# Metal-Semiconductor Ohmic and Schottky Contacts

Including Barrier Height Calculator and Depletion Width Calculator

Whenever a metal and a semiconductor are in intimate contact, there exists a potential barrier between the two that prevents most charge carriers (electrons or holes) from passing from one to the other.

Only a small number of carriers have enough energy to get over the barrier and cross to the other material. When a bias is applied to the junction, it can have one of two effects: it can make the barrier appear lower from the semiconductor side, or it can make it appear higher. The bias does not change the barrier height from the metal side.
The result of this is a Schottky Barrier (rectifying contact), where the junction conducts for one bias polarity, but not the other. Almost all metal-semiconductor junctions will exhibit some of this rectifying behavior.
Schottky Contacts make good diodes, and can even be used to make a kind of transistor, but for getting signals into and out of a semiconductor device, we generally want a contact that is Ohmic. Ohmic contacts conduct the same for both polarities.  (They obey Ohm's Law).
There are two ways to make a metal-semiconductor contact look ohmic enough to get signals into and out of a semiconductor (or doing the opposite makes a good Schottky contact).

1. Lower the barrier height
The barrier height is a property of the materials we use. We try to use materials whose barrier height is small.
Annealing can create an alloy between the semiconductor and the metal at the junction, which can also lower the barrier height.
2. Make the barrier very narrow
One very interesting property of very tiny particles like electrons and holes is that they can "tunnel" through barriers that they don't have enough energy to just pass over. The probability of tunneling becomes high for extremely thin barriers (in the tens of nanometers).
We make the barrier very narrow by doping it very heavily (1019 dopant atoms/cm3 or more).

## Metal-Semiconductor Barrier Height Calculator

 Lithium (Li)Beryllium (Be)Boron (B)Carbon (C)Sodium (Na)Magnesium (Mg)Aluminum (Al)Polysilicon    Doping of Polysilicon: /cm3     n or p type? n pPotassium (K)Calcium (Ca)Scandium (Sc)Titanium (Ti)Vanadium (V)Chromium (Cr)Manganese (Mn)Iron (Fe)Cobalt (Co)Nickel (Ni) Copper (Cu)Zinc (Zn)Gallium (Ga)Germanium (Ge)Arsenic (As)Selenium (Se)Rubidium (Rb)Strontium (Sr)Yttrium (Y)Zirconium (Zr)Niobium (Nb)Molybdenum (Mo)Technetium (Tc)Ruthenium (Ru)Rhodium (Rh)Palladium (Pd)Silver (Ag)Cadmium (Cd)Indium (In)Tin (Sn) Antimony (Sb)Tellurium (Te)Iodine (I)Cesium (Cs)Barium (Ba)Lanthanum (La)Cerium (Ce)Praseodymium (Pr)Neodymium (Nd)Promethium (Pm)Samarium (Sm)Europium (Eu)Gadolinium (Gd)Terbium (Tb)Dysprosium (Dy)Holmium (Ho)Erbium (Er)Thulium (Tm)Ytterbium (Yb) Lutetium (Lu)Hafnium (Hf)Tantalum (Ta)Tungsten (W)Rhenium (Re)Osmium (Os)Iridium (Ir)Platinum (Pt)Gold (Au)Mercury (Hg)Thallium (Tl)Lead (Pb)Bismuth (Bi)Polonium (Po)Francium (Fr)Radium (Ra)Actinium (Ac)Thorium (Th)Uranium (U)

NOTE: The majority of the values obtained for the work functions of the elements above were found from this publication:
"The work function of the elements and its periodicity", Herbert B. Michaelson, Journal of Applied Physics 48, 4729-4733, (1977).

n-Silicon
p-Silicon
n-Gallium Arsenide
p-Gallium Arsenide
n-Germanium
p-Germanium
n-Indium Phosphide
p-Indium Phosphide

 Barrier height is eV

The closer the barrier height is to 0, the more ohmic the contact
--A positive barrier height for an n-type semiconductor
means the current tends to flow more easily into the semiconductor.
--A positive barrier height for a p-type semiconductor
means the current tends to flow more easily into the metal.

## Metal-Semiconductor Junction Depletion Layer Width Calculator

Select a metal and semiconductor in the Barrier Height Calculator above, and input the doping level of your semiconductor here: /cm3

 The Depletion Layer is microns wide