Lecture 11:Introduction to Thin Film

Characterization: Structural and Morphological Characterization

B. D. Cullity, S. R. Stock, Stuart Stock, Elements of X-Ray Diffraction (3rd Edition) Prentice Hall; 3nd edition (February 5, 2001)

Harold P. Klug, Leroy E. Alexander, X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition Wiley-Interscience; 2 edition (May 1974) ISBN: 0471493694

C. Suryanarayana, M. Grant Norton,X-Ray Diffraction: A Practical Approach Plenum Publishing Corporation; (June 1, 1998) ISBN: 030645744X

David B. Williams and C. Barry Carter, Transmission Electron Microscopy I, II, III, IV (Plenum Press, New York, 1996).

John C. Vickerman, Surface Analysis – The Principal Techniques (John Wiley & Sons, New York, 1997).J.C. Vickerman and D. Briggs, ToF-SIMS: Surface Analysis by Mass SpectrometryEdited, IM Publications ISBN 1

901019 03 9

Briggs, D., Seah, M.P. Eds.; Practical Surface Analysis, 2nd ed.; John Wiley & Sons: New York, 1996;

J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, Jr., C. E. Lyman, C. Fiori, and E. Lifshin, Scanning Electron Microscopy and X-ray Microanalysis (Plenum Press, New York, 1990).

D. C. Joy, A. D. Romig, Jr., and J. I Goldstein, Principles of Analytical Electron Microscopy (Plenum Press, New York, 1989).

Frank A. Settle, Handbook of Instrumental Techniques for Analytical Chemistry (Prentice Hall PTR, New Jersey, 1997).

J. R. Tesmer, M. Nastasi, J. C. Barbour, C. J. Maggiore, and J. W. Mayer, Handbook of Modern Ion Beam Materials Analysis (Materials Research Society, Pittsburgh, 1995), Chap. 5, p.83.

W.-K. Chu, J. W. Mayer, and M.-A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978).

Bibliography

IonsElectronsPhotons

IonsElectronsPhotons

Vacuum

Primary beam (source)

Secondary beam (spectrometers, detectors)

imaging

High-power lithium-ion batteries failure mechanisms

spectroscopy

crystallography

elemental analysis

http://www.cea.com/

http://www.cea.com/

Diffraction of x-rays by a crystal

2n d sinλ = θBragg’s Law:

θ

d sinθ

A

B

C

d

plane normal1

2

1’

2’

{001}

{110}

{210}

ω-2θ (θ -2θ) scan geometryBragg-Brentano

“Powder” Diffraction

Glancing angle scan geometry

X-ray analysis of polycrystalline layers and powder materials

Bragg’s Law

dhkl = λ/2sin(θ)

•Bragg-Brentano or parallel beam x-ray analysis;

•Powders, polycrystalline films or nanostructures, mineralogy, cements, ceramics, pharmaceutics, polymers, biomaterials;

•Identification, quantification (w%) and structure determination of mixtures, impurities, multiple phases and amorphous fractions;

•Quantification of crystallinity, texture, twinning, grain size and strain;

•Pattern indexing, lattice parameters determination, unit cell refinement, atomic positions, bonds distances and angles;

•Pattern simulation and structure refinement (Rietveld analysis)

0.05%Strain:

> 1000 ÅCrystallite size:

82.9 w% LiNi0.7Co0.3O2, 17.1 w% CQuantitative analysis:

Ni-O: 1.9570 Å, Ni-Li: 2.8729 Å, Ni-Ni: 2.8629 Å, Co-O: 1.9570 Å, Co-Ni: 2.8629 Å, Co-Li: 2.8729 ÅLi-O: 2.1117 Å, Li-Li: 2.8629 Å, O-O: 2.7983 Å

Average bond distances (Rietveld):

a= 2.86285 Å; b= 2.86285 Å; c= 14.17281 Åα= 90o β= 90o γ= 120o

Unit cell volume: 100.6 (Å)3

Density: 4.8383 g cm-3

Linear Absorption Coefficient: 385.5 cm-1

Cell (Rietveld refinement):

Hexagonal R-3m (166) <1/3,2/3,2/3>, Z=1, hR4

Structure:

LiNi0.7Co0.3O2, major (minor: C graphite)Search / Match: Ni

O

Li

Co

Results obtained from the measured pattern:(006)

(113)

(110)

(018)(107)(015)

(104)

(012)

(101)

C(002)

(003)

Inte

nsity

(a.u

.)

