1. LEED
Low energy electron diffraction
Based on electron diffraction from Ni in the early experiments of Davisson and Germer (1925)

2. LEED
Low energy electron beam (~ eV) impinges at near normal incidence
From Ohring, Fig. 7-25, p. 343

3. LEED Low energy electrons are diffracted from near surface region
LEED pattern consists of spots where Ewald sphere intersects lattice rods
From Ohring, Fig. 7-27, p. 346

4. LEED
e.g., Si surface
From Ohring, Fig. 7-26(a), p. 345

5. Eliminate electron scattering by gas molecules
LEED
UHV required
Eliminate electron scattering by gas molecules
Eliminate sensitivity of diffraction to adsorbed impurities
Cannot be used during film growth due to obstruction of fluorescent screen
From
Ohring,
Fig. 7-27,
p. 346

6. Reflection high energy electron diffraction
RHEED
Reflection high energy electron diffraction
High energy electron beam (~5-100 keV) at grazing angle of incidence (~ few degrees)
Can be used during film growth
From Ohring, Fig. 7-25, p. 343

7. Glancing incidence electrons  interact with near surface region
RHEED
Glancing incidence electrons  interact with near surface region
High energy electrons → large diameter Ewald sphere
RHEED patterns consist of streaks for smooth surfaces
From Ohring,
Fig. 7-27,
p. 346

8. RHEED
Streak pattern indicates surface periodicity

9. RHEED Surface reconstruction phase diagram
from Semicond. Sci. Technol. 9, 123 (1994)

10. RHEED
from Semicond. Sci. Technol. 9, 123 (1994)

11. RHEED
RHEED patterns consist of spots for rough surfaces or streaks for smooth surfaces
From Herman et al, Fig. 10.4, p. 229

12. RHEED
From Ohring, Fig. 7-28, p. 347

13. RHEED
RHEED oscillations
From Ohring, Fig. 7-22, p. 340

14. RHEED
Vicinal surfaces
From Tsao, Fig. 6.5, p. 208

15. RHEED Step-flow growth Layer-by-layer growth
From Herman et al, Fig. 1.7, p. 10

16. RHEED
References :
D.K. Biegelson, R.D. Bringans, J.E. Northrup, and L.-E. Swartz, “Surface Reconstruction of GaAs(100) Observed by Scanning Tunneling Microscopy”, Phys. Rev. B 41, 5701 (1990).
H.H. Farrell and C.J. Palmstrom, “Reflection High Energy Electron Diffraction Characteristic Absences in GaAs (100) (2x4)-As : A Tool for Determining the Surface Stoichiometry”, J. Vac. Sci. Technol. B 8, 903 (1990).
S. Clarke and D. D. Vvedensky, “Growth Kinetics and Step Density in Reflection High-Energy Electron Diffraction During Molecular-Beam Epitaxy”, J. Appl. Phys. 63, 2272 (1988).
M. D. Pashley, “The Application of Scanning Tunneling Microscopy to the Study of Molecular Beam Epitaxy”, J. Cryst. Growth 99, 473 (1990).

17. RHEED
References :
5. B. A. Joyce, “The Evaluation of Growth Dynamics in MBE Using Electron Diffraction”, J. Cryst. Growth 99, 9 (1990).
6. J. H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, “Dynamics of Film Growth of GaAs by MBE from RHEED Observations”, Appl. Phys. A 31, 1 (1983).
7. L. Daweritz and K. Ploog, “Contribution of Reflection High-Energy Electron Diffraction to Nanometre Tailoring of Surfaces and Interfaces by Molecular Beam Epitaxy”, Semicond. Sci. Technol. 9, 123 (1994).
8. J. H. Neave, P. J. Dobson, B. A. Joyce, and J. Zhang, “Reflection High-Energy Electron Diffraction Oscillations from Vicinal Surfaces – a New Approach to Surface Diffusion Measurements”, Appl. Phys. Lett. 47, 100 (1985).

