Bruker AXS Good Diffraction Practice I - X-ray Reflectometry

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Good Diffraction Practice

Webinar Series

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X-ray Reflectometry – Jul 21, 2010

Two-Dimensional XRD – Aug 11, 2010

Powder XRD – Sep 30, 2010

www.bruker-webinars.com

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Welcome

Dr. Martin ZimmermannApplications Scientist, XRDBruker AXS GmbHKarlsruhe, Germanymartin.zimmermann@bruker-axs.de+49.721.595.4655

Peter LaPumaVice President of Sales & MarketingBruker AXS Inc.Madison, Wisconsin, USApeter.lapuma@bruker-axs.com+1.608.276.3000

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Overview

Introduction

Appropriate samples for XRR

Adapting the experimental setup

Performing an XRR experiment

Data interpretation

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What is X-ray Reflectometry (XRR)?

A surface-sensitive x-ray scattering technique

• Non-destructive method• Wavelength probes on nanometer scale• Works for crystalline and amorphous materials

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What is X-ray Reflectometry (XRR)?

A surface-sensitive X-ray scattering technique

• Non-destructive method• Wavelength probes on nanometer scale• Works for crystalline and amorphous materials

What does XRR provide?

• Layer thickness 0.1 nm – 1000 nm• Material density < 1-2%• Roughness of surfaces and interfaces < 3-5 nm

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The general scattering geometry

ikr fk

r

if kkqrrr

−=θ2

22 )exp()()( rdrqirqS

V

rrrrr∫∝ ρ θ

λsin2

=d

Probed quantity Probed lengthscale

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Wavevector transfer has a non-zero component perpendicular to the sample surface

For Cu-Kα (λ=1.54Å)

XRR probes the laterally averaged electron density

yxzyxz

,),,()( ρρ =

The specular XRR scattering geometry

q=(0,0,q )z

ki kf

θ θ

zx

θsin2kqz =

22 )exp()()( ∫∝ dzziqzqS zz ρ

][140/2 1−= nmqz θ

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The reflectivity from a substrate –in one minute

0 z

ρ( )z

exp(iqz)

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The reflectivity from a substrate –in one minute

0 z

ρ( )z

exp(iqz)

R exp(-iqz)

T exp(iQz)

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The reflectivity from a substrate –in one minute

0 z

ρ( )z

exp(iqz)

R exp(-iqz)

T exp(iQz)

ρπ erqQ 162 −=2

2)()(QqQqqRqr FF +

−==

Fresnel reflectivity

with

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Density dependency of the reflectivity

The higher the electron density ρ(z) of a material the higher the critical angle

The higher the electron density, the more intensity is scattered at higher angles

This limits the accessible angular range for light materials like soft-matter films

ρθ ∝c

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2⎟⎠⎞

⎜⎝⎛≈

θθcr

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Influence of roughness (1)

Wavinesssmall inclinations of the surface normalon a large scale of some 100 nm

wavinessbroadening of the specularreflected beam

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Influence of roughness (1)

Wavinesssmall inclinations of the surface normalon a large scale of some 100 nm

waviness

microscopicroughness

broadening of the specularreflected beam

Microscopic Roughnesslarge inclinations of the surface normal on an atomic scale of a few nanometers

leads to diffuse reflection of the incident beam the intensity of the specular reflected beam decreases

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Influence of roughness (2)

Modeling microscopic roughness

Interface is represented by an ensemble of sharp interfaces

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

2

2 2exp

21)(

σπσzzw

rms-roughness σ: = standard deviation of the Gaussian distribution

)(zw

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Influence of roughness (2)

Modelling microscopic roughness

Interface is represented by an ensemble of sharp interfaces

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

2

2 2exp

21)(

σπσzzw

rms-roughness σ: = standard deviation of the Gaussian distribution

modified reflection coefficients for rough interfaces:

( )2/exp 22zqσ−

)(zw

)()( zFz qRqR = Exponential decay

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Influence of roughness (3)

Roughness decreases the reflected intensity dramatically

XRR is highly sensitive to roughness

Roughness causes diffuse scattering

The interface roughness should not be larger than

2-3 nm.

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The interference of the waves reflected from the interfaces causes oscillations of period

The minimal observable thicknessis limited by the maximal measurable range

The maximal observable thicknessis limited by the instrumental resolution

The sample should have thicknesses observable with the

instrumental setup.

