X-ray analysis methods

2008 Advanced Materials Characterization Workshop X-ray analysis methods Mauro Sardela, Ph.D. The Frederick Seitz Materials Research Laboratory University of Illinois at Urbana-Champaign Sponsors: Sponsors: Supported by the U.S. Supported Department by the of Energy U.S. Department under grants of Energy DEFG02-07-ER46453 under grant DEFG02-91-ER45439 and DEFG02-07-ER46471 2008 University 2007 University of Illinois of Illinois Board of Board Trustees. of Trustees. All rights All reserved. rights reserved. 1 Outline X-rays interactions with the matter Fundaments of diffraction Powder diffraction methods Size / strain analysis Search / Match, structure determination Quantitative analysis, whole pattern fitting X-ray parallel beam methods Thin film crystallographic orientation Glancing / Grazing angle XRD methods Texture - preferred orientation methods Residual stress analysis methods High resolution XRD methods Rocking curve analysis Reciprocal lattice mapping X-ray reflectivity methods X-ray fluorescence methods X-ray analysis summary Comparison with other techniques Quick guide to the FS-MRL x-ray analysis facilities Recommended literature. 2 1

X-ray interactions with matter 125 γ X rays rays 0.01 0.125 10 UV λ(nm) Incident x-ray photons hν 0 E(keV) Visible 200 2 nm ~30 μm Coherent scattering Interaction volume hν 0 hν1 Fluorescence 50 μm 5 cm hν 2 Incoherent scattering e - e - Photoelectron Sample Auger electron hν: photon e - : electron Coherent Coherent scattering scattering (Thompson (Thompson scattering scattering / Incoherent / Incoherent scattering Fluorescence: scattering Fluorescence: diffraction): (Compton diffraction): (Compton scattering): (a) scattering): (a) K/L K/L shell shell e e - absorb - absorb incident incident incident incident photon photon hν hν o (a) interacts o (a) e e - energy absorbs - absorbs incident incident energy energy hν hν o energy hν hν o ; o ; interacts with with e e - o with - with no (excited no (excited photoelectron); (b) photoelectron); (b) outer outer shell shell e- e- cascade cascade down down energy loss and no phase (b) energy loss and no phase (b) part part of of the the energy energy is is emitted emitted at filling at filling the the holes holes causing causing secondary change different change different energy energy hν hν 1 and 1 and different secondary photons photons different phase. emission phase. emission (hν (hν 2 ). 2 ). Auger Auger electron electron emission: emission: Photoelectron Photoelectron emission: (a) emission: (a) incident incident hν hν 0 used 0 used to to eject eject e e - - from from atom; atom; hν hν 0 energy 0 energy is is used used to to eject eject electron electron e e - with (b) - with (b) 2 2 nd nd e e - - drops drops to to lower lower levels levels to to fill fill the the kinetic kinetic energy energy = = hν hν o o B.E.(binding B.E.(binding energy). hole energy). hole and and a a photon photon is is emitted; emitted; (c) (c) the the emitted emitted photon photon is is absorbed absorbed by by valance valance e e -, -, which which ionizes ionizes and and leaves leaves the the atom. atom. 3 Coherent scattering (Diffraction, Thompson or Rayleigh scattering) E 0 Photon X-ray interactions with matter (3) (1) (2) E 0 Electron Nucleus Incoherent scattering (Compton scattering) E 0 Photon (1) (3) (2) E 1 <E 0 Electron Nucleus (1) Incoming photon (2) Oscillating electron (3) Scattered photon No loss of energy. Fluorescence E 0 Photon (1) (2) (1) Incoming photon (2) Expelled electron (photoelectron) (3) Hole is created in the shell E 1 =E L -E K (3) (4) Nucleus Electron L shell (4) Outer shell electron moves to the inner shell hole (5) Energy excess emitted as characteristic photon. K E 0 (1) Incoming photon (2) Energy is partially transferred to electron (3) Scattered photon (energy loss). Auger electron (1) (2) L shell K (3) Nucleus Electron (1) Incoming photon excites inner shell electron (2) Excitation energy is transferred to outer electron (3) Electron ejected from atom (Auger electron) 4 2

Fundaments of diffraction Real space Set of planes F Reciprocal space Point (h k l) d h k l 2π/d origin M. von Laue 1879-1960 X-rays from crystals, 1912. 5 Fundaments of diffraction Real space F Reciprocal space d 2π/d origin 6 3

Fundaments of diffraction Real space F Reciprocal space origin 7 Fundaments of diffraction Real space F Reciprocal space Bragg s law Ewald s sphere Detector 2θ Diffracted beam Incident beam ω X-ray source q 2θ k 1 k 0 (= radius) 1862 1942 1890-1971 2 d sin θ = n λ Elastic (Thompson s) scattering q = k 1 k 0 q: scattering vector q = (4 π/λ) sinθ Paul P. Ewald 8 1888-1985 4

Fundaments of diffraction Real space Reciprocal space Detector scan Δ(2θ) 2θ/ω scan Δ(2θ/ω) Rocking curve (sample) scan Δ(ω) Rocking curve scan: to scattering vector Diffracted beam 2θ Scattering vector ω Incident beam Δ(ω) Detector Scan: around Ewald s sphere Δ(2θ) h k l Δ(2θ/ω) 2θ/ω scan: radial, // to scattering vector q k 1 h k l k 0 9 Fundaments of diffraction Real space Reciprocal space Diffracted beam Detector scan 2θ Δ(2θ) Scattering vector Glancing angle Constant sampled volume 2θ/ω scan Δ(2θ/ω) Incident beam h k l Rocking curve scan Δ(ω) Detector Scan: around Ewald s Phase analysis sphere ω Grain size analysis Δ(2θ) Unit cell determination Stress analysis Lattice distortion, strain q Composition, alloying Defects, material quality Rocking Mosaicity curve scan: Δ(ω) to scattering vector Texture Texture strength h k l k 1 Δ(2θ/ω) 2θ/ω scan: radial, // to scattering vector k 0 10 5

Typical contents from XRD pattern (diffractogram) Si powder sample PDF PDF (ICDD/JCPDS) Peak Peak position: identification, identification, structure, structure, lattice lattice parameter parameter Peak Peak width: width: crystallite crystallite size, size, strain, strain, defects defects Peak Peak area areaor or height height ratio: ratio: preferred preferred orientation orientation Peak Peak tails: tails: Diffuse Diffuse scattering, scattering, point point defects defects Background: amorphous amorphous contents contents 11 Powder diffraction methods Crystalline? Amorphous? What elements, compounds, phases are present? Structure? Lattice constants? Strain? Grain sizes? Grain orientations? Is there a mixture? What %? Powders, bulk materials, thin films, nanoparticles, soft materials. 12 6

Bragg-Brentano focusing configuration Focus Receiving slit Single crystal monochromator (λ) X-ray source Divergence slit Detector Focusing circle (variable during measurement) Angle of incidence (ω) Secondary Optics: Scatter and soller slits specimen Detector rotation (2θ) Diffractometer circle 13 (fixed during measurement) Bragg-Brentano focusing configuration Focus Receiving slit Single crystal monochromator (λ) X-ray source Divergence slit Detector Divergent beam not good for for grazing incidence analysis Focusing circle (variable during measurement) Angle of incidence (ω) Secondary Optics: Scatter and soller slits specimen Sample height positioning is is critical Detector rotation (2θ) Diffractometer circle 14 (fixed during measurement) 7

Instrumentation: powder diffraction Cu x-ray source Soller slits 2θ Rigaku D/Max-b x-ray diffractometer Bragg-Brentano configuration (top view) CMM XRD facilities Divergence slit θ sample Curved graphite monochromator 2θ Scatter slit Soller slits Receiving slit Δ2θ ~ 0.2 O Detector CMM instrument: Rigaku D/Max-b XRD system 15 Instrumentation: stress, phase analysis Bragg-Brentano configuration with programmable slits Top view Programmable anti-scatter slits 2θ φ sample ψ ω Vertical mask Programmable divergence slit [> (1/32) deg] Optional filter or attenuator X-ray source: Cu, line focus Programmable attenuator Detector Curved graphite monochromator Programmable receiving slits Programmable slits can be used for applications requiring limited or constant illuminated area in the sample. CMM instrument: Panalytical X pert #2 XRD system 16 8

