X-ray analysis methods Mauro Sardela, Ph.D. Frederick Seitz Materials Research Lab. University of Illinois at Urbana-Champaign

Transcription

1 Advanced Materials Characterization Workshop June 3 and 4, 2013 X-ray analysis methods Mauro Sardela, Ph.D. Frederick Seitz Materials Research Lab. University of Illinois at Urbana-Champaign

2 X-ray interactions with matter Incident x-ray photons hn 0 Coherent scattering hn 0 hn1 Incoherent scattering Fluorescence hn 2 e - e - Photoelectron Auger electron 2 nm ~30 mm Interaction volume hn: photon e - : electron 10 mm 5 cm Sample X-ray radiation mostly used in lab instruments: Cu radiation g rays X rays UV Visible Cu Ka: l= nm (8.05 kev, conventional resolution) Cu Ka1: (l= nm (high resolution) 2

3 X-ray interactions with matter Coherent scattering (Diffraction, Thompson or Rayleigh scattering) E 0 Photon (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 (1) Incoming photon (2) Energy is partially transferred to electron (3) Scattered photon (energy loss). Auger electron E 0 (1) (2) L shell (3) Nucleus K (4) (5) Electron (6) (1-4) Hole created (3) after photoelectron emission (2) is occupied by outer electron (4). (5) Excitation energy is transferred to electron (6) Electron ejected from atom (Auger electron)

4 Fundaments of diffraction Real space F Reciprocal space Set of planes Point (h k l) d h k l 2p/d origin M. von Laue X-rays from crystals,

5 Fundaments of diffraction Real space F Reciprocal space d 2p/d origin 5

6 Fundaments of diffraction Real space F Reciprocal space origin 6

7 Bragg s law and Ewald s sphere F Real space Reciprocal space Bragg s law Ewald s sphere 2q w q 2q k 1 k 0 (= radius) d sin q = n l Elastic (Thompson s) scattering q = k 1 k 0 q: scattering vector q = (4 p/l) sinq Paul 7 P. Ewald

8 Coupled 2theta-omega scans q X-ray source 2q k 1 w k 0 w 2q Detector d Sample 2q-w scan: Probes d-spacing variation Along q Phases id, composition, lattice constants Grain sizes, texture, strain/stress q 2q k 1 k 0 (= radius)

9 Information contents in the XRD pattern X-ray source Detector w 2q Sample Peak position: identification, structure, lattice parameter Peak width: crystallite size, strain, defects Peak area or height ratio: preferred orientation Peak tails: Diffuse scattering, point defects Background: amorphous contents

10 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. 10

11 Bragg-Brentano focusing configuration Focus Receiving slit Single crystal monochromator (l) X-ray source Divergence slit Detector Focusing circle (variable during measurement) Divergent beam not good for grazing incidence analysis Angle of incidence (w) Secondary Optics: Scatter and soller slits specimen Sample height positioning is critical Detector rotation (2q) Diffractometer circle 11 (fixed during measurement)

12 Ground to fine powder (random grain orientations) + Added amorphous phases (glass) to complicate things

13 Intensity (sqrt counts) XRD powder analysis walkthrough Crystalline phases Amorphous (zero background holder) theta (degrees), Cu K-alpha radiation

14 Intensity (sqrt counts) XRD powder pattern ~ 20 w% amorphous added No amorphous added theta (degrees), Cu K-alpha radiation

15 Intensity (sqrt counts) Peak fit and shape analysis Peak fit: Data + Peak + shape function Instrument resolution FWHM = f (2q) Crystallinity = Σ Peak areas = 81.7 % Total area Amorphous contents = 1 (crystallinity) = 18.3 % theta (degrees), Cu K-alpha radiation

16 Peak position + intensity ratio Search against Search / match ICDD PDF4 database ICSD, etc. Match! Fingerprinting identification of phases Hits Formula FOM PDF RIR Space group Calcite CaCO R-3c(167) Dolomite Ca 1.07 Mg 0.93 (CO 3 ) R-3(148)

