Curs Raze X 1

126A, Erou Iancu Nicolae Street, R-077190 , Bucharest, ROMANIA www.imt.ro [email protected] IMT @2009, All rights reserved

Tehnici moderne de masura si control Tehnici moderne de masura si control nedistructiv cu radiații Xnedistructiv cu radiații X

Ministry of Education, Research and InnovationNATIONAL INSTITUTE FOR RESEARCH AND DEVELOPMENT IN MICROTECHNOLOGIES IMT - Bucharest

Mihai Dănilă126A, Erou Iancu Nicolae Street, R-077190 , Bucharest, ROMANIA

PO-BOX 38-160, 023573, Bucharest, ROMANIA

[email protected]

Laboratorul de Nanotehnologii L1

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mailto:[email protected]



1. Teoria difractiei radiatiilor X si notiuni de Fizica Starii Condensate (background minimal)

2. Aplicatii ale metodelor XRD cu exemple– 1. Difracție pe pulberi (Materiale policristaline) X-Ray Powder Diffraction

• Compoziție de faze (phase composition analysis)• in situ XRD• % cristalinitate (analiza cantitativă&calitativă)• Dimensiune de cristalit • Incidență razantă GIXRD- glancing incident small angle X-ray diffraction of

mesostructures• Rafinarea parametrului de retea cristalina - lattice parameter refinement• Deformari si tensiuni reziduale - residual stress and strain• Microdifracție• Textură

– 2. Analiza filmelor subțiri• GIXRD glancing incident angle diffraction• Măsurători de reflectivitate de raze X –X - ray reflectivity • Filme epitaxiale (grosimi, tensiuni, compoziție, deformari)• Rocking curves – analiza perfecțiunii de monocristal

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Geometry – Structure - Analytic

Definitie Spectroscopia RX presupune analiza efectului interactiei radiatiei electromagnetice (foton RX – energie de ordinul keV, lungime de unda de ordinul 1 Angstrom) cu proba

Fotonul RX păstrează proprietatile radiatiei

electromagnetice

energia;

viteza;

amplitudinea;

frecventa;

unghiul de faza;

polarizarea;

directia de propagare.

Modificarea a cel putin una din

proprietati are loc la interactia

radiatiei electromagnetice X cu

proba

Lungine de unda Amplitudine

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• Hand mit Ringen (Hand with Rings): print of Wilhelm Röntgen's first "medical" X-ray, of his wife's hand, taken on 22 December 1895 and presented to Professor Ludwig Zehnder of the Physik Institut, University of Freiburg, on 1 January 1896[1][2]

Istoric (http://en.wikipedia.org/wiki/X-ray#History; http://en.wikipedia.org/wiki/X-ray#Crystallography;)

Descoperirea Wilhelm Conrad Röntgen - 1895 este creditat pentru descoperire, fiind primul care le-a studiat sistematic desi nu este primul care le-a observat efectele. Tubul cu raze X a fost inventat in 1875 - tubul Crookes, de catre fizicienii care studiau razele catodice – electronii de energii mari, accelerati la potentiale de ordinul 1-100 kV.

Ivan Pulyui, William Crookes, Johann Wilhelm Hittorf, Eugen Goldstein, Heinrich Hertz, Philipp Lenard, Hermann von Helmholtz, Nikola Tesla, Thomas Edison, Charles Glover Barkla, Max von Laue.

In April 1887-1892 Nikola Tesla began to investigate X-rays using high voltages and tubes of his own design. He invented and developed a special single-electrode X-ray tube which differed from other X-ray tubes in having no target electrode. The principle behind Tesla's device is called the Bremsstrahlung process in which a high-energy secondary X-ray emission is produced when concerning various experiments in his 1897 X-ray lecture before the New York Academy of Sciences. In this lecture Tesla stated the method of construction and safe operation of X-ray equipment. His X-ray experimentation by vacuum high field emissions also led him to alert the scientific community to the biological hazards associated with X-ray exposure.

