lecture 4: junctions · lecture outline 1. drawing energy band diagrams for junctions 2. different...
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Lecture 4:
Junctions
October 2018
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Lecture Outline
1. Drawing energy band diagrams for junctions
2. Different types of junction:
a) Metal-Semiconductor
b) pn-homojunction
c) pn-heterojunction
3. Deriving important junction parameters (Vbi, W)
4. Deriving the Diode equation
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Metal-SemiconductorL4
metal SC (n-type)
qφm
qφn
qχ
EG
EV
EC
EF
Schottky Junction
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Metal-SemiconductorL4
metal SC (n-type)
qφm
qφn
qχ
EC
EF E
F
EG
EV
Important Rule● Fermi level must be in equilibrium
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Metal-SemiconductorL4
metal SC (n-type)
qφm
qφn
qχ
EV
EC
EF E
F
qφm
qφn
qχ
EC
EV
metal SC (n-type)
EG E
G
“Contact”
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Metal-Semiconductor
metal SC (n-type)
qφm
qφn
qχ
EC
EV
EF
metal SC (n-type)
EG
qφn
qχ
EC
EV
EF
EG
qφm
qVoqφ
B
Vo = φm
-φn
φB= φ
m - χ
Barrier Height
Band Bending
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Metal-SemiconductorL4
metal SC (p-type)
qφm
qφp
qχ
EG
EC
EV
EF
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Metal-Semiconductor
metal SC (p-type)
qφm
qφp
qχ
EG
EC
EV
EF
qφp
qχ
EC
V
EF
EG
qφm
bi
qφB E
qV
metal SC (p-type)
Vbi = φm
- φp
φB= EG/q - (φ
m - χ)
