Energy bands, definition methods

The values of Vm and are key experimental quantities that are used to characterize the physical properties of semiconductor/metal interfaces. If Vbi or b can be determined, then W, Q, E(x), and most of the other important thermodynamic quantities that are relevant to the electrical properties of the semiconductor contact can be readily calculated using the simple equations that have been presented above. Methods to determine these important parameters can be found in the literature. However, it would be useful at this point in the discussion to consider what values of and Vbi are expected theoretically for a given semiconductor/metal interface. By definition, = (/ip.m - at the electrode surface (Figure 4b). Thus, in principle, the barrier height can be predicted if the energies of the semiconductor band edges and the electrochemical potential of the metal can be determined with respect to a common reference energy. 

The one-centre expansion (6.15) is specialised to the case where R = 0, and is valid inside the atomic sphere centred at the origin. It may be used to derive the LMTO equations and with the normalisation implied by (6.11) it is consistent with the secular matrices (5.46,47) in the ASA. In linear methods in band theory [6.2] Andersen presented the one-centre expansion in the form (6.15) and derived the LMTO formalism from that assumption. His LMTO formalism is equivalent to that presented here apart from the normalising factor [/S/2 (- -1)] 1 appearing in the definition (6.11) of the energy-dependent muffin-tin orbital. 

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