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http://en.wikipedia.org/wiki/Wilhelm_R%C3%B6ntgen

http://en.wikipedia.org/wiki/December_22

http://en.wikipedia.org/wiki/Ludwig_Zehnder

http://en.wikipedia.org/wiki/University_of_Freiburg

http://en.wikipedia.org/wiki/X-ray




http://en.wikipedia.org/wiki/Wilhelm_Conrad_R%C3%B6ntgen

http://en.wikipedia.org/wiki/Ivan_Pulyui

http://en.wikipedia.org/wiki/William_Crookes

http://en.wikipedia.org/wiki/Johann_Wilhelm_Hittorf

http://en.wikipedia.org/wiki/Eugen_Goldstein

http://en.wikipedia.org/wiki/Heinrich_Hertz

http://en.wikipedia.org/wiki/Philipp_Lenard

http://en.wikipedia.org/wiki/Hermann_von_Helmholtz

http://en.wikipedia.org/wiki/Nikola_Tesla

http://en.wikipedia.org/wiki/Thomas_Edison

http://en.wikipedia.org/wiki/Charles_Glover_Barkla

http://en.wikipedia.org/wiki/Max_von_Laue

http://en.wikipedia.org/wiki/Nikola_Tesla

http://en.wikipedia.org/wiki/New_York_Academy_of_Sciences


A Brief History of X-Ray Diffraction• 1895: Röntgen discovers X rays

– received the first Nobel prize in physics in 1901• 1912: Laue diffracts X rays from single crystal

– 1914 Nobel prize in Physics• 1912: Bragg’s analyze crystal structures

– 1915 Nobel prize in physics• 1917: Ewald develops dynamical theory of X-ray diffraction• 1918: Scherrer uses X rays to determine crystallite size of nanocrystalline gold• 1935: X-Ray powder diffractometer developed by Le Galley• 1947: first commercial powder diffractometer • Subsequently, Nobel prize winners used XRD

– 1962: Crick, Watson, and Wilkins: structure of DNA– 1962: Perutz and Kendrew: structure of moglobin and hemoglobin– 1964: Hodgkin: structure of insulin– 1976: Lipscomb: structure of boron hydrides– 1985: Karle and Hauptman: development of direct methods in XRD

analysis– 1988: Deisenhofer, Huber, and Michel: X-ray structure of proteins for

photosynthetic center– 1994: Shull and Brockhouse: Neutron diffraction

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X-rays can diffract from a periodic array of coherent scatterers, such as atoms in a crystal

c

a b

NaNaClCl

Halite

Fm3m (225): 5.64/5.64/5.64 <90.0/90.0/90.0> NaCl

• Diffraction occurs when objects in a periodic array scatter radiation coherently, producing concerted constructive interference at specific angles.

• Crystalline materials are characterized by orderly periodic arrangements of atoms.

– The electrons in an atom coherently scatter light.

• The distance between atoms is such that they diffract light in the X-ray spectrum.

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•

The atoms in a crystal are a periodic array of coherent scatterers and thus can diffract light.

• Diffraction occurs when each object in a periodic array scatters radiation coherently, producing concerted constructive interference at specific angles.

• The electrons in an atom coherently scatter light. – The electrons interact with the oscillating electric field of the light

wave. • Atoms in a crystal form a periodic array of coherent scatterers.

– The wavelength of X rays are similar to the distance between atoms.

– Diffraction from different planes of atoms produces a diffraction pattern, which contains information about the atomic arrangement within the crystal

• X Rays are also reflected, scattered incoherently, absorbed, refracted, and transmitted when they interact with matter.

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• The X-rays can be:– attenuated

• absorbed• fluoresced• incoherently scattered

– coherently scattered• refracted• reflected• diffracted

• The electromagnetic moment of X-ray photons interacts with the electrons in matter

• The change in X-ray photons due to interaction with electrons can be used to discern information about the matter

• Phase information is ussually lost

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Bragg’s law is a simplistic model to describe the conditions that are required for diffraction.

• For parallel planes of atoms, with a space dhkl between them, constructive interference only occurs when Bragg’s law is satisfied.

• In our diffractometers, the X-ray wavelength is fixed.– Each plane of atoms produces a diffraction peak at

a specific angle .• The direction perpendicular to the planes must bisect

the incident and diffracted beams.

sin2 hkld

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Powder diffractometers typically use theBragg-Brentano parafocusing geometry.

• The incident angle between the X-ray source and the sample is .• The diffraction angle, between the incident beam and the detector angle, is 22. • The Bragg-Brentano geometry constrains to be always ½ of the detector

angle 2– This constraint results in the incident angle the detector angle being equal

to – Do not get confused: this is an artificial constraint. Diffraction does not

rely on the incident and detector angles being equal.

X-ray tube

Detector

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2

A single crystal in a Bragg-Brentano diffractometer produces one family of

peaks in the diffraction pattern.

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The diffraction pattern consists of a record of photon intensity versus detector angle 2.

• The position, intensity, width, and shape of the observed diffraction peaks tells us about the crystal structure and, in some cases, microstructure of the sample.

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22 2

• For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams).

A polycrystalline sample should contain thousands of crystallites. All diffraction peaks should be observed.

