Transcript
Page 1: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

PART IV: EPITAXIAL SEMICONDUCTOR

NANOSTRUCTURES

PART IV: EPITAXIAL SEMICONDUCTOR

NANOSTRUCTURESProperties of low-dimensional quantum confined

semiconductor nanostructures

Fabrication techniques of low-dimensional semiconductor nanostructures

Formation and properties of self-assembled QDs

Growth of QWRs-QDs on patterned surfaces

Mechanisms of self ordering in epitaxial growth

Page 2: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Properties of low-dimensional quantum confined semiconductor

nanostructures

Properties of low-dimensional quantum confined semiconductor

nanostructures

Page 3: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Effect of quantum confinement on energy spectrum

Effect of quantum confinement on energy spectrum

Energy spectrum for electrons confined in 1, 2 or 3D with infinitely deep, rectangular potential wells with sizes tx, ty, tz:

tconfinemen 32

tconfinemen 222

tconfinemen 122

2

2

2

2

2

2

*

22

,,

*

22

2

2

2

2

*

22

,

*

222

2*

222

Dtn

tm

tl

mE

Dmk

tm

tl

mE

Dm

kk

tml

E

zyxnml

z

yxml

zy

xl

h

hh

hh

Page 4: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Electron DOS in low-D systemsElectron DOS in low-D systems

Lower D sharper DOS potential advantage for optical and electronic propertiesLower D sharper DOS potential advantage for optical and electronic properties

Energy Energy Energy Energy

Den

sity

of

Sta

tes

3D - bulk3D - bulk 2D - QW2D - QW 1D - QWR1D - QWR 0D - QD0D - QD

E

m2

2/32*

2/2

h l

lx

EEt

m

2

*

h

mlml

yx

EEtt

m

,

2/1,

2/1*2h

nml

nmlzyx

EEttt ,,

,,

2

Page 5: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Sizes needed to observe QCSizes needed to observe QC

At T = 0K electrons occupy all energy states up to EF, corresponding to de Broglie (Fermi) wavelength F = 2 / (32n)1/3, with n = electron density.

Quantum confinement for ti ≤ F

Metals: 1 electron / atom F ≈ 0.5nm

Semiconductors: much higher, depends on doping: e.g., n~1X1018cm-3 F = 29nm, ti ≈ 10nm is sufficient

Page 6: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Subband population in QC systemsSubband population in QC systems

If more subbands are populated, motion along confinement direction results only ground state must be populated, i.e., E12 > kBT

For infinite square QW, this means

For electrons in GaAs at T = 300K tx < 20nm

For holes, more complicated relations and mh>me smaller tx

Equivalent sizes for other confinement dimensions

Tkmt

Bx *

22

23 h

Page 7: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Uniformity requirements in QC structuresUniformity requirements in QC structures

Size non-uniformity inhomogeneous broadening of DOS

For ∞ wells, | Ei | / Ei = 2 ti / ti ; Ei << Ei ti << ti

Practical limit to observe QC: ti / ti < 10% ti ≈ 1nm

0

5

10

15

20 30 40 50 60 70

0 meV2 meV5 meV10 meV15 meV

nb

of

sta

tes

/ n

m

confinement energy (meV)

Calculated electron DOS in a GaAs/AlGaAs QWR with different Gaussian-shaped inhomogeneous broadening

Page 8: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Fabrication techniques of low-dimensional semiconductor

nanostructures

Fabrication techniques of low-dimensional semiconductor

nanostructures

Page 9: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

From Quantum Wells to Quantum Wires/DotsFrom Quantum Wells to Quantum Wires/Dots

?Planar (layer-by-layer) epitaxy

QWR - QD

Control overlateral

composition

QW

Page 10: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Main approaches for creation of lateral confinement

Main approaches for creation of lateral confinement

Top-down:Post growth patterning of epitaxially grown 2D quantum wells

Bottom-up:Formation of QWR / QD during growth by special epitaxial procedures

Page 11: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Post-growth patterning 1Post-growth patterning 1

EtchedRegrown

Advantages:

Flexibility of design (lithographic patterns)

Disadvantages:

Size: several 10nm

Uniformity (size and shape): several nm

Etching defects interface states75-nm quantum wires fabricated in GaAs/AlGaAs material by e-beam lithography and chemical etching

(M. L. Roukes et al.Phys. Rev. Lett. 59, 3011 (1987))

SEM image showing narrow pillars etched into a GaAs substrate.

