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Potentials of
Synchrotron Radiation Induced
X ray Standing Waves and
X ray Reflectivity Measurements
in Material Analysis
Markus Krämer
A thesis submitted in fulfillment of the requirements for
the degree of Doctor of Natural Sciences
in the subject of Physics
Department of Physics
at the
University of Dortmund
February 2007Contents
1. Introduction 1
2. Theoretical background 5
2.1. X ray scattering and X ray reflectivity (XRR) . . . . . . . . . . . . . . . . . . . 5
2.1.1. Specular X ray scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2. Diffuse (non specular) X ray scattering . . . . . . . . . . . . . . . . . . 12
2.1.3. Multilayer systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2. X ray fluorescence (XRF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1. X ray fluorescence analysis . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2. Total reflection X ray fluorescence analysis (TXRF) . . . . . . . . . . . 16
2.3. X ray standing waves (XSW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1. Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2. XSW at Bragg reflection and at normal incidence . . . . . . . . . . . . . 21
2.3.3. Lateral dimensions in XSW at grazing . . . . . . . . . . . . . 22
2.3.4. Calculation procedure for XSW . . . . . . . . . . . . . . . . . . . . . . 25
2.4. Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1. Debye Waller factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.2. Modified Fresnel coefficients . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.3. Effective density model . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.4. Implementation of roughness in the XSW calculation program . . . . . . 37
3. Samples 39
3.1. Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1. Semiconductor layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.2. Implantations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2. Bio organic samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1. Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2. Lipids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3. Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.4. Dendrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.5. Nitrobenzene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3. Other sample types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1. Periodic multilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
iContents
3.3.2. Ion distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4. Experiment 57
4.1. Measurement stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.1. TXRF spectrometer EXTRA II . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.2. DELTA synchrotron radiation source . . . . . . . . . . . . . . . . . . . 57
4.1.3. Beamline BL9 (SAW2) at DELTA . . . . . . . . . . . . . . . . . . . . . 58
4.1.4. Sample cell for liquid, vacuum and gas measurements . . . . . . . . . . 61
4.2. Experimental set ups and procedures . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.1. XRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2. TXRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.3. XSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5. Simulation 71
5.1. Calculation of X ray standing waves . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1.1. Required parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1.2. Optical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.3. Calculation of the 3D XSW field . . . . . . . . . . . . . . . . . . . . . . 73
5.1.4. Extraction of a 2D scan . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.5. Marker atom distributions . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.6. Geometrical effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.1.7. Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.1.8. Scaling of the measured curves . . . . . . . . . . . . . . . . . . . . . . . 80
5.1.9. Fit quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2. Evolutionary fitting algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1. General description of evolutionary algorithms . . . . . . . . . . . . . . 81
5.2.2. Implementation of ev in MXSW . . . . . . . . . . 83
5.3. Discussion of exemplary calculated intensity fields . . . . . . . . . . . . . . . . 84
5.3.1. Pure silicon wafer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.2. Germanium layers on silicon . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.3. Gold clusters on a polymer layer . . . . . . . . . . . . . . . . . . . . . . 87
5.3.4. Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6. Evaluation and results 89
6.1. Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.1. Semiconductor layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.2. Implantations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2. Bio organic samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.1. Proteins: Cytochrome . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.2. Lipids: Phospholipid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.3. Ion distribution: Buffer solution . . . . . . . . . . . . . . . . . . . . . . 105
6.2.4. Polymers: Gold and silver clusters on polymer films . . . . . . . . . . . 106
6.2.5. Dendrimers: Gold and DNA on PAMAM . . . . . . . . . . . . . . . . . 114
iiContents
6.2.6. Nitrobenzene: Thin films and nitrobenzene gold samples . . . . . . . . . 118