2-theta (o)

Pattern from a Li-Ni-based battery cathode

Data: Sardela, Abraham et al

Ta/SiO2 vs Ts

30 40 50 60 70 80 90 100

(212

)

(831

) (33

4)

(202

)(0

02)

(820

) (82

1)

(413

)

350 癈

Ts = 100 癈

Inte

nsity

(a.u

.)

2θ (deg)

430 癈

(311

)

(220

)

(211

)

(200

)

(110

)

tetragonal β-Tabcc α-Tat = 500 nm

fN2 = 0

Ta/SiO2/Si(001)

30 35 40 45 50 55 60

α-T

a 11

0

β-Ta

002

430 癈

Inte

nsity

(a.u

.)

2θ (deg)

α-T

a 11

0β-

Ta 2

02

β-Ta

002

350 癈

Ts = 100 癈 10 20 30

Inte

nsity

(a.u

.)

Γω = 3.5�

ω (deg)

10 20 30

Inte

nsity

(a.u

.)

Γω = 4.3�

ω (deg)

GA-XRD 2θ scans XRD ω-2θ scans

TaNx/SiO2 vs fN2

20 30 40 50 60 70 80

++0.013 (211

)

(200

)

(110

)

Inte

nsity

(a.u

.)

2θ (deg)

+

(101

)

0.025 (002

)

(112

)

(110

)

0.050

0.063

0.125

0.150

0.250

(311

)

(220

)

*

*

*

(200

)

fN2 = 1

(301

)

(200

)

(110

)

Ts = 100 癈t = 500 nm

(111

)

cubic TaN0.1

hexagonal γ-Ta2Ncubic δ-TaNbct-TaNx

+

*TaNx/SiO2/Si(001)GA-XRD 2θ scans TEM

δ-TaNx: ao = 0.443 nmbct-TaNx: a = 0.590 nm, c = 0.443 nm

N/Ta = 1.96

110

200

111

200 002

112

301

321220

400

fcc bct

Growth phase map for TaNx

Pure Ar: tetragonal β-Ta @ Ts < 150 °Cbcc α-Ta @ Ts > 400 °C.

fN2 < 0.1: three consecutive narrow lower nitride regions, defined by tilted boundaries toward higher fN2 with increasing Ts.

0.1 <fN2 < 0.3 and Ts ≤ 650 °C: single-phase δ-TaNx.

0.1 <fN2 < 0.3 and Ts > 650 °C:hexagonal ε-TaNx + δ-TaNx.

Pure N2: δ-TaNx + bct-TaNx.

0 0.1 0.2 0.3 1.00

200

400

600

800

1000= α-Ta= α-Ta + β-Ta= β-Ta = TaN0.1

= δ-TaN + ε-TaN= δ-TaN= δ-TaN + bct TaN

= Ta4N+TaN0.1

= Ta4N= γ-Ta2N = γ-Ta2N + δ-TaN

TaNx growth phase map

T s (癈

)

fN2

Stress measurements (sin2ψ method)

aψ is expected to depend linearly on sin2ψ.

[ ] ξ+ψδ=+ν−ψν+σ

=

σν

−ψσν+

=−

=ε

φψ

φφψ

ψ

20

20

2

0

0

sina2sin)1(E

aa

E2sin

E1

aaa

ψ

θ

Diffracting planes

Lφ,ψ

Film Normal

IncidentX-rays

ReflectedX-rays

ψ

θ

Diffracting planes

Lφ,ψ

Film Normal

IncidentX-rays

ReflectedX-rays

ψaψ

a0

a⊥

σφ

stressed

unstressed

film surfaceψ

aψ

a0

a⊥

σφ

stressed

unstressed

film surface

Stress measurement (sin2ψ method)

aψ is expected to depend linearly on sin2ψ.

[ ]

νσ−+ψ

ν+σ=+ν−ψν+

σ=

σν

−ψσν+

=−

=ε

φφφψ

φφψ

ψ

E2

1asinE

)1(aa2sin)1(

Ea

a

E2sin

E1

aaa

020

020

2

0

0

ψ

θ

Diffracting planes

Lφ,ψ

Film Normal

IncidentX-rays

ReflectedX-rays

ψ

θ

Diffracting planes

Lφ,ψ

Film Normal

IncidentX-rays

ReflectedX-rays

ψaψ

a0

a⊥

σφ

stressed

unstressed

film surfaceψ

aψ

a0

a⊥

σφ

stressed

unstressed

film surface

δ ξ

Stress measurement using XRD

0.0 0.2 0.4 0.6 0.8 1.04.515

4.520

4.525

4.530

4.535

4.540

sin2ψ

ξν++δνδ

=σ

ν+δν

+ξ=

φ )1(2E

12a0

ν+ν

=ψ12sin2

= −757.9 MPa (compressive stress)