(horizontal bars = 0.5 m(M. A. Reed et al., Phys. Rev. Lett. 60, 535

(1988))

Selective removal of QW by lithography, etching and regrowth

Lithography: holo, e-beam, X-ray

Etching: dry, wet depending on details of fabrication process

Regrowth: surface passivation

Page 12: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Post-growth patterning 2Post-growth patterning 2

Selective disordering of QWs

Patterning of QW band gap and refractive index

Methods: implantation or diffusion of impurities through a mask or with focused ion beams

Advantages:

Flexibility of design (lithographic patterns)

Disadvantages:

Size: several 10nm

Uniformity (size and shape): several nm

Impurities material contamination

Mask Disordered QWs

QWs

Page 13: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Post-growth patterning 3Post-growth patterning 3

Deposition of patterned “stressors” adjacent to the QW

Lateral band-gap modulation via strain effects

Advantages:

Flexibility of design (lithographic patterns)

Smooth, defect-free lateral interfaces

Disadvantages:

Size: several 10nm

Uniformity (size and shape): several nm

Stressor

Conduction Band

QW

Page 14: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Post-growth patterning 4Post-growth patterning 4

Lateral patterning of 2D electron gas structures

Creation of QWRs, quantum point contacts (QPCs) and QDs

Methods: Depletion by deposition of a metallic split-gate (top) Wet chemical etching and depletion by in-plane

gates (bottom)

Dielectric Metal gate

Patterned 2DEG

Advantages:

Flexibility of design (lithographic patterns)

Smooth, defect-free lateral interfaces

Easy electric contacts

Disadvantages:

Size: several 10nm

Uniformity (size and shape): several nm

Page 15: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Cleaved-edge overgrowthCleaved-edge overgrowth

Overgrowth on the Cleaved (011) Edge of a (multiple) QW or 2DEG structure (CEO) Cleave of the 2DEG in the MBE chamber Overgrowth of 2DEG on top of the cleaved edge

QWR at the point where the two 2DEGs intersect

lateral variation in the potential energy

1 regrowth: QWRs; 2 regrowths: QDs

2DConfinement

Edge-Regrowth

After cleavage the sampleis reoriented and growthis then resumed on topof the cleaved surface

AlG

aA

s

Ga

As

Growth direction

Growth direction

AlGaAs

GaAs

The process begins withthe usual growth of a

high-mobilityheterojunction

Cleave here

AlGaAs

GaAs

After this the sampleis cleaved inside the

vacuum chamber

A. R. Goni et al.APL. 61, 1956 (1992)

Page 16: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Cleaved-edge overgrowthCleaved-edge overgrowth

Advantages:

Size, uniformity: ML scale

Smooth, defect-free lateral interfaces

Disadvantages:

Low flexibility (difficult contacts on cleaved edge)

W. Wegscheider et al.PRL 71, 4071 (1993)

Page 17: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Spontaneous self-ordering 1Spontaneous self-ordering 1

Growth of fractional-layer SLs on vicinal substrates

Species-dependent surface diffusion and preferential attachment of adatoms to the step edges lateral and vertical definition, alignment

QWR formation: serpentine SL (growth rate modulations), accumulation at step bunches

Advantages:

1-step process (no processing)

Size: <10nm

Lateral interfaces formed during growth

Disadvantages:

Uniformity: 10-20% (imperfect step configuration and spacing, incomplete adatom segregation, growth rate variations)

Vicinal Substrate

Tilted SL

Stacked GaAs/AlGaAs QWR SL formed on step bunches on 3o off (110) GaAs.(T. Kato et al., APL 72, 465 (1998)

Page 18: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Spontaneous self-ordering 2Spontaneous self-ordering 2

Stranski - Krastanov growth of QDs in lattice-mismatched system (e.g., InGaAs/GaAs)

Advantages:

1-step process (no processing)

Size: <10nm

Lateral interfaces formed during growth

Disadvantages:

