Band-edge energies effect

It is often convenient to refer the Fermi level to reference levels that are close to the band edge energies. If we were to fill up the conduction band with electrons to a value equal to the effective density of states in the conduction band, N, then the Fermi level would shift until it was exactly equal to the energy of the bottom of the conduction band, E b- Our new reference level would then be the energy of the Fermi level at the bottom of the conduction band, that is, E = E h-That is. 

This is another way of saying that as the electron energy approaches that of a band edge, its effective mass, or the force needed to accelerate the electron, becomes very large. ... 

Tables 10.13a and b demonstrate the effect of the cychc-cluster increase for both HF and DFT-PWGGA methods, respectively. The main calculated properties are the total energy Etot (per primitive unit cell), one-electron band-edge energies of the valence-band top and conduction-band bottom e and Sc, MuUiken effective atomic charges q and full atomic valencies V. As is seen, the result convergence, as the supercell size increases, is quite different for the HF and DFT. We explain the much slower DFT convergence by a more covalent calculated electron-charge distribution, as compared to the HF case. For both methods, the convergence of local properties of the electronic structure is faster than that for the total and one-electron energies.

E is tire density of states between E and E + AE. A simpler way of calculating n is to represent all tire electron states in tire CB by an effective density of states at tire energy E (band edge). The electron density is tlien simply n = NJ (Ef. 

In the case where there is one single trap level, E, is the energy difference between this level and the delocalized band edge, and a the ratio between the effective density of slates at the delocalized band edge and the concentration of traps. If traps are energy distributed, effective values of N, and a must be estimated. 

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