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What can we do with XRD?• Identify phase composition• Measure unit cell lattice parameters• Estimate crystallite size, microstrain, and defect concentration• Measure residual stress• Measure texture and/or epitaxy• Evaluate thin film quality• Measure multilayer thin film thickness, roughness, and density• Determine orientation of single crystals• Solve or refine crystal structures• Analyze ordered meso- and nanostructures• Etc.

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X-Ray Analysis MethodsX-Ray Analysis MethodsSignificant Experimental Facts (affecting measurements)

Detector – Dynamic range & Speed X-Ray Source (tube) – High Power Beam Intensity (emited, on the sample and at the

detector) X-ray Optics (high resolution incident and receiving optics) – Resolution, Intensity,

Speed Any attempt to filter/monochromatize the incident X-Ray beam reduces intensity on the

sample by several orders of magnitude (typically with a factor of 10-2 - 10-6)

We need:

The plane monochromatic wave approximation to be fulfilled (for high resolution measurements,

multiple reflections: 2- 4 for monochromator, 2 reflections for the analyzer)

Measurements to be performed as fast as possible, maintaining high resolution options

FWHM of minimum 10-2 - 10-3 o for high resolution measurements;

An almost perfect (and sometimes impossible) combination of Detector, X-ray tube, goniometer,

incident X-ray optics, etc. must be chosen to minimize measurement time and increase resolution

and sensitivity (in order to detect changes in lattice parameter of

and beyond)

97 1010 dd

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Most XRD Analyses are Focus on Identifying the Phases Present in a Sample

• We collect the XRD pattern over a range that is suitable for the material we are studying

• typically 20 to 70 °2θ for inorganic specimens – typically 5 to 40 °2θ for organic specimens– data collection time ranges from 5 min to 1 hour for our

instruments• in the “real world”, these times are typically 30 min to 2 hours

• We compare the experimental data to a reference database of powder diffraction patterns

• The diffraction pattern of every phase is a unique ‘fingerprint’• A crystalline phase is identified by the set of interplanar d spacings• Each lattice plane gives a diffraction peak at a specific angular value

(related to atomic plane spacing by BRAGG law) and the relative intensities of those peaks are also a “fingerprint” of the crystalline phase

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Application of X-ray DiffractionApplication of X-ray DiffractionFrom Sciences to EngineeringFrom Sciences to Engineering

X-ray Powder diffraction (XRPD)

High resolution X-ray diffraction (HRXRD) (including multiple refflection HR-MRXRD)

X-ray reflectometry (XRR, including HRMR XRR )

Grazing incidence diffraction (GIXRD)

In-plane grazing incidence diffraction (IPGID)

Small angle X-ray scattering (SAXS)

Single crystal diffraction (SCD)

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X-Ray Diffraction and Scattering X-Ray Diffraction and Scattering PrinciplePrinciple

Debye cone

Sample

Incident beam

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Powder diffraction data consists of a record of photon intensity versus detector angle 2.

• Diffraction data can be reduced to a list of peak positions and intensities• Each dhkl corresponds to a family of atomic planes {hkl}• individual planes cannot be resolved- this is a limitation of powder

diffraction versus single crystal diffraction

{202}

{113}

{006}

{110}

{104}

{012}

hkl

1.41.9680

100.02.0903

1.92.1701

36.12.3852

85.82.5583

49.83.4935

Relative Intensity (%)

dhkl (Å)

328.000025.7200

380.000025.6800

456.000025.6400

732.000025.6000

1216.000025.5600

1720.000025.5200

2104.000025.4800

1892.000025.4400

1488.000025.4000

1088.000025.3600

752.000025.3200

576.000025.2800

460.000025.2400

372.000025.2000

Intensity [cts]

Position[°2]

Raw Data Reduced dI list

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You can use XRD to determine• Phase Composition of a Sample

– Quantitative Phase Analysis: determine the relative amounts of phases in a mixture by referencing the relative peak intensities

• Unit cell lattice parameters and Bravais lattice symmetry– Index peak positions– Lattice parameters can vary as a function of, and therefore give

you information about, alloying, doping, solid solutions, strains, etc.

• Residual Strain (macrostrain)• Crystal Structure

– By Rietveld refinement of the entire diffraction pattern• Epitaxy/Texture/Orientation• Crystallite Size and Microstrain

– Indicated by peak broadening– Other defects (stacking faults, etc.) can be measured by analysis

of peak shapes and peak width

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Databases such as the Powder Diffraction File (PDF) contain dI

lists for thousands of crystalline phases. • The PDF contains over 200,000 diffraction patterns.• Modern computer programs can help you determine what phases are

present in your sample by quickly comparing your diffraction data to all of the patterns in the database.

