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Characterization Of Layered Structures By X Ray Diffraction Techniques
 

Characterization Of Layered Structures By X Ray Diffraction Techniques

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    Characterization Of Layered Structures By X Ray Diffraction Techniques Characterization Of Layered Structures By X Ray Diffraction Techniques Presentation Transcript

    • X-Ray Scattering Methods for Characterization of Advanced Materials Workshop
      Characterization of layered structures by x-ray diffraction techniques
      Iuliana Cernatescu
      PANalytical Inc.
      Westborough, MA, USA
      1
    • Outline
      Thin films definition and XRD applications
      Reciprocal Space definition
      Characterization of Epitaxial Layers
      Characterization of Polycrystalline layers
      Overview of typical optics and resolutions by sample types and target analysis
      2
    • Thin Film Definition
      Nearly perfect epitaxy (thin film orientated to substrate parallel and perpendicular)
      Imperfect epitaxy (thin film partially orientated to substrate parallel and perpendicular)
      Textured polycrystalline (orientation unrelated to substrate but defined by growth)
      Non-crystalline layers (no correlation beyond a bond length)
      3
    • Epitaxial Layers
      Mismatch
      Relaxation
      Composition
      In-Plane Epitaxy
      Mosaic spread
      Super-lattice period
      Curvature
      Off-Cut
      Thickness
      Density
      Roughness
      } XRR
    • Polycrystalline Layers
      Phase ID
      Quantification
      Unit Cell refinement
      Residual stress
      Crystallite size & micro-strain
      Preferred orientation
      Depth profiling of stress, phases, microstructure
      Thickness
      Density
      Roughness
      } XRR
    • Amorphous Layers
      Thickness
      Density
      Roughness
      }XRR
    • Reciprocal Space
      1/
      S
      1/
      1/
      2



      7
    • The Reciprocal Lattice from Planes
      • Create reciprocal lattice (RL), where each point represents a set of planes (hkl)
      -The points are generated from the RL origin where the vector, d*(hkl), from the origin to the RLP has the direction of the plane normal and length given by the reciprocal of the plane spacing.
      002
      112
      1/d112
      001
      d*(112)
      111
      112
      002
      110
      000
      111
      110
      001
      8
    • Reciprocal Lattice and Scattering Vectors
      Reciprocal lattice vector d*hkl
      Length 1/d
      Direction, normal to hkl planes
      d*hkl
      S
      d*hkl
      kH
      k0
      Incident beam vector, k0,
      Length n/
      Direction,  with respect to sample surface
      k0

      2
      000
      kH
      Scattered beam vector, kH,
      Length n/ (user defined)
      Direction, 2 with respect to k0
      By rotating kH and kothe diffraction vector Scan be made to scan through reciprocal space.
      When S = d*hklthen Bragg diffraction occurs
      Diffraction vector, S,
      S = kH – k0
      S
      9
    • Scattering Vectors Related to a Real Experiment
      Psi
      Phi
      source
      Detector
      S

      2
      sample
      10
    • Reciprocal Lattice of a Single Crystal in 3D
      115
      -2-24
      • There are families of planes
      • All planes in the same family have the same length |d*|, but different directions
      • The family members have the same 3 indices (in different orders e.g. 400,040,004 etc)
      004
      224
      113
      d*
      | d*| = 1/dhkl
      -440
      440
      Just a few points are shown for clarity
      11
    • Characterization of epitaxial Layers
      12
    • Epitaxial Samples in RS
      • We investigate the fine structure of individual reciprocal lattice spots
      115
      004
      224
      113
      “Reciprocal space map”
      “Scan”
      -440
      440
      This requires high resolution instrumentation
      13
    • Thin Layers and Multi-layers
      115
      224
      004
      113
      -440
      • The reciprocal lattices of the crystals and the multilayer combine
      115
      004
      224
      113
      -440

