A Primer to Semiconductor-Metal Contacts

When a metal and a semiconductor (ideally with no surface states) are brought in contact and equilibrium is maintained, their Fermi levels will align. If the Fermi levels of the metal and the semiconductor were the same before contact, then there would be no change in the band structure after contact. Usually, matching the work functions is nearly impossible in part because the Fermi level in the semiconductor, and thus the work function, depends on the carrier concentration. 

In a metal-semiconductor junction, the electrons approaching the interface also experience an image-force lowering of the barrier. A negative charge at a distance x 

is the relative dielectric constant of the semiconductor and Eo is the permittivity of free space. Under the influence of the electric field applied normal to the surface, the confining barrier can be lowered, and the magnitude of this image- 

Clearly, the image-force lowering increases through a square root dependence with the electric field. The resulting effective barrier for electron escaping the metal can be expressed as 

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