Metal-semiconductor junctions
Work Function =
energy required to excite
an electron at the Fermi level
out of the material {φ})
Case 1 : n-material and metal, φm > φs , EFs > EFm
At equilibrium, Fermi level is constant
⇒ Potential in the semiconductor must increase
Diffusion of electrons from the semiconductor's
conducting band to the metal.
⇒ transition region created with wide W.
⇒ A contact potential is created :
V0 = φm - φs
Further diffusion from the semiconductor's conducting
band is opposed by the contact potential.
Electrons in the metal are prevented from entering
the semiconductor's conducting band by a barrier:
q φ B = ( φ m - χ) · q
(χ : electron affinity)
An external potential can change the barrier.
"Schottky barrier"
Case 1 describes a rectifying contact. Diodes made
with a metal - semiconductor junction are called
Schottky diodes
Case 2 : p - semiconductor and metal, φs > φm , EFm > EFs
Diffusion of electrons from the metal to the
semiconductor's valence band
⇒ transition region and contact potential
Schottky barrier opposes further diffusion
Case 2 also describes a rectifying contact.
Bias over a Schottky diode
Forward bias
•Barrier in Ec
reduced
•Large currents
Reverse bias
•Barrier in Ec
increased
•Very small currents
•Schottky barrier (qφm- χ) is constant
•No minority carrier injection
⇒ No storage delay time!
⇒ Good for fast "switching" applications
Metal-semiconductor, Ohmic contact
These contacts should
not be rectifying!
Ohmic :
• I ∝ V in both directions
• R small
Case 3 : n-semiconductor and metal, φm < φs , EFs < EFm
• Electrons move freely from semiconductor to metal
• Electrons also easily cross barrier from metal to semiconductor.
⇒ Current moves easily in both directions
No transition region!
Case 4 : p-semiconductor and metal, φs < φm , EFm < EFs
⇒ current moves freely in both directions
No transition region
Ohmic contact can also be improved
with high doping near the metal contact:
e.g. p+ n n+...
Extra topic: Heterojunctions
Junctions between two different semiconductors
Different properties: Band gap energy, refractive index, etc
e.g. GaAs has smaller bandgap and higher refractive index
than AlGaAs:
Heterojunctions have many practical uses, especially in
LEDs and diode lasers, and charge confinement around the
transition region.
Another interesting application: studies of 2D quantum
systems: