Transcript Semiconductors

Semiconductor Devices
 Metal-semiconductor junction
 Rectifier (Schottky contact or Schottky
barrier)
 Ohmic contact
 p – n rectifier
 Zener diode
 Photodiode (solar cell)
 Tunnel diode
 Transistor
 Other devices based on semiconductors (for
hybrid circuits)
 Resistor
 Isolator
 Capacitor
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Negative/Positive Charged Surface
Band structure of an n-type semiconductor
with negatively charged surface
Band structure of a p-type semiconductor
with positively charged surface
Near the surface, the concentration of free
electrons is lower – the negative charge of
the surface represents a potential barrier
for electrons
Near the surface, the concentration of “free
holes” is lower – the positive charge of the
surface represents a potential barrier for
free holes
Custom: the edges of energy bands are diagramed distorted, not the Fermi energy
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Contact: Metal and n-type Semiconductor
  M  S  EFM  EFS
 0
Potential barrier
Energy bands of a metal and a n-type
semiconductor (without contact)
Fermi energies are different




Electrons
Energy bands of a metal and a
n-type semiconductor (contact)
Electrons flow into the metal until the Fermi energies are equalized.
The surface of the metal charges negative.
Simultaneously, a potential barrier is formed.
In equilibrium, only one diffusion current exists (equal in both directions).
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Contact: Metal and p-type Semiconductor
  M  S  EFM  EFS
 0
Potential barrier
Energy bands:
The Fermi energies are different
Electrons
Energy bands of a metal and a
p-type semiconductor




Electrons flow into the semiconductor until the Fermi energies are equalized.
The surface of the metal charges positive.
Simultaneously a “negative” potential barrier is formed.
In the Equilibrium only one diffusion current exists (equal in both directions).
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Work functions
Metals
Material
Ag
Al
Au
Be
Ca
Cs
Cu
Fe
K
Li
Na
Ni
Zn
 [eV]
4,7
4,1
4,8
3,9
2,7
1,9
4,5
4,7
2,2
2,3
2,3
5,0
4,3
Semiconductors
Material
Diamond
Ge
Si
Sn
 [eV]
4,8
4,6
3,6
4,4
* Work function = vacuum electron affinity = vacuum ionization energy
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Electrical Currents
Diffusion current
Metal
Drift current
Metal
Semiconductor
Semiconductor
–
𝐼 = 0
+
𝐼 > 0
U
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Drift Current
Reverse bias
Forward bias
An external electric field
increases the potential barrier
An external electric field
decreases the potential barrier
Barrier for electrons
Acceleration of electrons
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Drift Current
Metal  Semiconductor
 Φ χ

I MS  AC T 2 exp  M
k
T
B


Semiconductor  Metal
 Φ  Φ S  eV
I SM  AC T 2 exp  M
k BT




𝐴 … area
𝐶 … Richardson
constants
𝑇 … temperature
𝜒 … affinity
Φ… work function
𝑘B … Boltzmann
constant
𝑉 … external voltage
𝑒 … elementary charge
Total current:

 Φ  Φ S  eV
I  I SM  I MS  AT 2 C  exp  M
k BT


 Φ  χ    eV  
 exp
  1
I  ACT 2 exp  M
k
T
k
T
B 
 B



 

saturation current

 Φ  χ 
  C  exp  M

k BT  


voltage dependency
enhanced
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Ohmic Contact
Electrons
Example:
Al / Ge : Al < Ge the contact Al / Ge exhibits good electrical conductivity
Technological example:
Al / Si or Al / SiO2
Al > Si  the contact Al / p-Si shows good electrical conductivity
the contact Al / n-Si can be used as a rectifier
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Ohmic Contact: Al / n-Si
n-semiconductor
n+-film
metal
Electron current
Quantum tunneling
The n+ slab has to be very thin.
Problem: electromigration
Material transport at high electric currents, due
to the momentum transfer between conducting
electrons and atoms or ions of the solid
Solution:
Al  Al + Cu, Al  Al + Si
Coating with gold
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p-n Junction (Diode)
In equilibrium (without
external voltage)
Diode with external voltage
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Electrochemical Potential
Diffusion current
Electrochemical potential in equilibrium state:
jfield  eEn   jdiff  eD
eE 
eD dn
μn dx
eE  e
Field current
U
; μ
dn
;
dx
j   D grad c
eD
k BT
dU k BT dn
d

 k BT ln n 
dx
n dx
dx
k BT
ln n  const.
e
… The electrochemical potential
of electrons is everywhere the
same in state of equilibrium
(without a current)
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p-n Junction (Diode)
Electrons
U
Holes
k BT
ln n  const.
e
U
k BT
ln p  const.
e
Potential difference (potential jump)
U 0   left   right 
p
k BT nright k BT
ln

ln left
e
nleft
e
pright
With external voltage
Without external
voltage
jdiff  jfield  j0
j  jfield  jdiff  0
U
 eU    
k BT
ln n   ; n  exp 

e
k
T
B


 eU 
 ;
jfield  nev  j0 exp
 k BT 
  eU  
  1
j  j0 exp
k
T
  B  
jdiff  j0
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Semiconductor Diode (Rectifier)
I
U
Abb. 14.61. Current-voltage-characteristic of a
rectifier diode
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Zener Diode
Used with reverse bias
Ionization process:
Avalanche-like increase of
the electric current
Generation of free electrons
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Photodiode (Solar Cell)
𝐸g
E  hν  E g
1 Eg
hc
 λ 
λ hc
Eg
𝐸g [eV]
Ge
0.7
Si
1.1
GaAs 1.5
𝜆 [m]
1.8
1.1
0.83
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Tunnel Diode
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Transistor (without external voltage)
B
E
C
Two potential barriers
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Transistor (with external voltage)
n
Potential
barrier
p
n
Acceleration in
the electric field
Amplifier
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Devices in Hybrid Circuits
Resistor: electrical conductivity as function of the doping in the p-zone
Capacitor: different electrical charges in p- and n-zone, separated by an
insulator (dielectric)
Technology
Source material: SiO2  Si  Czochralski method (monocrystalline silicon)
Diffusion process: diffusion of phosphorus (n) or boron (p) in silicon. Mask – SiO2.
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