6.3. Further samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3.1. Periodic multilayers: Laser mirror . . . . . . . . . . . . . . . . . . . . . 124
7. Summary and Outlook 127
A. List of Acronyms i
B. Physical and Optical Constants iii
B.1. Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
B.2. Optical of various materials . . . . . . . . . . . . . . . . . . . . . . . iv
B.3. X ray emission lines of elements used in this work . . . . . . . . . . . . . . . . vi
C. Sample preparation procedures vii
C.1. Cleaning procedure for quartz glass carriers . . . . . . . . . . . . . . . . . . . . vii
C.2. Preparation of cytochrome c films . . . . . . . . . . . . . . . . . . . . . . . . . ix
D. Calculations and approximations x
D.1. sin, cos, tan for small angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
D.2. Complex square root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
D.3. Energy and wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
D.4. Critical angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
D.5. Transmission angle of the penetrating beam . . . . . . . . . . . . . . . . . . . . xii
D.6. T angle in different notations . . . . . . . . . . . . . . . . . . . . . . xiii
D.7. Implementation of Debye Waller factor into matrix formalism . . . . . . . . . . xvi
D.8. Continuous transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
D.9. Aligning an MCA energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
D.10.Calculation of element fraction from the critical angle . . . . . . . . . . . . . . . xviii
E. Computer programs developed during this work xx
E.1. MXSW - XSW simulation program . . . . . . . . . . . . . . . . . . . . . . . . xx
E.2. TxrfTool - TXRF data converter and analyzer . . . . . . . . . . . . . . . . . . . xxii
E.3. D8opt - Analysis program for reflectivity and longitudinal diffuse scans . . . . . xxv
F. Publications and posters related to this work xxvii
F.1. Publications in referred journals . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii
F.2. Poster presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviii
F.3. Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix
F.4. Other talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxx
Bibliography xxxi
Index xlix
iiiContents
ivList of Figures
2.1. Electromagnetic wave at grazing incidence . . . . . . . . . . . . . . . . . . . . . 8
2.2. Calculated Fresnel reflectivity of a silicon/air interface . . . . . . . . . . . . . . 10
2.3. Real and imaginary part of the transmission angle for different angles of incidence 11
2.4. Angles at specular and diffuse scattering, in plane and out of plane . . . . . . . . 12
2.5. Multilayer system with layers of different indices of refraction . . . . . . . . . . 13
2.6. Calculated reflectivity for Si on Ge and Ge on Si . . . . . . . . . . . . . . . . . . 14
2.7. Schematic set up for TXRF measurements . . . . . . . . . . . . . . . . . . . . . 16
2.8. A typical TXRF spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.9. Definition of the transverse and longitudinal coherence length . . . . . . . . . . 20
2.10. Schematic illustration of the XSW triangle above a substrate . . . . . . . . . . . 22
2.11. Path length difference between incident and reflected beam . . . . . . . . . . . . 23
2.12. XSW intensity versus height above a Si substrate for different angles of incidence 25
2.13. XSW versus angle of incidence for different heights above a Si substrate 26
2.14. Multilayer system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.15. Illustration of roughness of an interface . . . . . . . . . . . . . . . . . . . . . . 34
2.16. Simulation of by a cosine shaped stepwise transition . . . . . . . . . . 37
3.1. Primary and tertiary structure of a protein . . . . . . . . . . . . . . . . . . . . . 41
3.2. Three dimensional representation of a cytochrome c molecule . . . . . . . . . . 42
3.3. Picture of quartz carriers covered with silane solution . . . . . . . . . . . . . . . 43
3.4. Schematic structure of a phospholipid molecule . . . . . . . . . . . . . . . . . . 44
3.5. Phospholipid bilayer and micelle . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6. Schematic structure of a bilayer on a glass/Mica substrate . . . . . 45
3.7. 3D representation of POPC and DOPC bilayers . . . . . . . . . . . . . . . . . . 45
3.8. Illustration of the Langmuir Blodgett technique . . . . . . . . . . . . . . . . . . 46
3.9. AFM image of DOPC phospholipids on a mica substrate . . . . . . . . . . . . . 47
3.10. Molecular structure of a polystyrene and a PBMA monomer . . . . . . . . . . . 49
3.11. Photos of the Ag PBMA Si sample . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.12. PAMAM dendrimer of the second generation . . . . . . . . . . . . . . . . . . . 50
3.13. Diameter, functional groups, molecular weight of PAMAM dendrimers . . . . . . 51
3.14. Structure of a nitrobenzene molecule . . . . . . . . . . . . . . . . . . . . . . . . 52
3.15. Orientations of molecules and gold atoms on the substrate . . . . . 53
3.16. Schematic illustration of ion distribution near a charged surface . . . . . . . . . . 56
vListofFigures
4.1. X ray spectrometer EXTRA II . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2. Layout of DELTA synchrotron facility . . . . . . . . . . . . . . . . . . . . . . . 59
4.3. Schematic representation of the set up of BL9 from source to detector . . . . . . 60