Uniformity: 10-20% in size and position (randomness of nucleation process)

Difficult contacting for transport

Strain field in the cap layer

Partiallystrained

island

Strain field in the substrate

STM image of self-assembled InAs QDs on a GaAs substrate

(M. E. Rubin et al. Phys. Rev. Lett. 77, 5268 (1996))

Improvement: growth on misoriented substrates QD formation on quasi-

periodic step edges

Page 19: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Seeded self-orderingSeeded self-ordering

Growth of QWs on lithographically patterned substrates Dielectric masks Nonplanar surfaces

Mechanisms: selective (masks) or anisotropic (nonplanar) growth rates material accumulation on preferential sites (“seeds”)

Advantages:

Size: <10nm

Uniformity: 5% (seeds)

Lateral interfaces formed during growth

Disadvantages:

2-step process (pre-patterning)

Nanostructures depend on growth habit

Patterned QW

Mask

Patterned QW

Nonplanar Substrate

TEM X-section of a stack of GaAs/AlGaAs QWRs grown on a V-grooved substrate

GaAsV-shapedsubstrate100nm

AlGaAsbarriers

GaAsQWR

Page 20: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Formation and properties of self-assembled QDs

Formation and properties of self-assembled QDs

Page 21: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Atomic arrangement in a QDAtomic arrangement in a QD

High resolution TEM of an uncapped InAs/GaAs QD (Chu et al., JAP85, 2355 (1999))

The lateral lattice constant in the upper part of the QD is clearly larger than in the lower part: strain relaxation in the 3D island.

When too much island material is deposited, the strain cannot be totally relieved elastically through islanding, and dislocations occur via plastic relaxation.

Page 22: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Formation stages of InAs/GaAs(001) QDsFormation stages of InAs/GaAs(001) QDs

1X1m2 AFM scans of different InAs coverages (1 to 4 ML) on GaAs (001) (Leonard et al., PRB 50, 11687 (1994))

a) Low coverages: InAs step-flow growth.

b)-c): ~1.7ML: pseudomorphic, defect free QDs, 10% uniformity. c): Higher density, smaller size than b).

d)-f): >2ML: dislocated islands by QD aggregation or by dislocations in a single QD.

Self-limiting effect

Page 23: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Critical thickness for QD formationCritical thickness for QD formation

QD density = 0 below critical layer thickness C

Sharp density increase after C

QD density = 0 (- C), C = 1.5ML, = 1.76: 1st order phase transition with an order parameter (Leonard et al., PRB 50, 11687 (1994))

Page 24: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Size distribution of QDsSize distribution of QDs

1.6ML

1.65ML

1.75ML

1.9ML

Diameter and height distribution for increasing InAs coverage

10% height and 7% uniformity for initial stages of QD formation (a)

Degraded uniformity for higher

Increasing : diameter decrease (~30nm to ~ 20nm), density increase

(Leonard et al., PRB 50, 11687 (1994))

Page 25: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Optical properties of QDsOptical properties of QDs

RT PL spectra for different

2-3 peaks corresponding to ground and excited states

Size distribution of the QDs -like DOS broad lines (inhomogeneous broadening)

(Chu et al., JAP85, 2355 (1999))

Page 26: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Optical properties of QDsOptical properties of QDs

RT PL intensity, energy and FWHM as a function of

Intensity: maximum for ~ 2.3ML

Energy: broad minimum for ~ 2.3-2.7ML ( largest QDs)

FWHM: minimum for ~ 2.6ML (30-35meV)

larger islands: better optical quality, higher homogeneity

> 2.7ML: formation of dislocations: decreased intensity, energy shift, broader lines.

(Chu et al., JAP85, 2355 (1999))

Previous experiment: higher homogeneity, slightly higher

size for lower (first stages of QD formation) high influence

of experimental conditions!

