High resolution x-ray analysis of the nano-structures

徐嘉鴻

國家同步輻射研究中心

Introduction of Synchrotron RadiationIntroduction of X-ray scatteringApplication of SR x-ray scattering -

Strain field and Compositional distribution of InGaAs quantum dots – iso-strain scattering and Resonant X-ray Scattering Structure determination of nano-thick HfO2 epi-layersStructure and composition determination of Y2O3 doped HfO2 thin films Epitaxial stablization of h-Gd2O3 on GaN (0001) and Thickness dependent structure transformation

清大物理 5/5/2011

The synchrotron produces light by accelerating electrons almost to the speed of light. Magnets put the electrons into circular paths. As the electrons turn, photons (little packets) of light are given off. The infrared, UV, and X-rays are sent down pipes called beamlines, to work areas where scientists run their experiments. The components of a synchrotron include an electron gun 電子槍, linear accelerator 線性加速器, a circular booster ring 增能環 (to increase the speed of the electrons), storage ring 儲存環(to re-circulate electrons), beamlines 光束線, and end stations 實驗站.

How does synchrotron radiation source work?

Electron Beam

N

S

N

S

SynchrotronRadiation Angular distribution of the radiation emitted by an

electron moving along a circular obit (dashed line) at a speed (a) much smaller than and (b) close to the speed of light.

a) b)

e-gunLINAC

transport line

bending maget

RF cavity

insertion device

BM beamline

ID beamline

Principal Components of a SR Light Source

Booster and Storage ring two-in-one

動畫astrid_total_v2.mov

103 101 10-1 10-3 10-5 10-7 10-9 10-11 10-13 10-15

10-9 10-7 10-5 10-3 10-1 101 103 105 107 109

無線電波

可見光

紅外線 紫外線 硬X射線 加瑪射線軟X射線微波

同步輻射源

(eV)

可探測到的物體

建築物

波長(米)

輻 射 源

粒子加速器

棒 球 昆 蟲 細 胞 病 毒 蛋白質 分 子 原子核質子 夸克？原 子

放射性源X射線管電 燈無線電天線 速度調制電子管

光子能量(電子伏特)

The Properties of Synchrotron Radiation• High Intensity & brightness

ISR > 106 * Itube

• Wide range of continuous Spectrum (NSRRC 35 keV > E > 0.05 eV)

x-ray far IR• Excellent Collimation • Low Emittance• Pulsed-time Structure (NSRRC)

bunch length: 25 pspulse separation: 2 nsno. of buckets: 200

• Polarizationlinear polarization, elliptical polarization

• Coherence (laser)

101 102 103 104 105

107

108

109

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

IASW6 (TLS)

SW6 (TLS)

W20 (TLS)

Bending (TLS)B

rillia

nce

(Pho

t/s/0

.1%

bw/m

m2 /m

r2 /0.4

A)

Photon Energy (eV)

Bending (TPS)

CU1.8 (TPS)

SW4.8 (TPS)

104 increase

Natural emittance: 1.6 nm-radStraight sections: 7 m (x 18); 12 m (x 6)

Taiwan Photon Source (TPS)3 GeV, 518.4 m, 500 mA

Taiwan Light Source (TLS)1.5 GeV, 120 m, 360 mA

Full capacity: 48 ports

Administration and Operation Center

Academic Activity Center

101 102 103 104 1051013

1014

1015

1016

1017

1018

1019

1020

1021

U280

Bending

CU18

IU20EPU46

EPU70EPU100

SW48

Bril

lianc

e (p

hoto

ns/s

/0.1

%bw

/mr2 /m

m2 /0

.4A)

Photon Energy (eV)

Cu Kα 8.0 keV 70 keV

101 102 103 104 1051013

1014

1015

1016

1017

1018

1019

1020

1021

70 keV

IASW60

U50EPU56

U90

SW60

W200

SWLS

Bending

Bril

lianc

e (p

hoto

ns/s

/0.1

%bw

/mm

2 /mr2 /0

.4A)

Photon Energy (eV)

Cu Kα 8.0 keV

Brightness comparison of TLS and TPSThe X-ray spectrum (photon energy 8 keV~70 keV)：the brilliance of bending magnet increases by >102.the brilliance of bending IDs increases by 4~6 orders of mag.