XRR from Multilayers: Thickness fringes (1)

dqz /2π=Δ

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Thickness fringes (2): Amplitude

Amplitude of the thick-ness fringes increases with increasing density contrast

XRR is quite sensitive to variations of the electron density

The sample should have a good contrast in the

electron density.

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X-ray ReflectometryDemands on Sample Properties

Golden Rule:

You should be able to see your reflection on the surface of the

sample!

Flat and lateral homogeneous - not structured

Sample roughness < 5nm

Good contrast in electron density for layered samples

Length of at least 2-5 mm in beam direction

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Audience poll

Please use your mouse to answer the question to the right of your screen:

What percentage of your samples match the criteria for XRR samples?

o < 10 %o 10 % - 30 % o 30 % - 50 % o 50 % - 80 % o 80 % - 100 %o 100 %

Criteria for XRR samples

Flat and lateral homogeneous -not structured

Sample roughness < 5nm

Good contrast in electron density for layered samples

Length of at least 2-5 mm in beam direction

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Instrumental resolution in XRR

qki

kf

θ θ

The ideal instrument

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Instrumental resolution in XRR

The scattering function S is convoluted with the resolution function R of the instrument:

Δθi Δθf

qki

kf

ΔqzΔqz

Δqx

θ θ

∫ −= dQQqRQSqI )()()( 2

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Rough estimation of the resolution: FWHM of the direct beam ΔΨ

Instrumental resolution in XRR

θθ Δ=Δ )cos(2kqz

The scattering function S is convoluted with the resolution function R of the instrument:

Δθi Δθf

qki

kf

ΔqzΔqz

Δqx

θ θ

θΔ=Δ zx qq

∫ −= dQQqRQSqI )()()( 2

2/ψθ Δ=Δ

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Rough estimation of the resolution: FWHM of the direct beam ΔΨ

Observation of thickness fringes requires resolution better than

Instrumental resolution in XRR

θθ Δ=Δ )cos(2kqz

The scattering function S is convoluted with the resolution function R of the instrument:

Δθi Δθf

qki

kf

ΔqzΔqz

Δqx

θ θ

θΔ=Δ zx qq

d2/λθ <<Δ∫ −= dQQqRQSqI )()()( 2

2/ψθ Δ=Δ

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The experimental setup for XRR

Parallel beam geometry

Setups with different resolutions

The footprint

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Simplest setup for XRR

Reasonable resolution requires slit of 50-100 µm Intensity is on the order of 107 cpsFull energy spectrum creates high background

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Principle of the Göbel Mirror

Mirror converts ≈0.35° into a parallel beam of 1.2 mm (60-mm mirror)Integrated intensity >109 cpsMainly Kα-radiation is reflected

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Handling the high flux: AutomatedAbsorber

Scintillation counters linear up to 2 x 105 cps

10,000 times more intensity from the tube side

4-position wheel with places for 4 different absorber foils

standard absorption factors:

1 - ~10 - ~100 - ~10000Rotary absorber

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The standard XRR setup for thin films

Slits can be easily exchanged to tune resolutionA reasonable resolution requires a slit size of 0.1 – 0.2 mm Integrated intensity ≈ 2x108 cps

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Reflectometry with different slits

with 0.1 mm slit

~ 6.5 h

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Reflectometry with different slits

with 0.6 mm slitwith 0.1 mm slit

~ 5 min~ 6.5 h

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XRR setup for very thin layers

Full beam on primary sideSoller with resolution down to 0.1°Integrated intensity ≈ 8x108 cps

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Limits of X-Ray Reflectometry Thin layers Example: LaZrO on Si

2θ [°]1412108642

Inte

nsity

[au]

-81*10

-71*10

-61*10

-51*10

-41*10

-31*10

-21*10

-11*10

01*10

Si (111)

6.7 nm LaZrO

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XRR with an analyzer crystal

Analyzer crystal separates Kα1, suppresses diffuse scattering and fluorescenceCrystal can accept the full incident beamIntegrated intensity ≈ 3x107 cps (for a 3-bounce analyzer)

Analyzer crystal improves the resolution:

1-bounce Ge(220)3-bounce Ge(220)

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XRR setup for thick layers

Analyzer crystal: 1-bounce Ge(220s)3-bounce Ge(220s)

Monochromator crystal: 4-bounce Ge

Monochromator cystals provide highly parallel and monochromatic beamCrystals can accept the full incident beam Integrated intensity ≈ 105 - 106 cps

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Limits of X-ray Reflectometry Thick layers example: SiO2 on Si