• The PDF card for an entry contains a lot of useful information, including literature references.

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Quantitative Phase Analysis• With high quality data, you can

determine how much of each phase is present– must meet the constant volume

assumption (see later slides)• The ratio of peak intensities varies

linearly as a function of weight fractions for any two phases in a mixture– need to know the constant of

proportionality• RIR method is fast and gives semi-

quantitative results• Whole pattern fitting/Rietveld

refinement is a more accurate but more complicated analysis

0

10

20

30

40

50

60

0 0,2 0,4 0,6 0,8 1

X(phase a)/X(phase b)I(p

hase

a)/I(pha

se b) ..

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Unit Cell Lattice Parameter Refinement

• By accurately measuring peak positions over a long range of 2theta, you can determine the unit cell lattice parameters of the phases in your sample– alloying, substitutional doping, temperature and pressure, etc

can create changes in lattice parameters that you may want to quantify

– use many peaks over a long range of 2theta so that you can identify and correct for systematic errors such as specimen displacement and zero shift

– measure peak positions with a peak search algorithm or profile fitting

• profile fitting is more accurate but more time consuming– then numerically refine the lattice parameters

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126A, Erou Iancu Nicolae Street, R-077190 , Bucharest, ROMANIA www.imt.ro [email protected] IMT @2009, All rights reserved23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

2 (deg.)

Inte

nsity

(a.u

.)

00-043-1002> Cerianite- - CeO2

Crystallite Size and Microstrain• Crystallites smaller than ~120nm create broadening of diffraction

peaks– this peak broadening can be used to quantify the average

crystallite size of nanoparticles using the Scherrer equation– must know the contribution of peak width from the instrument

by using a calibration curve• microstrain may also create peak broadening

– analyzing the peak widths over a long range of 2theta using a Williamson-Hall plot can let you separate microstrain and crystallite size

cos

2LKB

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Detectors• point detectors

– observe one point of space at a time• slow, but compatible with most/all optics

– scintillation and gas proportional detectors count all photons, within an energy window, that hit them

– Si(Li) detectors can electronically analyze or filter wavelengths

• position sensitive detectors– linear PSDs observe all photons scattered along a line from 2 to 10° long– 2D area detectors observe all photons scattered along a conic section– gas proportional (gas on wire; microgap anodes)

• limited resolution, issues with deadtime and saturation– CCD

• limited in size, expensive – solid state real-time multiple semiconductor strips

• high speed with high resolution, robust

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Commonly Used X-Ray DetectorsCommonly Used X-Ray Detectors

Point detectors (0-D)Point detectors (0-D)

Scintillation counter

Proportional counter

Si(Li) solid state detector

Ge solid state detectors

Silicon pin diodes

Silicon drift detectors

Ionization chambers

Linear detectors (1-D)Linear detectors (1-D)

Silicon strip detector

Single wire proportional

Counter

Image plate detector (IP)

Linear CCD

Photographic film

Area detectors (2-D)

Multi wire proportional counter (MWPC)

Image plate detector (IP)

CCD camera

Photographic film

Pixel detectors

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X- Ray Methods for structural AnalysisX- Ray Methods for structural Analysis

Amorphous Materials

CrystallineMaterials

Crystalline Materialsnew applications

X-ray investigations:

XRR: layer thickness, density, roughness, interface layers

XRD: thermal stability

XRD: phase analysis, crystal orientation and perfection, thermal stability

GIXRD: perfection of epitaxial cap-layers, ultra thin layers, etc

IPXRD: phase analysis, crystal orientation/perfection, thermal Stability, etc.

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Not only can we identify what phases are present, we can also determine how much of each phase is present

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 422 (deg.)

Inte

nsity

(Cou

nts)

Red Paint Pigment Mixture

28 wt% Hematite, 28 wt% Hematite, FeFe22OO33

21 wt% 21 wt% Anatase, TiOAnatase, TiO22

51 wt% Rutile, TiO51 wt% Rutile, TiO22

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From the ratio of peak intensities, we can determine how much of each phase there is

• The ratio of peak intensities varies linearly with the ratio of weight fractions

• K is not easily determined if we do not know the mass absorption coefficients of all phases in our sample

• We can determine K:– empirically, by building

calibration curves– by using published values

(I/Ic)– by simulating the diffraction

pattern: whole pattern refinement

XXK

II

0

200

400

600

800

1000

0 20 40 60 80 100

X (Al2O3)

MgSiO3:Al2O3

YSZ:Al2O3

X(b

)*I(

Al 2O

3)/I(

b)

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Amorphous content is difficult to quantify with XRD

• We cannot directly model the scattering from the amorphous content in a sample– at best, we can emperically fit the amorphous ‘hump’

• We do not know as much about the amorphous content as we know about the crystalline content– what is the mass absorption factor of the amorphous

material?• what is the composition of the amorphous material?• what is the density of the amorphous material?