TPSTLS

~102

>103

Wave

a snap shot of wave

Amplitude AThree key components of a wave: Wavelength λ (period in space)

Period τ (period in time)Phase φ = (kx-ωt+φ0)

plane wave:propagating along x )cos(

)(2cos

0

0

tkxA

txAA

ωτλ

π

−=

−= wave vector k = 2π/λangular frequency ω = 2π/τ

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

5 10 15 20 25 30

-1

0

1

x

X-ray: a from of electromagnetic wave with sinusoidally vibrating electric

and magnetic fields moving through space. (so is visible light) speed of light c = 299,792,458 m/sec ~ 3×108 m/sec (= in vacuum) Energy E = hc/λ = ħω

X-ray

3 key factors: wave vector (energy), amplitude, phase

plane wave: E(x,t) = E0 e-i(kx-ωt)

kω

crystal(periodic array of atoms)

= ⊗

lattice(periodicity)

basis(motif)

convolution

space group lattice point group(230) (14) (32)

Crystal: a repeated (periodic) array of atoms

A crystal structure consists of identical copies of the same physical unit, called the basis, located at all the points of a lattice. A lattice is defined as an array of equivalent points in 1, 2 or 3 dimensions. The environment of an atom placed on any one of these lattice points would be identical to that placed on any other lattice point. Therefore the lattice locates equivalent positions and shows the translational symmetry. The actual positions of atoms or molecules, however, is not provided.

= ⊗

(0 1)lattice

The crystal can be viewed as being made up of sets of parallel planes

(1/m 1/n): m and n are the intersections along a1 and a2

(0 2)a1

a2

A lattice can be described by sets of parallel planes.

Each set of parallel planes can be uniquely described by its• d-spacing : the distance between adjacent planes• orientation of plane normal

lattice

A lattice can be described by sets of parallel planes

a1

a2

(1 4)

intersection along a1: 1 intersection along a2: ¼

(1 4) plane

(1 2)

low index planes: more dense, more widely spacedhigh index planes: less dense, more closely spaced

lattice planes in real space

(1 0 0)

(1 0 0)

(2 1 0)

(2 1 0)

(3 2 0)

(3 2 0)

(3 1 0)

(3 1 0)

(110)

(110)

(0 1 0)

(0 1 0)

lattice points in reciprocal space

A crystal can be described by sets of evenly spaced parallel planes.Represent each set of planes by its and 2π/dhkl, a vector (point) in reciprocal space.

There is a one-to-one correspondence between R’s and G’s.n̂

Effect due to Lattice Constant Change(Strain Effect)

2π (a2-1- a1

-1) ≥ R-1

2 atoms

5 atoms

Diffraction Pattern of A Row of Atoms

Domain size Peak width

Scherrer equation L = 0.9λ/(Bcos θB)

(Elastic) X-ray Scattering

Ei = Ef i.e. λi = λf (elastic scattering)

wave vector k = 2π/λ ; | ki | = | kf |

2θ

qr

fkr

ikr

q = 4π sin(θ)/λif kkqrrr

−=

scattering vector

Bragg Law 2d sinθ = λ

Real space Reciprocal space

hkldπθ

λπ 2sin22 =

qkfki

Condition for Bragg reflection

θθ

θdhkl d sinθd sinθ

θ

ki kf

Path Difference L = 2dhkl sinθConstructive interference: L = nλphase difference φ = k L

hklhkl

Gnd

qqvv === ˆ2ˆsin4 πθ

λπ

FT

a1

a2

a1=a

a1’a2’

a1’=2π/a

Texture - Pole figures

Ag/NaCl(001)<220> pole figure

[001]Ag || [001]NaCl[100]Ag || [100]NaCl

With fixed |q|, measure the diffraction intensity while rotating the sample orientation over a hemisphere. Spatial distribution of orientations.

|q|= |G220| = 2π/d220

H

K

L

H

K

L

(202)(-202)

(022)(0-22)

(220)

(-220)

(2-20)

(-2-20)

Ag: fcc structure

Experimental method:With a given, 2θ, a series of φ scans is performed at regularly incremented χ values.

Texture - Pole figures

Pole figures show the stereographic projection of the locations where a selected crystallographic plane, defined by its interplanar distance d value, is in a reflection position.

To define the orientation of a crystal, we usually specify the directions of a crystallographic plane, such as the (001) plane of a cubic system.

H

K

L

r = R tan(χ/2)X = r cos φY = r sin φχ

φ

X

Y

(rcosφ rsinφ)

Texture - Pole figures (epitaxial)With fixed |q|, measure the diffraction intensity while rotating the sample orientation over a hemisphere. Spatial distribution of orientations.

