1. THIN FILM CHARACTERIZATION TECHNIQUES
OPTICAL* TECHNIQUES (EP727)
ION BEAM TECHNIQUES (EP727)
ELECTRON MICROSCOPY (MSE731)
Diffraction
X-ray diffraction (XRD)
Reflection/Transmission
Optical microscopy
Ellipsometry
Absorption/Emission
Photoluminescence
Photoconductivity
Fourier transform infrared spectroscopy (FTIR)
Raman spectroscopy
Ultraviolet photoelectron spectroscopy (UPS)
X-ray photoelectron spectroscopy (XPS)
Rutherford backscattering spectrometry (RBS)
Elastic recoil detection (ERD)
Ion induced x-ray spectroscopy (IIX)
Nuclear reaction analysis (NRA)
Channeling
Secondary ion mass spectrometry (SIMS)
Low energy electron diffraction (LEED)
Reflection high energy electron diffraction (RHEED)
Scanning electron microscopy (SEM)
Transmission electron microscopy (TEM)
ELECTRICAL
TECHNIQUES (EP727)
SCANNING PROBE MICROSCOPY (Chem733)
ANALYTICAL ELECTRON MICROSCOPY (MSE732)
Resistivity & Hall effect
Capacitance-voltage (C-V)
Deep level transient spectroscopy (DLTS)
Langmuir probe
Scanning tunneling microscopy (STM)
Atomic force microscopy (AFM)
Auger electron spectroscopy (AES)
Energy dispersive x-ray analysis (EDX)
Electron energy loss spectroscopy (EELS)
OTHER TECHNIQUES
Positron annihilation spectroscopy (PAS)
Electron paramagnetic resonance (EPR)
Contact angle measurements
* Optical techniques refers to all regions of the electromagnetic spectrum from IR to X-rays

2. Used to determine film structure, composition, thickness, etc.
THIN FILM CHARACTERIZATION TECHNIQUES
Mass, energy, or wavelength of reflected or transmitted particles are measured
Used to determine film structure, composition, thickness, etc.
Incident electrons, ions, or photons
Reflected or emitted particles
Sample
Transmitted particles

3. Film Structure
Direct Imaging
Diffraction
(electrons, x-rays)
SPM
LEED
RHEED
XRD
Electron
Microscopy

4. Crystal Structures
14 Bravais lattices
From Kittel, Fig. 11, p. 14

5. Crystal Structures From Kittel, Table 1, p. 15
From Kittel, Fig. 12, p. 15

6. Miller Indices for Crystal Planes
c/l
b/k
a/h
Lattice vectors are a, b, c
(hkl) are the Miller indices for the plane with intercepts a/h, b/k, c/l
Spacing between planes with Miller indices (hkl) is denoted ahkl
For cubic crystal with lattice constant a,
ahkl = a / (h2 + k2 + l2)½

7. Diffraction Incident wave, k = 2p/l
Incident particles (electrons, x-rays) treated as a plane wave (large distances, R; far-field or Fraunhofer diffraction condition)
Amplitude of incident wave at point P in crystal (polar notation):
ψP(r,t) = A e i k·(R+r) – iwt
phase
Incident wave,
k = 2p/l R O r
crystal P

8. Diffraction Amplitude at detector D due to scattering from point P :
ψD,P(r,t) = ψP(r,t)r(r) e i k´·(R´-r)
R´- r 
scattering density = electron probability density
In structural analysis we are interested in determining r(r) S D R R´
R´ - r O r
crystal P

9. ψD,P(r,t) = ψP(r,t)r(r) e i k´·(R´-r)
Diffraction
ψD,P(r,t) = ψP(r,t)r(r) e i k´·(R´-r)
 R´- r 
w´ = w  Forced oscillation; elastic scattering S D R R´
R´ - r O r
crystal P

10. For large R´ (far-field or Fraunhofer diffraction condition):
ψD,P(r,t) = ψP(r,t)r(r) e i k´·(R´-r)
= [(A/R´)e-iwt ei(k·R+k´·R´)] r(r)ei(k-k´)·r R´ S D R R´
R´ - r O r
crystal P

