XRD polykrystalick tenk vrstvy Conventional BraggBrentano symmetric geometry
XRD polykrystalické 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
Bragg-Brentano conventional powder diffraction geometry 3 h 3 k 3 l 3 Symmetric - 2 scan 2 h 2 k 2 l 2 1 h 1 k 1 l 1 Information from the grains oriented with the corresponding planes parallel to the surface
Absorpce a 2 - a b b Lineární absorpční koeficient Energie z hloubky t za 1 s
Asymmetric powder diffraction geometry 3 h k l 3 3 3 h 2 k 2 l 2 2 2 scan 1 h 1 k 1 l 1 Small constant angle of incidence g Parallel beam g = 2 – 10 Picture from Seifert poster
XRD Seifert - FPM Monochromator Detector Parallel plate collimator Slits X-ray tube Sample holder
C. Bragg-Brentano asymmetric powder diffraction geometry 3 h 3 k 3 l 3 hkl 2 2 1 h 1 k 1 l 1 - 2 scan -goniometer Y-goniometer Texture Stress
Philips X’Pert MRD Eulerian cradle Sample stage Parallel plate collimator Detector X-ray tube Goebel mirror Polycapillary
Texture and Stress
Omega sken FWHM Korekce na absorpci a defokusaci
- sken
Texture, stress
2 D reciprocal space scan -2 scan 2 2 scan Ideal single crystal Ideal polycrystal Textured polycrystal 0
Zbytková napětí Homogenní napětí 1. druhu (s). Může být určováno přímo známou metodou sin 2 y, kdy musí být vzorek nakláněn na různé úhly y 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 n … Poissonovo číslo, E … Youngův modul Elasticky izotropní materiály Elastická anizotropie + Reussův model ( = konst. maximální závislost na hkl ) tlakové napětí a 222 400 311 200 111 a 0 Hodnota bez napětí cos cot Back
2 sken 422 goniometr
Crystallite Group Method BB - y = 0 BB - y = y 0 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).
Hloubka průniku Nekonečná tloušťka Poměr energií difraktovaných tenkou vrstvou na povrchu a tenkou vrstvou v hloubce t Hloubka průniku Efektivní hloubka průniku Informační hloubka Přispívající tloušťka Ekvivalentní tloušťka
- 2 (B-B) Hloubka průniku 2 (SB, PB)
Rutile P 42/mnm 4. 5977 2. 9564 Anatase I 41/amd 3. 7710 9. 430 Brookite Pbca 9. 174 5. 449 5. 138
Rutile Anatase Brookite
Parallel beam geometry Bragg-Brentano symmetric geometry Thickness - 0. 6 mm Anatase Amorphous
Williamson-Hall plot Crystallite size > 100 nm Microstrain ~ 0. 15 % ~ microstrain ~ 1/crystallite size Apparent crystallite size Lattice strain e=Dd/d
Texture indices Thicker Thinner 2. 0/250 2. 0/300 1. 7/300 1. 5/300 1. 2/300 101 1. 2 1. 6 1. 7 004 3 2. 1 1. 3 1. 1 112 0. 5 0. 8 1 Fiber texture 0. 9 200 1. 2 0. 9 0. 7 1 105 1. 6 1. 2 1. 1. 0. 9 1 211 0. 6 0. 5 0. 6 0. 9
Residual stress • • • isotropic elastic constants (E = 190 GPa, ν = 0, 31) tensile stress at 500 C drop of 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
Stress Thick ness [nm] [MPa] 300 C 200 350 C 500 C 341 151 630 187 42 800 219 209 - 1000 184 154 - 1500 240 163 - 1700 280 232 - 2000 293 252 -
Stress anisotropy
105 Diffraction peaks For different inclinations 211 300 ºC Tensile stress ~ 200 MPa 500 ºC no stress
X-ray reflectivity Refraction index electron density Total reflection absorption length re = 2. 818 10 -15 m - wavelength Critical angle
Surface roughness, film thickness ~ 1/t Perfectly smooth surface Visible up to ~ 300 nm Kiessig maxima 0. 3 nm roughness Reflectivity is sensitive only to the projection of the surface profile to its normal direction It cannot distinguish between mechanically and chemically rough surface
Ti. O 2 200 nm 250 ºC 350 ºC 450 ºC Increasing roughness with annealing temperature
Ti. O 2 200 nm 250 ºC Ω scans
Ti. O 2 1 700 nm 350 ºC Ω scan
Reflectivity curves 2 q Increase of roughness with film thickness Reduction of very thin surface layer with annealing temperature
Reflectivity curves fitting 0, 8 m 300 C Two layer model necessary Surface porous layer 0, 054 m 350 C Experimental Fitted
Surface roughness Thickness [nm] Fitted thickness [nm] Electron density [g. cm-3] Roughness [nm] 54 57 3. 42 1. 2 100 93 3. 58 1. 7 200 3. 48 1. 8 630 569 3. 53 4. 1 57 3. 64 7 968 3. 89 2 49 3. 68 5 1791 3. 89 2 55 3. 74 5 2 nd layer 1000 2 nd layer 1700 2 nd layer
