Schottky barrier

A Schottky barrier, named after Walter H. Schottky, is a potential energy barrier for electrons formed at a metal–semiconductor junction. Schottky barriers have rectifying characteristics, suitable for use as a diode. One of the primary characteristics of a Schottky barrier is the Schottky barrier height, denoted by ΦB (see figure). The value of ΦB depends on the combination of metal and semiconductor. 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.

Physics of formation

When a metal is put in direct contact with a semiconductor, a so called Schottky barrier can be formed, leading to a rectifying behavior of the electrical contact. 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. At the basis of the description of the Schottky barrier formation through the band diagram formalism, there are three main assumptions:

The contact between the metal and the semiconductor must be intimate and without the presence of any other material layer (such as an oxide). No interdiffusion of the metal and the semiconductor is taken into account. There are no impurities at the interface between the two materials. 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. For an isolated metal, the work function Φ M {\displaystyle \Phi _{M}} is defined as the difference between its vacuum energy E 0 {\displaystyle E_{0}} (i.e. the minimum energy that an electron must possess to completely free itself from the material) and the Fermi energy E F {\displaystyle E_{F}} , and it is an invariant property of the specified metal:

Φ M = E 0 − E F {\displaystyle \Phi _{M}=E_{0}-E_{F}}

On the other hand, the work function of a semiconductor is defined as:

Φ S = χ + ( E C − E F ) {\displaystyle \Phi _{S}=\chi +(E_{C}-E_{F})}

Where χ {\displaystyle \chi } is the electron affinity (i.e. the difference between the vacuum energy and the bottom energy E C {\displaystyle E_{C}} of the conduction band). 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.

When the two isolated materials are put into intimate contact, the equalization of the Fermi levels brings to the movement of charge from one material to the other, depending on the values of the work functions. Charge collects at the interface between the materials, leading to the creation of an energy barrier. For electrons, the barrier height Φ B n {\displaystyle \Phi _{B_{n}}} can be easily calculated as the difference between the metal work function and the electron affinity of the semiconductor:

Φ B n = Φ M − χ {\displaystyle \Phi _{B_{n}}=\Phi _{M}-\chi }

While the barrier height for holes is equal to the difference between the energy gap of the semiconductor and the energy barrier for electrons:

Φ B p = E gap − Φ B n {\displaystyle \Phi _{B_{p}}=E_{\text{gap}}-\Phi _{B_{n}}}

In reality, what can happen is that charged interface states can pin the Fermi level at a certain energy value no matter the work function values, influencing the barrier height for both carriers. This is due to the fact that the chemical termination of the semiconductor crystal against a metal creates electron states within its band gap. The nature of these metal-induced gap states and their occupation by electrons tends to pin the center of the band gap to the Fermi level, an effect known as Fermi level pinning. 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. 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.

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