11. Diffraction ψD,P(r) ~ r(r) ei(k-k´)·r ~ r(r) e -i K·r
scattering vector, K = k´ - k S D R R´
R´ - r O r
crystal P

12. Diffraction Total amplitude of wave scattered from crystal:
ψ ~ ∫ r(r) e - i K·r dr
Amplitude is the Fourier transform of the scattering density
Total intensity:
I ~ ∫ r(r) e - i K·r dr 2
phase problem : we measure intensity not amplitude
must determine structure by comparison of experimental diffraction pattern with simulated pattern from model structure V

13. Diffraction
Incident wave is elastically scattered by atomic array
Constructive interference occurs in specific directions
Incident wave,
k = 2p/l
Scattered Waves
k' = 2p/l a

14. Same physics as diffraction grating
slit N
...
Optical path length difference q q
... P
slit 1

15. Constructive interference occurs when: Path length difference = ml
Diffraction
Constructive interference occurs when:
Path length difference = ml
2ahkl sinq = ml
(Bragg condition)
m = diffraction order = 1, 2, 3, …
q’s that satisfy the Bragg condition are called Bragg angles, qb k' k k' k q A
ahkl r B

16. Note : q defined relative
Diffraction
Note : q defined relative
to surface plane, not the surface normal (as in optics) k' k k' k q A
ahkl r B

17. Constructive interference occurs when Df = 2p or K = (2p/ahkl) n
Diffraction
Phase difference between plane waves reflected from atoms such as A and B is
Df = (k' – k)•r = K•r
Constructive interference occurs when
Df = 2p or
K = (2p/ahkl) n
(Laue condition)
n = unit vector along surface normal k' k k' k q A
ahkl r B

18. ghkl = (2p/ahkl)n is called a reciprocal lattice vector
Diffraction
K = (2p / ahkl) n
(Laue condition)
ghkl = (2p/ahkl)n is called a reciprocal lattice vector
ghkl is normal to the hkl set of crystal planes
K = ghkl k'
ghkl = (2p / ahkl) n qb qb k qb

19. Miller Indices ghkl c/l b/k a/h Lattice vectors are a, b, c
Reciprocal lattice vectors are a*, b*, c*
ghkl = (ha* + kb* + lc*) is orthogonal to hkl plane; h, k, l are integers

20. The set of all ghkl points is called reciprocal space
Diffraction
The set of all ghkl points is called reciprocal space
ghkl defines a point in reciprocal space for each set of crystal planes in real space with spacing ahkl
ghkl
Origin, O

21. Diffraction Superimpose Laue condition on reciprocal space (hkl) k'
ghkl
2qb k O

22. Diffraction
Sphere of radius k= 2p/l is called the Ewald sphere C
 k = 2p/l O

23. Diffraction K = ghkl (Laue condition)
Laue condition is satisfied by any reciprocal lattice point that intersects the Ewald sphere
(hkl) k'
ghkl C
2qb k O

24. Diffraction
Crystal
Crystal =
Unit cell
+ Basis
(e.g., fcc)

25. Diffraction r = rm + rn + ra ra rn rm
position vector from centre of charge distribution within each atom
position of mth unit cell
position of nth atom in each unit cell ra rn rm O

26. Diffraction Total scattering amplitude is
ψ ~ ∫ r(r) e -i K·(rm + rn + ra) dr
= S [ ∫ rn(ra) e-iK·ra dra] e-iK·(rm+rn)
= S fn e-iK·rn S e-iK·rm
phase difference
m,n A
atomic scattering factor, fn
Tabulated for each element n m
structure factor, F
shape factor

27. Diffraction Amplitude of wave scattered from a single unit cell:
F = Σ fn exp -iK·rn
position of atom n in unit cell
Structure factor n
phase difference
scattering factor from atom n
summation over n atoms in unit cell
Assumes electrons only scatter once (kinematic approximation)

28. Diffraction
Amplitude of wave diffracted from unit cell at Bragg angle (Laue condition):
F = Σ fn exp -i ghkl·rn
Diffraction spots will appear when F ≠ 0
F (the diffraction pattern) is the Fourier transform of fn (the crystal structure)
F = Σ fn exp -i K·rn n  n

29. Diffraction e.g., fcc lattice
4 atoms per unit cell (one at each lattice point) at
r1 = (0a + 0b + 0c)
r2 = (½a + ½b + 0c)
r3 = (½a + 0b + ½c)
r4 = (0a + ½b + ½c) c 4 3 b 2 1 a