– is the amorphous composition homogeneous?

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10 15 20 25 30 352 (deg.)

Inte

nsity

(Cou

nts)

Determining % Crystallinity without adding a standard

• If we know/assume that the mass absorption coefficient of an amorphous phase is the same as the crystalline content, we can sometimes use the ratio of intensities to determine % crystallinityArea Crystalline Peaks: 108322 ctsArea Amorphous Hump: 124621 cts

% Crystalline: 46.5%% Amorphous: 53.5%

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Bragg-Brentano vs PB measurements Bragg-Brentano vs PB measurements Classical sealed X-Ray tube compared to Classical sealed X-Ray tube compared to

Rotating Anode Rotating Anode

Sealed 2.3 kWX-ray tube

Rotating anode 9kW

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9kW rotating anode, 200mm wafer

Triple axis, vertical goniometer

Independent Theta - Theta rotation

Horizontal sample position

X-Y Micro Area Mapping

Chi, Phi, Omega Eulerian Cradle

Bragg-Brentano (+focussing option)

Parallel beam (FWHM 0.1 to 0.003o)

XRR variable resolution (depth profiling)

HRMR-XRD [PB, Ge(220)x2, x4]

Texture Analysis and Pole Figures

GIXRD, In-plane, (GI)SAXS, RSM

D-texUltra high speed detector

CBO-f : 0.4 mm2 colimated parallel beam for increased intensity on sample and /or X-Y mapping

Capababities of the XRD system Capababities of the XRD system installed at IMT Bucharest installed at IMT Bucharest 5-10 January 2009 5-10 January 2009

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Essential Parts of the Diffractometer

• X-ray Tube: the source of X Rays• Incident-beam optics: condition the X-ray beam

before it hits the sample• The goniometer: the platform that holds and moves

the sample, optics, detector, and/or tube• The sample & sample holder• Receiving-side optics: condition the X-ray beam

after it has encountered the sample• Detector: count the number of X Rays scattered by

the sample

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Most of powder diffractometers use the Bragg-Brentano

parafocusing geometry.• A point detector and sample are

moved so that the detector is always at 2q and the sample surface is always at q to the incident X-ray beam.

• In the parafocusing arrangement, the incident- and diffracted-beam slits move on a circle that is centered on the sample. Divergent X rays from the source hit the sample at different points on its surface. During the diffraction process the X rays are refocused at the detector slit.

• This arrangement provides the best combination of intensity, peak shape, and angular resolution for the widest number of samples.

F: the X-ray sourceDS: the incident-beam divergence-limiting slitSS: the Soller slit assemblyS: the sampleRS: the diffracted-beam receiving slitC: the monochromator crystalAS: the anti-scatter slit

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X-radiation for diffraction measurements is produced by a sealed tube or rotating anode.

• Sealed X-ray tubes tend to operate at 1.8 to 3 kW.

• Rotating anode X-ray tubes produce much more flux because they operate at 9 to 18 kW. – A rotating anode spins the anode

at 6000 rpm, helping to distribute heat over a larger area and therefore allowing the tube to be run at higher power without melting the target.

• Both sources generate X rays by striking the anode target wth an electron beam from a tungsten filament.– The target must be water cooled.– The target and filament must be

contained in a vacuum.

Cu

H2O In H2O Out

e-

Be

XRAYS

windowBe

XRAYSFILAMENT

ANODE

(cathode)

AC CURRENT

window

metal

glass

(vacuum) (vacuum)

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The wavelength of X rays is determined by the anode of the X-ray source.

• Electrons from the filament strike the target anode, producing characteristic radiation via the photoelectric effect.

• The anode material determines the wavelengths of characteristic radiation.

• While we would prefer a monochromatic source, the X-ray beam actually consists of several characteristic wavelengths of X rays.

KL

M

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Spectral Contamination in Diffraction PatternsK1

K2

KW L1

K1

K2 K1

K2

• The Ka1 & Ka2 doublet will almost always be present– Very expensive optics can remove the Ka2 line– Ka1 & Ka2 overlap heavily at low angles and are

more separated at high angles• W lines form as the tube ages: the W filament

contaminates the target anode and becomes a new X-ray source

• W and lines can be removed with optics

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The X-ray beam produced by the X-ray tube is divergent. Incident-beam optics are used to limit this divergence

• X Rays from an X-ray tube are: – divergent– contain multiple characteristic wavelengths as well as Bremmsstrahlung

radiation• neither of these conditions suit our ability to use X rays for analysis

– the divergence means that instead of a single incident angle q, the sample is actually illuminated by photons with a range of incident angles.

