X-Ray Interferometry for Dimensional Metrology World Interferometry Day Andrew Yacoot 14 April 2021 [email protected] Layout of Talk
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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 linear regions of x regions linear in fixed held can be of XRI position (PID loop) control a servo Using of displacement measure a gives fringes through Scanning - ray fringes ray x-ray fringes 24000 22000 20000 18000 16000 14000 12000 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 4000 2000 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161 166 171 176 181 186 191 196 201 206 211 216 221 226 231 236 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.