6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-1
Lecture 17 - Metal-Semiconductor Junction
March 14, 2007
Contents:
1. Ideal metal-semiconductor junction in TE
2. Ideal metal-semiconductor junction outside equilib­
rium
Reading assignment:
del Alamo, Ch. 7, §§7.1, 7.2
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-2
Key questions
• What happens when you bring together a metal and a semicon­
ductor in intimate contact?
• What happens in a metal-semiconductor junction when you ap­
ply a voltage to the metal with respect to the semiconductor?
• In a metal-semiconductor junction under bias, is there current
flow? If so, how exactly does it happen?
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-3
1. Ideal metal-semiconductor junction in TE
� First, ideal metal-metal junction in TE:
Eo
Eo
WM1
WM2
EF2
EF1
a) two metals far apart
Eo
Eo
WM1
WM2
EF2
EF1
b) two metals just before contact
Eo
qφbi
WM1
WM2
EF
c) two metals in intimate contact
dipole charge at interface → built-in potential
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-4
Spatial extent of SCR in MM junction: a few nm
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-5
Can define local work function
Think of photoelectric experiment vs. position:
-
hυ
metal 1
metal 2
hυth
WM1
WM2
x
metal 1
metal 2
hυth
WM1
WM2
x
Can define local vacuum energy Eo
Shape of Eo identical to potential energy ⇒
1
φbi = (WM1 − WM2 )
q
� Ideal metal-semiconductor junction in TE
Energy band line up depends on choice of metal and semiconductor.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-6
Do metal/n-type semiconductor with WM > WS :
WS = χ + qϕn
Eo
Eo
χ
WS
WM
Ec
EF
qϕn
EF
Ev
a) metal and semiconductor far apart
M S
Eo
qφbi
WM
EF
qϕBn
WS
Eo
χ
Ec
EF
qϕn
Ev
b) metal and semiconductor in intimate contact
1
φbi = (WM − WS )
q
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Eo
Lecture 17-7
qφbi
WM
EF
qϕBn
WS
Eo
χ
Ec
EF
qϕn
Ev
Most important parameter of MS junction: Schottky barrier height:
qϕBn = WM − χ
Also:
qϕBn = qφbi + qϕn
Warning: simple theory not followed due to surface states
⇒ In practice, rely on measurements for qϕBn.
Still can use:
qϕBn = qφbi + qϕn
Typical Schottky barrier height: qϕB ∼ 0.4 − 0.8 eV (depends on
metal and doping type).
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-8
� Electrostatics in TE
In semiconductor:
• close to the M-S interface: space-charge region
• farther away: quasi-neutral region
ρ
depletion approximation
qND
exact
0
0
xd
x
ε
xd
0
0
x
εmax
φ
xd
0
0
x
−φbi
log po, no
ND
no
po
ni2
ND
0
x
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-9
Do depletion approximation:
• Volume charge density:
ρ(x) � qND
ρ(x) � 0
in SCR: 0 ≤ x < xd
in QNR: xd < x
• Electric field:
qND
(x − xd)
�
E(x) � 0
E(x) �
in SCR: 0 ≤ x ≤ xd
in QNR: xd ≤ x
• Electrostatic potential, with φ(bulk) = 0:
φ(x) = −
φ(x) = 0
qND 2
(x − 2xdx + x2d )
2�
in SCR: 0 ≤ x ≤ xd
in QNR: xd ≤ x
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-10
xd obtained by demanding φ(0) = −φbi:
xd =
�
�
�
�
�
2�φbi
qND
Maximum field:
|Emax| =
�
�
�
�
�
qND xd
2qND φbi
=
�
�
Key dependencies:
• ND ↑ → xd ↓→ |Emax| ↑
• φBn ↑ → xd ↑→ |Emax| ↑
Also in TE, Boltzmann relation:
no(x) = ND exp
qφ(x)
kT
no (0) = ND exp
−qφbi
kT
At x = 0:
Depletion approximation valid if no (0) � ND , or φbi � 3 kT
, easy!
q
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-11
2. Metal-semiconductor junction outside equilibrium
Apply voltage across:
• forward bias: metal positive with respect to semiconductor
• reverse bias: metal negative with respect to semiconductor
[notation reversed for metal/p-semiconductor junction]
Voltage can drop in four distinct regions:
• metal
• metal-semiconductor interface on metal side
• semiconductor SCR
• semiconductor QNR
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-12
Key to drawing energy band diagram: battery grabs on majority­
carrier quasi-Fermi level [will see when we discuss ohmic contacts].