– the spectral contamination means that the smaple does not diffract a single wavelength of radiation, but rather several wavelengths of radiation.

• Consequently, a single set of crystallographic planes will produce several diffraction peaks instead of one diffraction peak.

• Optics are used to:– limit divergence of the X-ray beam– refocus X rays into parallel paths– remove unwanted wavelengths

sin2 hkld

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Divergence slits are used to limit the divergence of the incident X-ray beam.

• The slits block X-rays that have too great a divergence.

• The size of the divergence slit influences peak intensity and peak shapes.

• Narrow divergence slits:– reduce the intensity of the X-ray

beam– reduce the length of the X-ray beam

hitting the sample– produce sharper peaks

• the instrumental resolution is improved so that closely spaced peaks can be resolved.

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Other optics:

• limit divergence of the X-ray beam– Divergence limiting slits– Parallel plate collimators– Soller slits

• refocus X rays into parallel paths– “parallel-beam optics”– parabolic mirrors and capillary

lenses– focusing mirrors and lenses

• remove unwanted wavelengths– monochromators– Kb filters

Parallel Plate Collimator & Soller Slits block divergent X-rays, but do not restrict beam size like a divergent slit

Göbel Mirrors and capillary lenses collect a large portion of the divergent beam and refocus it into a nearly parallel beam

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Monochromators remove unwanted wavelengths of radiation from the incident or

diffracted X-ray beam.• Diffraction from a crystal monochromator can be used to

select one wavelength of radiation and provide energy discrimination.

• An incident-beam monochromator might be used to select only Ka1 radiation for the tube source.

• A diffracted-beam monochromator may be used to remove fluoresced photons, , or W-contamination photons from reaching the detector.– Without the RSM slit, the monochromator removes ~75% of

unwanted wavelengths of radiation.– When the RSM slit is used, over 99% of the unwanted

wavelengths of radiation can be removed from the beam.

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Wavelengths for X-Radiation are Sometimes Updated

2.084920 Å2.08487ÅCr K0.632305 Å0.632288ÅMo K

2.293663 Å2.293606ÅCr K20.713609 Å0.713590ÅMo K2

2.289760 Å2.28970ÅCr K10.709319 Å0.709300ÅMo K1

ChromiumAnodes

MolybdenumAnodes

1.620830 Å1.62079ÅCo K1.392250 Å1.39220ÅCu K

1.792900 Å1.792850ÅCo K21.544426 Å1.54439ÅCu K2

1.789010 Å1.788965ÅCo K11.540598 Å1.54056ÅCu K1

Holzer et al.(1997)

Bearden(1967)

CobaltAnodes

Holzer et al.(1997)

Bearden(1967)

CopperAnodes

• Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Phys. 39 (1967) are incorrect.

– Values from Bearden (1967) are reprinted in international Tables for X-Ray Crystallography and most XRD textbooks.

• Most recent values are from Hölzer et al. Phys. Rev. A 56 (1997)

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High Resolution Measurement Types available

Hardware - In-plane difraction

- (GI)SAXS, RSM, RC

- Ge (220) 2 bounce monochromator

- Ge (220) 4 bounce monochromator

- Ge (220) 2 bounce analyzer

- CBO-f unit*

-DTexUltra high speed detector*

(* by the end of 2009, September)

Options

(future financing from other projects)

- Ge (440)x2/ x4 monocromator

- 2D Detector

- High/Low temperature chamber

- Simultaneous DSC/XRD chamber

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Crystallite Size Broadening

• Peak Width B(2q) varies inversely with crystallite size• The constant of proportionality, K (the Scherrer constant) depends

on the how the width is determined, the shape of the crystal, and the size distribution– the most common values for K are 0.94 (for FWHM of spherical

crystals with cubic symmetry), 0.89 (for integral breadth of spherical crystals with cubic symmetry, and 1 (because 0.94 and 0.89 both round up to 1).

– K actually varies from 0.62 to 2.08– For an excellent discussion of K, refer to JI Langford and AJC

Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size,” J. Appl. Cryst. 11 (1978) p102-113.

cos94.02

LB

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Factors that contribute to peak broadening

• Instrumental Broadening• Crystallite Size• Microstrain (lattice distortions)• Faulting• Dislocations• Antiphase Domain Boundaries• Grain Surface Relaxation• Solid Solution Inhomogeneity• Temperature Factors

• The peak profile is a convolution of the profiles from all of these contributions

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Lattice Parameters

The position of the diffraction peaks are a product of the space between planes of

atoms. Consequently, we can use XRD to probe

anything that affects that interplanar spacing.