Crystallite size analysis Scherrer s equation: k * λ Size = cos (θ) * (FWHM) k : shape factor (0.8-1.2) λ: x-ray wavelength FWHM: full width at half maximum (in radians) Not accounting for peak broadening from strain and defects Measured along the specific direction normal to the (hkl) lattice plane given by the 2θ peak position Peak width (FWHM) Measurement Fit Peak position 2θ 2θ 17 FWHM vs. integral breadth It does not take into account the lower part of the profile I max (½)I max FWHM (deg) The square-topped profile has the same area and peak height as the measured curve. Integral breadth = (total area) / (peak height) Integral breadth (deg) 18 9

Peak shape analysis Peak fit: Gaussian Lorentzian Pearson-VII (sharp peaks) Pseudo-Voigt (round peaks) Information from fit: Position Width (FWHM) Area Deconvolution Skewness Measurement Fit Measurement Fit 19 Correction for instrument resolution Use FWHM curve as a function of 2θ from standard sample (NIST LaB 6 ) - specific for each diffractometer FWHM: β β D = (β meas ) D (β instr ) D D: deconvolution parameter Measurement Instrument function D : 1 (~ Lorentzian) β = (β meas ) (β instr ) D : 2 (~ Gaussian) β 2 = (β meas ) 2 (β instr ) 2 D : 1.5 β 1.5 = (β meas ) 1.5 (β instr ) 1.5 Software: MDI s Jade + 8.0 20 10

Potential artifacts in size determination Measured peak width ( o ) FWHM: β β D = (β meas ) D (β instr ) D Size, nm D = 1 (Lorentzian) Size, nm D = 1.5 Size, nm D = 2 (Gaussian) Assume: Instrument resolution ~ 0.15 o 2θ = 40 o Cu radiation 0.3 0.5 56.4 24.2 38.0 19.2 32.6 17.7 Large difference (up to 48%!) for narrow peaks (large sizes) 0.75 14.1 12.0 11.5 1 1.5 2 10.1 6.3 4.6 8.8 5.8 4.3 8.6 5.7 4.2 Smaller difference (~ 10%) for broad peaks (small sizes) 21 Strain effects in diffraction lines d No strain Macrostrain uniform strain (lattice distortion) Uniform strain Δ(2θ) Peak position shift (lattice constant change) Microstrain nonuniform strain (lattice distortion) FWHM Peak width change Nonuniform strain 22 11

Size and strain in peak shape analysis (FWHM)*cos(θ) = kλ/(size) + (strain)*sin(θ) (FWHM)*cos(θ) Williamson-Hall Method Acta Metall. 1 (1953) 22. sin(θ) Intercept ~ 1/(size) 1/(size) Slope Slope ~ micro micro strain strain FWHM strain = 4*(strain)*tanθ 23 Other methods of grain size analysis Rietveld Rietveld refinement refinement method: method: Refines Refines the the whole whole diffraction diffraction pattern pattern (including (including background) background) Needs Needs detailed detailed data data over over a a wide wide angular angular range range Gives Gives one one average average size size value value Works Works better better for for powder powder samples samples (not (not well well with with films films with with strong strong preferred preferred orientation) orientation) Data Data processing processing (refinement (refinement and and play play with with parameters) parameters) is is time time consuming. consuming. H. Rietveld (1932-) Warren-Averback Warren-Averback method: method: Standard Standard sample sample -> -> Instrumental Instrumental Broadening Broadening -> -> Correct Correct measured measured peaks peaks assuming assuming error -type error -type of of function function (main (main assumption) assumption) I I ~ exp(-pφ) exp(-pφ) 2 2 -> -> Use Use Scherrer s Scherrer s equation equation Jones Jones method: method: Measured Measured profile profile = = convolution convolution ( pure, ( pure, instrument) instrument) Use Use Fourier Fourier integrals integrals for for all all the the profiles profiles (measured, (measured, pure, pure, instrument) instrument) Use Use ratio ratio of of the the integrals integrals to to determine determine sizes. sizes. 24 12

Pattern treatment, S/M and structure refinement Intensity 1. Background treatment 2. Peak fit 3. Search/Match ( PDF ) 4. Composition (w%) 5. Grain sizes, lattice parameters 6. Structure determination refinement Weight % of parts in the mixture 2θ( o ) Software: MDI s Jade + 8.0 25 Intensity (a.u.) Whole pattern fitting and structure refinement Pattern from a Li-Nibased battery cathode (003) C(002) (101) (104) (012) (006) (015) 2-theta ( o ) Pattern treatment: * Peak profile fit * Search / Match * Pattern Indexing * Cell Refinement * Pattern Simulation * RIR w% quantification * Rietveld structure refinement Data: Sardela, UIUC Sample: Abraham et al, ANL (018) (107) (110) (113) 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). Search / Match: Structure: Cell (Rietveld refinement): Average bond distances (Rietveld): Quantitative analysis: Crystallite size: Strain: Results obtained from the measured pattern: LiNi 0.7 Co 0.3 O 2, major (minor: C graphite) Hexagonal R-3m (166) <1/3,2/3,2/3>, Z=1, hr4 a= 2.86285 Å; b= 2.86285 Å; c= 14.17281 Å α= 90 o β= 90 o γ= 120 o Unit cell volume: 100.6 (Å) 3 Density: 4.8383 g cm -3 Linear Absorption Coefficient: 385.5 cm -1 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 Å Li-O: 2.1117 Å, Li-Li: 2.8629 Å, O-O: 2.7983 Å 82.9 w% LiNi 0.7 Co 0.3 O 2, 17.1 w% C > 1000 Å 0.05% Ni O Li Co 26 13

New: S/M assisted by whole pattern fitting Multi-phase mixture powder data Software: MDI s Jade + 8.0 27 New: S/M assisted by whole pattern fitting Whole pattern fitting using possible pdf hits in search for best phase id s R is being minimized (whole pattern fitting) Possible Possible pdf pdf hits hits after after S/M S/M 28 14

New: S/M assisted by whole pattern fitting Unmatched peaks are now fitted New New pdf pdf hits hits are are now now automatically added added 29 New: S/M assisted by whole pattern fitting Whole pattern fitted R: 45.5 w%, XS: 463 nm H: 31.0 w%, XS: 273 nm A: 23.5 w%, XS: 28 nm R H A 3 phases matched: Rutile, Hematite, Anatase 30 15

X-ray parallel beam methods Rough, irregular surfaces Film / Substrate systems α Near surface region Glancing / grazing angle applications. Phase, stress gradients (depth profiles) 31 Parallel beam configuration Negligible Negligible sample sample displacement displacement issues issues (rough (rough and and curved curved samples samples OK) OK) Specific Specific optics optics to to maximize maximize intensities intensities Detector X-ray source Primary Optics: mirror, slits, lens Parallel plates collimation Single crystal monochromator (λ) Parallel beam Detector rotation (2θ) Angle of incidence (ω) Excellent Excellent for for glancing glancing angle angle (fixed (fixed ω) ω) applications applications specimen 32 16