17 Peak position + intensity ratio Search against Search / match ICDD PDF4 database ICSD, etc. Match! Fingerprinting identification of phases Hits Formula FOM PDF RIR Space group Calcite CaCO R-3c(167) Dolomite Ca 1.07 Mg 0.93 (CO 3 ) R-3(148)

18 Search / match Second round Focus on unmatched peaks Hits Formula FOM PDF RIR Space group Calcite CaCO R-3c(167) Dolomite Ca 1.07 Mg 0.93 (CO 3 ) R-3(148)

19 Search / match Second round Focus on unmatched peaks Search / Match Identify additional phases (~ > 1 w%) Hits Formula FOM PDF RIR Space group Calcite CaCO R-3c(167) Dolomite Ca 1.07 Mg 0.93 (CO 3 ) R-3(148)

20 Intensity (sqrt counts) Ratio of crystalline phases 1 Quant: RIR reference intensity ratio ( ) ( ) ~ Ratio of peak areas corrected by RIR of each phase RIR ~ I / I corundum 2 Ratio of crystalline phases: Calcite: 79.2 w% Dolomite: 20.8 w% (no amorphous included) theta (degrees), Cu K-alpha radiation

21 Rietveld refinement Non-linear least square minimization For each data point i: H. Rietveld (1932-) Minimize this function: Sum over n data points n data points p phases m Bragg reflections for each data i w i, b i, K l, Y l,j weight, background, scale factor and peak shape function Data + preliminary structure: Refinement parameters: Background Sample displacement, transparency and zero-shift correction Peak shape function Unit cell dimensions Preferred orientation Scale factors Atom positions in the structure Atomic displacement parameters Minimize and converge figures of merit/quality: R

22 Intensity (sqrt counts) Rietveld refinement Peak fit: Data + Peak + shape function Instrument Calcite: resolution 80.7 w% Dolomite: FWHM = f (2q) 22.2 w% Amorphous: 17.1 w% Crystallinity Crystallite Peak areas = Σ size: = 81.7 % Calcite: Total area 56.8 nm Dolomite: 35.6 nm Amorphous = 1 (crystallinity) = 18.3 % contents theta (degrees), Cu K-alpha radiation

23 Intensity (sqrt counts) Rietveld refinement Peak fit: Data + Peak + shape function Instrument resolution FWHM = f (2q) Crystallinity = Σ Peak areas = 81.7 % Total area Amorphous _ Calcite, = 1 (crystallinity) = 18.3 % contents CaCO 3, hexagonal, R3c (167) nm/ nm / nm <90.0/90.0/120.0> theta (degrees), Cu K-alpha radiation

24 Intensity (sqrt counts) Rietveld refinement Peak fit: Data + Peak + shape function Instrument resolution FWHM = f (2q) Crystallinity = Σ Peak areas = 81.7 % Total area Amorphous = 1 (crystallinity) = 18.3 %_ Dolomite, contents Ca 1.07 Mg 0.93 (CO 3 ) 2, hexagonal, R3 (148) nm/ nm / nm <90.0/90.0/120.0> theta (degrees), Cu K-alpha radiation

25 Scherrer s equation: Size = k * l cos (q) * (FWHM) Crystallite size analysis Simplistic approximation! Not accounting for peak broadening from strain and defects k : shape factor ( ) l: x-ray wavelength FWHM: full width at half maximum (in radians) Directional measurement! Measured along the specific direction normal to the (hkl) lattice plane given by the 2q peak position Peak width (FWHM or integral breadth) Measurement Fit Peak position 2q 25

26 Intensity(Counts) Intensity(Counts) Crystallite size analysis Intensity(Counts) 6.5 o 0.5 o 2 nm Fe 3 O 4 nanoparticle 20 nm (111) grains in Cu foil Two-Theta (deg) Two-Theta (deg) 145 nm Si powder 0.17 o Two-Theta (deg) 26