      Fourier transform
      Reflectivity is known as the 000 reflection
      14
    • RSM features bulk crystals
      CTR = sample surface streak (and white radiation streak)
      M = monochromator (or source) streak, parallel to diffracted beam
      A = analyser (or detector) streak, parallel to tangent of Ewald sphere
      S = Mosaic spread, curvature
      (A)
      (A)
      S
      S
      M
      (M)
      CTR
      CTR
      15
    • surface normal
      high quality substrate -sharp peak
      broadening normal to sample surface
      thin layers
      d spacing variation
      broadening parallel to surface
      mosaic structure
      variable tilts (curvature or dislocations)
      Shapes in RS
      16
    • layer
      substrate
      thick layer with grading and overall curvature
      thin
      layer
      mosaic
      layer
      Examples Symmetric Reflections
      17
    • 4.8o
      InGaAs tensile and compressive alternating multilayer on 001 InP substrate.
      Bent multilayer sample
      Samples with Bend or Tilt
      18
    • 19
      Buffer Layer Structures
      Relaxed Buffer layers as virtual substrates:e.g. Si/Ge on Si InGaAs on GaAs GaN on Sapphire
      Substrate and surface layer lattice parameter calculations from reciprocal lattice coordinates (Bragg’s Law)
      d*substrate
      d*cap
      d*layer
      tilt
      InP capping layer
      Graded InxGa(1-x)As Buffer layer with dislocations
      GaAs substrate
      P. Kidd et al, J. Crystal growth, (1996) 169 649-659
    • layer thickness
      Tilt, thickness and lateral width
      symmetric
      asymmetric
      Spread due to finite size effects
      Range of tilts
      In-plane
      20
    • Broadening effects on symmetric reflections
      Omega broadening due to
      Size effects
      Omega broadening due to tilts
      (s-x,sz)
      (sx,sz)
      (s-x,sz)
      (sx,sz)

      1/L
      000
      000

      L
      21
    • Strained Layer
      Q
      at=aS
      Layer
      006
      Substrate
      L
      004
      224
      -2-24
      002
      aS
      S
      fully
      strained
      220
      110
      Q||
      22
    • Relaxed Layer
      Q
      Layer
      Substrate
      006
      at= aL
      L
      aL
      004
      224
      -2-24
      002
      S
      220
      110
      fully
      relaxed
      Q||
       at
      23
    • Relaxed layers RSM
      24
    • Scans in reciprocal space (1)
      /2 scan
      2’
      ’
      25
    • Scans in reciprocal space (2)
      2’’
      ’’
      26
    • Scans in reciprocal space (3)
      q varied
      2’’’
      ’’’
      27
    • Scans in reciprocal space (1)
      Rocking curve
      2
      ’
      28
    • Scans in reciprocal space (2)
      Rocking curve
      2
      ’
      29
    • Scans in reciprocal space (3)
      q constant
      2
      ’’’
      30
    • Scans in reciprocal space (4)
      2
      ’’’
      31
    • In-plane definition
      Symmetrical
      Diffraction
      Gonio Scan
      Grazing Incidence
      Diffraction
      2 theta scan
      In-plane
      Diffraction
      Phi scan
      Coupled scan
      32
    • In-Plane Diffraction
      In-plane diffraction is a technique for measuring the crystal planes that are oriented perpendicular to the surface
      | d*| = 1/dhkl
      115
      -2-24
      224
      004
      113
      d*
      110
      -1-10
      220
      -2-20
      33
    • In-Plane Diffraction
      2Theta/Omega scan
      115
      -2-24
      224
      004
      113
      d*
      110
      -1-10
      220
      -2-20
      34
    • In-Plane Diffraction
      2Theta/Omega scan
      115
      -2-24
      224
      004
      113
      d*
      110
      -1-10
      220
      -2-20
      35
    • In-Plane Diffraction – phi scan
      115
      -2-24
      224
      004
      113
      d*
      110
      -1-10
      220
      -2-20
      36
    • RS Mapping
      0
      +
      +