4.4. of the experimental hutch of BL9 . . . . . . . . . . . . 60
4.5. Design drawing of the sample cell . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6. Photos of the sample cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7. Schematic illustration of the set up in XRR measurements . . . . . . . . . . . . 63
4.8. Illustration of the reduced reflectivity due to a footprint effect . . . . . . . . . . . 65
4.9. Experimental set up for XSW . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.10. Fluorescence energy spectrum for a Ge layer on Si . . . . . . . . . . . . . . . . 68
5.1. XSW field above a pure Si wafer . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2. XSW field at fixed angle or fixed height . . . . . . . . . . . . . . . . . . . . . . 75
5.3. Extraction of the measured XSW scan from the 3D XSW field . . . . . . . . . . 76
5.4. Different models of marker distribution . . . . . . . . . . . . . . . . . . . . . . 77
5.5. Influence of beam footprint and detector length . . . . . . . . . . . . . . . . . . 77
5.6. XSW field above a pure Si wafer . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.7. Calculated XSW scan of a pure Si wafer . . . . . . . . . . . . . . . . . . . . . . 86
5.8. Simulated 3D XSW fields for Ge layers of various thicknesses . . . . . . . . . . 86
5.9. 3D XSW field for a polystyrene layer on silicon covered with gold . . 87
5.10. XSW field above a Si wafer with of different roughnesses . . . . . . 88
6.1. XSW scan curves of Ge layers on Si . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2. XSW calculation for a 100 nm Ge layer on Si . . . . . . . . . . . . . . . . . . . 91
6.3. Schematic illustration of implanted ion distribution . . . . . . . . . . . . . . . . 91
6.4. Calculated 3D XSW field for As implantations in Si . . . . . . . . . . . . . . . . 92
6.5. and measured XRR and XSW scans for As implantations in Si . . . . 93
6.6. Reflectivity and XSW scans for different implant concentrations . . . . . . . . . 94
6.7.vity and XSW scans for different angles . . . . . . . . . . . . . . 96
6.8. Reflectivity and XSW scans for different double implantations . . . . . . . . . . 97
6.9. TXRF scan of silane/cytochrome samples . . . . . . . . . . . . . . . . . . . . . 99
6.10. Energy spectrum of c sample fluorescence . . . . . . . . . . . . . . . 100
6.11. XSW and XRR scans of a cytochrome film . . . . . . . . . . . . . . . . . . . . 101
6.12. Evaluation of phospholipid scans . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.13. Analysis of the layer structure of the phospholipid bilayer . . . . . . . . . . . . . 103
6.14. XSW scan and fit of P in phospholipid . . . . . . . . . . . . . . . . . . . . . . . 104
6.15. XSW scan and fit of Cl and K in buffer solution . . . . . . . . . . . . . . . . . . 105
6.16. Marker distribution in phospholipid/buffer sample . . . . . . . . . . . . . . . . . 106
6.17. XSW and XRR scans for different PS films on Si . . . . . . . . . . . . . . . . . 107
6.18. XSW field of the Au PS SiO Si sample . . . . . . . . . . . . . . . . . . . . . . 1092
6.19. XSW and XRR scans and fits for a polystyrene layer on Si/SiO with Au clusters 1092
6.20. XRR for PS on Si/SiO with Au clusters in 2002 and 2004 . . . . . . . . . . . . 1112
6.21. Comparison of dispersion profiles 2002 and 2004 . . . . . . . . . . . . . . . . . 111
viListofFigures
6.22. Reflectivity scan of the Ag PBMA Si sample . . . . . . . . . . . . . . . . . . . 112
6.23. XSW scan of the sample . . . . . . . . . . . . . . . . . . . . . . . 114
6.24. Fluorescence energy spectrum for PAMAM sample 617 . . . . . . . . . . . . . . 115
6.25. XSW scan and fit for PAMAM sample 617 . . . . . . . . . . . . . . . . . . . . 116
6.26. XRR scans and fits for P samples 616 and 617 . . . . . . . . . . . . . . . 116
6.27. Reflectivity scan of the pure Si substrate . . . . . . . . . . . . . . . . . . . . . . 118
6.28.vity scan of a nitrobenzene film on a Si substrate . . . . . . . . . . . . . 119
6.29. Fit and dispersion profile of the reflectivity scan of the nitrobenzene film on Si . . 120
6.30. Soft X ray XSW measurements of nitrobenzene on silicon . . . . . . . . . . . . 121
6.31. Reflectivity scan andδ profile of the NB film on Si with Au . . . . . . . . . . . . 123
6.32. XSW scan and fit of the nitrobenzene film on Si with Au . . . . . . . . . . . . . 124
6.33. XSW scan of a multilayer laser mirror and oscillation wavelength spectrum . . . 125
6.34. Ratio of calculated and measured total layer thickness in the multilayer mirror . . 126
D.1. Comparison ofsin(z),erf(z) andtanh(z) . . . . . . . . . . . . . . . . . . . . . xvii
E.1. Screenshots of MXSW program: Enter sample and experimental parameters . . . xx
E.2. of Beampath and angle cut . . . . . . . . . . . . . xxi
E.3. Screenshots of MXSW program: Calculated 3D and 2D XSW curves . . . . . . . xxi
E.4. Screenshot of TxrfTool Plot of scan end selected emission lines . . . . xxiv
E.5. Screenshots of D8opt program: Reflectivity and LD scans with(out) overlap . . . xxv
E.6. of Conversion intoq space . . . . . . . . . . . . . xxvi
E.7. Screenshots of D8opt program: Difference between reflectivity and LD scan . . . xxvi
F.1. Cover picture of Journal of Analytical Atomic Spectrometry 21 (2006) . . . . . . xxvii
F.2. Poster presentations 2005 and 2006 . . . . . . . . . . . . . . . . . . . . . . . . xxix
viiListofFigures
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