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
Properties of low-dimensional quantum confined semiconductor
nanostructures
Properties of low-dimensional quantum confined semiconductor
nanostructures
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
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
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
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
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
Fabrication techniques of low-dimensional semiconductor
nanostructures
Fabrication techniques of low-dimensional semiconductor
nanostructures
From Quantum Wells to Quantum Wires/DotsFrom Quantum Wells to Quantum Wires/Dots
?Planar (layer-by-layer) epitaxy
QWR - QD
Control overlateral
composition
QW
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
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
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
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
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
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)
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)
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)
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
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
Formation and properties of self-assembled QDs
Formation and properties of self-assembled QDs
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.
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
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))
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))
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))
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!
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))
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))
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)
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)
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)
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)
Growth of QWRs and QDs on patterned surfaces
Growth of QWRs and QDs on patterned surfaces
Grating fabrication for QWRsGrating fabrication for QWRs
5 µm
MaskUV light
Exposure
Development
[100]
[011][011]
Etching H2SO4:H2O2:H2O
Photoresist
Substrate
Coating
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
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
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).
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
Mechanisms of self ordering in epitaxial growth
Mechanisms of self ordering in epitaxial growth
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
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
Example: sinusoidal chemical potentialExample: sinusoidal chemical potential
(x) = sin (x)
j(x) - ’(x) = -cos(x)
R(x) ”(x) = -sin(x)
jj jj
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.
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% ()
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
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
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).
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).
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).
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).
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).
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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