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Important characteristics of samples for XRPD

• a flat plate sample for XRPD should have a smooth flat surface– if the surface is not smooth and flat, X-ray absorption

may reduce the intensity of low angle peaks– parallel-beam optics can be used to analyze samples

with odd shapes or rought surfaces• Densely packed• Randomly oriented grains/crystallites• Grain size less than 10 microns• ‘Infinitely’ thick

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Texture analysis is the study of orientation of crystallites within a sample

• Random Orientation– All crystallites are randomly

oriented– there is an even distribution of

all possible orientations• Textured

– the orientation of crystallites are distributed in a non-random manner

– preferred orientation: texture that is not wanted

• Epitaxial– all crystallites are perfectly

oriented in exactly the same way

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Intro to X-ray Pole Figures

• X-ray diffraction; pole figures; measures average texture at a surface (µm penetration); projection (2 angles).

• Neutron diffraction; type of data depends on neutron source; measures average texture in bulk (cms penetration in most materials) ; projection (2 angles).

• Electron [back scatter] diffraction; easiest [to automate] in scanning electron microscopy (SEM); local surface texture (nms penetration in most materials); complete orientation (3 angles).

• Optical microscopy: optical activity (plane of polarization); limited information (one angle).

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Preferred Orientation (texture)• Preferred orientation of crystallites can create a systematic variation

in diffraction peak intensities– can qualitatively analyze using a 1D diffraction pattern– a pole figure maps the intensity of a single peak as a function of

tilt and rotation of the sample• this can be used to quantify the texture

(111)

(311)(200)

(220)

(222)(400)

40 50 60 70 80 90 100Two-Theta (deg)

x103

2.0

4.0

6.0

8.0

10.0

Inte

nsity

(Cou

nts)

00-004-0784> Gold - Au

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Preferred orientation

• If the crystallites in a powder sample have plate or needle like shapes it can be very difficult to get them to adopt random orientations– top-loading, where you press the powder into a

holder, can cause problems with preferred orientation• in samples such as metal sheets or wires there is almost

always preferred orientation due to the manufacturing process

• for samples with systematic orientation, XRD can be used to quantify the texture in the specimen

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Pole figure measurementsPole figure measurements

2

2 defines the Bragg angle planes of diffraction

0 30 60 90 120 150 180

Alpha

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Line

0 90 180 270 360

Beta

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Circle

– sample rotation – sample inclination

= 90°-

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Si 111 pole figure / projectionSi 111 pole figure / projection

0 30 60 90 120 150 180

Alpha

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Line

0 90 180 270 360

Beta

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Circle

layer structurePerfect Si

0 30 60 90 120 150 180

Alpha

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Line

0 90 180 270 360

Beta

1e+4

1e+6

Ave

rage

Inte

nsity

Cut Circle

111 spots 180° rotated + additional spots !

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By controlling the incident angle, we can control the depth of penetration of X-rays

• GIXRD can be used to optimize the diffractometer for the analysis of surface layers of a sample

• Varying incident angles can be used to probe different depths, providing depth profiling

– Penetration depth is a function of the mass absorption coefficient, composition, density, and packing density of the sample

• This technique can be combined with all of the analyses that have been previously discussed

0

20

40

60

80

100

120

140

0 1 2 3Incident Angle

Pene

tratio

n De

pth

C (m

icron

s)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Pene

tratio

n De

pth

PZT

(micr

ons)

GraphitePZT

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High Resolution Diffraction is used to evaluate epitaxial multilayer thin films

• In a single layer epitaxial thin film, high resolution XRD (HRXRD) can be used to evaluate the quality of the thin film

• Rocking curves compare the distribution of intensity of a diffraction peak as a function of the tilt of the sample

30.6 30.7 30.8 30.9 31.0 31.1 31.2 31.3 31.42 (deg.)

Inte

nsity

(a.u

.)