Int. [a

u]

5

10

100

1000

1e4

2θ [°]

0.11 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Si

1014 nm SiO2:H

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For Cu-Kα radiation: λ ≈ 1.54 ÅValues for Δθ were obtained by scanning the direct beamObtained from the rough estimation

Resolution of differents setups

θλ Δ≈ 2/d

Tube side Detector side Δθ [deg] dmax [nm]

GM + 1.2mm 0.2° soller 0.06° 73

GM + 0.2mm 0.2mm slits 0.029° 150

2xGe(220a) 0.2mm slits 0.026° 170

GM 3xGe(220s) 0.013° 340

2xGe(220a) 3xGe(220s) 0.01° 440

4xGe(220s) 3xGe(220s) 0.006° 735

4xGe(440s) 3xGe(220s) < 0.006° > 735

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Please use your mouse to answer the question to the right of your screen:

What is the typical film thickness of your XRR samples?

o Very Thin layers < 10 nm

o Thin layers 10 nm – 100 nm

o Medium 100 nm – 200 nm

o Thick layers 200 nm – 350 nm

o Very Thick layers > 350 nm

Audience Poll

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Influence of X-ray wavelength on the reflectivity

Higher wavelength + better resolution of fringes and higher critical angle- high air-absorption reduces intensity + air scattering

290 nm boron on silicon

(2.29Å)

(1.54Å) Poll Results

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Adapting the optics to the sample

brings the best results

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Easy change of the resolution on the tube side…

Rotary absorber

X-ray tube

Goebel mirrorslit-holder

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…and more resolution…

Rotary absorber

Goebel mirrorslit-holder

X-ray tube

2-bounce Ge(220a)

monochromator

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…and even more resolution

Rotary absorber

Goebel mirrorslit-holder

X-ray tube

4-bounce Ge(220s)

monochromator

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Automated change of the resolution on the detector side

Motorized switch between• one high-resolution beam path• and two high-flux beam paths

PATHFINDERoptics

Motorized slit Use of multiple beampath optics allows changing the resolution within seconds

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Automated change of the resolution on the detector side

Soller + slit Motorized slit

Double slit system for intermediate resolution

Analyzer

Analyzer crystal with high resolution

Soller for high flux / low resolution

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Documentation of the experimental setup

A detailed documentation of the experimental setup is mandatory for proper data-analysis

• Resolution function• Footprint correction

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Geometrical corrections –The footprint (1)

d : beam widthL : sample length || beamD : illuminated area

L

d

θ

D

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Geometrical corrections –The footprint (1)

)/arcsin( LdB =θ)sin(/)sin( BB θθ=

θsin/dD =

d : beam widthL : sample length || beamD : illuminated area

L

d

θ

D

Footprint of the beam on surface

Beam matches the sample size at

Below θB the intensity is reduced by

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Geometrical corrections –The footprint (2)

Beamsize : 200 µm

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Controlling the footprint – The Knife Edge Collimator (1)

The KEC allows the removal of the footprint effect by making the probed area smaller than the sample sizeFor higher angles, the KEC needs to be lifted from the surface to gain fluxThe measurement with KEC will be upscaled to the curve without KEC

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0,0 0,5 1,0 1,5 2,0104

105

106

107

108

with KECwithout KEC

Inte

nsity

2θ [deg]

Controlling the footprint – The Knife Edge Collimator (2)

Measurement with KEC must be performed up to at least 2θB

The high-angle measure-ment without KEC must have an overlap with the KEC – measurement to rescale the data properly

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Performing an XRR measurement

Sample alignment procedure

Measurement strategy• Statistics• Diffuse scattering

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Sample alignment in 5 steps…

Ideal sample alignment

Situation after sample mounting

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Sample alignment (1): Defining the 2θ scale

2θ

2 =0°θ

Detector scan without sample

2θ aligned to primary beam

0I

θΔ2Instrumental resolution

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z

I(z )=I /21/2 0

Sample alignment (2): First height alignment

2/0I

2/1z

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ω

Sample alignment (3): Coarse alignment of the surface normal

maxω maxω

2/maxI

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z

I(z )=I /21/2 0

Sample alignment (4): Fine height alignment

2/0I

2/1z

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Sample alignment (5): Alignment of the reflection condition

ω

ω–offset of surface relative to drive:

max2/2 ωθω −=Δ

°= 4.02θ

maxω

Waviness /domains on the sample surface

θΔ

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Sample alignment: Remarks

Bθω

Determination of the footprint angle θB

If the rocking-curve in reflection condition is slighty distorted, e.g. peak shoulders, align the sample at higher angles (reduction of the illuminated area)

If the triangle is not symmetric, the sample is not centered along the beam.