27 Peak shape analysis Peak fit functions: Gaussian Lorentzian Pearson-VII (sharp peaks) Pseudo-Voigt (round peaks) Measurement Information from fit: Position Width (FWHM) Area Deconvolution Skewness Fit Measurement Fit 27

28 Correction for instrument resolution Use FWHM curve as a function of 2q from standard sample (NIST LaB 6 ): specific for each diffractometer FWHM: b b D = (bmeas) D (binstr) D D: deconvolution parameter Measurement Instrument function D : 1 (~ Lorentzian) b = (bmeas) (binstr) D : 2 (~ Gaussian) b 2 = (bmeas) 2 (binstr) 2 D : 1.5 b 1.5 = (bmeas) 1.5 (binstr)

29 Potential artifacts in size determination FWHM: b b D = (bmeas) D (binstr) D For this calculation assume: Instrument resolution ~ 0.15 o 2q = 40 o Cu radiation Measured peak width ( o ) Size, nm D = 1 (Lorentzian) Size, nm D = 1.5 Size, nm D = 2 (Gaussian) Large difference (up to 48%!) for narrow peaks (large sizes) Smaller difference (~ 10%) for broad peaks (small sizes) 29

30 Strain effects in diffraction lines d No strain Macrostrain uniform tensile or compressive stress (lattice expansion or contraction) Uniform strain D(2q) Peak position shift (lattice constant change) Microstrain nonuniform strain (both tensile and compressive stresses) (lattice distortion). Dislocations, vacancies, defects, thermal effects. Nonuniform strain FWHM Peak width change (symmetric broadening) 30

31 Size and strain in peak shape analysis FWHM strain = 4 * (strain) * tan q (FWHM)*cos(q) = kl/(size) + (strain)*sin(q) Williamson-Hall Method Acta Metall. 1 (1953) 22. (FWHM)*cos(q) Intercept ~ 1/(size) Slope ~ micro strain sin(q) 31

32 X-ray parallel beam methods Rough, irregular surfaces Film / Substrate systems a Near surface region Glancing / grazing angle applications. Phase, stress gradients (depth profiles) 32

33 Parallel beam configuration Negligible sample displacement issues (rough and curved samples OK) Specific optics to maximize intensities Detector X-ray source Primary Optics: mirror, slits, lens Parallel plates collimation Single crystal monochromator (l) Parallel beam Detector rotation (2q) Angle of incidence (w) Excellent for glancing angle (fixed w) applications specimen 33

34 Intensity (a.u.) MgO 002 Thin film orientation analysis Intensity (a.u.) 2q/w scan (surface normal direction) -TaN x /MgO(001) t = 500 nm T s = 600 C J i /J Ta = 11 f N2 = TaN 002 -TaN (002) 40 ev, w = 0.95 <001> TaN <001> MgO MgO (002) Example: TaN film MgO(001) substrate Cube on cube epitaxy: (001) TaN //(001) MgO (100) TaN //(100) MgO f scan (in-plane surface direction) (220) f scans TaN MgO <110> <110> -TaN 1.17 /MgO(001) t = 500 nm T s = 600 C 30 ev, w = ev, w = TaN -TaN 8.5 ev, w = q (deg) Data: Shin, Petrov et al, UIUC MgO f (deg) MgO

35 Glancing angle x-ray analysis Detector X-ray source 2q w (fixed) 2q w Sample surface normal grains w constant (~ o ) + : conventional Bragg-Brentano configuration 2q-w scans probe only grains aligned parallel to the surface : parallel-beam glazing incidence configuration 2q scans probe grains in all directions

36 X-ray penetration depth vs. angle of incidence Low angle region -Type of radiation - Angle of incidence - Material (Z, A, r, m) 36

