Reappraising the Need for Bulk Heterojunctions in Polymer ...
Semiconductor Heterojunctions - University of Oxfordrtaylor/teaching/devices/... · 2006. 5....
Transcript of Semiconductor Heterojunctions - University of Oxfordrtaylor/teaching/devices/... · 2006. 5....
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HRTEM image of a 6.4 nm AlGaAs/InGaAsstrained layer heterostructure
Semiconductor HeterojunctionsSemiconductor Heterojunctions
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Lattice Parameter (Å)
Energy gap vs lattice parameterEnergy gap vs lattice parameter
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MBE Growth ChamberMBE Growth Chamber •Growth, preparation and loadlock chambers
•Stainless steel•Copper gasket seals
•Ion, turbo- and cryopumps•LN2 cryoshield (400L/day)
•Very long bakes at 200oC•Outgassing of sources•Outgassing of substrates
•Ultra-high vacuum•10-11mbar total
•Pressure of impurities •10–15 mbar
•Growth of thick layers to bury contamination – up to 6 months to clean up.
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Production MBE SystemProduction MBE SystemVG VG SemiconSemicon V150V150
•Launched 1999
•Automated
•Simultaneous growth on four 6 inch wafers
•20,000 6 inch wafers per year
•Laser diodes, LEDs, HBTs, PHEMTs
•Cost £2M
VG Semicon
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)101(2x4 pattern direction
RHEED OscillationsRHEED Oscillations(Observation of growth monolayer by monolayer)(Observation of growth monolayer by monolayer)
8s
GaAs 1μm/hr
AlAs 0.5μm/hr
AlGaAs1.5μm/hr
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MOCVD Growth SystemMOCVD Growth System
• Chemical reaction of elements bonded in volatile organic compounds
• e.g. (CH3)3Ga + AsH3 →GaAs + 3CH4
• Reaction takes place on a heated substrate and growth is also ‘epitaxial’
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strain due to lattice mismatchstrain due to lattice mismatch
*
GaAs
InGaAs
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EC2
χ2
χ1
ΔEV
Evac
EG2EG
1
ΔECEC
1
EV1
EV2
Material 1 Material 2
Energy band offsetsEnergy band offsets
Electron affinity χ: Energy required to remove an electron from the conduction band and take it to the vacuum.
1 2
1 2
= -
= - -
C
V G G C
E
E E E E
χ χΔ
Δ Δ
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Type I: straddlingeg In0.53Ga0.47As-InP
Heterostructure band alignmentHeterostructure band alignment
Type II: staggered eg InP-In0.52Al0.48As
Type III:broken gapeg InAs-GaSb
These examples of band alignment show how the potential barrier across a pn junction may be increased (Type I), electronic states can be made "spatially indirect" (Type II), or semi-metallic behaviour can be produced due to overlapping conduction and valence bands (Type III).
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A single heterojunctionA single heterojunction
ΔEC
E1
E0W
Vd
Ed EF
++
++
+++
E0
E1
E2
wavefunctionswavefunctionsenergy bandsenergy bands
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A single heterojunctionA single heterojunction
( )
( )
0
1/32 2 2
*
2 /3
1/3 2 /32
*
0
3 / 4
3 / 4
and for 0 for a triangular well:
( ) so solving Schrodinger's equation gives:
2
3, 0,1,
2
3and eliminating
2 2
s
r
n n
n
n
N ez
z z
eE a
m
a n n
eE n
m
E
ε ε
ϕ
π
π
ℑ = >
= −ℑ
⎛ ⎞ℑ= −⎜ ⎟
⎝ ⎠
⎡ ⎤≅ − + =⎢ ⎥⎣ ⎦
⎛ ⎞ ℑ⎡ ⎤≅ + ℑ⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠
≅
…
2 /31/3 22
*0
9
2 8s
r
e N
m
πε ε
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠
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A perfect junction?A perfect junction?
High Resolution TEM GaAs/AlGaAsinterface (T Walther, Materials)
TEM of GaAs/AlGaAs 2DEG structure with superlatticebuffer (W M Stobbs, Materials)
GaAs
AlGaAs
GaAs
2.5nm AlGaAs/2.5nm GaAssuperlattice
2DEG
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Quantum Well Quantum Well -- Type IType I
Typical Materials: 1: GaAs(Eg = 1.5 eV)
2: (Al0.35Ga0.65)As(Eg = 2.0 eV)
Energy levels are quantized in z-direction with values En for both electrons and holes ∴
E = En + 2k⊥2/2m* ↑ ↑
1-D 2-D
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V0
2 2
02( ) ( )
2 n n nw
V x xm x
ψ ε ψ⎛ ⎞∂− − =⎜ ⎟∂⎝ ⎠
2 2
2( ) ( )
2 n n nb
x xm x
ψ ε ψ⎛ ⎞∂− =⎜ ⎟∂⎝ ⎠
( ) cos 2
exp 22
exp 22
n x A kx for x w/
w B -K x - for x w/
w B K x for x w/
ψ = <
⎡ ⎤⎛ ⎞= >⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞= + + < −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
( ) sin 2
exp 22
exp 22
n x A kx for x w/
wB -K x - for x w/
wB K x for x w/
ψ = <
⎡ ⎤⎛ ⎞= >⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞= + + < −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
particle in a finite potential wellparticle in a finite potential well
The continuity conditions at the interfaces are
that ψ and should be continuous.1 ∂ψm ∂x
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cos 2
sin2
tan2
w b
w b
kwA B
k kw KBA
m m
k kw K
m m
⎛ ⎞ =⎜ ⎟⎝ ⎠
⎛ ⎞ =⎜ ⎟⎝ ⎠
⎛ ⎞∴ =⎜ ⎟⎝ ⎠
sin2
cos2
cot2
w b
w b
kwA B
k kw KBA
m m
k kw K
m m
⎛ ⎞ =⎜ ⎟⎝ ⎠
⎛ ⎞ = −⎜ ⎟⎝ ⎠
⎛ ⎞∴ =−⎜ ⎟⎝ ⎠
0
0
2 00 2
cos for tan 02 2
sin for tan 02 2
2
kw k kw( )
k
kw k kw( )
k
mVk
= >
= <
=
even
odd
mw≠ mb mw= mb
Eigenvalues for finite potential wellEigenvalues for finite potential well
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Density of StatesDensity of States
Travelling waveseikx (eik.r)
Periodic boundary conditionsψ(x) = ψ(x + L)
∴ eikL = 1 → k = ±2nπ/L→ δk = 2π/L
ε = 2k2/2m*,dε = ( 2/2m*) 2k dk
g(k)dk g(ε)dε3-D
2-D
1-D
( ) ( )εε
πππ dmV
Ldkk 2/1
2/3
223
2 *22/2
4⎟⎠⎞
⎜⎝⎛
( )ε
πππ dmA
Ldkk
⎟⎠⎞
⎜⎝⎛
22*2
4/22
εεππ
dmLL
dk 2/12/1
2
*22/2
2 −⎟⎠⎞
⎜⎝⎛
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2 22 22 2 2
22 2 2yx
n * * *
kkπ nE
m w m m= + +
Two-dimensional density of statesTwo-dimensional density of states
Ee1
Ee2
Ee3
E
k
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Quantum well lasersQuantum well lasers
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Band structure engineering of a quantum well laser
Band structure engineering of a quantum well laser