18. X-ray Diffraction (XRD)
Structural characterization technique:
Composition
Lattice constant
Film thickness
Strain and relaxation
Crystalline perfection
Interface quality
Non-destructive
Best strain sensitivity, 10-7

19. XRD
Collimated (parallel beam), monoenergetic beam of x-rays diffract from sample
From Panish & Temkin, Fig. 6.1(a), p. 174

20. XRD ahkl … Atoms scatter incident x-rays
Constructive interference occurs in specific directions
lateral resolution ~ mm to mm
ahkl
Penetration depth ~ 10 mm …

21. XRD Large penetration depth compared to electrons
 narrower diffraction peaks
 better strain sensitivity
 less surface sensitivity
Use glancing incidence x-ray scattering (GIXS) for surface sensitivity (similar to RHEED)
Difficult to focus x-rays
 electrons are better for imaging
 electrons have higher resolution (nm’s) compared to x-rays (mm’s to mm’s)

22. XRD
Crystal planes act as diffraction grating
Constructive interference occurs when
2ahkl sinqb = ml
(Bragg’s law)
qb = Bragg angle
m = diffraction order = 1, 2, 3, …
Caution: q defined relative to surface plane not the surface normal (as in optics) qb
ahkl

23. XRD
2ahkl sinqb = ml
sinqb ≤ 1
l < 2ahkl (first order, m = 1)
Need l ~ Å

24. XRD
X-ray source
Electrons are produced by thermionic emission from a filament
Electrons are accelerated by a potential ~ 30 kV towards a solid target (usually Cu)
Electrons produce core shell ionization, resulting in characteristic x-ray emission
From Dunlap, Fig. 13.5, p. 328

25. XRD X-ray detectors Proportional counters
x-ray ionizes gas in a tube; ion current is measured by negative electrode
Scintillation counters
scintillator converts x-rays to optical photons; PMT detects optical photons
Solid-state detectors
electron-hole pairs created in reverse-biased p-n junction

26. XRD X-ray nomenclature: Ka : L → K Kb : M → K La : M →L
Energy transition
Terminating energy level Ka Kb La
Letters denote principal quantum numbers (K: n = 1, L: n=2, etc.)
adapted from Loretto, Fig. 2.3, p. 30

27. XRD
From Dunlap, Fig. 13.2, p. 325
From Dunlap, Table 13.1, p. 326

28. XRD X-ray detector Scintillator-PMT
Solid-state detector (Si p-n junction diode)
From Panish & Temkin, Fig. 6.1(a), p. 174

29. XRD a Usually use (hkl) = (400) for III-V epilayers
e.g., a (400) for InP = Å/4 = Å a
From Sze, Fig. 3(a), p. 5

30. XRD
2ahkl sinqb = ml
lCuKa1 = Å
a(400) InP = Å
qb = º
qb varies with ahkl
Can measure qb to determine ahkl

31. Sample and detector are rotated through the Bragg angle
XRD
Sample and detector are rotated through the Bragg angle
Maintain q – 2q geometry
From Panish & Temkin, Fig. 6.1(a), p. 174

32. Measure x-ray intensity versus angle for a specific Bragg reflection
XRD
Measure x-ray intensity versus angle for a specific Bragg reflection
 x-ray rocking curve
From Panish & Temkin, Fig. 6.2, p. 176

33. XRD
2a┴ sinqb = ml
qb is different for substrate and epilayers due to strain (remember the Posisson effect)
qb,epilayer
qb,substrate
epilayer
(compression)
substrate

34. a┴ increases with compressive strain
XRD
2a┴ sinqb = ml
a┴ increases with compressive strain
→ qb decreases (layer peak left of substrate peak)
a┴ decreases with tensile strain
→ qb increases (layer peak right of substrate peak)
From
Ohring,
Fig. 7-1,
p. 308

35. XRD
Measure diffraction angle of film relative to substrate, Dq
Differentiate Bragg’s law to derive perpendicular mismatch from Dq :
(Da/a)┴ = - Dq / tan q
Can use Poisson’s ratio to determine natural (unstrained) lattice constant of film :
(Da/a)┴ = [(1+n)/(1-n)] (Da /a)o

36. Diffraction peaks have finite width
XRD
Strain sensitivity :
Diffraction peaks have finite width
From Panish & Temkin, Fig. 6.2, p. 176

37. XRD
Strain sensitivity :
Diffraction peaks have finite width
Source is not perfectly monochromatic (Cu Ka dispersion ~ Å = difference between Ka1 and Ka2 lines)
Source is not perfectly collimated (require angular divergence < few arcseconds)
Layers have finite thickness
Layers may be bent due to strain
Layers may be partially relaxed