37 Regular 2q-w scan vs. glancing angle 2q scan Regular 2q-w scan Glancing angle 2q scan Probe depth: Variable (deep) Constant (shallow) w (fixed, small) Regular 2q-w scan Glancing angle 2q scan Grain orientations Directions to surface Various directions Depth resolution Constant, many mm From few nm to mm Depth profiling possible by varying angle of incidence Sensitive to surface Ideal for ultra-thin layers Best configuration Bragg Brentano Parallel beam Parallel beam (less sensitive to sample displacement) 37

38 Glancing angle x-ray analysis Example: Poly-Si gate in CMOS Poly-Si (~ 100 nm) Si(001) substrate Glancing angle 38

39 Texture and preferred orientation methods Anisotropy in grain orientation distribution What is the preferred orientation? % of random grains? Strength / sharpness of the texture? Crystallographic relationship between film and substrate? 39

40 Determination of preferred orientation Method Measurement Principle Results Lotgering factor (L hkl ) 2q-w scans Compare I peak or A peak with expected values from random samples (PDF) L hkl as measure of texture strength March- Dollase (MD) 2q-w scans Use I peak or A peak with MD formalism % of grains that are more oriented along a specific direction Rocking curve w scans Measure FWHM from w scan for a particular (hkl) FWHM decreases with stronger texture Pole figure f scans at various tilts y Pole plots of intensities from a particular (hkl) Texture distribution for a single (hkl) Orientation Distribution Function (ODF) Pole figures from various (hkl) s Calculate ODF from various pole figures with background and defocussing correction % of grain orientation distribution in all directions (Euller angles). 40

41 Pole plot projections Equatorial plane Pole Wulff projection (stereographic or equal-angle projection) Side view (normal to equatorial plane) O y r W Equatorial plane O A Schmidt projection (equal-area projection) y B r S AB = AS Side view (normal to equatorial plane) Top view (parallel to equatorial plane) O W f O S f Top view (parallel to equatorial plane) OW = r tan(y/2) OS = 2 r tan(y/2) 41

42 Basics of pole figure analysis Surface normal f y Example: (100) cubic crystal f Pole figure plot y hkl hkl y(radial / tilt) f (azimuthal rotation) (100) Pole figure (111) Pole figure (110) Pole figure f f y f y y Azimuth f= 0, 90 o, 180 o, 270 o Tilt y= 0, 90 o y: [100],[100] Azimuth f= 45 o, 135 o, 225 o, 315 o Tilt y= 54.7 o y: [100],[111] Azimuth f= 0, 90 o, 180 o, 270 o,45 o, 135 o, 225 o, 315 o Tilt y= 45 o,90 o 42 y: [100],[110]

43 X-ray pole figure analysis of textured materials Texture results from a rolled Cu foil Pole figures y 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. F 2 Orientation distribution function (ODF) f detector 2q f sample w y (111) Inverse pole figures F 1 F y f Data: Sardela, UIUC F 43

44 Residual stress analysis methods Residual stress? How much? (MPa GPa) Type? Direction (s)? Stress gradients? XRD measures strain (Dd) Hooke s law Elastic properties (E,n) Stress tensor 44

45 Interplanar spacing d (Angstroms) X-ray analysis of residual stress Intensity (a.u.) film surface a unstressed stressed y a y a 0 s f Incident X-rays Film Normal y q L f,y Reflected X-rays Diffracting planes Tilt y: +60 o +45 o +30 o +15 o 0-15 o -30 o -45 o -60 o Dd d = s (1+n) sin 2 y E theta ( o ) Quantification of residual stress. Compressive (-) and tensile (+) stress. Crystallographic orientation of stress Slope: Stress = -199 MPa (compressive) sin 2 (y) Stress results from a steel sample Data: Sangid et al, UIUC Sin 2 y method. Linear for rotationally symmetric biaxial stress where the only non-zero components are s 11 = s 22 = s // y and w scan methods. Glancing angle method (texture). Determination of stress tensor. Requires crystallinity (no amorphous). 45

