Schottky barrier

[1][2] Not all metal–semiconductor junctions form a rectifying Schottky barrier; a metal–semiconductor junction that conducts current in both directions without rectification, perhaps due to its Schottky barrier being too low, is called an ohmic contact.

[3] At the basis of the description of the Schottky barrier formation through the band diagram formalism, there are three main assumptions:[4] To a first approximation, the barrier between a metal and a semiconductor is predicted by the Schottky–Mott rule to be proportional to the difference of the metal-vacuum work function and the semiconductor-vacuum electron affinity.

It is valuable to describe the work function of the semiconductor in terms of its electron affinity since this last one is an invariant fundamental property of the semiconductor, while the difference between the conduction band and the Fermi energy depends on the doping.

This leads to the creation of an energy barrier, since at the interface between the materials some charge get collected.

can be easily calculated as the difference between the metal work function and the electron affinity of the semiconductor:

This is due to the fact that the chemical termination of the semiconductor crystal against a metal creates electron states within its band gap.

Thus the heights of the Schottky barriers in metal–semiconductor contacts often show little dependence on the value of the semiconductor or metal work functions, in strong contrast to the Schottky–Mott rule.

[5] Different semiconductors exhibit this Fermi level pinning to different degrees, but a technological consequence is that ohmic contacts are usually difficult to form in important semiconductors such as silicon and gallium arsenide.

Non-ohmic contacts present a parasitic resistance to current flow that consumes energy and lowers device performance.

This gives the barrier a high resistance when small voltage biases are applied to it.

Under large voltage bias, the electric current flowing through the barrier is essentially governed by the laws of thermionic emission, combined with the fact that the Schottky barrier is fixed relative to the metal's Fermi level.

The current-voltage relationship is qualitatively the same as with a p-n junction, however the physical process is somewhat different.

While the tunneling current density can be expressed, for a triangular shaped barrier (considering WKB approximation) as:[citation needed]

From both formulae it is clear that the current contributions are related to the barrier height for both electrons and holes.

If a symmetric current profile for both n and p carriers is then needed, the barrier height must be ideally identical for electrons and holes.

For very high Schottky barriers where ΦB is a significant fraction of the band gap of the semiconductor, the forward bias current may instead be carried "underneath" the Schottky barrier, as minority carriers in the semiconductor.

Introducing a second semiconductor/metal interface and a gate stack overlapping both junctions, one can obtain a Schottky barrier field effect transistor (SB-FET).

The gate steers the carrier injection inside the channel modulating the band bending at the interface, and thus the resistance of the Schottky barriers.

This kind of device has an ambipolar behavior since when a positive voltage is applied to both junctions, their band diagram is bent downwards enabling an electron current from source to drain (the presence of a

In the opposite case of a negative voltage applied to both junctions the band diagram is bent upwards and holes can be injected and flow from the drain to the source.

One of the main limitations of such a device is strongly related to the presence of this current that makes it difficult to properly switch it off.

A clear advantage of such a device is that there is no need for channel doping and expensive technological steps like ion implantation and high temperature annealings can be avoided, keeping the thermal budget low.

However the band bending due to the voltage difference between drain and gate often injects enough carriers to make impossible a proper switch off of the device.

Because the junction voltage of the Schottky barrier is small, the transistor is prevented from saturating, which improves the speed when used as a switch.

A MESFET or metal–semiconductor FET uses a reverse-biased Schottky barrier to provide a depletion region that pinches off a conducting channel buried inside the semiconductor (similar to the JFET where instead a p–n junction provides the depletion region).

By analyzing the speed at which the capacitance responds to changes in voltage, it is possible to obtain information about dopants and other defects, a technique known as deep-level transient spectroscopy.

1N5822 Schottky diode with cut-open packaging. The semiconducting silicon (center) makes a Schottky barrier against one of the metal electrodes, and an ohmic contact against the other electrode.
Band diagram for n -type semiconductor Schottky barrier at zero bias (equilibrium) with graphical definition of the Schottky barrier height , Φ B , as the difference between the interfacial conduction band edge E C and Fermi level E F . [For a p -type Schottky barrier, Φ B is the difference between E F and the valence band edge E V .]
Metal and semiconductor band diagrams when separated (up) and when in intimate contact (down)
For a very high Schottky barrier (in this case, almost as high as the band gap), the forward bias current is carried by minority carrier injection (the white arrow shows the injection of an electron hole into the semiconductor's valence band).
Band diagrams of the SBFET operations. From left to right: negative applied voltage bend the band diagram enabling a hole tunneling current (p-type); without any voltage applied only thermionic emission is allowed for carriers (off-state); a positive gate voltage enables electrons to tunnel due to the downwards band bending (n-type).
Schottky transistor effective circuit