HRTEM image of a 6.4 nm AlGaAs/InGaAsstrained layer heterostructure
Semiconductor HeterojunctionsSemiconductor Heterojunctions
Lattice Parameter (Å)
Energy gap vs lattice parameterEnergy gap vs lattice parameter
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.
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
)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
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’
strain due to lattice mismatchstrain due to lattice mismatch
*
GaAs
InGaAs
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
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).
A single heterojunctionA single heterojunction
ΔEC
E1
E0W
Vd
Ed EF
++
++
+++
E0
E1
E2
wavefunctionswavefunctionsenergy bandsenergy bands
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
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠
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
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
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
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
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 −⎟⎠⎞
⎜⎝⎛
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
Quantum well lasersQuantum well lasers
Band structure engineering of a quantum well laser
Band structure engineering of a quantum well laser