OUTLINE

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Lecture 10

• OUTLINE
• Poissons Equation
• Work function
• Metal-Semiconductor Contacts
• equilibrium energy-band diagram
• depletion-layer width
• Read Chapter 5.1.2,14.1, 14.2

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Poissons Equation
Gausss Law
area A
?s permittivity (F/cm) ? charge density
(C/cm3)
E(x)
E(xDx)
Dx
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Charge Density in a Semiconductor

• Assuming the dopants are completely ionized
• r q (p n ND NA)

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Work Function
E0 vacuum energy level
FM metal work function
FS semiconductor work function
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Metal-Semiconductor Contacts

• There are 2 kinds of metal-semiconductor
  contacts
• rectifying
• Schottky diode
• non-rectifying
• ohmic contact

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Ideal MS Contact FM gt FS, n-type
Band diagram instantly after contact formation
Schottky Barrier
Equilibrium band diagram
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Ideal MS Contact FM lt FS, n-type
Band diagram instantly after contact formation
Equilibrium band diagram
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Ideal MS Contact FM lt FS, p-type
p-type Si
metal
Eo
cSi

Ec
FM
EF
Ev
FBp c EG - FM
FBp
qVbi FBp (EF Ev)FB
W
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Effect of Interface States on FBn
FM gt FS
n-type Si
metal

• Ideal MS contact
• FBn FM c
• Real MS contacts
• A high density of allowed energy states in the
  band gap at the MS interface pins EF to the range
  0.4 eV to 0.9 eV below Ec

Eo
cSi
FM

qVbi FB (Ec EF)FB
FBn
Ec
EF
Ev
W
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Schottky Barrier Heights Metal on Si

• FBn tends to increase with increasing metal work
  function

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Schottky Barrier Heights Silicide on Si
Silicide-Si interfaces are more stable than
metal-silicon interfaces. After metal is
deposited on Si, a thermal annealing step is
applied to form a silicide-Si contact. The term
metal-silicon contact includes silicide-Si
contacts.
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The Depletion Approximation

• The semiconductor is depleted of mobile carriers
  to a depth W
• In the depleted region (0 ? x ? W )
• r q (ND NA)
• Beyond the depleted region (x gt W )
• r 0

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Electrostatics
E

• Poissons equation
• The solution is

E
E
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Depleted Layer Width, W
At x 0, V -Vbi

• W decreases with increasing ND

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Summary Schottky Diode (n-type Si)
FM gt FS
n-type Si
metal
Depletion width
Eo
cSi
FM

qVbi FBn (Ec EF)FB

• Equilibrium (VA 0)
• -gt EF continuous, constant
• FBn FM c

FBn
Ec
EF
Ev
W
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Summary Schottky Diode (p-type Si)
FM lt FS
p-type Si
metal
Eo
Depletion width
cSi

Ec
FM
Equilibrium (VA 0) -gt EF continuous,
constant FBp c EG - FM
EF
Ev
FBp
qVbi FBp (EF Ev)FB
W