Instrumentation: thin film, texture, stress analysis Parallel plate collimator configurations Top view 0.27 o - parallel plates collimator 2θ φ sample ψ ω Crossed slits (slit+mask) Vertical mask Primary optics option 1: Crossed-slit collimator Optional filter or attenuator X-ray source: Cu, line or point focus Primary optics option 2: x-ray lenses Δθ ~ 0.03-0.2 o Detector Optional 0.1mm slit Flat graphite monochromator Programmable divergence slit Programmable attenuator Primary optics option 3: programmable divergence slit + programmable attenuator CMM instrument: Panalytical X pert #2 XRD system 33 Thin film orientation analysis Intensity (a.u.) 2θ/θ scan (surface normal direction) δ-tan x /MgO(001) t = 500 nm T s = 600 C J i /J Ta = 11 f N2 = 0.125 δ-tan 002 δ-tan (002) 40 ev, Γ ω = 0.95 30 ev, Γ ω = 0.75 20 ev, Γ ω = 0.60 8.5 ev, Γ ω = 0.68 <001> φ scan (in-plane TaN Example: surface direction) <001> MgO MgO 002 MgO (002) 41.0 41.5 42.0 42.5 43.0 43.5 2θ (deg) TaN film MgO(001) substrate Data: Shin, Petrov et al, UIUC Cube Cube on on cube cube epitaxy: (001) (001) TaN //(001) TaN //(001) MgO MgO (100) (100) TaN //(100) TaN //(100) MgO MgO Intensity (a.u.) (220) φ scans TaN MgO <110> <110> δ-tan 1.17 /MgO(001) t = 500 nm T s = 600 C δ-tan δ-tan MgO MgO 0 50 100 150 200 250 300 350 φ (deg) 34 17

Glancing angle x-ray analysis surface normal ω (fixed) Incident x-ray beam Diffracted x-ray beam grains : conventional Bragg-Brentano configuration 2θ-ω scans probe only grains aligned parallel to the surface + : parallel-beam grazing incidence configuration 2θ scans probe grains in all directions 35 X-ray penetration depth vs. angle of incidence Low angle region -Type of radiation - Angle of incidence - Material (Z, A, ρ, μ) 36 18

X-ray penetration and information depths t z I 0 α d 1 d 2 I 0 exp(-μl) 2θ α l = d 1 + d 2 = sin z + z α sin (2θ α) Absorption (sample w/ finite thickness) Absorption factor = Absorption (sample w/ infinite thickness) For θ/2θ configuration: A θ2θ = 1 exp(-2μ/sinθ) For GIXRD configuration:a GIXRD = 1 exp(-μtk α ) k α = 1/sinα + 1/sin(2θ α) t: thickness z: depth from surface μ = μ m ρ = linear absorption coefficient μ m = mass absorption coefficient (tables) ρ: mass density α c : critical angle β: λμ / 4π (imaginary part of refractive index) δ = ½(α c 2 ) (1) Penetration depth τ 1/e : depth for Intensity = I o /e ~ 37% I o τ 1/e = (sinα) / μ (2) Penetration depth τ 63 : depth for A GIXRD = 1-1/e (~ 63%, μtk α =1) sinα sin(2θ α) τ 63 = 1 / μk α = μ [sinα + sin(2θ α)] Bragg peak (2θ) dependent penetration depth! (3) Information depth τ : weighted average of sampling depth 1 τ = + 1 μkα 1 exp(μtk α ) It will not exceed the thickness value! (4) Penetration depth τ 1/e for α ~ α c : Includes correction with refractive index n = 1- δ -iβ τ 1/e = 2 λ 4π [(α 2 α c 2 ) 2 + β 2 ] -1/2 (α 2 - α c 2 ) Excel spreadsheet calculator available at: http://www-ssrl.slac.stanford.edu/materialscatter/gixs-calculator.xls 37 X-ray penetration and information depths t z I 0 α d 1 d 2 I 0 exp(-μl) 2θ α 500 nm thick TiO 2 rutile film (μ = 0.0528 μm -1, Cu Kα radiation) 2θ range: 22 60 o Angle of incidence α ( o ) Penetration depth τ 1/ε (nm) Information depth τ (nm) 0.9 298 180-182 1.8 595 (>t!!) 212 214 2.7 892 (>t!!) 224 226 From: M. Birkholz, Thin Film Analysis by X-ray Scattering Wiley-VCH 2006 (1) Penetration depth τ 1/e : depth for Intensity = I o /e ~ 37% I o τ 1/e = (sinα) / μ (2) Penetration depth τ 63 : depth for A GIXRD = 1-1/e (~ 63%, μtk α =1) sinα sin(2θ α) τ 63 = 1 / μk α = μ [sinα + sin(2θ α)] Bragg peak (2θ) dependent penetration depth! (3) Information depth τ : weighted average of sampling depth 1 τ = + 1 μkα 1 exp(μtk α ) It will not exceed the thickness value! (4) Penetration depth τ 1/e for α ~ α c : Includes correction with refractive index n = 1- δ -iβ τ 1/e = 2 λ 4π [(α 2 α c 2 ) 2 + β 2 ] -1/2 (α 2 - α c 2 ) Excel spreadsheet calculator available at: http://www-ssrl.slac.stanford.edu/materialscatter/gixs-calculator.xls 38 19

Grazing angle vs. Bragg-Brentano configurations Grazing incidence analysis with with parallel beam optics Detect Detect grains grains in in various various orientations orientations (including (including tilted tilted to to the the sample sample surface). surface). Fixed Fixed incident incident angle: angle: constant constantprobed depth depth in in the the sample sample during during analysis. analysis. Low Low angle angle of of incidence: incidence: high high sensitivity sensitivityto to (ultra) (ultra) thin thin films; films; avoid avoid artifacts artifacts from from substrates; substrates; can can be be used used for for depth depth profiling profiling at at different different incidences. incidences. Slightly Slightly lower lower 2θ 2θresolution: ok ok for for broad broad peaks. peaks. Thin Thin film film collimation collimation optics: optics: enhanced enhanced sensitivity sensitivity to to thin thin films. films. Parallel Parallel beam: beam: insensitive insensitiveto to sample sample displacement displacementerrors. errors. Conventional analysis with with focusing configuration Detect Detect only only grains grains with with orientation orientation parallel parallel to to the the sample sample surface. surface. Sample Sample probed probed depth depth may may vary vary during during the the analysis. analysis. Lower Lower sensitivity sensitivity to to (ultra) (ultra) thin thin films; films; substrate substrate artifacts artifacts are are problem. problem. Very Very good good 2θ 2θresolution resolutionand and wellknowknown mathematical mathematical formalism. formalism. well- Typical Typical optics optics are are ideal ideal for for powder powder samples samples and and thick thick films films with with no no preferred preferred orientation. orientation. Focusing Focusing configuration: configuration: very very sensitive sensitive to to sample sample displacement displacementerrors errors 39 Example: Glancing angle x-ray analysis Poly-Si (~ 100 nm) Si(001) substrate Substrate Substrate Glancing angle Conventional 2θ/θ XRD 2-theta (degrees) 40 20

Grazing incidence x-ray analysis Depth from surface (Å) 2θ detector XRD penetration depth surface normal (hkl) ω α (Incidence angle) / (critical angle) sample x-ray source Grazing incidence X-ray scattering (GIXS) analysis uses low angle of x-ray beam incidence relative to the surface in order to enhance diffraction from very thin layers. Analysis of ultra-thin films (<10 nm), nanostructures or topmost surface regions of the material. Allows structure determination and quantification of lattice parameters, rocking curve widths and crystallite size along the surface direction (different from conventional XRD, which probes surface normal directions). GIXS from a ScN thin film on MgO (001): The results allow the determination of in-plane lattice parameter and crystallite size; Notice the differences in the relative intensities of the film and substrate peaks at different in-plane angles of incidence α. Intensity (a. u.) Angle of incidence: 0.50 1.00 1.40 1.80 2.25 2.75 Data: Sardela, Shin, Petrov, Greene et al, UIUC ScN(220) MgO(220) 57 58 59 60 61 62 63 64 65 2θ ( o ) 41 Texture and preferred orientation methods Preferred orientation Texture / Preferred orientation: anisotropy of grain orientation distribution. Are the grain orientations distributed randomly? Or is there a preferred orientation? What is the preferred orientation? What is the % of random grains? How strong and sharp is the texture? For film / substrate systems: what is the crystallographic orientation between the substrate and the layers? 42 21

