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Also shown: Fermi level E F, valence band edge E V, work function W. In a semiconductor, the work function is sensitive to the doping level at the surface of the semiconductor. Since the doping near the surface can also be controlled by electric fields, the work function of a semiconductor is also sensitive to the electric field in the vacuum.
This happens both when the semiconductor is n-type and its work function is smaller than the work function of the metal, and when the semiconductor is p-type and the opposite relation between work functions holds. [3] At the basis of the description of the Schottky barrier formation through the band diagram formalism, there are three main ...
The first practical application of semiconductors in electronics was the 1904 development of the cat's-whisker detector, a primitive semiconductor diode used in early radio receivers. Developments in quantum physics led in turn to the invention of the transistor in 1947 [ 7 ] and the integrated circuit in 1958.
At the junction of a semiconductor and metal, the bands of the semiconductor are pinned to the metal's Fermi level. At the junction of a conductor and vacuum, the vacuum level (from vacuum electrostatic potential) is set by the material's work function and Fermi level. This also (usually) applies for the junction of a conductor to an insulator.
In fact, empirically, it is found that neither of the above extremes is quite correct. The choice of metal does have some effect, and there appears to be a weak correlation between the metal work function and the barrier height, however the influence of the work function is only a fraction of that predicted by the Schottky-Mott rule. [6]: 143
Shown to the right is a diagram of band-bending interfaces between two different metals (high and low work functions) and two different semiconductors (n-type and p-type). Volker Heine was one of the first to estimate the length of the tail end of metal electron states extending into the semiconductor's energy gap. He calculated the variation ...
If the metal work function is larger than that of the semiconductor (), that is >, the electrons will flow from the semiconductor to the metal, thereby lowering the semiconductor Fermi level and increasing that of the metal. Under equilibrium the work function difference vanishes and the Fermi levels align across the interface.
While the work function of a semiconductor can be changed by doping, the electron affinity ideally does not change with doping and so it is closer to being a material constant. However, like work function the electron affinity does depend on the surface termination (crystal face, surface chemistry, etc.) and is strictly a surface property.