= 4.5280 Å

δ = -0.01751ξ = 4.53503

a (Å

)

HfN1.18/SiO2

a0

orientation plane ψ 2θ sin2ψ

1 1 1 0 01 1 1 70.529 0.88892 0 0 54.736 39.853 0.66672 2 0 35.264 57.601 0.33333 1 1 29.496 0.24243 1 1 58.518 0.72733 1 1 79.975 0.96971 1 1 54.736 34.333 0.66672 0 0 0 39.853 02 2 0 45 57.601 0.53 1 1 25.239 0.18181 1 3 72.452 0.9091

2 0 0

34.333

1 1 1

68.825

68.825

1.0 1.1 1.2 1.3 1.4 1.5 1.64.50

4.52

4.54

4.56

4.58

a 0 (A)

x

Stress and a0 of HfNX/SiO2

1.0 1.1 1.2 1.3 1.4 1.5 1.6-2

-1

0

1

2

σ φ (GPa

)

x

• X ≤ 1.17 : (111) preferred orientation, tensile stress

• X ≥ 1.18 : (200) preferred orientation, compressive stress

• X ↑ ⇒ a0 ↑

(200) P.O.(111)

HfNX/SiO2

X-ray analysis of textured materials

Texture results from a rolled Cu foil

•Texture orientation and quantification•Volume fraction of textured grains,

twinning and random distributions•Texture strength and sharpness•Crystallographic orientation•Crystallographic relationship between

layers and substrate

x-ray source

Pole figures

Orientation distribution

function (ODF)

φ

ψ

ψφ

(111)

Φ2

Φ1

Φ

Φ

Data: Sardela et al

φ

ψdetector

2θ sample

Si1-xGex on Si(001)

Si1-xGex on Si(001)

substratesubstrate

film

film

thicknessfringes

(224) (224)

0.1 nm-1 0.1 nm-1

Mosaicity(diffuse

scattering)

∆q001

∆q110

substrate substrate

film film

a// = as

a┴

as as

a// ≠ as

a┴

X-ray analysis of lattice mismatched epitaxial films•High resolution reciprocal lattice mapping requires multi-reflection monochromator and analyzer crystal in order to separate strain from mosaicity

•Sensitive to lattice distortions within 10-5

•Accurate lattice parameter determination (in and out of plane)

•Determination of strain and composition variations, strain relaxation, mosaic size and rotation, misfit dislocation density, nanostructure dimensions, lattice disorder and diffuse scattering

No strain relaxation: Strain relaxation:

Data: Sardela et al

HR-XRD and TEM: CeN /MgO(001):fN2 = 0.25, Ji/JMe = 15, Ei = 30 eV

Cube on cube epitaxial relationship:(001)CeN||(001)MgO with [100]CeN||[100]MgO

aCeN = 5.021 Å, aTiN = 4.242 Å

0 90 180 270 360

MgO(113)

CeN(113)

I (a.

u.)

φ(deg)

MgOCeN

000 020

022002

2.16°

17 18 21 220

10

20

30

40

50

60

t = 70 nm MgO(002)

CeN(002)

CeN/MgO(001)TS = 700 癈

I (10

4 cou

nts s

-1)

ω−2θ (deg)

I (

coun

ts s-1

)

0

1

2

3

15 18 210

10

20

30

ω (deg)

I (co

unts

s-1)

HR-RLM

The degree of in-plane layer relaxation:

|||| k2a =

⊥⊥ = k3a

+−

−=⊥

⊥⊥ ν)1(a

)aaν(2 1aa ||

o

so

s||L a-a

aaR

−=

Relaxed lattice constant:

for 113 reflection

0.04 nm-1

TaN

MgO 113

∆(ω

−2θ)

∆(ω)k

k (nm )-1

(nm

)-1

δ-TaN /MgO(001)1.17

T = 600 癈s

113 RL = 94±4% for δ-TaNx (1.0 ≤ x ≤ 1.37)

X-ray reflectometry of thin films

•Film thickness measurements: 2 – 300 nm

•Applicable to ultra-thin films, amorphous or crystalline materials, multilayers and liquids

•Simulation and fitting: determination of interface roughness (rms) at each interface, and roughness correlation.

•Very sensitive to density variations

•Determination of critical angle, refractive index and density

2 4 6 8 10 12

Log

inte

nsity

(a.u

.)