Determination of preferred orientation Crystalline grains in a material may be preferentially distributed along one orientation (preferred orientation). This may complicate the analysis using conventional XRD methods derived from powder techniques. Methods: 1. 1. Compare Compare relative relative peak peak height heightor or area areaobtained from from a 2θ/θ 2θ/θscan with with the the expected expected relative relative intensity intensity from from a standard standard (same (same material) material) with with no no preferred preferred orientation orientation (~ (~ powder): powder): Lotgering Lotgering factors. factors. 2. 2. Use Use the the relative relative intensity intensitymethod above above combined combined with with March-Dollase March-Dollasepreferred orientation orientation corrections corrections to to obtain obtain % grains grains that that are are more more oriented oriented in in a specific specific direction. direction. 3. 3. Use Use the the rocking rocking curve curveanalysis of of a strong strong film film diffraction. diffraction. The The width width of of the the rocking rocking curve curve peak peak is is used used as as texture texture parameter. parameter. 4. 4. Perform Perform pole pole figures figuresto to determine determine the the presence presence of of grains grains of of a a certain certain orientation orientation in in all all sample sample directions. directions. 5. 5. Use Use multiple multiple pole pole figures figures from from multiple multiple orientations orientations to to obtain obtain Orientation Orientation Distribution Distribution Functions: Functions: % of of grain grain orientation orientation distributions distributions in in all all wafer wafer directions. directions. 43 X-ray pole figure analysis of textured materials Texture results from a rolled Cu foil (111) Pole figures ψ φ 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. detector 2θ φ sample ω x-ray source ψ Φ 2 Orientation distribution function (ODF) Inverse pole figures Φ 1 Φ ψ φ Data: Sardela, UIUC Φ 44 22

Pole plot projections Equatorial plane Pole Wulff projection (stereographic or equal-angle projection) Side view (normal to equatorial plane) O ψ r W Equatorial plane O Schmidt projection (equal-area projection) A ψ B r S AB = AS Side view (normal to equatorial plane) Top view (parallel to equatorial plane) O W φ O S φ Top view (parallel to equatorial plane) OW = r tan(ψ/2) OS = 2 r tan(ψ/2) 45 Surface normal φ Basics of pole figure analysis ψ Example: (100) cubic crystal φ Pole figure plot ψ hkl hkl ψ(radial / tilt) φ (azimuthal rotation) (100) Pole figure (111) Pole figure (110) Pole figure 0-1 0 φ φ φ ψ 1-1 0-1 -1 1 1-1 1-1 -1 0 ψ 0-1 1 ψ -1 0 0 0 0 1 1 0 0 1 1 1-1 0 1-1 1 1 0 1 1 1 0 1-1 1 0 1 1 0 0 1 0 Azimuth φ= 0, 90 o, 180 o, 270 o Tilt ψ= 0, 90 o ψ: [100],[100] Azimuth φ= 45 o, 135 o, 225 o, 315 o Tilt ψ= 54.7 o ψ: [100],[111] Azimuth φ= 0, 90 o, 180 o, 270 o,45 o, 135 o, 225 o, 315 o Tilt ψ= 45 o,90 o 46 ψ: [100],[110] 23

Basics of pole figure analysis Surface normal φ hkl (100) Pole figure φ ψ 0 0 1 0 1 0 Azimuth φ= 30 o, 150 o, 270 o Tilt ψ= 54.7 o ψ Example: (111) cubic crystal φ Pole figure plot ψ hkl ψ(radial / tilt) φ (azimuthal rotation) (111) Pole figure (110) Pole figure φ φ 0-1 1 ψ 1-1 1 ψ -1 0 1 1 0 1 1 0 0 1 1 1-1 1 1 0 1 1 1 1-1 -1 1 0 1 1 0 1-1 0-1 0 1 0 1-1 ψ: [111],[100] Azimuth φ= 90 o, 210 o, 330 o Tilt ψ= 0, 70.5 o ψ: [111],[111] Azimuth φ= 60 o, 120 o, 240 o, 300 o, 90 o, 210 o, 330 o. Tilt ψ= 35.3 o, 90 o ψ: [111],[110] 47 Example: Cu thin film on Si (001) substrate Conventional 2θ/θ scan: Fiber texture analysis Cu(111) Si Grains: 56 nm Cu(222) 48 24

Example: Cu thin film on Si (001) substrate Conventional 2θ/θ scan: Fiber texture analysis ψ = 70.53 o (111) Pole figure: Cu(111) Grains: 56 nm Si ψ = 0 (200) (200) Pole figure: (220) (311) ψ = 54.74 o Cu(222) All grains are <111> oriented along the film growth direction. Grains are randomly oriented along the surface 49 Fiber texture analysis 2θ Detector Sample ω ψ <111> (111) Fiber plot Cu film on Si (001) substrate HWHM: 1.09 o (texture sharpness) Data after background subtraction <111> Fiber texture: Texture direction X-ray source 3.5% <5 7 13>+<112> +<225> twinning 4.6% <511> twinning Random Random 9.0% random grains Random Random 50 25

Residual stress analysis methods Residual stress? How much? (MPa GPa) Type? Direction (s)? Stress gradients? 51 X-ray analysis of residual stress a unstressed stressed Film Normal L Incident φ,ψ X-rays ψ Reflected X-rays film surface ψ a ψ a 0 σ φ θ Tilt ψ: +60 o Interplanar spacing d (Angstroms) 1.173 1.172 1.171 1.170 1.169 1.168 Stress = -199 MPa Δd/d = σ [(1+ν)/E] sin 2 ψ 0.0 0.2 0.4 0.6 0.8 sin 2 (ψ) Stress results from a steel sample Diffracting planes Intensity (a.u.) +45 o +30 o +15 o 0-15 o -30 o -45 o -60 o 79 80 81 82 83 84 85 2-theta ( o ) Quantification of residual stress. Compressive (-) and tensile (+) stress. Crystallographic orientation of stress. Sin 2 ψ and RIM methods. ψ and ω scan methods. New glancing angle method (texture). Determination of stress tensor. Requires crystallinity (no amorphous). Data: Sangid et al, UIUC 52 26

Residual stress analysis: the sin 2 ψ method a unstressed stressed Incident X-rays Film Normal ψ L φ,ψ Reflected X-rays film surface ψ a ψ a 0 σ φ θ Diffracting planes a ψ (Å) 4.55 4.54 4.53 2ν sin 2 ψ = 4.52 1 + ν 4.51 HfN 1.05 /SiO 2 δ = -0.03074 ξ = 4.54521 a [ ] ξ 0.0 0.2 0.4 0.6 0.8 1.0 sin 2 ψ ε ψ aψ ao = a o 1+ ν = σ E φ 2 2ν sin ψ σφ E aoσφ 2 2 aψ = (1 + ν)sin ψ 2ν + ao = δsin ψ + E 2δν a o = ξ + = 4.533 Å 1+ ν Eδ σφ = = 1.47 GPa (Compressive) 2δν + (1 + ν) ξ 53 Data: Petrov et al, UIUC High resolution XRD methods Single crystals: α γ b Accurate measurements of a, b, c, α, β, γ a β c Detailed peak shapes: defects, mosaicity. a + Δa Film / substrate epitaxial systems: Measure small variations Δa, Δc, (~ 10-5 ). c + Δc Measure layer tilts Δφ,... c Δφ Detailed peak shapes: defects, strain, mosaicity. a 54 27