30. Diffraction F = Σ fn exp -i ghkl·rn ghkl = (ha*+ kb*+ lc*)
r1 = (0a + 0b + 0c)
r2 = (½a + ½b + 0c)
r3 = (½a + 0b + ½c)
r4 = (0a + ½b + ½c)
F = f [ 1 + e-ip(h+k) + e-ip(h+l) + e-ip(k+l) ]
0 if h, k, l are mixed (even &
odd) integers
4f if h, k, l are unmixed (all
even or all odd)
e.g., (400) → F = 4f
e.g., (211) → F = 0 n
F =

31. Diffraction F = 0 are called forbidden reflections
Not all reciprocal lattice points satisfying the Laue condition will result in a diffraction spot
(hkl) k'
ghkl C qb k O

32. Diffraction e.g., bcc lattice 2 atoms per unit cell at
r1 = (0a + 0b + 0c)
r2 = (½a + ½b + ½c)
F = f [1 + e-ip(h+k+l) ]
0 if h+k+l is odd
2f if h+k+l is even
F = c 2 b 1 a

33. Diffraction A unit cell may have a basis with different atoms
e.g., bcc structure for NiAl
rNi = (0a + 0b + 0c)
rAl = (½a + ½b + ½c)
F = fNi + fAle-ip(h+k+l)
fNi – fAl if h+k+l is odd
fNi + fAl if h+k+l is even
Weak spots appear called superlattice peaks or spots
The more intense peaks are called the fundamentals
F =

34. Diffraction
The symmetry and forbidden reflections of the diffraction pattern can be used to determine the crystal structure
Structure
Forbidden Reflections
Simple cubic
None
fcc
h, k, l mixed (odd and even)
bcc
h+k+l odd
Zincblende
h, k, l mixed odd and even
Sodium Chloride
Diamond
h, k, l all even and h+k+l not divisible by 4; or h, k, l mixed odd and even

35. Diffraction Total scattering amplitude near the Bragg angle is
ψ = Σ fn exp -i(ghkl + s)·(rn + rm)
Position of atom n in unit cell
n,m
Small deviation from Laue condition
Position of mth unit cell in crystal
Sum over all unit cells, m, in sample and all atoms, n, per unit cell

36. Diffraction s k'
ghkl C k O

37. Diffraction Total scattering amplitude near the Bragg angle is
ψ = Σ fi exp -i(ghkl+s)·(rn + rm)
= Σ[Σ fnexp -i(gkhl+s)·rn]exp -i(ghkl+s)·rm
= F Σ exp -i(ghkl·rm) exp -i(s·rm)
n,m m n
= structure factor, F, since s << ghkl m
= 1
since ghkl = (ha* + kb* + lc*)
rm = (n1a + n2b + n3c)
where h, k, l, n1, n2, n3 = integer
ghkl·rm = 2p (n1h + n2k + n3l)

38. Diffraction ψ = F Σ exp -i (s·rm)
For rectangular crystal with dimensions xa, yb, zc :
ψ = F sin(½sxxa) sin(½syyb) sin(½szzc)
½sxxa ½sy yb ½sz zc
V = sample volume = xaybzc
For a thin film z << x, y
Assume sx = sy = 0
ψ = F sin (½szzc)
V ½sz m
shape factor

39. Diffraction ψ = F sin (½szzc) V ½sz Now zc = film thickness, t
ψ = F sin (½szt)
V ½sz
Intensity of diffracted wave is :
I = ψ2 = (F/V)2 [( sin(½szt) )/(½sz)]2
= (tF/V)2 sinc2(½szt)

40. Diffraction I = ψ2 = (tF/V)2 sinc2(½szt) I = 0 when x = ±pp 2p 3p
I = 0 when x = ±p
width, 2p = 2 (½szt) = szt
sz = 2p / t

41. Diffraction
Due to finite thickness of the film, each reciprocal lattice point may be considered as streaks with length 2p/t
2p/t k'
ghkl C k O

42. The thinner the film the greater the “streaking”
Diffraction
The thinner the film the greater the “streaking”
Lattice points become lattice rods for very thin films (monolayers)
from
Ohring,
Fig. 7-27,
p. 346

43. Diffraction
From Tom Ryan, MRS short course (1990)