1. ## Metal-Semiconductor Junctions

Chapter 17 ¡V page 1Metal-Semiconductor Junctions
This chapter concerns metal-semiconductor junctions. They are also called Schottky contacts to honor Walter Schottky, a pioneer in metal-semiconductor junctions.
Introduction
„h Importance of metal-semiconductor junctions is due to
1) Ohmic metal-semiconductor junctions (e.g. for metal interconnects contacting a Si device in an integrated circuit)
2) Rectifying metal-semiconductor junctions = Schottky diodes (e.g. for high-speed rectifier diodes)
„h History:
o Ferdinand Braun in the late 1800s experimented with metal-semiconductor contacts
„X Ease of fabrication
„X Deposition of a metal film on a semiconductor
„h Experiment: Removal of an electron from a hydrogen atom
Illustration shows hydrogen atom core and electron
Chapter 17 ¡V page 2
Illustration shows the removal of the electron:
Work will be required to remove the electron to overcome coulombic attraction.
Work that is required to remove one electron: W F r
r
d
0 „Å
„V
ƒ*
ƒ*
The work required is called the Rydberg energy: ERydberg = 13.6 eV
The work required to remove an electron from a hydrogen atom is equal to the Rydberg
energy.
„h The Work Function and Einstein¡¦s photoemission experiments (Photoelectric Effect)
Experiment:
Result of experiment:
Chapter 17 ¡V page 3
Experimental finding: Ekin ƒ* hƒÞ ƒ{eƒ¶m
eƒ¶m = ¡§threshold energy¡¨ required to remove one electron from a solid
ƒ¶m = Work function
dimension {ƒ¶m } = V
o Example: Work function of some metals
Aluminum, Al: ƒ¶m = 4.3 V
Gold, Au: ƒ¶m = 4.8 V
Recall: Band diagram for a metal
Recall: Band diagram for a metal and a semiconductor
Chapter 17 ¡V page 4
Schottky model for metal-semiconductor junctions
„h Schottky barrier
o When a metal and a semiconductor get into contact a Schottky Barrier forms
o The Schottky-barrier height is measured in eV
o In the Schottky model, the Schottky-barrier height is equal to the difference of metal
work function and semi-conductor electron affinity.
o The illustration below shows the band diagram of a metal and a semiconductor
before and after being brought into contact
o Schottky-barrier height (Schottky model):
eƒ¶B ƒ* eƒ¶m ƒ{ e ƒÓs (1)
ƒ¶B = Schottky barrier height
Chapter 17 ¡V page 5
o Electrons transfer to metal (Driving force: Diffusion)
o Electron transfer lasts until Fermi levels are equal on both sides of the junction
o An electric field is generated
o Depletion approximation: Layer of width WD is depleted of free carriers. Transition
regions are abrupt.
o VD= Diffusion potential
eVD ƒ* eƒ¶B ƒ{ (EC ƒ{ EF) (2)
Recall: E E kT n N ( ) /
c
e C F ƒ{ ƒ{ ƒ* (3)
Chapter 17 ¡V page 6
Bardeen model for metal-semiconductor junctions
„h Bardeen¡¦s model takes into account interface charges or interface states (Bardeen states)
„h Atomic model
Due to different atomic structure and chemistry, electronic dipoles will form at the interface.
Chapter 17 ¡V page 7
o Schottky-barrier height (Bardeen model):
e ƒ¶B ƒ* e ƒ¶m ƒ{ e ƒÓs ƒy e ƒ¶dipole (4)
Comparison of the Bardeen model with the Schottky model reveals that the Bardeen
model has one additional term. This term is due to the dipoles forming at the
interface.
ƒ¶dipole cannot be easily calculated.
EF is ¡§pinned¡¨ near the middle
of the forbidden gap for most
metal-semiconductor junctions
Chapter 17 ¡V page 8
Rectifying metal-semiconductor junctions
o IV characteristic:
(e 1) /
ƒ* s ƒ{ eV kT I I (5)
Reverse saturation current:
e kT I /
s
e B ƒ{ ƒ¶ „f (6)
Chapter 17 ¡V page 9
o Depletion layer width (n-type semiconductor):
( )
2
D
D
D V V
e N
W ƒ{
ƒÕ
ƒ* (7)
o Maximum electrics field:
( )
2
D
D
max V V
e N
ƒ{
ƒÕ
E ƒ* (8)
o Eqns. (7) and (8) can be derived by using Poisson¡¦s equation, Gauss¡¦s equation,
and the depletion approximation
o Band diagram:
o There is no minority carrier injection in metal-semiconductor junctions (Schottky
contacts)
o There are no holes in the metal
o Therefore, there is no diffusion capacitance
o There is only a depletion capacitance
o Due to the absence of the diffusion capacitance, Schottky diodes are inherently
fast.
Chapter 17 ¡V page 10
Ohmic Contacts
Ohmic contacts are highly doped Schottky contacts
o Band Diagram:
o Transport through barrier by tunneling
o IV characteristics:

2. ## Re: Metal-Semiconductor Junctions

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