XRD polykrystalické tenké vrstvy

1. XRDpolykrystalické tenké vrstvy • Conventional Bragg-Brentano symmetric geometry – θ/2θ scan • Asymmetric BB geometry – θ/2θ scan • Parallel beam geometry – 2θ scan Phase analysis Lattice parameters Size, strain Texture

2. Bragg-Brentano conventional powder diffraction geometry Symmetric  - 2 scan h3k3l3 3 h2k2l2 2 1 h1k1l1 Information from the grains oriented with the corresponding planes parallel to the surface

3. Absorpce a b Lineární absorpční koeficient a b Energie z hloubky t za 1 s

4. Asymmetric powder diffraction geometry 3 2 scan Small constant angle of incidence g h3k3l3 h2k2l2 2 h1k1l1 1 Parallel beam g = 2 – 10  Picture from Seifert poster

5. XRD Seifert - FPM Monochromator Detector Slits Parallel plate collimator X-ray tube Sample holder

6. C. Bragg-Brentano asymmetric powder diffraction geometry  - 2 scan h3k3l3 -goniometer 3 h2k2l2 2 h1k1l1 1 Y-goniometer Texture Stress

7. Philips X’Pert MRD Eulerian cradle Sample stage X-ray tube Parallel plate collimator Goebel mirror Polycapillary Detector

8. Texture and Stress

9. Omega sken FWHM Korekce na absorpci a defokusaci

10.  - sken

11. Texture, stress

12. 2D reciprocal space scan q-2q scan 2q 2q scan q scan Ideal single crystal Ideal polycrystal Textured polycrystal q 0

13. Zbytková napětí Homogenní napětí 1.druhu(s). Může být určováno přímo známou metodou sin2y, kdy musí být vzorek nakláněn na různé úhlyy ze symetrické polohy tak, aby difraktovaly atomové roviny různě skloněné vůči povrchu. Uvedený výraz platí přesně pouze pro jednoosá napětí (y = 0 pro symetrickoul Braggovu-Brentanovu geometrii). Rtg elastické konstanty Elasticky izotropní materiály Elastická anizotropie + Reussův model ( s = konst.  maximální závislost nahkl ) n … Poissonovočíslo, E … Youngův modul tlakovénapětí 222 311 a 111 311 400 200 a0 Hodnota bez napětí cos q cot q Back

14. 2  sken 422 422  goniometr  goniometr

15. Crystallite Group Method BB - y = 0 BB - y = y0 For thin films and some bulk materials the orientation of grains with respect to the surface may be very important. Differently oriented grains can have very different defect content and/or be in very different stress state. Therefore it is desirable to measure various crystallite families (texture components) rather than individual planes. Of course, as it is not the case of single crystals, other crystallites always contribute to the profile (less for strong texture).

16. Hloubka průniku Nekonečná tloušťka Poměr energií difraktovaných tenkou vrstvou na povrchu a tenkou vrstvou v hloubce t

17. q - 2q(B-B) Hloubka průniku 2q (SB, PB)

18. RutileP42/mnm 4.59774.5977 2.9564 BrookitePbca 9.1745.449 5.138 AnataseI41/amd 3.77103.77109.430

19. Rutile Anatase Brookite

20. Parallel beam geometry Bragg-Brentano symmetric geometry Thickness - 0.6 mm Anatase Amorphous

21. Williamson-Hall plot Crystallite size > 100 nm Microstrain ~ 0.15 % ~ microstrain ~ 1/crystallite size Apparent crystallite size Lattice strain e=Dd/d

22. Texture indices Thicker Thinner Fiber texture

23. Residual stress • isotropic elastic constants(E=190 GPa, ν=0,31) • tensile stress • at 500 C drop of stress • stresses ~ 200 - 300 MPa • typical stress anisotropy 1,54 m at 300 C for (215) Typical linear dependence Isotropic stress, absence of tri-axial stresses

24. Stress

25. Stress anisotropy

26. 105 211 300 ºC Tensile stress ~ 200 MPa Diffraction peaks For different y inclinations 500 ºC no stress

27. X-ray reflectivity Refraction index Total reflection electron density absorption length re = 2.818  10-15 m  - wavelength Critical angle

28. Surface roughness, film thickness ~ 1/t Perfectly smooth surface Visible up to ~ 300 nm Kiessig maxima 0.3 nm roughness Reflectivity is sensitive onlyto the projection of the surface profileto its normal direction It cannot distinguish betweenmechanically and chemically rough surface

29. TiO2 200 nm 250 ºC 350 ºC 450 ºC Increasing roughness with annealing temperature

30. TiO2 200 nm 250 ºC Ωscans

31. TiO2 1 700 nm 350 ºC Ωscan

32. Reflectivity curves 2q Increase of roughness with film thickness Reduction of very thin surface layer with annealing temperature

33. Reflectivity curves fitting Two layer model necessarySurface porous layer 0,8 m 300 C 0,054 m 350 C Experimental Fitted

34. Surface roughness

35. thickness – 1 mm Depth profiling Different angles of incidence () Rutile 110 Anatase 101

37. Reflection on multilayers Bragg maxima of multilayer Period d d = T Kiessig maxima Number of ML periods Total thickness T

38. Kinematical approx: No total reflection region, wrong positions of the satellites (refraction not considered) 10x(GaAs 7nm/AlAs 15 nm), CuKa1 Annealing of amorphous9x(5 nm Si/ 1 nm W)

39. Experimental set-up Detector X-ray tube CuK Göbel mirror Slit 0.05 mm Secondary graphite monochromator Slit 0.1mm Sample

40. Diffuse scatteringnon-specular conditions Thermal fluctuationsCorrelated layer distortions Height-height correlationfunction Effective cut-off length of theself-affine surface For multilayers Vertical interface roughnesscorrelation

41. Fe/Au (70Å/21Å)x13 Low correlation of the interface roughness -1.67 -1.11 -0.56 0 -0.56 1.11 1.67 3.33 Detector angle 2.22 1.11 Sample inclination

42. Dynamická difrakce Dynamical diffraction Shift from the kinematical Bragg position (due to refraction) Finite width of the diffraction curve (even for T→0) Asymmetry of the maximum – due to the Borrmann effect

43. Wavefields in crystal Weakly interacts with the atoms – Anomalously low absorption Strongly interacts with the atoms – Anomalously high absorption The Borrmann effect

44. Epitaxní vrstvy strain Tloušťka

45. Implantace Si – B+ D = 3,1.1014 D = 6,2.1015 a žíhání 1000 ºC D = 6,2.1015 bez implantace

46. X-ray grazing incidence diffraction

48. W ~ 1.8 nm na Al2O3 w sken a|| = 0.3184 nm a0 = 0.3165 nm e|| = 0.6 % <D||> 5 nm Mozaiková rozorientace ~ 1.1º

49. MBE Mo 22 nm (111) na (001) GaAs Tři domény Mo[110] || GaAs [110] GaAs [1-10] GaAs [100] Mismatch B || -10.2 % ┴ +3.7 % C ┴ +27 % <D> ~ 13 nm Jedna doména Nb[110] || GaAs [100]Nb(001) || GaAs (001) Mismatch 21.1 %

50. Standing waves