Perfect Single Crystal Substrate

Good Epitaxial Thin FilmPoor Epitaxial Thin Film

Horrible Quality, Not Epitaxial At All, Thin Film

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The general problem:

substrate crystal lattice, e.g. Si

d,Substrate

d,Substrate

d,Layer

d,Layer

Epitaxial layer with d,L d,S

Diffusion or implantation layers with modified lattice spacing

Characterization of epitaxial layersCharacterization of epitaxial layers

d/ d = f(z) - depth profile

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Multilayer thin films create dynamic interference fringes produced by the multilayer

superstructure• Form and perfection of the

multilayer superstructure– layer thickness, superlattice

period, compositional profile, miscut angle and direction

• Quality of surfaces and interfaces– heterointerface transition,

interdiffusion, interface roughness

• Crytalline properties– elastic lattice distortion, strain

relaxation, porosity, structure defects such as misfit dislocations

-1000 -500 0 500 1000 1500Omega/2Theta (s)

0.1

1

10

100

1K

10K

100K

1M

10Mcounts/s

GeSi on Ge0 0 4

Omega 32.938602Theta 66.17160

Phi 0.00Psi 0.19

X 9.00Y -10.00

S

L

004 GeSi on Ge.xrdml

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Direct information from a Rocking Direct information from a Rocking Curve SpectraCurve Spectra

-3000 -2000 -1000 0 1000

10-6

10-5

10-4

10-3

10-2

10-1

100

Cap: (53.2 ± 1.0) nmSiGe: (118.0 ± 0.5) nmx: (19.80 ± 0.08) %

Ref

lect

ivity

Delta Theta [arcsec]

exp. sim.

Simulation with IHP program RCRefSimW,

Prof. P. Zaumseil

Ge concentration

(more general: d/d )

Ge:

d/d = 0.005x2+0.03675x

Layer thickness

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SiGe HBT structureSiGe HBT structure

-3000 -2000 -1000 0 1000

10-6

10-5

10-4

10-3

10-2

10-1

100

0 20 40 60 80 100 1200

5

10

15

20

Ref

lect

ivity

Delta Theta [arcsec]

exp. sim.

19.48 %

31.6855.42

Ge

cont

ent

[ % ]

Depth [nm]

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Reciprocal space map

-1.0 -0.8 -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6 0.8 1.0Omega/2Theta

-0.8

-0.6

-0.4

-0.2

-0.0

0.2

0.4

0.6

0.8

Omega

GaInAs on GaAs 4 4 4

Omega 15.156002Theta 140.55000

Phi 90.00Psi 0.27

X 0.00Y 0.00 Map444b.a00

1.6

2.7

4.6

7.9

13.7

23.6

40.7

70.1

120.8

208.1

358.7

618.2

1065.4

1836.3

3164.8

5454.5

9400.6

16201.9

27923.6

48125.8

82944.0

7600 7650 7700 7750 7800 7850Qx*10000(rlu)

5250

5300

5350

5400

5450

5500

Qy*10000(rlu)

GaInAs on GaAs 4 4 4

Omega 15.156002Theta 140.55000

Phi 90.00Psi 0.27

X 0.00Y 0.00 Map444b.a00

1.6

2.7

4.6

7.9

13.7

23.6

40.7

70.1

120.8

208.1

358.7

618.2

1065.4

1836.3

3164.8

5454.5

9400.6

16201.9

27923.6

48125.8

82944.0

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Metallization / formation of cobalt Metallization / formation of cobalt silicide on Sisilicide on Si

»

TwoTheta converted to netplane spacing D

10 nm Co deposited on Si,

annealed at different temperatures

different phases (CoSi and CoSi2) are

formed as a function of temperature.

optimization of thermal process budget

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•

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Meas. dataSimulation

10-6

10-5

10-4

10-3

10-2

10-1

100

0.0000 1.0000 2.0000 3.0000 4.0000

REFLECTIVITY PROFILE

2theta angle (deg.)

Ref

lect

ivity

(a.u

.)

Density distr.

0.00000

10.00000

20.00000

30.00000

40.00000

0.000 10.000 20.000 30.000 40.000 50.000

Density Distr.

Depth (nm)

Den

sity

(g/c

m3)

1 Au t = 41.968(3)nm ρ = 19.3g/cm3 σ = 1.028(2)nm

1 Glass - ρ = 2.213g/cm3 σ = 0.6nm

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Metallization /thickness control Metallization /thickness control TaTa22OO33/Ta/TaN/SiO/Ta/TaN/SiO22/Si/Si

Simulation with IHP simulation program

RCRefSimW

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XRR of very thin Si3N4 layer on SiXRR of very thin Si3N4 layer on SiSmartLab measurement + RCRefSimW fitting

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XRR of 120 nm Ge layer on SiXRR of 120 nm Ge layer on SiSmartLab measurement + RCRefSimW fitting

dGe = (121.2 ± 0.2) nm, = 0.4 nm

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XRR determination of layer thicknessXRR determination of layer thickness

Ultra-high resolution XRR at SmartLab and simulation with RCRefSimW 1.08

dSi = 287.5 nm

dY2O3 = 26.0 nm

dPr2O3 = 6.6 nm

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