When a metal contacts a semiconductor, two types of devices can be formed. The first is an ohmic contact, which behaves pretty much like a small resistor. Ohmic contacts are used by the millions in integrated circuits to contact semiconductor devices. The second type of device is the Schottky diode, which has a current vs. voltage characteristic very similar to that of the p-n diode. Schottky diodes aren't all that popular in modern integrated circuits, though they are essential in some high-speed BiCMOS circuits.

Schottky diodes are formed when two conditions are satisfied:

• The work function of the metal is greater than that of the semiconductor if the semiconductor is n-type or smaller if the semiconductor is p-type.
• The semiconductor is not doped so heavily that carriers can tunnel from the semiconductor to the metal.

A detailed analysis of the Schottky diode would require some background in semiconductor physics and would involve diagrams with curvy energy bands, so I will skip this analysis. A reference is given at the bottom of this writeup, but any book on semiconductor physics should do.

The I-V equation for an ideal Schottky diode is the following:

I = Is(eqV/kT -1)
Is = RAT2e-Φ/kT

R is known as Richardson's constant and is equal to 120 A/(cm2K2)
T is temperature in Kelvins
Φ is equal to the work function of the metal minus the electron affinity of the semiconductor
A is the cross-sectional area of the junction, V is the applied voltage, k is Boltzmann's constant, and q is the charge of an electron in Coulombs.

For many applications the Schottky diode is superior to the more well-known p-n diode. The Schottky diode has a far speedier transient response and a smaller turn-on voltage. These advantages make the Schottky diode useful as a "clamp" across the collector-base junction of a bipolar junction transistor (BJT), preventing the BJT from entering its saturation regime and increasing the speed of bipolar digital circuits. Since the MOSFET has all but made the BJT obsolete in digital circuits, the most common location of Schottky diodes in modern digital integrated circuits is at a failed ohmic contact.

Reference: Semiconductor Device Fundamentals by Robert Pierret