coupling i.e., Stokes shift. Polarization of the dangling bond electrons creates the mid-gap states and band tails, which lowers the quantum efficiency of photon emission hydrogenation could annihilate such defect states. 

The Hamiltonian determines and correlates the properties intrinsically, and therefore, it is appropriate to consider the change of all the properties relating to the Hamiltonian rather than separate one phenomenon at a time from another. The size-induced quantum entrapment and polarization modulates the Hamiltonian, and therefore, the entire band structure of nanostructured semiconductors [1]  

Relaxation of the Chemical Bond, Springer Series in Chemical Physics 108, DOI 10.1007/978-981-4585-21-7 17, Springer Science+Business Media Singapore 2014 

Electron-phonon coupling shifts the intrinsic bandgap Eq to the EpA or the Epp by an addition or subtraction of the Stokes shift that also changes with solid size [23]. 

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