Page 27: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Effect of growth temperature (MBE)Effect of growth temperature (MBE)

Increasing T (480-530C) decreasing energy larger QDs

Explanation: larger diffusion length there is a larger nucleation-free area around islands ( nucleation centers, adatom sinks) where adatoms can be collected by the island

550C: In desorption (smaller QDs), In-Ga intermixing higher energy

Increasing T: stronger, narrower lines better material quality

Ground state – 1st subband separation (530C): ~ 70meV

(Chu et al., JAP85, 2355 (1999))

Page 28: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Effect of V/III ratio (MBE)Effect of V/III ratio (MBE)

T=480, different As4 flux: enhanced In diffusion for lower As4/In ratios

Lower As4 fluxes: increased QD quantum efficiency

Lower As4 fluxes: small redshift increased QD size ( larger diffusion length, coherent with T dependence)

(Chu et al., JAP85, 2355 (1999))

Page 29: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Lithographic positioning of SA QDsLithographic positioning of SA QDs

Self-assembled Ge islands on Si(001) pre-patterned with oxide lines

Increased uniformity in size and separation

Possible mechanisms:

Diffusion barrier on the stripe edge

Reduced strain energy at the stripe edge

T. I. Kamins and R. S. Williams, APL 71, 1201 (1997)

Page 30: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Lithographic positioning of SA QDsLithographic positioning of SA QDs

Preferential formation of InAs QDs in shallow, sub-m-size GaAs holes defined by electron-beam (a) 1.4ML, b) 1.8ML InAs)

Holes with (111)A and B faces, QDs formed on B faces (favorable nucleation sites for In atoms).

S Kohmoto, MSEB 88, 292 (2002)

Page 31: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Vertical stacking of QDsVertical stacking of QDs

Coherent InAs islands separated by GaAs spacer layers exhibit self-organized growth along the growth direction.

The island-induced evolving strain fields provide the driving force for self-assembly provided the spacer is not too thick

Bright field TEM pictures taken along [011] azimuth of five sets of InAs islands separated by 36 ML GaAs spacer layers.Q. Xie et al., PRL 75, 2542 (1995) X-STM constant current topography

image of two stacks of InAs QDs.D. M. Bruls et al., APL 82, 3758 (2003)

Page 32: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Lithographic positioning of stacked QDsLithographic positioning of stacked QDs

Twofold stacked InGaAs/GaAs QD layers grown on GaAs(001) substrates patterned with square arrays of shallow holes ((a)(-d): 100-200nm period).

The second QD layer responds to the lateral strain-field interferences generated by the buried periodic QD array: vertically-aligned QDs or satellite QDs placed on strain energy minima.

Base size and shape, and lateral orientation are predefined by the Estr distribution on the underlying surface.

H. Heidemeyer et al., PRL 91, 196103 (2003)

Page 33: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Growth of QWRs and QDs on patterned surfaces

Growth of QWRs and QDs on patterned surfaces

Page 34: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Grating fabrication for QWRsGrating fabrication for QWRs

5 µm

MaskUV light

Exposure

Development

[100]

[011][011]

Etching H2SO4:H2O2:H2O

Photoresist

Substrate

Coating

Page 35: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

MOCVD on V-grooved substratesMOCVD on V-grooved substrates

Stable facets forming in the groove:

sidewalls:{111}A ~ 5-10° off towards (100)

top and bottom regions:(100) + {311}A

Different surface crystalline structure

different diffusion & nucleation rates

growth rate R depends on orientation

Rtop, Rbottom < Rsidewall

expansion at top,

sharpening at bottom

BUT: profile stabilizes at the bottom at the 10nm-level

BUT: profile stabilizes at the bottom at the 10nm-level

{111}A

(100)

{311}A

sidewalls

GaAssubstrate

Page 36: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

QWR formation on V-grooved substratesQWR formation on V-grooved substrates

AlGaAs self-limiting profile

independent of lithographic details

recovers after QWR deposition

~ 10nm

GaAs QW profile bottom region thickens and expands

QWR formation

[100]

[011]

[011]Patterned

GaAsSubstrate 20 nm

GaAsQWR

AlGaAsBarriers

lateralGaAs QW

AlGaAs vertical QW

Page 37: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Profile evolution during self-limiting growthProfile evolution during self-limiting growth