[100]NaCl

[010]NaCl

|q|=2π/d220

Ag/NaCl(001) Ag{220} pole figure

[001]Ag || [001]NaCl[100]Ag || [100]NaCl

(2 0 2)

(-2 0 2)

(0 2 2)(0 -2 2)

(2 2 0)

(-2 -2 0)

(2 -2 0)

(-2 2 0)

a1’

a2’

a3’

Azimuthal Scans (Epitaxial Relationship)With fixed |q|, rotate sample against surface normal or crystalline

a1’

a2’

a3’

a3’

a1’ a2’

(101)

(111)

0 50 100 150 200 250 300 350

10-3

10-2

10-1

100

101

102

103

104

I (sr

b. u

nit)

φ (deg)

film (101) substrate (111)

cubic-on-cubic growth

(001)

substrate

film

In-plane 45° rotation, i.e.<100>film || <110>sub

Texture – pole figure (preferred orientation)

Si cubic a =5.431ÅZnO Wurtzite (hexagonal)

(101)ZnO

Si]011[

Si]211[

ZnO/Si(111) (0001)ZnO || (111)Si

Columnar growth, no fixed in-plane orientation

a1’

a2’

a3’

120°

Texture - Pole figures

For a powder sample, you will see a uniform intensity distribution over the entire sphere. Each angular position corresponds to a crystalline.

H

K

L

Pole figure bears the information about crystalline orientation and symmetry

X

Y

Example 1: Strain field and compositional distribution of InGaAs quantum dots

3Dbulk semiconductor

2Dquantum well

1Dquantum wire

0Dquantum dot

Nano Materials Definition: 1 nm < size < 100 nm

Size, Strain, Shape, Composition Energy levels & physical properties

Ge QDCNT

VCSEL G. Medeiros-RebeiroHewlett-Packard Labs.

Sander Tans Delft University of Technology

QWBulk

self-assembled semiconductor quantum structures

Elastic Strain Relaxation during the S-K Growth(2-D followed by 3-D)

Uniformly Strained Layer

Dislocation Relaxed Islands

Coherently Strained Islands

increasing coverage

Issues of InterestApplication: uniform size, high density, regular arrangementFundamental: to understand and control the formation of quantum dots

coherent (dislocation free) dots/wires grown via the S-K mode

“Coherently Strained” Quantum Materials Fabricated by Heteroepitaxial Growth

narrow size distributionpreferred shapecorrelated spatial distributionsensitive to the details of growth condition

Nucleation phase (growth kinetics)Growth of islands (energetic balance)Ostwald ripening

strain relaxation, chemical intermixing, inter-dot interaction, surface energy

Uncapped In0.5Ga0.5As Quantum Dots

In0.5Ga0.5As 5ML/ Ga (4x2)

AFM image

n ~ 5.3x1010 cm-2

J. Cryst. Growth, 175/176, 777 (1997).

Grown by MEE

grown @ 520oC 0.1ML/s.

GaAs buffer layer 200 nm

GaAs (001)

aInAs = 6.0583ÅaGaAs = 5.65325Å

mismatch = 7.2 %

qa

qr

qz

ki

kf(HK0)

αι

αf

αf2θ

kf

zy

xqy

GIRSMGISAXS

qz

qx

Scattering geometry of Grazing Incidence X-ray Scattering

αi ~ αc

GIRSMq ~ (H K 0)

Strain sensitivestrain profilecomposition

GISAXSq ~ 0

Strain independentshape

spatial correlation

ki: incident wave vector.kf: scattered wave vector.q : scattering vector.αi: incident angle αf: outgoing angle

Pene

tratio

n de

pth

Λq c

0.5 1 1.5 2 2.5q/qc or α/αc

Penetration depth vs. incident angle α or q

Grazing Incidence Small Angle X-ray Scattering (GISAXS)

q||

qz

direct beambeam stopper• inter-dot spacing ~ 48 nm• symmetric profile & azimuthal invariant• isotropic distribution & ω-symmetric shape

-0.05 0.00 0.05

1E-4

1E-3

I (ar

b. u

nit)

q|| (A-1

)

interference peak

qz=0.l08Å-1 kf

q

αι

ωki

n

tthαf

PRB 63, 35318 (2001) by I. Kegel et al.

2π (a2-1- a1

-1) ≥ R-1

Iso-strain slab: region of constant lateral lattice parameter al

For given G = (HK0), x-ray scattered by a slab

with al distributes around .222 KHa

ql

r +=π

large al ⇔ small qr

alqr

Reconstruct Quantum Dots Structure from Reciprocal Space Map (RSM)

Shape and Strain Distribution of In0.5Ga0.5As QDs

0.0 0.2 0.4 0.6 0.8 1.00.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

I (ar

b. u

nit)

αf (deg)

αc=0.325o

0.99750.9950.9850.9750.96-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06

1E-5

1E-4

1E-3

0.01

3.75

3.80

3.85

3.90

3.95

4.00

I (arb. unit)

K (r

lu)

H (rlu)

GaAs(040)al

qr

R=2.78/FWHM(follwoing the sin(x)/x law)

