X-ray interferometry for dimensional metrology World Interferometry Day Andrew Yacoot 14 April 2021 [email protected] Layout of talk

▪ Introduce NPL ▪ Traceability for length and nanometrology ▪ How the SI has adapted to changing requirements for length metrology at the nanoscale? ▪ Introduction to x-ray interferometry ▪ Applications ▪ Conclusion Punch line: an x-ray interferometer is a ruler where the graduations are the atoms in a crystal UK’s national metrology institute provides measurement expertise underpinning economic growth and quality of life in the UK. From new antibiotics and more effective cancer treatments, to unhackable quantum communications and superfast 5G, technological advances must be built on a foundation of reliable measurement to succeed.

As a national laboratory, our advice is always impartial and independent, meaning consumers, investors, policymakers and entrepreneurs can always rely on the work we do. UK’s national metrology institute

▪ Responsible for realisation of the SI in the UK providing traceability to the 7 base units from which others are derived Kilogram

Candela Metre

Mole Second

Kelvin Ampere Measurement traceability

“property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties” Traceability chain

One calibration by NPL against a national measurement standards for an accredited calibration laboratory

Commercial services from accredited calibration and testing laboratory

Traceable calibration of hundreds of instruments for use in industry

Thousands of traceable measurements and instrument calibrations by industry Traceability chain for realisation of the metre The metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second

Realised through known laser frequencies

e.g I2 stabilised He Ne laser

optical interferometry for displacement metrology

m cm mm μm nm pm The Taniguchi extrapolation – from 1983 Adapted from: Taniguchi, 1983, Annals of the CIRP, 32/2 25 - 30 year time lag between precision levels

Mechanical comparators, micrometers, dial gauges

Optical comparators

Laser measuring instruments, roundness testers Metal bar

High precision laser instruments, Krypton lamp surface analyzers

HeNe Electron microscopes, electron diffraction, ion analyzers, X-ray micro analyzers, Auger analyzers, plasmonics, scanning probe microscopes Nanometrology for the future? ▪ Stage and sensor manufacturers are claiming sub-nm capability but require independent performance verification ▪ Quantum metrology exploits quantum mechanical effects and will require precise construction of nanostructures who properties depend on device dimensions ▪ Linewidths for semiconductor industry requiring nanometre tolerances ▪ Drive towards miniaturization; reduced measurement tolerances ▪ There is a requirement to measure at nanometre level with low uncertainty e.g. AFMs Traceability for nanometrology

▪ Metre realized through I2 stabilized laser l=633 nm ▪ 1 fringe in l/4 interferometer 158 nm ▪ Metrology at nanometre and sub nanometre level requires interpolation ▪ 10 pm> non-linearities <1.0 nm Traceability required for Surface texture, lithography, space, sensors, nanopositioning, microscopy …… Main route for traceability is via optical interferometry and this supports other areas of metrology

Nanoindentation Piezo actuator Hydrophone calibration characterisation Some uses for Dimensional metrology Sensor calibration interferometry measurement services in

Vibration Kibble Balance (kg realisation) measurements But many interferometers have errors due to non-linearity that can range from ~ pm-- nm Who oversees the SI? The Metre Convention was signed on the 20th May 1875 in Paris and led to formation of BIPM:

BIPM is the intergovernmental organization through which Member States act together on matters related to measurement science and measurement standards ▪ Via committees coordinated by BIPM, they produce Mise en pratique for units: a set of instructions that allows the definition to be realized in practice at the highest level, i.e. primary realizations based on top-level primary method ▪ Consultative Committee for Length & Working Group on Nanometrology identified need for new routes to traceability for nanometrology Silicon lattice: an alternative ruler for nanometrology • Two interpenetrating face centred cubic unit cells • Same crystal structure as diamond • Available in defect free high purity form • Extensively studied to support semiconductor industry • Lattice spacing quoted in Committee on Data for Science and Technology Silicon Unit Cell (CODATA) d220=192 pm The Si {220} lattice spacing, -12 d220 = 192.015 571 4 × 10 m Δ푑/푑 = 1.67 × 10–8

So if we want to use the lattice spacing of silicon as a ruler, we have to ‘count the atoms’ The Taniguchi extrapolation – from 1983 Adapted from: Taniguchi, 1983, Annals of the CIRP, 32/2 25 - 30 year time lag between precision levels

Mechanical comparators, micrometers, dial gauges

Optical comparators

Laser measuring instruments, roundness testers Metal bar

High precision laser instruments, Krypton lamp surface analyzers

HeNe Electron microscopes, electron diffraction, ion analyzers, X-ray micro analyzers, Auger analyzers, Si lattice plasmonics, scanning probe microscopes X-ray interferometry; a ruler where the atoms are the lines on the ruler • Developed by Bonse and Hart in 1960s • Three parallel equally spaced lamellae (< 1 mm thick) • Orientation such that x-rays are diffracted from a set of crystallographic planes, usually the (220) • At first lamella (S) two diffracted beams produced • At second lamella (M) two more pairs of beams produced. • Inner beams from each pair recombine at third lamella to form an interference pattern. • Fringe spacing equal to lattice spacing of planes • NOT wavelength • Too small to see, but use of third lamella gives a Moire fringe pattern • As 3rd lamella translated, x-ray intensity varies to produce a fringe pattern • Analogous with an optical encoder How do we know the lattice spacing so well? Avogadro constant, the kg and X-ray interferometry:

▪ At NMIs work done to determine the Avogadro constants and support mass metrology ▪ requires an accurate measurement of the lattice parameter of silicon ▪ Via XRI with separated crystal Interferometer ▪ Translate 3rd lamella and count the number of x-ray fringes in many optical fringes

E Massa et al New J.Phys. 11 (2009) 053013 Measurement of the lattice parameter of a silicon crystal Moire Fringe pattern:

…

As lower grating is translated, transmitted intensity varies

Fringe period corresponds to grating pitch Moire Fringe pattern: twist of a grating

Twist of one grating gives unwanted fringes Effect of twist on x-ray fringe

1/4 of lattice How much twist can we tolerate? spacing=50 pm Assume no more than 0.25 of a fringe 50×10−12 Arctan( ) 5×10−3 Height of x-ray = 1 x 10-8 rad≡0.002 arc seconds!! beam 5 mm Alignment tolerances very high

(London- New York by air 5585 km Equivalent to pinpointing landing position of a rocket to 6 cm from London) Temperature stability expansion coefficient of silicon= 2.6 x 10-6 ◦C-1 L = 5 mm

L-L0=L0αΔT) 50 x 10-12 = 5x10-3(2.6 x 10-6 ΔT) ΔT = 3.8 mK Construction of an x-ray interferometer Strict alignment tolerances between lamella tolerances mean monolithic construction is favoured Single crystal of silicon CNC machining of lamella and flexure stage around 3rd lamella Flexure stage limited to a few micrometres of motion

Flexure stage driven by pzt actuator Optical mirrors on side of XRI for interfacing to optical interferometer X-ray interferometer

▪ Atomic scale ruler/translation stage ▪ Moiré fringe pattern period given by lattice spacing NOT wavelength of x-rays

▪ d (220)= 0.192 nm ▪ Range of 10 m ▪ Displacement TRACEABLE ▪ Flexure stage driven by pzt actuator ▪ Three optical mirrors on side of XRI XRI Signal

▪ Scanning through fringes gives a measure of displacement ▪ Using a servo control (PID loop) position of XRI can be held fixed in linear regions of x-ray fringes x-ray fringes

24000

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10000 counts per second 8000 mean count rate 16250 counts per Servo on positive flank Can also servo on negative flank second, contrast ~40% 6000

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101 106 111 116 121 126 131 136 141 146 151 156 161 166 171 176 181 186 191 196 201 206 211 216 221 226 231 236 reading

21 Quantized positioning of the XRI

Fringe stepping x-ray interferometer

•Lock XRI onto an x-ray fringe •Allow the optical interferometer to •Displace the moving lamella by a follow the motion of the x-ray whole number of x-ray fringes interferometer Half fringe steps 96 pm ½ fringe steps

single fringe 10 steps up and 20 half steps down steps Combined Optical & X-ray Interferometer (COXI)

▪ calibration of displacement transducers ▪ Range up to 1 mm ▪ x-ray interferometry to interpolate between optical fringes Long range high resolution displacement sensor calibration

Readings every 20 nm Limits of optical interferometry For single pass OI with HeNe laser, an optical fringe, λ/2, equivalent to 316 nm, for a double pass system 158 nm

Single and double pass configurations Fringes can be subdivided & electronics available today gives us plenty of resolution eg If 1 fringe is represented by +/- 10 V and 16 bit analogue to digital conversion 216 so 20 V/ 216 = 0.3 mV resolution 0.3 mV x158 nm /20 V = 0.002 nm ≡ 2 pm

However, Limits of optical interferometry • This assumes a noise free signal and a noise free detection system. • Sources of noise include: bit noise on the A/D ~1 bit of resolution, detector noise, electronic noise, mechanical noise (vibration) No optical component is perfect so there will be stray reflections in the interferometer that interfere with the reference and measurement beams. This effect depends on individual set up. Maximum intensities of the reference and measurement beams may be unequal. Lissajous for which phase extracted Phase difference between the two beams may (hence displacement is an ellipse) no be exactly 90º leading to periodic non-linearity error ~ pm-nm. Some of this (but not all) can be corrected using the Heydemann correction to convert ellipse back to a circle, so some non-linearity remains

P.L.M. Heydemann, Determination and correction of quadrature fringe measurement errors in interferometers. Appl. Opt., 1981. 20, p. 3382-3384 K.P. Birch, Optical fringe subdivision with nanometric accuracy. Prec. Eng., 1990. 12, p. 195-198. The NPL Jamin interferometer

▪ Traceability route for many NPL instruments ▪ Homodyne interferometer ▪ 1 fringe equivalent to l/4 ▪ Common path design ▪ Sine & cosine outputs that are optimised ▪ Separate analysis performed for each fringe scanned ▪ Data fitted to an ellipse ▪ Heydemann algorithm to fit data to a circle Interferometer fitted with unstabilized laser & scanned over 5 optical fringes