2-theta (o)0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log

inte

nsity

(a.u

.)Theta (o)

0 2 4 6 8 10 12

Log

inte

nsity

(a.u

.)

2-theta (o)

Metallic multilayer

2.3 nm thick polymer on Si

AmorphousPZT film

Log

Ref

lect

ivity

RR ~ θ -4

One sharp surface(density ρe variation: step function at surface)

One rough interface (“broad”ρe variation

at surface)∆θ = λ/[2*(thickness)]

∆I ~∆ ρe

decay ~ roughness

Critical angle θc

Two interfaces

Thickness fringes

θ

θ

Data: Heitzman et al Data: Sardela, Auoadi et al Data: Mikalsen et al

Atomic Force MicroscopyAtomic Force Microscopy

Schematic of a typical AFM system

AFM is a technique which uses a smalltip to physically scan the sample surfacetopography on a sub-nm scale and produce a quantitative map of height vs location.

Atomic Force Microscopy

AFM: Surface morphology evolution during Ge MBEAFM: Surface morphology evolution during Ge MBE

(c) t = 1000 � (d) t = 2300 �

(b) t = 500 �(a) t = 250 �

[100][100] 1000 � Universal Scaling Theory

M aterial β γ ξG e* 1 0.4 0.02Fe** 0 .16 0.16 0.1T iN 0.25 0.25 0.006

β = roughening exponent

γ = coarsening exponent

ξ = aspect ratiodw

td

tw

=ξ

∝

∝

γ

βTiN/TiN(001)TiN/TiN(001)

( )2

i jG( ) h hρ = −

Surface Morphological Evolution of TM NitridesSurface Morphological Evolution of TM Nitrides

Ti1-xCexN/ SiO2, x = 0 - 0.25Ji/JMe ≈ 16, Ei ≈ 14eV, TS= 350 ºC

Si(0

02)

2 phases

1 phase

Ti1-xCexN/SiO2 (x = 0 - 0.23), TS = 350 ºC, Ji/JMe = 15, Ei = 14 eV

x 0.1:• a0 increases linearly with x.• Γ2θ (FWHM) remains small.• ρ increases linearly with x.

x > 0.1:• extensive CeN segregation• 2 phases (TiN-rich / CeN-rich)• Γ2θ jumps and then increases

linearly with x.• ρ increases faster than x < 0.1.

2 cosvKDθ

λθ

⋅=

Γ ⋅Dv = Volume weighted crystallite size,K = Scherrer constant (0.87-1.0),λ = The wavelength of the radiation,Γ2θ= The integral breadth of a reflection

(in radians 2θ) located at 2θ.

Ti1-xCexN (14 eV) surface morphology f(x)

w = surface width (RMS roughness)

x > 0.1:• CeN segregation.• 2 phases (TiN-rich & CeN-rich).• w drops below 2 nm.• w reaches 0.32 nm when x = 0.2.

x = 0

w = 6.82 nm w = 4.57 nm

x = 0.1

w = 1.31 nm

x = 0.15

w = 0.32 nm

0.5 µm

x = 0.2

SiO2100 nm100 nmSiO2100 nm

XTEM as f(x) at Ei = 14 eVTiN Ti0.9Ce0.1N Ti0.8Ce0.2N

Kinetic roughening:• Low adatom mobility in the

presence of Ehrlich barriers* Eb.• Local epitaxial growth in

individual columns facetsatomic shadowingunderdense structure.

*G. Ehrlich, Surf.Sci. 331-333, 865 (1995).

Eb

Polycrystalline ScN/MgO(001)

MgO(001)ScN

30 35 40 450

100

200

300

400 Ts = 750 oCt = 180 nm

x 500 ScN(002)

ScN(111)

MgO(002)

ScN/MgO(001)

Inte

nsity

(arb

. uni

ts)

2θ (degrees)

ScN layers on MgO(001) are polycrystalline with 111- and 002-oriented grains, as observed by x-ray diffraction θ-2θscans.

7%mismatch

Plan-view electron diffraction pattern

12-fold symmetry is due to 4-different azimuthal orientations of the ScN three-fold 111-grains on MgO(001)

X-ray Diffraction Pole Figures and Electron Diffraction Patterns

ScN(111)(2θ = 34.415°)

Pole figure

ScN(002)/MgO(001) ScN(111)/MgO(001)

Nucleation of 111- and 002-oriented ScN grains

Competitive Columnar Growth

(e)

(d)(a)

(b) (c)

Initially both 111- and 002-oriented grains nucleate. However the 111-grains overgrow the 002-grains in a competitive growth mode.

002 dark-field image

111 dark-field image