38. From MRS Short Course (1990)
DCXRD
Double crystal XRD or High resolution XRD (HRXRD)
Uses a reference crystal to filter and collimate the incident x-rays
Only x-rays satisfying the Bragg condition are reflected to sample
e.g., InP crystal aligned to 31.67º fixes l at Å
From MRS Short Course (1990)

39. Double Crystal XRD or High Resolution XRD (HRXRD)
DCXRD
Double Crystal XRD or High Resolution XRD (HRXRD)
Acts as monochromator
From Panish & Temkin, Fig. 6.1(b), p. 174

40. Linewidth of substrate peak ~ 12 arcsecs
DCXRD
Linewidth of substrate peak ~ 12 arcsecs
Strain sensitivity, Da/a ~ 10-4
From Panish & Temkin, Fig. 6.3, p. 176

41. DCXRD
Pendellosung fringes
From Panish & Temkin, Fig. 6.3, p. 176

42. DCXRD
Pendellosung fringes :
Diffraction corresponding to total film thickness
2t sinqb = ml
lDm = 2tcosqb
t = l / (2Dqcosqb) for Dm = 1 qb t

43. Can measure spacing of fringes to determine film thickness
DCXRD
t = l / (2Dqcosqb)
Can measure spacing of fringes to determine film thickness Dq
From Panish & Temkin, Fig. 6.3, p. 176

44. HRXRD
Can use more than one crystal to further improve resolution → multi-crystal diffractometers
From Panish & Temkin, Fig. 6.8(b), p. 181

45. Superlattices
From Panish & Temkin, Fig. 6.6, p. 179

46. Superlattices
Satellite peaks are produced corresponding to the periodicity of the superlattice
Experiment
Model
From Panish & Temkin, Fig. 6.10(b), p. 183

47. Monolayer resolution from HRXRD (> 2 crystals)
Superlattices
Monolayer resolution from HRXRD (> 2 crystals)
From Panish & Temkin, Fig. 6.10(b), p. 183

48. Interface roughness and grading
Superlattices
Interface roughness and grading
From Panish & Temkin, Fig. 6.17(a), p. 193

49. Superlattices
From Panish & Temkin, Fig. 6.15, p. 191

50. Superlattices
The intensities of the peaks contains information on the interface composition
The satellite peaks correspond to the Fourier transform of the superlattice structure
 sinusoidal structure: only 1 pair of satellite peaks
 perfect square wave: infinite number of odd satellite peaks
Higher order peaks (corresponding to higher order Fourier components) are sensitive to the interface composition
Varying the compositions is like varying the structure factors in the unit cells

51. Other Effects Mismatch Misorientation Dislocation Content
from
Bowen,
Fig. 3.1,
p. 51
Mismatch
Misorientation
Dislocation
Content
Mosaic Spread
Curvature
Relaxation
Inhomogeneity

52. Other Effects Change beam position Rotate sample
from Bowen, Table 3.1, p. 52

53. Other Effects
Use different reflections to probe broadening of reciprocal lattice points
From Tom Ryan, MRS Short Course (1990)

54. Asymmetric Reflections
Can use assymetric reflections (e.g., 224 or 115) to measure in-plane lattice parameter

55. Asymmetric Reflections
Can separate broadening effects in k (e.g., due to superlattice effects) and k (e.g., due to dislocations)
2q-w ~ 90°  sensitive to k
2q-w ~ 0°  sensitive to k

56. Asymmetric Reflections
Can measure very thin layers
(~ 10 nm with a conventional anode source) using glancing incidence or glancing exit

57. Advanced X-ray Techniques
X-ray diffraction can be made surface sensitive by using grazing angles of incidence
 GIXS, GIXD
Reciprocal space mapping
X-ray standing waves (XSW)
Diffraction anomalous fine structure (DAFS)
X-ray reflectivity

58. XRD References
P. F. Fewster and C. J. Curling, “Composition and Lattice-Mismatch Measurement of Thin Semiconductor Layers by X-ray Diffraction”, J. Appl. Phys. 62, 4154 (1987).
P. F. Fewster, “X-ray Diffraction from Low-Dimensional Structures”, Semicond. Sci. Technol. 8, 1915 (1993).