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-0.05 Difference nm Difference

-0.1 Displacement (nm) Align optical interferometer to X-ray interferometer Generate a displacement in steps of x-ray fringes and compare with XRI Calculate least square difference Initial measurements of non-linearity ±40 pm Non-linearity in NPL interferometer Based on measurements obtained using the x-ray interferometer modifications were made to the optical interferometer to reduce the non-linearity.

peaks correspond to fringe fractions Red curve: before modification Black curve: after modification DC offset due to drift

After modification all peaks <<5 pm Investigation of non-linearity in Heidenhain encoder •Signal generated by interference of different Light source diffraction orders Collimating lens •Signal period: 128 nm Detectors

•Resolution 30 pm Index grating Corner cube (pitch = 1.024 µm) •Grating placed above moving lamella •4 periods –readings 5 x-ray fringes (0.96 nm)

Scale (pitch = 0.512 µm) Non-linearity

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100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 displacement (nm) Fabry Perot system l • Relies on multiple reflections from two parallel mirrors with high reflectivity • Higher resolution than conventional OI. • Separation of fringes Δλ related to θ n

distance between mirrors Multiple reflections from • Much higher resolution mirrors

4휋푛푙푐표푠(휃) 훿 = 휆

휆2 Δ휆 ≈ 0 2푛푙푐표푠(휃) Differential Fabry Perot optical interferometer • Developed by UME • reduced sensitivity to environment • ECLD λ=780 nm • Super Invar construction

Çelik M, Hamid R, Kuetgens U and Yacoot A 2012 Picometre Displacement Measurements using a Differential Fabry - Perot Optical Interferometer and an X-ray Interferometer Meas. Sci. Technol. 23 085901 X-ray fringe and half fringe stepping Fabry Perot measurements

80 s period, amplitude ~2- 4 pm

Scan over 850 x-ray fringes Variations in step size as measured by FPI Spread of values

X-ray intensity fluctuations? Separate measurements showed fluctuations over 300 s causing equivalent displacement of 1.1 pm

Effect in control system for laser diodes

FWHM 8 pm c.f. 5 pm res of electronics Phase relationship between signals from XRI •Introduce a p/2 phase shift between top and bottom of both beams •Quadrature signals are obtained c.f. optical interferometer • Lissajous figure •Bi-directional fringe counting with sub-fringe resolution. Phase plate •Fringe spacing 192 pm c.f. 158000 pm for l/4 optical interferometer(with HeNe illumination) Heydemann correction of x-ray fringes

1 fringe= 192 pm cf 158 000 for λ/4 optical interferometer (with HeNe)

8000 pm Quadrature output from XRI: 1 fringe 192 pm

±1.5 nm Combined XRI & STM: XRI as a translation stage Mise en pratique: Secondary methods of realizing the metre for Dimensional Nanometrology:

-12 The Si {220} lattice spacing, d220 = 192.015 571 4 × 10 m, may be used as a secondary realisation of the definition of the metre, for dimensional nanometrology applications, using the following techniques, and with the associated caveats and uncertainty limits:

A) Measurement of a displacement by reference to the d220 lattice plane, using an X-ray interferometer can be made using either a monolithic interferometer or an interferometer comprising two parts. Both types of interferometer have uncertainties associated with them. Previous experience shows an uncertainty of 10 pm is realistic with a 10 μm displacement from a monolithic interferometer …

B) Calibration of TEM magnification by reference to a single crystal silicon artefact, where the crystal lattice is visible in the field of view of the TEM and the size or width of the single crystalline nanostructure can thus be determined by counting the number of lattice planes in the nanostructure. By this method U < 1 nm for the widths of line structures smaller than 200 nm could be achieved.

C) Measurement of step height standard artefacts manufactured from single crystal silicon, where the height range of multiple monoatomic steps currently is limited up to 10 nm and the uncertainties of the monoatomic step heights are 5 pm under UHV conditions and 15 pm under ambient conditions. Traceability chain for realisation of the metre The metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second

Realised through Realised through laser wavelength x-ray interferometry

Mise en Pratique (MeP) for optical interferometry for metre May 2019 Si lattice displacement metrology: spacing as realisation 192.015 supporting meas. services 5714 pm Δd/d= 1.67 x 10-8 and research

m cm mm μm nm pm The metre from platinum-iridium to silicon The x-ray interferometer Conclusions

• X-ray interferometry a practical tool for dimensional nanometrology • Fundamental role in update to the Si for length metrology with new secondary metre realisation • Evaluate traceably errors in optical interferometers & other nano-displacement sensors • Traceable generation of sub nano-displacements of bulk objects • Will play a key role in evaluation of novel displacement sensors for nanometrology Acknowledgements

NPL: Nigel Cross, John Mountford, Angus Bridges PTB: Ulrich Kuetgens, Ludger Koenders UME: Mehmet Celik, Ramiz Hamid INRIM: Giovanni Mana The National Physical Laboratory is operated by NPL Management Ltd, a wholly- owned company of the Department for Business, Energy and Industrial Strategy (BEIS).