X-ray Scattering from Thin Films Experimental methods for thin films analysis using X-ray scattering Conventional XRD diffraction Glancing angle X-ray diffraction X-ray reflectivity measurement Grazing incidence X-ray diffraction X-ray diffraction study of real structure of thin films Phase analysis Residual stress analysis Crystallite size and strain determination Study of the preferred orientation Study of the crystal anisotropy 1

Conventional X-ray diffraction Diffracting crystallites + Reliable information on the preferred orientation of crystallites the crystallite size and lattice strain (in one direction) - No information on the residual stress (constant direction of the diffraction vector) - Low scattering from the layer (large penetration depth) 2

Glancing angle X-ray diffraction GAXRD Gold, CuKa, m  4000 cm-1 Symmetrical mode GAXRD 3

Other diffraction techniques used in the thin film analysis Conventional diffraction with W-scanning qy=0 Grazing incidence X-ray diffraction (GIXRD) qz»0 Conventional diffraction with C-scanning qx=0 4

Penetration depth of X-rays L.G. Parratt, Surface Studies of Solids by Total Reflection of X-rays, Physical Review 95 (1954) 359-369. Example: Gold (CuKa) d = 4.2558 10-5 b = 4.5875 10-6 5

X-ray reflectivity measurement Calculation of the electron density, thickness and interface roughness for each particular layer r t [Å] s [Å] 0.68 19.6 5.8 0.93 236.5 34.0 1.09 14.1 2.7 1.00 5.0 2.7 1.00 2.8 Mo Edge of TER Mo Kiessig oscillations (fringes) Mo W Si The surface must be smooth (mirror-like) 6

Experimental set-up Used for XRR, SAXS, GAXRD and symmetrical XRD Scintillation detector Flat monochromator Sample Goebel mirror X-ray source Sample rotation, f Normal direction Diffraction vector Diffraction angle, 2q Angle of incidence, g Sample inclination, y 7

Information on the microstructure of thin films Phase analysis Residual stress analysis Crystallite size and strain determination Study of the preferred orientation Study of the anisotropy in the lattice deformation Investigation of the depth gradients of microstructure parameters

Uranium nitride – phase analysis Sample deposition PVD in reactive atmosphere N2 Heated quartz substrate (300°C) Phase composition UN, 80-90 mol.% Fm3m, a = 4.8897 Å U2N3, 10-20% mol.% Ia3, a = 10.64 - 10.68 Å Schematic phase diagram 800 T(°C) 400 U UN U2N3 UN2 0 Atomic Percent Nitrogen 50 60 67 9

Cannot be distinguished in thin films U2N3 versus UN2 U2N3 (Ia3), a = 10.66 Å U: 8b (¼, ¼, ¼) U: 24d (-0.018, 0, ¼) N: 48e (0.38, 1/6, 0.398) UN2 (Fm3m) a = 5.31 Å U: 4a (0, 0, 0) N: 8c (¼, ¼, ¼) Cannot be distinguished in thin films U N 10

Uranium nitride – residual stress analysis UN a0 = (4.926 ± 0.015) Å Compressive residual stress s = - (1.8 ± 0.8) GPa Strong anisotropy of lattice deformation U2N3 a0 = (10.636 ± 0.002) Å Compressive residual stress s = - (6.2 ± 0.1) GPa No anisotropy of lattice deformation GAXRD at g=3° 11

Uranium nitride – anisotropic lattice deformation UN a0 = (4.9270 ± 0.0015) Å s = - (1.0 ± 0.1) GPa 111 easy hard directions 12

UN – anisotropic lattice deformation Dependence of the lattice deformation on the crystallographic direction R.W. Vook and F. Witt, J. Appl. Phys., 36 (1965) 2169. Related to the anisotropy of the elastic constants 13

UN versus U2N3 U N UN (Fm3m) a = 4.93 Å U: 4a (0, 0, 0) N: 4b (½, ½, ½) Anisotropy of the mechanical properties is related to the crystal structure U2N3 (Ia3), a = 10.66 Å U: 8b (¼, ¼, ¼) U: 24d (-0.018, 0, ¼) N: 48e (0.38, 1/6, 0.398) U N 14

Methods for the size-strain analysis using XRD Crystallite size Fourier transformation of finite objects (with limited size) Constant line broadening (with increasing diffraction vector) Lattice strain Local changes in the d-spacing Line broadening increases with increasing q (a result of the Bragg equation in the differential form) (011) (011) (111) (111) (001) (001) (110) (110) (000) (100) (000) (100) Scherrer Williamson-Hall Warren-Averbach Krivoglaz P. Klimanek (Freiberg) R. Kuzel (Prague) P. Scardi (Trento) T. Ungar (Budapest) 15

UN – anisotropic line broadening The Williamson-Hall plot It recognises the anisotropy of the line broadening It is robust (weak intensity, overlap of diffraction lines) It is convenient if the higher-order lines are not available (nanocrystalline thin films, very thin films, GAXRD) 100 111 16

UN – texture measurement Reciprocal space mapping Preferred orientation {110} 17

Reciprocal space mapping -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 1 1 -1 1 1 2 0 0 2 2 0 -2 2 0 3 1 1 3 -1 1 3 -1 -1 2 2 2 -2 2 2 4 0 0 3 3 1 -3 3 1 3 3 -1 4 2 0 4 -2 0 4 2 2 4 -2 2 4 -2 -2 3 3 3 5 1 1 5 -1 1 5 -1 -1 q x [1/A] z {111} A highly textured gold layer Measured using CuKa radiation 18

Epitaxial growth of SrTiO3 on Al2O3 SrTiO3: Fm3m 111  axis -3  001 Al2O3: R-3c Reciprocal space map Atomic ordering in direct space Sr O in SrTiO3 Ti O in Al2O3 Al 19

SrTiO3 on Al2O3 Atomic Force Microscopy Pyramidal crystallites with two different in-plane orientations 111 111 _ 110 _ 110 AFM micrograph courtesy of Dr. J. Lindner, Aixtron AG, Aachen. 20

Depth resolved X-ray diffraction TiC TiN TiN TiC WC TiCN Absorption of radiation 21

Surface modification of thin films Gradient of the residual stress in thin TiN coatings (CVD) implanted by metal ions: Y, Mo, W, Al and Cr 22

Functionally graded materials W. Lengauer and K. Dreyer, J. Alloys Comp. 338 (2002) 194 Nitrogen – in-diffusion from N2 N-rich zone of (Ti,W)(C,N)  Ti(C,N) N-poor zone of (Ti,W)(C,N)  (Ti,W)C SEM micrograph courtesy of C. Kral, Vienna University of Technology, Austria 23

Study of concentration profiles The lattice parameter must depend on concentration Copper radiation Penetration depth: 1.8 mm Molybdenum radiation Penetration depth: 12.5 mm 24

Summary Benefits of X-ray scattering ... for investigation of the real structure of thin films Length scale between 10-2Å and 103Å is accessible (from atomic resolution to the layer thickness) Small and variable penetration depth of X-ray into the solids (surface diffraction, study of the depth gradients) Easy preparation of samples, non-destructive testing Integral measurement (over the whole irradiated area) 25