Bonding in Crystalline Solids Introduction to Band Theory

Bonding in Crystalline Solids Introduction to Band Theory 

The electron-occupied band is known as the valence band, whereas the unfilled band is referred to as the conduction band. The energy gap, if present, between these 

At absolute zero, the highest occupied energy level is referred to as the Fermi level (in 3-D Fermi surface), derived from Fermi-Dirac statistics.The Fermi-Dirac distribution function, f(E), describes the probability that a given available energy state will be occupied at a given temperature  

In metals, the position of the Fermi level provides information regarding the thermal motion of conduction electrons, known as electron velocity v, through the extended crystal lattice (Eq. 36 me = electron mass 9.1066 x 10 g). For instance, the Fermi energies for copper (7 eV) and gold (5.5 eV) correspond to velocities of 1.6 x 10 m/s and 1.4 x 10 m/s, respectively. However, it should be noted that the average speed of electron flow, known as the drift velocity, within electrical wires is much less, typically on the order of 100 pm/s (i.e., 6 mm/min) for DC voltage - much slower than one would think °  

The potential energy of an electron in a crystal lattice depends on its location, which will be periodic due to the regular array of lattice atoms. The periodic wavefunctions that result from solving the Schrodinger equation are referred to as 

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