      -
      +
      2-
      0
      Omega offset
      -
      -
      2Theta/omega
      Reciprocal lattice view
      Angular view
      37
    • Reciprocal Space Map
      Qz
      AlGaN/GaN MQW
      GaN(0002)
      Qx
      38
    • 12/1/2009
      Si (224) - 1D-mode with PIXcel
      • Reduced collecting time (1/10)
      • High dynamic range
      Si
      SiGe
    • X-ray diffraction - rocking curve
      monochromator (collimator)
      AlGaN layer
      X-ray
      source
      Peak positions
      /  d/d  composition,
      strain
      f thickness
      Peak shape thickness
      defects
      curvature
      GaN
      
      Substrate
      f
      Layer
      40
    • Characterization of Polycrystalline layersspace
      41
    • 42
      Definitions: Orientations of crystallites
      Random orientation
      Single crystal
      Preferred orientation
    • Polycrystalline random oriented
      113
      000
      hkl
      0 0 4
      A sufficient number of randomly oriented crystals forms a reciprocal “lattice” of spherical shells
      43
    • Textured samples
      • Non uniform reciprocal lattice
      • Different intensities at different directions
      Spherical shell radius 1/dhkl
      S
      2
      2
      1/dhkl
      S = 1/dhkl
      44
    • Characterization of Polycrystalline thin films
      Phase ID
      Phase ID with depth profiling
      Residual stress
      Residual stress with depth profiling
      Texture analysis
      45
    • Symmetric 2Theta/Omega “powder” scans
      Phase ID in polycrystalline samples
      2Theta/Omega scan
      scattering vector S
      46
    • Symmetric 2Theta/Omega “powder” scans
      2Theta/Omega scan
      111
      47
    • Symmetric 2Theta/Omega “powder” scans
      2Theta/Omega scan
      111
      220
      311
      48
    • Symmetric 2Theta/Omega “powder” scans
      2Theta/Omega scan
      111
      220
      311
      331
      004
      49
    • Symmetric 2Theta/Omega “powder” scans
      2Theta/Omega scan
      111
      220
      311
      422
      331
      004
      511
      50
    • Symmetric scan for thin films
      In the case of very thin films the scattering volume will become smaller and smaller as the symmetric scan progresses to higher angles.
      The diffraction pattern of the substrate will dominate the diffractogram and could complicate the pattern analysis.
      51
    • Glancing Incidence Diffraction - 2Theta scan
      Phase ID in thin film polycrystalline samples
      52
    • Glancing Incidence Diffraction - 2Theta scan
      Phase ID in thin film polycrystalline samples
      53
    • Glancing Incidence Diffraction - 2Theta scan
      Phase ID in thin film polycrystalline samples
      54
    • Glancing Incidence - Diffraction 2Theta scan
      Phase ID in thin film polycrystalline samples
      55
    • 56
      GIXRD - Thin film depth profiling phase analysis
      , Incident angle

      ZnO
      CIGS
      0.45 deg
      Mo
      1.00 deg

      ZnO
      ZnO
      CIGS
      Mo
      2.00 deg

      ZnO
      ZnO
      CIGS
      Mo
    • 57
      GIXRD - Thin film depth profiling phase analysis
      , Incident angle

      ZnO
      CIGS
      0.45 deg
      Mo
      1.00 deg

      ZnO
      ZnO
      CIGS
      Mo
      2.00 deg

      ZnO
      ZnO
      CIGS
      Mo
    • 58
      GIXRD - Thin film depth profiling phase analysis
      , Incident angle
      ZnO
      =0.45
      CIGS
      0.45 deg
      Mo
      1.00 deg
      ZnO
      =1
      ZnO
      CIGS
      Mo
      2.00 deg
      ZnO
      =2
      ZnO
      CIGS
      Mo
    • GIXRD in Reciprocal Space
      powder
      single crystal
      Sampling only the random component of the studied sample.
      59
    • Residual Stress in Polycrystalline thin films
      Non uniform reciprocal lattice
      Different d-spacings at different directions
      Polycrystalline components subjected to external mechanical stresses
      Spherical shell distorted
      (not to scale!)
      S
      2
      2
      1/dhklnot constant