Depth profiling thickness – 1 mm Different angles of incidence ( ) Rutile 110 Anatase 101
Reflection on multilayers Bragg maxima of multilayer Period d d=T Kiessig maxima Total thickness T Number of ML periods
10 x(Ga. As 7 nm/Al. As 15 nm), Cu. Ka 1 Kinematical approx: No total reflection region, wrong positions of the satellites (refraction not considered) Annealing of amorphous 9 x(5 nm Si/ 1 nm W)
Experimental set-up Detector X-ray tube Cu. K Göbel mirror Slit 0. 05 mm Secondary graphite monochromator Slit 0. 1 mm Sample
Diffuse scattering non-specular conditions Thermal fluctuations Correlated layer distortions Height-height correlation function Effective cut-off length of the self-affine surface For multilayers Vertical interface roughness correlation
Fe/Au (70Å/21Å)x 13 Low correlation of the interface roughness -1. 11 -0. 56 0 -0. 56 1. 11 1. 67 3. 33 2. 22 1. 11 Sample inclination Detector angle -1. 67
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
Wavefields in crystal Weakly interacts with the atoms Anomalously low absorption Strongly interacts with the atom Anomalously high absorption The Borrmann effect
Epitaxní vrstvy strain Tloušťka
Implantace Si – B+ D = 3, 1. 1014 D = 6, 2. 1015 a žíhání 1000 ºC bez implantace
X-ray grazing incidence diffraction
W ~ 1. 8 nm na Al 2 O 3 a|| = 0. 3184 nm a 0 = 0. 3165 nm e|| = 0. 6 % <D||> 5 nm w sken Mozaiková rozorientace ~ 1. 1º
MBE Mo 22 nm (111) na (001) Ga. As Tři domény Mo[110] || Ga. As [110] Ga. As [1 -10] Ga. As [100] Mismatch B || -10. 2 % ┴ +3. 7 % C ┴ +27 % <D> ~ 13 nm Jedna doména Nb[110] || Ga. As [100] Nb(001) || Ga. As (001) Mismatch 21. 1 %
Standing waves
Standing waves Amplitude of diffracted wave Phase of (Eh/E 0) Amplitude of incoming wave Reciprocal lattice vector Reflection curve – 1 Phase – 2 Intensity at atomic planes – 3 Maximum interaction for a = 0, at high angle side of reflection curve
Monolayer of adsorbed atoms High sensitivity to displacement of layer ~ 1 % !!! Yield of the fluorescent radiation
Adsorbed layers Three adatoms at 0, 1/3, 2/3 Parallel planes Inclined planes
Experiment Measurements of secondary radiation under the condition of diffraction Fluorescence Photoelectrons Auger electrons Compton radiation Chemical selectivity Spatial resolution on atomic scale Depth-resolved studies Determination of coherent position – mean plane of the adsorbed atoms and coherent fraction – static and dynamic displacement of atoms from the coherent position
Organic materials Long-period standing waves are necessary Bragg diffraction from layered synthetic microstructures with large period 10 -200 layer pairs (low and high electron density) Fixed period XSW Total reflection SW is formed as an interference between incident and specularly reflected waves q = 0. 1 qc q = qc Height dependence of electric field intensity generated during specular reflection of an X-ray plane wave from the mirror surface at three angles of incidence Marker atom A – two E-field maxima marker atom B – five E-field maxima
XSW application Monitoring of membrane-related dynamic processes membrane-lipid phase transitions ion movement in membrane Protein folding Membrane-protein insertion Lipid and/or protein distributions Surface binding Distribution of marker atom above the substrate surface Theoretical model Experimental fluorescence, Reflectivity data Layered model of refractive index based on the known structure Adjusting of interfacial roughness
Features of XSW Resolution ~ 1 % of LSM d (for 50 Å - 0. 3 Å, 925 Å - 3 Å) Element specificity (not suitable for light elements, O, P, S) Structure-determination measurement on isolated lipid membranes (protein monolayers ~ 10 pmol (100 ng) of cytochrome c) Calculation of the angle-dependent electric-field profile and fluorescence-yield profile normal to the surface Adjusting two parameters Membrane-topology measurements on minimally perturbed systems (Fe XSW on Fe-cytochrome c)
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