ECE606: Solid State Devices Lecture 17 SchottkyDiodeee606/downloads/ECE6… · ·...
Transcript of ECE606: Solid State Devices Lecture 17 SchottkyDiodeee606/downloads/ECE6… · ·...
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
ECE606: Solid State Devices
Lecture 17
Schottky Diode
Gerhard [email protected]
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Reference: Semiconductor Device Fundamentals, Chapter 14, p. 477
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Metal-semiconductor Diode
M N
Symbols
DN
Metal Wire
N
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Applications of M-S Diode ….
Originally, Gelena (PbS), Si as semiconductor and
Phospor Bronze for metal (cat’s whisker)
Detectors
www.fz-juelich.de/ibn/index.php?index=674
STM(scanning tunneling microscope)
on semiconductor
Original Bipolar CNT(carbon nanotube)
Transistors
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Drawing Band Diagram in Equilibrium…
1P P P
pr g
t q
∂ = − ∇ • − +∂
J
( )D AD q p n N N+ −∇ • = − + −
P P Pqp qD pµ= − ∇J E
1N N N
nr g
t q
∂ = ∇ • − +∂
J
N N Nqn qD nµ= + ∇J E
Equilibrium
DC dn/dt=0Small signal dn/dt ~ jωtn
Transient --- full sol.
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band-Diagram
DN
Vacuum level
EC
EV
EF
A p D nN x N x=
ΦM
Since NA is large,xp is negligible ..
χ
1. EF flat in equilibrium2. EC/EV in Metal3. Vacuum level in Metal4. Ec/Ev in semiconductor5. Vacuum level in semiconductor
6. Connect vacuum levels
7. duplicate the connections down to Ec/Ev
Charge(metal) = charge(semiconductor)
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Built-in Potential: bc @Infinity
b MiqVχ∆ + = Φ+ ( )M BbiqV χ= ≡− − ∆Φ Φ − ∆
BC
BDN
k T lnN
= −Φ
qVbi
∆χ
ΦM
ΦB
non-degenerate
neglect
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Depletion Approximation
ρ
qND
Xn
QM =-QDQD = NDXn
x
Actual Xn
E
x
max
D
0 0
Q D n
s s
qN x
K Kε ε= = −E
xXn
BqφCE
VE
Area negligible
integrate
integrate
Analytical Solution (Simple Approach)
Notice how we neglect xp here, is there a proof?
x
Xn
max
max 2nxφ = − E
φΦmax=qVbi
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Charge
E-field
Potential
xp
xn
+-
Position
Position
Position ( ) ( )22
0 0
0 0
2 2
2 2
bi
MD
n
pn
s s
pqV
qNqN
k k
xx
xx
ε ε
− +
= +
= +
E E
( )
( )0
0
0
0 ?
nD
s
M
s
D
p
n pM
qN
k
qN
k
N
x
xN
x
x
ε
ε
+
−
=
=
⇒ =
E
E
Complete Analytical Solution
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Depletion Regions
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0 02 2pMD
bs
ni
s
qNqNqV
k
x
k
x
ε ε= +
pD MnxN N x=( )
0 02 2 1s sMbi bi
D M D Dn
k kNV V
q N N N q Nx
ε ε= →+
( )02
0s Dbi
M M Dp
k NV
q N Nx
N
ε= →+
xnxp
DN
NM ∞
This is why we can neglect xp
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band Diagram with Applied Bias…
1P P P
pr g
t q
∂ = − ∇ • − +∂
J
( )D AD q p n N N+ −∇ • = − + −
P P Pqp qD pµ= − ∇J E
1N N N
nr g
t q
∂ = ∇ • − +∂
J
N N Nqn qD nµ= + ∇J E
This works for doping-modulated
Semiconductors.
Does not work for heterostructures
(when the conduction band is not
continuous)
Metal-Semiconductor is a HS
Need theory of thermionic
emission
Band diagram …
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Depletion Regions with Bias
( ) ( )0 02 2 1s M sn bi bi A
D M D D
k N kx V V V
q N N N q N= → −
+ε ε
( )02
0s Dp bi
M M D
k Nx V
q N N N= →
+ε
xnxp
DN
Forward bias: xn decreaseReverse bias: xn increase
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band-diagram with Bias
VA
EC-EF
EC-EF
qVbi
qVbi-V
VA
EC-EF
Forward Bias
Reverse Bias
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
I-V Characteristics
Forward Bias
Reverse Bias
Metal N-typeSemi.