� Forward bias (V > 0):
Eo
q(φbi-V)
WM
Ef
χ
Eo
WS
qϕBn
Ec
Efe
qV
Ev
Main consequence of voltage application:
φbi → φbi − V < φbi
Then:
xd(V ) < xd(V = 0)
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-13
� Reverse bias (V < 0):
Eo
q(φbi-V)
WM
qϕBn
Ef
Eo
χ
WS
qV
Ec
Efe
Ev
Also:
φbi → φbi − V > φbi
Then:
xd(V ) > xd(V = 0)
Otherwise, electrostatics not substantially changed.
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-14
� Summary of electrostatics under bias:
ρ
qND
V>0
V=0
V<0
0
xd(V)
x
ε
xd(V)
0
x
εmax(V)
φ
xd(V)
0
x
−(φbi-V)
Reuse main results from TE but φbi → φbi − V :
xd (V ) =
|Emax(V )| =
�
�
�
�
�
�
�
�
�
�
�
2�(φbi − V )
V
= xd(V = 0) 1 −
qND
φbi
�
�
�
�
�
�
�
�
�
�
qND xd (V )
qND (φbi − V )
V
=
= |Emax(V = 0)| 1 −
�
�
φbi
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-15
� Depletion capacitance
Examine change in SCR charge differentially:
ρ
qND
ΔQ
V
+Q
V+ΔV
0
x
xd(V)
-Q
Δρ
+ΔQ
xd(V)
0
x
−ΔQ
SCR behaves as capacitor of capacitance per unit area:
C(V ) =
�
xd(V )
Or:
C(V ) =
�
�
�
�
�
�
�qND
C(V = 0)
= �
2(φbi − V )
1 − φV
bi
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-16
Same result obtained if:
C=
dQ
dV
with:
�
Q(V ) = qND xd(V ) = 2qND �(φbi − V )
Q
1
C
C2
-
2
εqN
D
φbi
V
0
0
φbi V
0
φbi
V
C
C-V technique to extract φbi and ND :
1
2(φbi − V )
=
C2
�qND
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-17
1
2(φbi − V )
=
C2
�qND
2
1.8
1.6
Capacitance (10−11 F)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−40
−35
−30
−25
−20
−15
Voltage (V)
−10
−5
0
5
0.7
data
0.6
ideal Schottky diode theory with
φbi = 0.95 V
ND = 2.15*1017 cm−3
0.5
1/C2 (1023 F−2)
A = 1.86*104 µm2
0.4
0.3
0.2
0.1
0
−10
−9
−8
−7
−6
−5
−4
Voltage (V)
−3
−2
−1
0
1
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 17-18
Key conclusions
• Junction of dissimilar materials ⇒ dipole charge at interface ⇒
built-in potential.
• Relative band alignment between metal and semiconductor char­
acterized by Schottky barrier height, qϕBn.
• Simple theory for qϕBn does not apply ⇒ must use experimen­
tally determined values.
• In M-S junction, charge dipole occurs at interface; typically a
depletion region is created on semiconductor side.
• Built-in potential of M-S junction:
φbi = ϕBn − φn
• Application of voltage to M-S junction impacts φbi directly ⇒
xd(V ), E(V ).
• Modulation of depletion region width with voltage gives rise to
capacitive effect.
• Order of magnitude of key parameters in Si at 300K:
– Schottky barrier height: qϕB ∼ 0.4 − 0.8 eV (depends on
metal and doping type).
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
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