If the rocking-curve in reflection condition is strongly distorted, e.g. multiple peaks, rotate the sample 90° or translate the sample along the beam

No improvement: Reduce the beam size/width and/or if available use KEC

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Proper analyses require that the statistics is better than the amplitude of the oscillations

The decay of the reflected intensity requires longer counting time at larger angles to keep the statistics good

Keeping the statistics high – Variable counting time

)()( θθ II ±

1000 count level

CPS

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What do we measure?

Data provided by S. Tiemeyer, TU Dortmund

GaAswafer

Can we analyze this measurement

properly?

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Measuring the diffuse background

XRR

ki kf

Δqx

θ θ

Δθ

longitudinaldiffuse scan

diffuse scattering

Imperfections - like roughness - cause diffuse scattering

Diffuse scattering contributes to the reflectivity

Theory of XRR does not account for diffuse scattering

Perform a longitudinal diffuse scan to estimate the diffuse scattering in the specular direction

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True specular reflectivity

Diffuse scattering limits the accessible 2θ range

Measurement of the diffuse scattering is time-consuming

Choose large step-size and interpolate

Extracting the true specular reflectivity

Data provided by S. Tiemeyer, TU Dortmund

)2()2()2( θθθ diffXRRTS III −=

GaAswafer

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Analysis of XRR curves

Fitting of XRR curves

Examples

Limitations

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Account for the instrumental setup

Analytical calculation of the resolution functionCalculation of the footprint-correction

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Evaluation of SampleFitting Procedure

Sample Model parameterized by {p1,…pN}

Tolerance

XRR Simulation

Comparison with Experiment, χ2 cost function

Minimization of χ2 using Genetic Algorithm, Levenberg-Marquardt, Simplex,Simulated Annealing, etc. in view of {p1..pN}

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Amorphous HfO2 film – Ultra thin films

θ [degees]

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XRR on MEMS – Ru/SiN film

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GMR Heterostructure – 8 Layers

Sample courtesy of Dr. Schug, IBM Mainz

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Limits of XRR: Uniqueness of the solution (1)

Data provided by S. Tiemeyer, TU Dortmund

Everything depends

on the sample model...

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Limits of XRR: Uniqueness of the solution (2)

0 1 2 3 4 5 6

100

101

102

103

104

105

106

107

meas sin-function (2-layers)

Inte

nsity

[a

.u.]

2θ [degrees]

007.02 =χ

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0 1 2 3 4 5 6

100

101

102

103

104

105

106

107

meas error-function (3-layers)

Inte

nsity

[a

.u.]

2θ [degrees]

007.02 =χ

Limits of XRR: Uniqueness of the solution (3)

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Limits of XRR: What can we really have access to?

0 1 2 3 4 5 6

100

101

102

103

104

105

106

107

meas simulation

Inte

nsity

[a

.u.]

2θ [degrees]

006.02 =χ

What does the sample-modellook like???

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Limits of XRR: What can we really have access to?

0 1 2 3 4 5 6

100

101

102

103

104

105

106

107

meas simulation

Inte

nsity

[a

.u.]

2θ [degrees]

006.02 =χ

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Choose the right optics

Align the sample properly

Remember to account for diffuse scattering

Do not over-interpret your data

Never forget about the limited spatial resolution

Summary

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Summary

Choose the right optics

Align the sample properly

Remember to account for diffuse scattering

Do not over-interpret your data

Never forget about the limited spatial resolution

Thank you for your attention…

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Any Questions?

Please type any questions you may have in the Q&A panel and then

click Send.

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To Learn More About XRD and XRR

Bruker Training Central (BTC) – Online Training CoursesWeb-based training courses delivered through your browserInclude slides, audio, video and participant Q&AUpcoming live:• Aug 11 – Good Diffraction Practice II: Two-Dimensional XRD (1 hr)• Sep 30 – Good Diffraction Practice III: Powder XRD (1 hr)• Oct 5-6 – X-ray Reflectometry (2 hrs)

On-demand:• Fundamentals of Powder XRD• Powder XRD Data Acquisition & Analysis• Basics of Two-Dimensional XRD• Getting Started with LEPTOS• Getting Started with TOPAS www.brukersupport.com

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