Instrument resolution in reciprocal space Beam angular divergence, detector acceptance and diffractometer sampling volume Diffracted beam sample ω Incident beam Angular acceptance of the secondary optics Diffractometer sampling volume 2θ ω Primary beam divergence (from primary optics) Ewald sphere 55 Instrumentation: high resolution configuration 3-bounce analyzer crystal Lower detector (triple axis: 12 arc-sec acceptance) 2θ φ sample ψ ω Δθ =12 arc-sec Δλ/λ = 5x10-5 4-reflection Ge(220) monochromator Crossed slits (variable slit+mask) Programmable attenuator Upper detector (open: < 1 o acceptance) slit x-ray mirror x-ray source slit High resolution configuration with mirror and 4-reflections monochromator Line focus; Parabolic x-ray mirror; 4-reflection monochromator (12 arc-sec resolution); Open detector or analyzer crystal. CMM instrument: Panalytical X pert #1 XRD system 56 28

Instrumentation: high-resolution configuration 3-bounce analyzer crystal Lower detector (triple axis: 12 arc-sec acceptance) 2θ φ sample ψ ω Δθ =30 arc-sec Programmable attenuator Upper detector (open: < 1 o acceptance) Hybrid Mirror (2-bounce monochromator + X-ray mirror) Mask x-ray source slit High resolution configuration with hybrid mirror Line focus; Hybrid mirror (30 arc-sec resolution); Open detector or analyzer crystal. CMM instrument: Panalytical X pert #2 XRD system 57 High resolution x-ray analysis High resolution methods using multi-reflection monochromator and possibly analyzer crystal (Δθ = 0.003 o ). Sensitive to lattice distortions within 10-5. Rocking curve analysis. Film thickness measurements. Strain relaxation and lattice parameter measurements. Determination of alloy composition and superlattice periods. Dynamical scattering simulation to determine composition variations and interface smearing in heterostructures. Single crystals Epitaxial films Heterostructures Superlattices Quantum dots InAs / GaAs multilayer Data: Wu et al, UIUC SiGe / Ge superlattice Data: Sardela, UIUC InAs quantum dots on GaAs Data: Zhang et al Log intensity (a.u.) Log intensity (a.u.) Log intensity (a.u.) 58 60 62 64 66 68 2-theta / omega ( o ) 62 64 66 68 70 2-theta / omega ( o ) 62.5 63.0 63.5 64.0 64.5 2-theta / omega ( o ) 58 29

High resolution x-ray analysis Example: strained In x Ga 1-x As on GaAs (001) substrate Lattice structure High resolution 2θ/θ scan near GaAs(004) In x Ga 1-x As (004) GaAs (004) Thickness fringes a film > a substrate a // film = a substrate (004) In x Ga 1-x As (004) GaAs Δa a 0.07 o = sin θ(substrate) -1 sin θ(film) 0.04 o Thickness = λ 2 Δθ cosθ a substrate Data: Sardela 59 Sample: Highland, Cahill, Coleman et at, UIUC High resolution x-ray analysis Example: strained In x Ga 1-x As on GaAs (001) substrate High resolution 2θ/θ scan near GaAs(004) and dynamical scattering simulation In x Ga 1-x As (004) GaAs (004) Lattice structure a film > a substrate a // film = a substrate (004) In x Ga 1-x As (004) GaAs 0.76 at% In 243 nm Takagi-Taupin dynamical scattering simulation a substrate Data: Sardela 60 Sample: Highland, Cahill, Coleman et at, UIUC 30

substrate High resolution reciprocal space mapping No strain relaxation: film a // = a s a s a High resolution reciprocal lattice mapping requires multireflection 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. Strain relaxation: a a // a s a s film substrate (224) substrate (224) film thickness fringes film Δq 110 0.1 nm -1 0.1 nm -1 Si 1-x Ge x on Si(001) Δq 001 Data: Sardela et al substrate Mosaicity (diffuse scattering) Si 1-x Ge x on Si(001) 61 High resolution reciprocal space mapping Layer structure Strained Si (top layer, very thin) Relaxed Si 1-x Ge x (thick, many microns) Example: strained Si layer on Si 1-x Ge x / Si substrate Si(001) substrate Lattice structure Strained Si Relaxed Si 1-x Ge x (virtual substrate) Si(001) substrate (004) (224) Strain? Lattice distortion? % of relaxation? at % of Ge? Defects? Δq Reciprocal lattice (004) (224) Strained Si Si substrate Si 1-x Ge x Δq // 62 31

High resolution reciprocal space mapping High resolution 2θ/θ scan near Si(004) Layer structure Strained Si (top layer, very thin) Relaxed Si 1-x Ge x (thick, many microns) Si 1-x Ge x Si substrate Example: strained Si layer on Si 1-x Ge x / Si substrate Strained Si Si(001) substrate Lattice structure Strained Si Strain? Reciprocal lattice (004) Lattice distortion? (004) (224) Relaxed Si 1-x Ge x (virtual substrate) (224) % of relaxation? at % of Ge? Δq Strained Si Si substrate Si(001) substrate Defects? Si 1-x Ge x Δq // 63 High resolution reciprocal lattice map Strained Si (top layer) Relaxed Si 1-x Ge x Si(001) substrate Map near Si(224) 0.1 nm -1 [001] [110] Data: Sardela Sample: Zuo, UIUC 64 32

High resolution reciprocal lattice map Strained Si ε = - 0.77% ε // = 0.64 % Si substrate Strained Si (top layer) Relaxed Si 1-x Ge x Si(001) substrate 4.60 at% Ge 7.52 at% Ge Map near Si(224) 11.45 at% Ge Relaxed Si 1-x Ge x 18.70 at% Ge 100% strain relaxation 0.1 nm -1 [001] [110] Data: Sardela Sample: Zuo, UIUC 65 High resolution reciprocal lattice map Finite size Composition and strain gradients Strained Si (top layer) Relaxed Si 1-x Ge x Si(001) substrate Map near Si(224) Analyzer streaks Mosaicity and dislocations Coherent length in any direction: 2π / Δq i i = x, y, z, //, 0.1 nm -1 [001] [110] Data: Sardela Sample: Zuo, UIUC 66 33

High resolution reciprocal lattice map Finite size Vertical coherent length: 14 nm Composition and strain gradients Strained Si (top layer) Relaxed Si 1-x Ge x Si(001) substrate Map near Si(224) Analyzer streaks Mosaicity and dislocations Misfit dislocations: average separation : 21 nm density: 5 x 10 5 cm -1 0.1 nm -1 [001] [110] Coherent length in any direction: 2π / Δq i i = x, y, z, //, Data: Sardela Sample: Zuo, UIUC 67 Comparison with TEM EDS line scan Data: Zuo s group, UIUC 68 34

The shape of the reciprocal lattice point 004 ω scan 224 Changes in lattice parameter (radial direction) Lateral sub-grain boundaries (along q // ) [001] 000 (ω/2θ) scan [110] G 224 CTR, finite layer thickness, superlattice (along q ) Mosaicity, curvature, orientation (circumferential direction) 69 X-ray reflectivity methods Bulk materials: Near surface region Liquids: Multilayered systems: Near surface and interface information on: Density Porosity Roughness Thickness in films (ultra thin to thick) Amorphous or crystalline materials 70 35

X-ray reflectivity Angle of incidence relative to the surface (omega or theta) Incident x-ray beam Sample Scattered x-ray beam Detector Detector rotation: angle 2-theta Log Reflectivity R Critical angle θ c R ~ θ -4 Thickness fringes Δθ = λ/[2*(thickness)] decay ~ roughness ΔI ~Δ ρ e θ One sharp interface (density ρ e variation: δ function at interface) θ One rough interface ( broad ρ e variation at interface) Two interfaces Intensity Angle ω, θ or 2θ 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, roughness correlation and film porosity. Very sensitive to density variations. Determination of critical angle, refractive index and density. 71 X-ray reflectivity analysis of thin films Log intensity (a.u.) Ultra-thin 2.3 nm thick polymer on Si Log intensity (a.u.) Complex multilayers Data: Sardela, UIUC Sample: Auoadi et al, SIU n=1 2 3 4 Metallic multilayer Log intensity (a.u.) Non crystalline Amorphous PZT film 0 2 4 6 8 10 12 2-theta ( o ) Data: Heitzman et al, UIUC Intercept: refractive index η 2 4 6 8 10 12 2-theta ( o ) sin 2 θ Slope: periodicity d n 2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Theta ( o ) Data: Mikalsen et al, UIUC sin 2 θ = (λ 2 /2d) 2 n 2 (η 2-1) (modified Bragg s law to include refractive index) 72 36