46 High resolution XRD methods Single crystals: a g b Accurate measurements of a, b, c, a, b, g a b c Detailed peak shapes: defects, mosaicity. Film / substrate epitaxial systems: c + Dc c Df Measure small variations Da, Dc, (~ 10-5 ). Measure layer tilts Df,... Detailed peak shapes: defects, strain, mosaicity. a 46

47 Instrument resolution in reciprocal space Beam angular divergence, detector acceptance and diffractometer sampling volume sample w Angular acceptance of the secondary optics Diffractometer sampling volume 2q w Ewald sphere Primary beam divergence (from primary optics) 47

48 Instrumentation: high resolution configuration f y 4-reflection Ge(220) monochromator slit x-ray mirror x-ray source w slit 3-bounce analyzer crystal 2q Dq =12 arc-sec Dl/l = 5x10-5 Triple axis detector (triple axis: 12 arc-sec acceptance) Or: Open detector (open: < 1 o acceptance) Line detector 1D mode for ultra-high speed 48

49 Log intensity (a.u.) High resolution x-ray analysis Log intensity (a.u.) Log intensity (a.u.) Lattice distortions within Rocking curve analysis. Film thickness. Strain relaxation and lattice parameter measurements. Alloy composition and superlattice periods. Interface smearing in heterostructures (dynamical simulation). Single crystals Epitaxial films Heterostructures Superlattices Quantum dots InAs / GaAs multilayer SiGe / Ge superlattice InAs quantum dots on GaAs Data: Wu et al, UIUC Data: Sardela, UIUC Data: Zhang et al theta / omega ( o ) theta / omega ( o ) theta / omega ( o ) 49

50 High resolution x-ray analysis Example: strained In x Ga 1-x As on GaAs (001) substrate High resolution 2q/q scan near GaAs(004) In x Ga 1-x As (004) GaAs (004) Lattice structure Thickness fringes a // film = a substrate 0.07 o 0.04 o (004) a film > In x Ga 1-x As a substrate (004) GaAs Da a = sin q(substrate) - 1 sin q(film) Thickness = l 2 Dq cosq a substrate Data: Sardela 50 Sample: Highland, Cahill, Coleman et at, UIUC

51 High resolution x-ray analysis Example: strained In x Ga 1-x As on GaAs (001) substrate High resolution 2q/q scan near GaAs(004) and dynamical scattering simulation In x Ga 1-x As (004) GaAs (004) Lattice structure a film a // film = a substrate (004) 0.76 at% In 243 nm > In x Ga 1-x As a substrate (004) GaAs a substrate Takagi-Taupin dynamical scattering simulation Data: Sardela 51 Sample: Highland, Cahill, Coleman et at, UIUC

52 No strain relaxation: a // = a s film substrate High resolution reciprocal space mapping a a s Separation of strain and mosaicity Lattice distortions within Accurate lattice parameters in and out of plane Strain and composition gradients Strain relaxation Mosaic size and rotation Misfit dislocation density Nanostructure dimensions, Lattice disorder and diffuse scattering. a s Strain relaxation: a a // a s film substrate (224) substrate (224) film substrate thickness fringes 0.1 nm -1 film Si 1-x Ge x on Si(001) Dq 001 Dq nm -1 Mosaicity (diffuse scattering) Si 1-x Ge x on Si(001) Data: Sardela et al 52

53 High resolution reciprocal space mapping Example: strained Si layer on Si 1-x Ge x / Si substrate High resolution 2q/w scan near Si(004) Layer structure Si 1-x Ge x Si substrate Strained Si (top layer, very thin) Relaxed Si 1-x Ge x (thick, many microns) 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? % of Ge? Dq Strained Si Si substrate Si(001) substrate Defects? Si 1-x Ge x Dq // 53

54 High resolution reciprocal lattice map Strained Si (top layer) Map near Si(224) Relaxed Si 1-x Ge x Si(001) substrate (224) Strained Si Si substrate Dq Si 1-x Ge x Dq // [001] 0.1 nm -1 [110] Data: Sardela Sample: Zuo, UIUC 54