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Metal-Semiconductor
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Semiconductor-Semiconductor
qφp
qχp
EG
EF
p n
qφn
qχn
EV
EG
p-n homojunction
EC
EF
L4
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Semiconductor-Semiconductor
qφp
qχp
EG
EF
p n
qφn
qχn
EV
EG
p-n homojunction
EF
EF
EC
EF
L4
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Semiconductor-Semiconductor
qφp
qχp
EG
EF
p n
qφn
qχn
EV
EF
EG
p-n homojunction
qφp
qχp
qφn
qχn
EG
p n
EG
EV
EC
EC
EC
EF
EF
EV
L4
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Semiconductor-Semiconductor
qφp
qχp
EG
EF
p n
qφn
qχn
EV
EF
EG
p-n homojunction
EF
EF
p n
qVbi
L4
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Semiconductor-Semiconductor
qφp
qχp
EG
EF
p n
qφn
qχn
EV
EF
EG
p-n homojunction
EF
EF
p n
qVbi
Ei
Ei
Defining Electrostatic potential, Ψ, for a SC●
iDifference between E and E
f
qΨn
qΨp
Vbi
= Ψn - Ψ
p
Ele
ctr
osta
tic P
ote
ntial,Ψ
Ele
ctr
on e
nerg
y,E
Coming back here shortly to get a more physical picture
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Semiconductor-Semiconductor
Everybody's favourite homojunction - Silicon
p-type n-type
http://electronics.howstuffworks.com/diode1.htm
Extrinsically doped
Every bit of electronics you own is jam packed with silicon homojunctions
iPhone 5:1 billion transistors!~ 45 nm wide
Mono-C solar cells~750 μm thick cell size = 1 cm2
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Semiconductor-Semiconductor
qφp
qχp
EFp
p n
qφn
qχn
EFn
p-n heterojunction: Different band gaps
ΔEV
ΔEC
wide gap narrow gap
EF
1. Align the Fermi level. Leave some space for transition region.
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Semiconductor-Semiconductor
qφp
qχp
EFp
p n
qφn
qχn
EFn
p-n heterojunction: Different band gaps
ΔEV
ΔEC
wide gap narrow gap
EF
2. Mark out ΔEC
and ΔEC
at mid-way
points
ΔEC
ΔEC
L4
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Semiconductor-Semiconductor
qφp
qχp
EFp
p n
qφn
qχn
EFn
p-n heterojunction: Different band gaps
ΔEV
ΔEC
wide gap narrow gap
EF
Barrier to hole transport
3. Connect the C.B. and V.B. keeping the band gap constant in each material
Difference in band gaps give rise to discontinuities in band diagrams. This limits the carrier transport by introducing potential barriers at the junction
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Semiconductor-Semiconductor
http://pubs.rsc.org/en/content/articlehtml/2013/ee/c3ee41981a#cit111
Examples of p-n heterojections
Most thin-film PV technologies
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Semiconductor-Semiconductor
Examples of p-n heterojections
III-V multi-junction devices
Being able to control the band offsets of a material can help eliminate barriers
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Physical Picture
Drawing band schematics for junctions all day is fun, but what is actually going on here?
http://www.youtube.com/watch?v=JBtEckh3L9Q
Excellent qualitative description6:27 – Didactic Model of Junction formation
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Physical Picture
J = J (drift ) +J (diffusion)= 0
http://en.wikipedia.org/wiki/File:Pn-junction-equilibrium.png
Equilibrium Fermi Levels – Explained – our one rule for drawing band schematics!
In thermal equilibrium, i.e. steady state: not net current flows
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Physical Picture
Lets look at hole current:
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Physical Picture
Lets look at hole current:
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Physical PictureL4
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Physical Picture
dEF =0dx
The same is true from consideration of net electron current, Jn
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Abrupt JunctionL4
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Abrupt JunctionL4
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Abrupt JunctionL4
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Abrupt JunctionL4
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Abrupt JunctionL4
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Abrupt JunctionL4
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Under Bias
What happens to our ideal p-n junction if we put a forward or reverse bias across it?
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Under Bias
p n
0 wn-wp
W
EF
ZERO BIAS
Vbi
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Under Bias
p n
0 wn-wp
W
EF
FORWARD BIAS
Vbi - V
EF
+ -
●
●
●
●
●
Electron energy levels in p side lowered relative to those in n side Energy barrier qVbi reduced by V
Flow of electrons from n to p increasesFlow of holes from p to n increasesDepletion width decreases
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Under Bias
p n
0 wn-wp
W
EF
REVERSE BIAS
Vbi + V
EF
- +
●
●
●
●
Electron energy levels in p sideraised relative to those in n sideEnergy barrier qVbi increased by V
Flow of electrons from n to p reducedJunction width increases
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Ideal Dark JV curveL4
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Ideal Dark JV curve
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Deriving Shockley Equation
Steady State again (i.e. no bias) Consider electron drift current
– Ieo from p to n
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Deriving Shockley Equation
Steady State again (i.e. no bias) Consider electron drift current
– Ieo from p to n
W
Le
L4
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Deriving Shockley Equation
Steady State again (i.e. no bias) Consider electron drift current
– Ieo from p to n
W
Le
L4
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Deriving Shockley Equation
Steady State again (i.e. no bias) Consider electron drift current
– Ieo from p to n
W
Le
L4
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Deriving Shockley Equation
What happens under forward bias?
●
●
Drift (p to n)? - Nothing. No potential barrier in this directionDiffusion (n to p)? - Increases by exponential factor:
If we assume occupation of states in CB is given by Boltzmann distribution
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Deriving Shockley Equation
What happens under forward bias?
●
●
Drift (p to n)? - Nothing. No potential barrier in this directionDiffusion (n to p)? - Increases by exponential factor:
If we assume occupation of states in CB is given by Boltzmann distribution
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Deriving Shockley EquationL4
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Deriving Shockley EquationL4
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Deriving Shockley EquationL4
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Deriving Shockley EquationL4
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Lecture SummaryL4
1. Drawing energy band diagrams for junctions
2. Different types of junction:
a) Metal-Semiconductor
b) pn-homojunction
c) pn-heterojunction
3. Deriving important junction parameters (Vbi, W)
4. Deriving the Diode equation