VA
IEc
EV
EFEFS
EFM
Ec
EV
EFEFS
EFM
I
1,2,3
6,7
4
51 – diffusion control2 – ambipolar3 – resistance drop6 – defects – trap assist7 – Esaki
4 – generation current5 – impact ionization
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
EC-EF
qVbi
Current Flow Concept
In Equilibrium:and
are equal
ΦB
VA
EC-EF
Reverse Bias
ΦB
BarrierThe same!M=>S current unchanged!
VA
EC-EFqVbi-VA
Forward Bias
ΦB
Partition problem in2 currentsM=>S S<=M
BarrierThe same!M=>S current unchanged!
q(Vbi+VA)
Barrier smallerM<=S increased
Barrier biggerM<=S decreased
M=>S current Independent
of bias!19
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Left Boundary Condition
VA
ECq(Vbi-VA)
( )
(
(( ) )
( )0)m s A s m A
s m As
T
m
A J V
J
J VJ
J
V
V→
→
→
→
= −= −
(0)(
(
(0)
(
0
0 )) 0
0) s m
s m
m
m s
T sA J
JJ
J V J →
→
→
→
= = = −⇒ =
( ) (0) ( )T A s m s m AJ V J J V→ →= −
(detailed balance)
M=>S current independent of bias
We use thermionic emission because:1. EC is not continuous here2. There’s no minority carriers!
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Semiconductor to Metal Flux
(0)AV
s m
q
kTeJ →=
( )2
bi AV Vq
s khs
TA tm
nq eJ V
−−
→ = − υ
VAEC-EF
q(Vbi-VA)
2
bi AqV qVs th kT kT
nq e e
−= − ×υ
( (0)2
0)biV
s m m s
qs kT
th JqJn
e υ−
→→ = − =
(0)AV
m s
q
kTeJ →=
Only half of them goes to the right
Only the ones above the barrier goes to the right
(0)
( )2
Bqm kT
th
m s
m s A
nJ qV e
J
υ
→
→
Φ−
=
= − M
2
B Aq qVm th kT kT
nq e e
Φ−
= − υ M
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(0) ( )m Aq qV
m th kT kTm s AT s m
qnJ J e eJ V
υ→ →
− Φ = = −
− M
BΦ
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Diffusion vs. Thermionic Emission
Fp
Fn
∆n
Fp
Fn
Check that both gives the
same result for a diode…
Thermionic Emission theory is a more general approach, can be used for device so small that no scattering occur (can’t use diffusion!).
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Schottky barrier diode is a majority carrier device of great historical importance.
There are similarities and differences with p-n junction diode: for electrostatics, it behaves like a one-sided diode, but current, the drift-diffusion approach requires modification.
The trap-assisted current, avalanche breakdown, Zenertunneling all could be calculated in a manner very similar to junction diode.
Intermediate Summary
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Energy Resolved Thermionic Flux
( )min
34F
s x xmE E
y zJ q dk edk dkυ
β υπ
∞ ∞− −
→−∞
−
−∞−∞
Ω= − ∫ ∫ ∫
VA
EC-EF
q(Vbi-VA)
~ DOS
minυ
x
Occupation(non-denegerate)
Only movement in thex direction will contribute
to the current flux
2min
*
2
1 υm<Energy
will be bounced back
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Thermionic Flux from Semi to Metal ..
( )min
34F
s m x y z xE EJ q dk dk edk β
υ
υπ
−∞ ∞
→−
∞ −∞ −∞
−
−
Ω= − ∫ ∫ ∫
( ) ( ) ( ) ( ) ( )min2 2 2* *
2
*
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x y
c F
z
x y zm m m
xE E
d m d m d mqe e
υυ υββ
υυ υ υυ
π
−∞ ∞−−
−∞ −∞ −∞
+−
+Ω= ∫ ∫ ∫
ℏ ℏ ℏ
( ) ( )
2 22min
3 * ***2 22
3 34
y xz
c F
m mm
E Es m y z x x
q mJ e e d e d d e
υ υυβ βυββ υ υ υ υ
π
− ∞ ∞− −− − −
→−∞ −∞ −∞
Ω =
∫ ∫ ∫ℏ
( ) * 2 * 2 * 21 1 1
2 2( ) ( )
2C x y zC F C FF E E E EE E m m mE E υ υ υ− + ++− =− −= +
EECEF
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Thermionic Current …
( )* 2
203
4bF C i A AE E qV qV Vq
s m
qm kJ T e e A e
hβ β βπ
→− −= =
π
( ) ( )
2 22min
3 * ***2 22
3 34
y xz
c F
m mm
s m y z xE E
x
q mJ e e d e d d e
υ υυ υβ βββ υ υ υ υ
π
− ∞ ∞− −− − →
−∞ ∞ −∞
−
−
Ω =
∫ ∫ ∫ℏ
π ( )1
2bi AV Vqe β−−
( )min *
2bi A
qV V
m= −υ
( )0 1AqT s m m s
VJ J J A e β→ →= − = −
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam 28
Some insight of the Thermionic Current …
Compare to the current of p-n diodes…
( )22
1An i
p
qVT
p i
DA n
D n
W N
D n
W NJ q e β
= − + −
( )0 1AqT s m m s
VJ J J A e β→ →= − = − Schottky diode
p-n diode
Both of them depends exponentially on VA, however current of p-n diodes depends more on temperature (since ni depends strongly on Eg), where the Schottky diode doesn’t have that dependence.