55 High resolution reciprocal lattice map Strained Si e = % e // = 0.64 % Si substrate Strained Si (top layer) Relaxed Si 1-x Ge x Si(001) substrate 4.60 at% Ge Map near Si(224) 7.52 at% Ge at% Ge Relaxed Si 1-x Ge x at% Ge 100% strain relaxation [001] 0.1 nm -1 Data: Sardela Sample: Zuo, UIUC [110] 55

56 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: 2p / Dq i i = x, y, z, //, 0.1 nm -1 [001] [110] Data: Sardela Sample: Zuo, UIUC 56

57 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 nm -1 [001] [110] Coherent length in any direction: 2p / Dq i i = x, y, z, //, Data: Sardela Sample: Zuo, UIUC 57

58 The shape of the reciprocal lattice point Changes in lattice parameter (radial direction) Lateral sub-grain boundaries (along q // ) [001] 000 CTR, finite layer thickness, superlattice (along q ) Mosaicity, curvature, orientation (circumferential direction) [110] 58

59 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 59

60 Reflectivity Log Intensity X-ray source w 2q Detector Angle w, q or 2q Sample

61 Log Reflectivity R X-ray reflectivity Critical angle q c One sharp interface (density r e variation: function at interface) q Thickness fringes Dq = l/[2*(thickness)] One rough interface ( broad r e variation at interface) Two interfaces DI ~Dr e q Film thickness measurements: 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. 61

62 Log intensity (a.u.) X-ray reflectivity analysis of thin films Log intensity (a.u.) Log intensity (a.u.) Ultra-thin 2.3 nm thick polymer on Si n=1 2 3 Complex multilayers Data: Sardela, UIUC Sample: Auoadi et al, SIU 4 Metallic multilayer Non crystalline Amorphous PZT film theta ( o ) Data: Heitzman et al, UIUC Intercept: refractive index sin 2 q 2-theta ( o ) Slope: periodicity d n Theta ( o ) Data: Mikalsen et al, UIUC sin 2 q = (l 2 /2d) 2 n 2 ( 2-1) (modified Bragg s law to include refractive index) 62

63 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 63

64 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 nm, 2.19 g/cm 3 Si substrate Data Best fit 64

65 X-ray reflectivity: summary * Non destructive method * Applicable to whole wafers (wafer mapping option) * Fast method (in most cases) * Do not depend on crystalline quality of the films (can also be used in amorphous layers). Quantification of: * Layer thickness in thin films and superlattices: 1 nm ~ 1 mm (± 0.5-1%). * Layer density and porosity (± 1-2%). * Interface roughness: nm (model dependent; reproducibility ~ 3%). * Layer density gradients (variations > 2%). * Interface roughness correlation in superlattices and 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). 65

66 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 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: > at % (may require depth profiling). SIMS: > 1 ppm (requires sputtering depth profiling). EDS: > w % over small volume 1mm 3. Little with phase information; averages over small lateral areas (< 100 mm). o Better than within 10-5 o TEM: estimates ~ 10-3 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. 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.

67 Comparison with other techniques X-ray analysis methods Other techniques Texture Residual Stress Depth dependent information Surface or Interface roughness Defects 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 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). Instrument cost Portable instruments ~ $ 60 K. Average well-equipped: ~ $ 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~ 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.

68 X-ray analysis summary Information contents Detection limits > w% Depth information Lateral resolution Angular resolution Sample requirement % 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 Up to 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) 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 * 68

69 X-ray analysis summary (+) Non destructive Quantitative Finger printing (chemical info) Very accurate crystalline structure info Averages over large volume (~ 30 mm x cm s) Levels of complexity: simple to complex Trends: microdiffraction, pair distribution function, fast areal detectors (-) Non crystalline materials Localized info (below 100 mm) Defects identification and quantification Direct imaging 69

70 Acknowledgments 2013 University of Illinois Board of Trustees. All rights reserved. 70