X-ray reflectivity information content Critical angle: density, porosity θ critical = (2δ) 1/2 Refractive index = 1-δ+iβ Reflectivity intensity (counts per sec.) Thickness (Kiessig) fringes: angular separation between oscillations gives thickness Slope / shape of the decay of the curve: used to quantify interface roughness in all interfaces t = (λ/2) / (sinθ 2 sinθ 1 ) = ~ (λ/2) / Δθ Two sets of oscillations: gives thickness of two layer structure Amplitude of fringes: interface roughness, density variations Angle of incidence (degrees) 73 X-ray reflectivity from superlattices Example: 20 periods [1 nm SiO 2 / 1 nm Si ] superlattice on Si wafer Reflectivity intensity (counts per sec.) Critical angle: gives density of each layer in the superlattice (model dependent) Thickness fringes: angular separation gives total superlattice thickness Number of fringes gives the total number of layers in the superlattice Superlattice main peaks: angular separation gives period thickness Slope: gives interface roughness for each layer in the superlattice (model dependent) Angle of incidence (degrees) 74 37

X-ray reflectivity data fitting in ultra-thin films Polymer (few nm) 1,3,5-tribromo-2-nanyloxybenze: C 15 H 21 Br 3 SiO 3 SiO 2 (~ 100 nm) Si substrate SiO 2 thickness Polymer thickness Data: Sardela Sample: Zhang, Rogers et al, UIUC 75 X-ray reflectivity data fitting rms: 0.26 nm rms: 0.45 nm rms: 0.24 nm Best fit Polymer 2.0 nm, 1.30 g/cm 3 SiO 2 98.9 nm, 2.19 g/cm 3 Si substrate Data Best fit 76 38

X-ray reflectivity data fitting Fitting sensitivity to the polymer thickness (best fit: 2.00 nm) 2.2 nm (+ 10 %) simulation Data 1.8 nm (- 10 %) simulation 77 X-ray reflectivity data fitting Fitting sensitivity to the polymer top roughness (best fit: 0.26 nm) 0.2 nm (- 0.06 nm) simulation Data 0.4 nm (+ 0.14 nm) simulation 78 39

X-ray reflectivity data fitting Data Fitting sensitivity to the polymer density (best fit: 1.3 g/cm 3 ) 1.4 g/cm 3 (+ 8 %) simulation 1.2 g/cm 3 (- 8 %) simulation 79 X-ray reflectivity: summary * Non Non destructive destructive method method ** Applicable Applicable to to whole whole wafers wafers (wafer (wafer mapping mapping option) option) ** Fast Fast method method (in (in most most cases) cases) ** Do Do not not depend depend on on crystalline crystalline quality quality of of the the films films (can (can also also be beused in in amorphous amorphous layers). layers). Quantification Quantification of: of: ** Layer Layer thickness thicknessin in thin thin films films and and superlattices: superlattices: 1 nm nm ~ 1 μm μm (± (± 0.5-1%). 0.5-1%). ** Layer Layer density densityand and porosity porosity (± (± 1-2%). 1-2%). ** Interface Interface roughness: roughness: 0.1 0.1 10 10 nm nm (model (model dependent; dependent; reproducibility reproducibility ~ 3%). 3%). ** Layer Layer density density gradients gradients (variations (variations > 2%). 2%). ** Interface Interface roughness roughness correlation correlationin in superlattices superlattices and and multilayers. multilayers. Alternative techniques: * Thickness: optical methods (TEM, SEM) poor contrast issues. * Density: RBS (issues for ultra thin layers). * Interface roughness: AFM (surface only not buried interfaces). 80 40

X-ray fluorescence methods Bulk materials: Liquids: Which elements are present down to ppm levels? What is the elemental composition (%)? Fast, accurate. Liquids, solids, amorphous, crystalline materials. Multilayered systems: 81 X-ray fluorescence (XRF) Data: Panalytical (www.panalytical.com) K Kα 2 Kα1 Kβ 1 L I L II L III M I M II M III M IV M V Transition notation: Lα 1 Lα 2 Lβ 1 IUPAC: <element>< hole shell>< originating shell> Ex.: Cr-KL III Intensity (a.u.) Siegbahn: <element>< hole shell><α,β,γ, etc.> Ex.: Cr-Kα 1 (for L III to K transition in Cr) Ti-Kα Mn-Kβ 1 1 Fe-Kα 1 K-Kα Ba-Lα 1 1 Fe-Kβ 1 K-Kβ 1 Energy (kev) Typical Typical plot: plot: Intensity Intensity vs. vs. Energy. Energy. Line Line position position associated associated to to element element and and specific specific transition transition Line Line positions: positions: fingerprint fingerprint of of the the element. element. Element Element identification identification Na-U Na-U or or Be-U. Be-U. Peak Peak assignment assignment uses uses database database and and search/match. search/match. Peak Peak area/height: area/height: composition composition (sub (sub ppm ppm to to 100%). 100%). Peak Peak overlap overlap requires requires deconvolution. deconvolution. Composition Composition determination determination requires requires standards, standards, calibration. calibration. Fast Fast data data acquisition acquisition (seconds (seconds to to ½ hr). hr). Solids, Solids, liquids, liquids, powders, powders, thin thin films, films, Minimum Minimum or or no no sample sample preparation preparation required. required. 82 41

EDXRF and WDXRF X-ray tube Energy Dispersive XRF (EDXRF) Sample Peak assignment: search/match software Concentration: down to sub-ppm Secondary target Detector Wavelength Dispersive XRF (WDXRF) Sample X-ray tube Analyzer crystal Collimator Detector 2θ Energy resolution: 5-20 ev (WDXRF) 150-300 ev (EDXRF) Data: Horiba Jobin Yvon http://www.jyinc.com/spain/esdivisions/xray/tutorial.htm 83 EDXRF and WDXRF EDXRF WDXRF Dispersive system Raw data Basic set up Elemental Range Detection limit Sensitivity Resolution Cost Measurement Moving parts Detector Qualitative analysis Energy Intensity vs. Energy (kev) X-ray tube (Secondary Target) Sample Detector Na U Good for heavier elements (less optimum for light elements) Good for heavier elements (less optimum for light elements) Good for heavy elements (less optimum for light elements) Moderate Simultaneous No Solid state detector Peak area Wavelength Intensity vs. Detector angle (2θ). X-ray tube Sample Collimator ( for // beam) Analyzer Crystal Detector (+ goniometer) Be U Good for all range Moderate for light elements. Good for heavy elements. Good for light elements (less optimum for heavy elements) Relatively expensive Sequential (moving detector on goniometer) Simultaneous (fixed detector) Crystal, goniometer Gas-filled (for Be Cu) Scintillation (for Cu U). Peak height 84 42