However, Eg hides in…
( )* 2
203
4bF C i A AE E qV qV Vq
s m
qm kJ T e e A e
hβ β βπ
→− −= =
The information of material hides in m* The information of doping concentration hides in EF-EC
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Recombination/Generation/Impact-ionization
SAME technique as in p-n junction except integrate to xp only
Ec
EV
EFEFS
EFM
EFM
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Series Resistanc
e
Conductance
Diffusion Capacitance
Junction Capacitance
AC response
We will not have Diffusion Capacitance here…
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
( )( )/ 1A Sq V R I moI I e −= −β
0
1
( )SFB
mR
g q I I= +
+β
0
ln ( ) /oA S
I Iq V R I m
I
+ = − β
( )A
So
m dVR
q I I dI= −
+β
gFB
Forward Bias Conductance
m depends on which operation regime you are
RS
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Junction Capacitance (Majority Carriers)
Junction Capacitance
0sJ
AC
W
κ ε=
0
02( )
sJ
sbi A
D
AC
V VqN
κ εκ ε
=−
Response time – dielectricVery fast propagation
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
No Diffusion Capacitance in Schottky Diode
No minority carrier transport and therefore no diffusion capacitance ..
p-n Diode Schottky diode
VA
n
x
When electrons reach the metal side, they quickly scatter and join the majority carriers there. Nothing is diffusing…
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Reducing diffusion capacitance in p-n diode
Short minority carrier lifetime in p-n junction diode equivalent to rapid energy relaxation in SB diode.
p-n Diode Schottky diode
VA
n
x
Provide lots of traps
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Presentation Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams
3) DC Thermionic current (simple derivation)
4) Intermediate Summary
5) DC Thermionic current (detailed derivation)
6) AC small signal and large-signal response
7) Additional information
8) Conclusions
37
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Ohmic Contact vs. Schottky contacts ..
n-Si
n+
OxideMetal
Low Doping Moderate Doping
High Doping
What if we just want the p-n junction? How to reduce the barrier of Metal-Semiconductor?
For majority carriers: there’s not barrier For minority carriers: high doping allows them to tunnel throughMetal will just act like Ohmic Contact
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Lowering of Schottky Barrier
Ref. Sze/Ng., p. 143
E
qφ1qφB
Semi
x
Metal
---
---
-
-Surface Charge
x
ElectronImage Charge
Metal Semi
qφ1qφB
The fields on the metal must be perpendicular(otherwise there will be tangential current flow which is impossible)as if there’s an image charge(positive) in the metal, results in lowering the barrier height
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Fermi-level Pinning
Full
Full
Density of States
EcEfEv
Metal MetalSemiconductor
Regardless the workfunction, no modulation in potential. (e.g. Modern high-k dielectrics)
A B
Full
Metal
Full
Metal
EcEf
Ev
Shift in the Band edge
Why sometimes we don’t get conductance at all?
surface states bends EC/EV so that the Fermi level is at the center of the bandgap, they exchange carriers with metals, blocking the bulk semiconductor insideno modulation in potentialbarrier even you connected to different metals.
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Conclusion
1) Schottky diodes have wide range of applications in
practical devices.
2) The key distinguishing feature of Schottky diode is that
it is a majority carrier device.
3) We use a different technique to calculate the current in
a majority carrier device.
=> thermionic emission.
4) Elimination of diffusion capacitance make the response
of the diodes very fast.
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