      S = 1/dhkl

      One hkl reflection
      60
    • “Stress” Measurement
      A stress measurement determines dhkl at a series of Psi positions
      The sample is stepped to different  positions, 2 scan at each position to obtain peak position
      Repeated for different  positions as required
      Spherical shell distorted

      One hkl reflection
      S
      2
      2
      1/dhklvaries with position
      61
    • Classical Residual Stress
      Single hkl






      62
    • Calssical Residual stress
      Measure (very small) peak shifts as a function of the sample tilt angle ‘psi’
      Plot d-spacing as a function of sin2(psi)
      Fit straight line
      63
    • Multiple hkl residual stress analysis
      Analysis
      Determine peak positions
      Calculate offsets
      (w-q)=wfixed- ½ (2q)peak
      Calculate sin2y values
      y=(w-q)
      Full range scan needed
      Low 2q small sin2y (40 o2q sin2y ~0.11)
      High 2q large sin2y (140 o2q sin2y ~0.87)
      hkl
      hkl
      hkl
      2q
      w
      64
    • Stress depth gradient
      Very small angle of incidence
       analyzing stress near surface
      Coating
      Substrate
      65
    • Stress depth gradient
      Larger angle of incidence
       analyzing stress near surface AND deeper
      Coating
      Substrate
      66
    • Stress depth gradient
      Largest angle of incidence
       analyzing average stress whole coating
      Coating
      Substrate
      67
    • Stress Gradient example - MgO on Glass
      68
    • Pole Figure Measurement
      A Pole figure maps out the intensity over part of the spherical shell
      2 stays fixed, the sample is scanned over all  at different  positions


      One hkl reflection
      S
      2
      2
      69
    • Pole figure example: Aligned ZnO wires
      70
    • Pole figures of ZnO


      000l
      71
    • Few typical Diffractometer configurations
      72
    • Epi characterization
      • For this type of analysis typicaly the diffraction geometry if parallel beam.
      • The incident beam side is monochromated and the type of monochromator depends on the needed resolution.
      • For the diffracted beam side there are choises of TA, RC/open detector or line detector depending on the resolution needed.
      73
    • Powders characterization
      • In the case of powder samples where we are scanning in a symmetrical manner Bragg-Brentano geometry is used due to its optical resolution.
      • Powder are often time analyzed with parallel beam, micor-spot beam, depending on the type of analysis required.
      74
    • Configuration for Texture and stress analysis
      Texture measurements require a point like source due to the tilting in Psi during the data collection of a pole figure.
      In this case the tube was rotated to point focus in order to avoid defocusing error and have better intensity.
      75
    • Configuration for GIXRD, XRR and Residual Stress
      Soller slits
      Thin layers
      X-ray tube
      (line focus)
      Sample
      X-ray mirror
      Parallel plate
      collimator
      Soller slits
      Detector
      Monochromator (optional)
      76
    • Summary [1]
      crystal block size
      residual stress
      Perfect epitaxy
      Nearly perfect epitaxy
      Imperfect epitaxy
      Textured polycrystalline
      Perfect polycrystalline
      Non-crystalline layers
      defects
      orientation
      distortion
      composition
      relaxation
      thickness
      77
    • Summary [2]
      source
      Detector
      S

      2 
      sample
      An instrument
      Provides X-rays
      Aligns a sample
      Detects diffraction pattern
      A Material
      Reciprocal “Lattice” Structure
      An Experiment
      Designed to suit the material
      Designed to answer the question
      78