Basic EDXRF system configuration Automatic 16 samples changer Ta or Ag collimator Si (Li) detector Filter Automatic secondary target changer Automatic filter changer Two configurations: --- direct collimated --- secondary target Automatic x-ray tube position changer CMM instrument: Kevex Analyst 770 XRF system * * X-ray X-ray tube: tube: Rh Rh (side (side window) window) 3.3mA, 3.3mA, 60kV. 60kV. * * Secondary Secondary targets: targets: Gd, Gd, Sn, Sn, Ag, Ag, Ge, Ge, Fe, Fe, Ti. Ti. * * Filter: Filter: Gd Gd (6 (6 mil), mil), Sn Sn (4 (4 mil), mil), Ag Ag (2 (2 mil). mil). * * Detector Detector collimators: collimators: Ag, Ag, Ta. Ta. * * Samples: Samples: 16 16 samples samples up up to to 2 2 diameter, diameter, or or 2 2 square square mounts, mounts, or or 1.25 1.25 diameter diameter (inserts). (inserts). * * Detector: Detector: Si Si (Li) (Li) 30mm 30mm 2 2 active active area. area. * * Energy Energy resolution resolution ~ ~ 165 165 ev. ev. 85 XRF application Spectroscopy investigation of icons painted on canvas Lj. Damjanovic et al, Belgrade http://www.srs.ac.uk/scienceandheritage/prese ntations/olgica_marjanovic.pdf Surface sample: Original made of Au. Restoration with Au imitation Schlagmetal (Cu and Zn). Fe: natural Fe-Al-silicate red bole used for gilding the icon. The Virgin and the Child, Unknown author Museum of the Serbian Orthodox Church, Belgrade XRF and IR results show pigments and binders widely used in the XIX century confirming that the work is from late XIX to XX centuries Frame sample: Cu and Zn (no Au) -> Schlagmetal 86 43

Information contents Detection limits Depth information Lateral resolution Angular resolution Sample requirement X-ray analysis summary % of crystallinity and amorphous contents Identification and quantification of phases and mixtures Chemical information (if crystalline) Texture (type and strength) and fraction of random grains Grain / crystallite size (> 2 nm) Strain (> 10-5 ) Stress (type, direction and value) Relative crystallographic orientation Lattice constants and unit cell type Structure determination Thickness (1.5 nm 3 mm) Roughness (including buried interfaces) Density and porosity Relative fraction of domains Defects and dislocation densities Mosaic tilts and sizes > 0.1 0.5 w% Up to 20 50 mm (typical) > 10 nm and variable with glancing angle XRD ~ a few cm (typical) 10 mm (microdiffraction) 5 cm 0.1 o 2q (typical powder diffraction) 0.003 o 2q (high resolution methods) Mostly non destructive Sample sizes from ~ 50 mm to many cm No vacuum compatibility required Solids, liquids, gels * Semiconductors * Coatings * Pharmaceutical Cements * Metals * Ceramics * Geology * Archeology * Biosciences * Forensics * Medical applications * Nanotechnology * Polymers * Food science * Combustion * Energy * 87 Comparison with other techniques X-ray analysis methods Other techniques Sample preparation and vacuum compatibility Composition and impurity determination and quantification Lattice constants Thickness in thin films Grain size o No vacuum compatibility required (except XRF on vacuum). o Any sample size (depends on the goniometer size/weight capability). o Rough surfaces acceptable (parallel beam configuration). o No sample preparation required (prep recommended for the detection of unknown phases or elements in XRD/XRF). ~ 0.1 w % (XRF > ppm); may require standards. XRD: also phase information and % of crystallinity. Data averaged over large lateral area. o Better than within 10-5 HR-XRD or XRR: direct measurement (no modeling for single or bi-layers). Requires flat interfaces. o Measures Crystallite Size. o Typically ~ 1-2 nm microns, requires size/strain assumptions/ modeling. o Volume average size. o Surface analysis and electron microscopy techniques will require vacuum compatibility and in many cases sample preparation. o Optical techniques will do analysis on air. XPS: > 0.01 0.1 at % (may require depth profiling). SIMS: > 1 ppm (requires sputtering depth profiling). EDS: > 0.1 1 w % over small volume 1μm 3. Little with phase information; averages over small lateral areas (< 100 μm). o TEM: estimates ~ 10-3 RBS: > 10 nm (requires modeling). Ellipsometry: requires modeling. TEM: requires visual contrast between layers. o SEM: grain size distribution averaged over small area. o TEM/SEM: number average size. 88 44

Comparison with other techniques X-ray analysis methods Other techniques Texture Residual Stress Depth dependent information Surface or Interface roughness Defects Instrument cost o Type and distribution averaged over large sample volume. 10 MPa, averaged over large sample volume (large number of grains). Needs crystallinity. Measures strain and obtains stress from Hooke s law. Averages macro and micro stresses over large area of a layer. Phase, grain sizes, texture and stress depth profiling requires x-ray information depth modeling XRR: interface roughness 0.01 5 nm, including buried interfaces Misfit dislocations (HR-XRD). Point defects (diffuse scattering with model). Extended defects (powder XRD with model). Average over larger sample area (> mm). Portable instruments ~ $ 60 K. Average well-equipped: ~ $ 200 300 K. Top of the line ~ $ 500 K (including microdiffraction and 2D detectors). o EBSD: within grain sizes dimensions, better sensitivity at the surface. Wafer curvature: No need for crystallinity. Direct measurement of stress, but only interlayer stress between film and substrate (macrostress). Surface analysis depth profiling: compositional depth profiles. SPM: top surface only; rsm~ 0.01-100 nm. TEM: accurate identification of defects and their densities; average over small sample area. Sample preparation may introduce artifacts. Surface analysis instruments > $ 500 K. Electron microscopes ~ $ 300 K 1 M. RBS ~ $ 2 M. Raman, ellipsometry > $ 100 K. 89 Amazing x-ray samples Pieces from Egyptian mummy Powder from Inca ruins Corrosion in pipes from IL water supply Rocks from Mississippi river Mud from a cadaver s shoes Dove chocolate Corn starch Train tracks Heavy machinery valves 100 μm micro chips 10 μm superconductor single crystal Next generation CPU processors Micro extraction from Dutch paintings Virus, bacteria, DNA, proteins Powder from Mars terrain Gasoline, electrical car battery Bone implants Pork tissue 90 45

Amazing x-ray samples W. C. Roetgen wife s hand (1895) Science and Society Picture Library / Science Museum A. Bertha Roetgen (1833-1919) Wedding ring It frightened Bertha terribly as a premonition of death After Boston Globe 11/6/95 W.C. Roetgen (1845-1923) 1 st Physics Nobel 91 Quick guide to our x-ray analysis instruments (1) X-ray analysis instrumentation available as user facility in the FS-MRL Instrument Panalytical X pert (#1) Panalytical X pert (#2) Set up Source:Cu Kα1, line or point focus. High resolution configuration. 4 or 2 reflection Ge monochromator (12 or 30 arc-sec parallel beam). 3 reflection Ge analyzer crystal (12 arc-sec parallel beam). Eulerian cradle. Proportional detectors. Source:Cu Kα1+Kα2, line or point focus. Crossed slit collimator (variable aperture). X-ray lens. Programmable divergence slit. Eulerian Cradle. Parallel plate collimator and flat graphite monochromator Programmable receive and scatter slits and graphite monochromator. Proportional detectors. Applications High resolution XRD capabilities. Rocking curve. Single crystals, epitaxial systems. Reciprocal space mapping. Reflectivity. Curvature, wafer mapping, miscut, diffuse scattering. Topography. Glancing angle. Parallel beam applications. Max sample size: 10 cm diameter x 2 cm thick..phase, size, strain, stress, texture, crystallinity.parallel beam applications.bragg-brentano applications.general thin film analysis.glancing/grazing angle.max sample size: 10 cm diameter x 2 cm thick 92 46