R(100) > R{ijk}

(100) expanding

R(100) > R{ijk}

(100) expanding

R(100) > R{ijk}

conformal growth

R(100) > R{ijk}

conformal growth

layer A: t100 > t311 > ts expansion of (100) and {311}A facets

layer B: t100 = t311 = ts stable facets, self-limiting growth

layer A: t100 > t311 > ts expansion of (100) and {311}A facets

layer B: t100 = t311 = ts stable facets, self-limiting growth

25 nm

(100){311}A

sidewall

A

B

AlGaAs

GaAst{ijk}

G. Biasiol et al., APL 71, 1831 (1997).

Page 38: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Optical Properties of GaAs-AlGaAs QWRs*Optical Properties of GaAs-AlGaAs QWRs*

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

QWR

PHOTON ENERGY (eV)

LUM

INE

SC

EN

CE

INTE

NS

ITY

QW

AlGaAs Barrier

QWR - 2.5nm8 K

0

1

PLE, Excit. pol. //PLE, Excit. pol. PL

1.55 1.6 1.65 1.7 1.75

QWR - 2.5nm

0

1

LU

MIN

ES

CE

NC

E IN

TE

NS

ITY

PHOTON ENERGY (eV)

e1-h

1

e2-h

2

e3-h

3e

4-h

4

e1-"lh

1"

e5-h

5

e6-h

6

e7-h

7

e9-h

9

e8-h

8

•hh and lh related transitions observed•polarization anisotropy in e-lh/e-hh ratio•hh and lh related transitions observed•polarization anisotropy in e-lh/e-hh ratio

*F. Vouilloz et al. ICPS 23, Berlin, 1996

PL FWHM of QWR ~ 6meVPL FWHM of QWR ~ 6meV

Photoluminescence Photoluminescence Excitation

Page 39: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Mechanisms of self ordering in epitaxial growth

Mechanisms of self ordering in epitaxial growth

Page 40: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Driving force for lateral epitaxyDriving force for lateral epitaxy

Chemical potential (driving force for epitaxy supersaturation):

µ

Lateral variations of lateral variations of growth rate

Page 41: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Chemical potential growth rateChemical potential growth rate

Diffusion towards areas of lower

Growth rate: increased at lower , decreased at higher

coordinate lateral tcoefficiendiffusion surface

density surface adatom

)()(

xDn

B x

x

Tk

nDxj

fluxgrowth 0

00)(

)()(

Jx

xjxJxR

Nernst-Einstein relation

Continuity equation

2

2

00)(

)()(x

x

Tk

nDxJxR

B

Page 42: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Example: sinusoidal chemical potentialExample: sinusoidal chemical potential

(x) = sin (x)

j(x) - ’(x) = -cos(x)

R(x) ”(x) = -sin(x)

jj jj

Page 43: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

How self-ordering is establishedHow self-ordering is established

Need for an equilibrating action between non-uniform chemical potential (stress, shape, composition) and another

factor that drives atoms away from chemical potential minima.

As growth proceeds, this should bring to steady-state growth profile.

Any change in growth parameters (materials, temperature, fluxes, growth rates...) should bring to a new steady-state

profile, independent of the initial one.

Page 44: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Stressed surface self-ordering of QDsStressed surface self-ordering of QDs

1. SK growth mode: adatom flux towards islands island coarsening

2. Strain energy (chemical potential) Es:

Flux away from islands

Es larger for larger islands dissolution rate larger as island size increases

3. 1 + 2: kinetic mechanism stabilizing the island size: slowing of the growth rate of large islands and increase of the adatom density away from them, thus enhancing nucleation of new islands (with small Es faster growth).

4. narrow island size distribution in the system (for f = 5 and 7.5%).

1D KMC model, A.L. Barabasi, APL 70, 2565 (1997)

f =

7.5% ()5 ()

2.5% ()0% ()

Page 45: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Pairing probability between 1st and 2nd layer of dots decreases with thicker spacers

Model: atoms of 2nd InAs layer arrive on stressed region (I) of width 2ls ( strain-driven diffusion towards top of 1st islands) or unstressed region (II) of width l-2ls ( random island formation)

ls increases as GaAs spacer is thinner

Surface diffusion model pairing probability as a function spacer thickness, dependent on island size and density (measured), lattice mismatch and strain (calculated) and In diffusion length LD (fit parameter)

Very good match with exp data for LD = 280nm (@ T=400C)

Full calculations in Q. Xie et al., PRL 75, 2542 (1995)

