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Fermi Level Calculation by Free Electronic Band Model

Three different kinds of crystal structures,face centered cubic(fcc),body centered cubic(bcc),and hexagonal close packed(hcp) structures with eight valence electrons in each primitive unit cell were studied.In the framework of free electron approximation,their Fermi level E F were determined by Fermi sphere according to the theory of free electron gas,and the average bond energies E m were calculated by free electronic band model.The calculated results of E F and E m indicate that the average bond energies E m of three different crystal structures (therefore their electron densities are different) correspond to their Fermi levels E F respectively.In the semiconductor energy band,the average bond energy E m is defined as the mid point of the energy gap between E b (bonding orbital energy) which is the avergage valence band level of the four highest valence band levels,and E a (anti bonding orbital energy) which is the average conduction band level of the five lowest conduction band levels in the whole Brillouin zone eigenvalues.It is the reference energy level in our theoretical calculation of heterojunction band offset.Therefore,the relationship between E F and E m found here is helpful to understand the physical concept of average bond energy E m and the reason why it aligns at the two sides of the heterojunction interface.It also suggests a new method to calculate the Fermi level E F of free electron systems through free electronic band model.