)cos(1 max

maxc

ak

zα

αα

=DWBA

Shape and Strain Distribution of In0.5Ga0.5As QDs

(▓) height Z and ( ) misfit vs. radius R measured along [040]

misfit = (aexp - aGaAs)/aGaAs, where aGaAs denotes the lattice parameter of bulk GaAs

4 6 8 10 12 14 16 18 20 22

0

1

2

3

4

5

6

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Z (n

m)

R (nm)

misfit (%)

Structure factor is a simple linear combination of atomic scattering factors and atomic percentage of consisting elements

Composition of Iso-Strain Region

))(2

exp()1( LKHiffxfxF AsGaInHKL +++−+=π

2

200

400

))(1()())(1()()(

AsGarInr

AsGarInrr ffqxfqx

ffqxfqxqII

−−++−+

=

0.0 0.2 0.4 0.6 0.8 1.00.1

1

10

100

I

In concentration x

I400

I200

0.0 0.2 0.4 0.6 0.8 1.00

50100150200250300

I 400/I 20

0ab

c

InxGa1-xAs: FCC structure Ga, In: (0,0,0), As: (1/4,1/4,1/4)

Ratio of intensity around (400) and (200) ⇔ In concentration

disadvantages: multiple valuesadditional contribution from interference

1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00

1E-4

1E-3

I

K (rlu)

E=10.2 keV

-0.05 0.00 0.05

1E-4

1E-3

I (ar

b. u

nit)

q|| (A-1

)

GaAs(020)

Anomalous X-ray Scattering

Chemical composition and/or electronic states

Atomic scattering factor f (q,E)= f0(q) + f’(E)+ i f”(E)= f1+i f2

Intensity

E/Eedge

f1

f2

22

iHKL rqi

iiHKL efFI

vv ⋅⋅=≈ ∑

10.0 10.2 10.4 10.6 10.8

1

2

3

4

5

6

7

8

9

10.0 10.2 10.4 10.6 10.80

1

2

3

4

5

6

7

8

9

Nor

mal

ized

I (a

rb. u

nit)

E (keV)

x=0.0

x=0.2

x=0.25

x=0.35

x=0.5(200)

E (keV)

x=0.3

x=0.4

(400)

x=0.15

x=0.1

AsGaIn ffxfxF −−+= )1(200 AsGaIn ffxfxF +−+= )1(400

Simulated Spectra of the (200) and (400) Reflections of the InGaAs

weak reflection: H + K + L = 4n +2 strong reflection: H + K + L = 4n

peak

dip

narrower dipshift to larger E

Ga K-edge

Resonant X-ray Scattering around GaAs(020)

1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00

1E-4

1E-3

I

K (rlu)

E=10.2 keV

10.25 10.30 10.35 10.40 10.450.01

0.1

1

10

(0.24; 0.075)

(0.375; 0.065)

(0.48; 0.055)

(0.54; 0.04)

(0.31; 0.07)

E (keV)

(x = 0.13, Δx = 0.08)

1.97

1.96

1.951.94

1.975

K = 1.99 rlu

Inte

nsity

(a.u

.)

Ga K-edge (10.367 keV)

∫ ′Δ′−−′= xxxxxEFxEQF d]/)(exp[),,(),,( 2222 Q

),(),(LP),,(),,( 2 EAExEFxEI QQQQ =

4 6 8 10 12 14 16 18 20 22

0

2

4

610 20 30 40 50 60 70 80

Z (n

m)

R (nm)

In concentration (%)

( ) In concentration and ( ) radius R vs. height Z

Compositional Distribution

x increases monotonicallywith Z

x << 0.5 at the basex > 0.5 near the top

Ecoh = 2μ [(1+ν)/(1-ν)] ε||2

μ : shear modulusν : poisson’s ratioε|| : strain (in-plane)

Elastic Energy

10 20 30 40 50 60 70 80

0

1

2

3

4

5

6-1 0 1 2 3 4 5

Z (n

m)

x (%)

Ecoh (meV)

(▲) elastic energy and ( ) In concentration x vs. height Z

Taking both strain and composition into account

J. Y. Tsao, Materials Fundamentals of Molecular Beam Epitaxy (1993)

Conclusions (InGaAs QDs)• X-ray Scattering is a powerful technique of characterizing the strain, shape, composition and spatial correlation of In0.5Ga0.5As QDs.

• Progressive lattice relaxation accompanied by severe variation in chemical composition as a function of height was observed. Beside the increase of lattice parameter, an enhancement in intermixing is a major mechanism to minimize the total energy.

• In concentration near the top of the dot is higher than the nominal composition. In surface segregation has additional contribution in reducing the system total energy and stabilizing the structure of self-assembled QDs.

• Grazing incidence resonant X-ray scattering is a powerful technique for composition characterization, especially for systems with strongly correlated surface morphology.