Quick guide to our x-ray analysis instruments (2) X-ray analysis instrumentation available as user facility in the FS-MRL Instrument Rigaku D/Max b Rigaku Laue Set up Source:Cu Kα1+Kα2, line focus. Bragg-Brentano focusing configuration. Theta/2theta goniometer. Divergence, soller, scatter and receiving slits. Curved graphite monochromator. Scintillation detector. Source:Mo point focus. Four circle sample stage (manual). Polaroid film camera detection system. Applications Phase, size, strain, crystallinity. Bragg-Brentano applications. Rietveld analysis. Mostly for powder, bulks and thin film with small preferred orientation. Single crystal orientation. Miscut information. Crystallographic alignment prior to crystal cutting. Bruker / Siemens D5000 (Fall 2008) Kevex Analyst 700 XRF Source:Cu Kα1+Kα2, line focus. Bragg-Brentano focusing configuration. Theta / theta goniometer. Horizontal sample load. No sample movement required during analysis. Divergence, scatter and receiving slits. Scintillation detector..source: Rh (side window) 3.3mA, 60kV.6 secondary targets, 2 detector collimators, 3 filters..si (Li) solid state detector..energy resolution 165 mev. Ideal for powder and soft samples (horizontal load). Phase, size, strain, crystallinity. Bragg-Brentano applications. Rietveld analysis. Mostly for powder, bulks and thin film with small preferred orientation..elemental identification: Na U..Liquids, solids, powder samples..composition: > ppm (some standards available). 93 Recommended literature Residual stress and stress gradients: Basic applications of x-ray diffraction: Residual stress and stress gradients: Basic applications of x-ray diffraction: Residual Stress: Measurement by Diffraction and Interpretation, I. C. Noyan X-ray diffraction a practical approach, C. Suryanarayana and M.G. Norton. Residual Stress: Measurement by Diffraction and Interpretation, I. C. Noyan X-ray diffraction a practical approach, C. Suryanarayana and M.G. Norton. and J. B. Cohen, Springer-Verlag, 1987. Introduction to X-Ray Powder Diffractometry, R. Jenkins and R. Snyder, and J. B. Cohen, Springer-Verlag, 1987. Introduction to X-Ray Powder Diffractometry, R. Jenkins and R. Snyder, Residual stress/strain analysis in thin films by X-ray diffraction, I.C. Wiley-Interscience; 1996. Residual stress/strain analysis in thin films by X-ray diffraction, I.C. Wiley-Interscience; 1996. Noyan, T.C. Huang and B.R. York, Critical Reviews in Solid State and Materials X-ray characterization of materials, E. Lifshin, Wiley-VCH, 1999. Noyan, T.C. Huang and B.R. York, Critical Reviews in Solid State and Materials X-ray characterization of materials, E. Lifshin, Wiley-VCH, 1999. Sciences, 20 (1995) 125 177. Sciences, 20 (1995) 125 177. Sample Preparation Methods: Sample Preparation Methods: X-ray analysis of clay minerals: A practical guide for the preparation of specimens for x-ray fluorescence and x- X-ray analysis of clay minerals: A practical guide for the preparation of specimens for x-ray fluorescence and x- X-Ray Diffraction and the Identification and Analysis of Clay Minerals, D.M. ray diffraction analysis, V.E. Buhrke, R. Jenkins and D.K. Smith; Wiley-VCH, X-Ray Diffraction and the Identification and Analysis of Clay Minerals, D.M. ray diffraction analysis, V.E. Buhrke, R. Jenkins and D.K. Smith; Wiley-VCH, Moore and R.C. Reynolds, Oxford University Press, 1997. 1998. Moore and R.C. Reynolds, Oxford University Press, 1997. 1998. X-ray fluorescence: Rietveld Analysis: X-ray fluorescence: Rietveld Analysis: Quantitative x-ray spectrometry, R. Jenkins, R.W. Gould and D. Gedcke, The Rietveld Method ed. By R.A. Young, Oxford Press, 2000. Quantitative x-ray spectrometry, R. Jenkins, R.W. Gould and D. Gedcke, The Rietveld Method ed. By R.A. Young, Oxford Press, 2000. Marcel Dekker Inc, 1995 Marcel Dekker Inc, 1995 Quantitative x-ray fluorescence analysis theory and application, G.R. Lachance Thin Analysis by X-ray: Quantitative x-ray fluorescence analysis theory and application, G.R. Lachance Thin Analysis by X-ray: and F. Claisse, Willey, 1995. Thin Films Analysis by X-ray Scattering, M.Birkholz, Wiley-VCH, 2006 and F. Claisse, Willey, 1995. Thin Films Analysis by X-ray Scattering, M.Birkholz, Wiley-VCH, 2006 Laue methods: High-resolution X-ray analysis: Laue methods: High-resolution X-ray analysis: Laue Method, J.L. Amoros, Academic Press Inc., 1975. X-ray scattering from semiconductors, P. Fewster, Imperial College, 2001. Laue Method, J.L. Amoros, Academic Press Inc., 1975. X-ray scattering from semiconductors, P. Fewster, Imperial College, 2001. High Resolution X-Ray Diffractometry And Topography, D.K. Bowen and B. High Resolution X-Ray Diffractometry And Topography, D.K. Bowen and B. Two-dimensional XRD (with areal detectors): K. Tanner, CRC, 1998. Two-dimensional XRD (with areal detectors): K. Tanner, CRC, 1998. Microdiffraction using two-dimensional detectors, B.B. He, Powder Diffraction High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures Microdiffraction using two-dimensional detectors, B.B. He, Powder Diffraction High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures 19 (2004) 110-118. (Advanced Texts in Physics), U. Pietsch, V. Holy and T. Baumbach, Springer; 19 (2004) 110-118. (Advanced Texts in Physics), U. Pietsch, V. Holy and T. Baumbach, Springer; 2004. 2004. Fundaments of x-ray scattering: Fundaments of x-ray scattering: X-ray diffraction, B.E. Warren, Addison-Wesley, 1962. Industrial applications of x-ray analysis: X-ray diffraction, B.E. Warren, Addison-Wesley, 1962. Industrial applications of x-ray analysis: X-ray diffraction procedures for polycrystallines and amorphous materials, H.P. Industrial Applications of X-Ray Diffraction by F. Smith (Editor), CRC, 1999. X-ray diffraction procedures for polycrystallines and amorphous materials, H.P. Industrial Applications of X-Ray Diffraction by F. Smith (Editor), CRC, 1999. Klug and L.E. Alexander, Wisley-Interscience, 1974. X-Ray Metrology in Semiconductor Manufacturing, D.K. Bowen and B.K. Klug and L.E. Alexander, Wisley-Interscience, 1974. X-Ray Metrology in Semiconductor Manufacturing, D.K. Bowen and B.K. Elements of x-ray diffraction, B.D. Cullity, Addison-Wesley, 1978. Tanner, CRC, 2006. Elements of x-ray diffraction, B.D. Cullity, Addison-Wesley, 1978. Tanner, CRC, 2006. Elements of Modern X-ray Physics, J. Als-Nielsen (Author), D. McMorrow, Elements of Modern X-ray Physics, J. Als-Nielsen (Author), D. McMorrow, Wiley, 2001. Glancing/grazing incidence methods and reflectometry: Wiley, 2001. Glancing/grazing incidence methods and reflectometry: Coherent X-Ray Optics (Oxford Series on Synchrotron Radiation), D. Paganin, Thin film and surface characterization by specular X-ray reflectivity, E. Coherent X-Ray Optics (Oxford Series on Synchrotron Radiation), D. Paganin, Thin film and surface characterization by specular X-ray reflectivity, E. Oxford University Press, 2006. Chason and T. M. Mayer, Critical Reviews in Solid State and Materials Oxford University Press, 2006. Chason and T. M. Mayer, Critical Reviews in Solid State and Materials Sciences, 22 (1997) 1 67. Sciences, 22 (1997) 1 67. Web resource: www.ccp14.ac.co.uk (free x-ray data analysis programs and Review on grazing incidence X-ray spectrometry and reflectometry, K.N. Web resource: www.ccp14.ac.co.uk (free x-ray data analysis programs and Stoev Review and K. on Sakurai, grazing incidence Spectrochimica X-ray Acta spectrometry B: At Spectros, and reflectometry, 54 (1999) 41-82. K.N. tutorials) tutorials) Stoev and K. Sakurai, Spectrochimica Acta B: At Spectros, 54 (1999) 41-82. 94 47

Acknowledgements Sponsors: Frederick Seitz Materials Research Laboratory is supported by the U.S. Department of Energy under grants DEFG02-07-ER46453 and DEFG02-07-ER46471 95 48