Semiconductor Heterojunctions - University of Oxfordrtaylor/teaching/devices/... · 2006. 5....

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