Vertical self-ordering of stacked QDsVertical self-ordering of stacked QDs

200 )(

2x

E

Page 46: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Surface chemical potential on a patterned, faceted substrate

Surface chemical potential on a patterned, faceted substrate

Diffusion towards the bottomDiffusion towards the bottom

Growth rate: increased at the bottom, decreased at the topGrowth rate: increased at the bottom, decreased at the top

µt

µs

µb

j(x)nD

kBT

x

R(x)0 J0 (x) j(x)x

t 0 0

l t;

s 0 ;

b 0 0

lbOzdemir and Zangwill, JVSTA 10, 684 (1992)lb

lt

Page 47: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Mechanism of self-limiting growthMechanism of self-limiting growth

Capillarity Growth rate anisotropy

= Self-limiting growth

G. Biasiol and E. Kapon, PRL 81, 2962 (1998),G. Biasiol et al., PRB 65, 205306 (2002).

Page 48: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Self-Limiting Growth: AlxGa1-xAsSelf-Limiting Growth: AlxGa1-xAs

AFM cross section of a V-groove AlxGa1-xAs heterostructure

200 nm

x=0.21

x=0.49

0 1.5 nm

VQW

Ls(Ga) > Ls(Al)

stronger Ga capillarity to the bottom

Ga-rich AlxGa1-xAs vertical quantum well

Ls(Ga) > Ls(Al)

stronger Ga capillarity to the bottom

Ga-rich AlxGa1-xAs vertical quantum well

Nonuniform composition

ordered phase increase of the entropy of

mixing to be included in the model

Nonuniform composition

ordered phase increase of the entropy of

mixing to be included in the model

G. Biasiol and E. Kapon, PRL 81, 2962 (1998),G. Biasiol et al., PRB 65, 205306 (2002).

Page 49: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Composition dependence of self-limiting bottom width

Evidence for entropic contributions

Composition dependence of self-limiting bottom width

Evidence for entropic contributions

lbsl lb

sl X;lslA , lsl

G ,r A ,r G ,LsG lb

sl lbsl X;lsl

A , lslG ,r A ,r G ,Ls

G fixed by

experimentfitted, Ls

G =175±20nm

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1

l bs

l (

nm

)

x

without entropy of mixing

with entropy of mixing

exp. data

AlXGa1-XAs;T = 700°C

G. Biasiol and E. Kapon, PRL 81, 2962 (1998),G. Biasiol et al., PRB 65, 205306 (2002).

Page 50: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Temperature dependence Arrhenius plots

Temperature dependence Arrhenius plots

lslG Ds

G1 /3 exp EBG /3kBT

lsl X lsl X;DsA ,DsG fit: EB

G = 1.9±0.3eV

fit: EBA = 2.3±0.2eV

GaAs:

AlXGa1-XAs:

4

6

810

30

11.5 12 12.5 13

x=0x=.19x=.29x=.47

sl ~

l sl (

nm

)

1/kBT (eV)

G. Biasiol and E. Kapon, PRL 81, 2962 (1998),G. Biasiol et al., PRB 65, 205306 (2002).

Page 51: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

Evolution to self-limiting profilesEvolution to self-limiting profiles

slbbbb

slbb

b

slbb

lll

b

l

lXr

dt

dl

l

lr

dt

dl

3

30

30

1

1

Modeling of experimental data; T = 700°C

20

40

60

80

100

120

0 50 100 150 200

l b (

nm

)

zn (nm)

lb

sl (GaAs)

lb

sl (Al0.3

Ga0.7

As)

GaAs:

AlXGa1-XAs:

G. Biasiol and E. Kapon, PRL 81, 2962 (1998),G. Biasiol et al., PRB 65, 205306 (2002).

Page 52: PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES  Properties of low-dimensional quantum confined semiconductor nanostructures  Fabrication techniques

QDs on etched tetrahedral pyramidsQDs on etched tetrahedral pyramids

QDs at the intersection of 3 QWRs

3D diffusion model [ µ(x,y) ]

QDs at the intersection of 3 QWRs

3D diffusion model [ µ(x,y) ]A. Hartmann et al.

APL 71, 1314 (1997)

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