Table Of ContentVolume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
[J.Res.Natl.Inst.Stand.Technol.106,1–23(2001)]
Length and Dimensional Measurements
at NIST
Volume 106 Number 1 January–February 2001
Dennis A. Swyt Thispaperdiscussesthepast,present, rangeofareasofdimensionalmetrology.
andfutureoflengthanddimensional Theseinclude:large-scalecoordinate
National Institute of Standards and measurementsatNIST.Itcoversthe systems;complexform;microform;
Technology, evolutionoftheSIunitoflengththrough surfacefinish;two-dimensionalgrids;
Gaithersburg, MD 20899-8201 itsthreedefinitionsandtheevolutionof optical,scanning-electron,atomic-force,
NBS-NISTdimensionalmeasurement andscanning-tunnelingmicroscopies;
[email protected] fromearlylinescalesandgageblocksto atomic-scaledisplacement;andatom-
afutureofatom-baseddimensional basedartifacts.
standards.Currentcapabilitiesinclude
dimensionalmeasurementsoverarange Keywords: atomic-force;dimensional;
offourteenordersofmagnitude.Uncertain- interferometry;length;measurements;
tiesofmeasurementsondifferenttypes microscopes;optical;scanning-electron;
ofmaterialartifactsrangedownto scanning-tunneling;traceability.
7(cid:1)10–8mat1mand8picometers(pm)
at300pm.Currentworkdealswithabroad Availableonline:http://www.nist.gov/jres
Contents
1. Introduction...................................... 2
1.1 TheEvolutionoftheMeterSince1901............ 2 2.2 ResearchandDevelopmentinDimensional
1.1.1 TheRe-DefinitionsoftheMeter............ 2 MetrologyatNISTToday....................... 7
1.1.2 NISTContributionstotheRe-definitions 2.2.1 TheFirst-PrinciplesMethodofNIST
oftheUnitofLength .................... 3 DimensionalMeasurements................ 7
1.2 TheEvolutionofDimensionalMetrologySince1901. 3 2.2.1.1 TheArtifact .................... 8
1.2.1 TwoHistoricalDimensionalMeasurements... 3 2.2.1.2 TheMeasuringMachine........... 8
1.2.1.1 MeasurementofLinescales 2.2.1.3 TheTheoreticalModel............ 10
Since1901 ..................... 3 2.2.1.4 TheMeasurementAlgorithm....... 11
1.2.1.2 MeasurementofPrecisionGage 2.2.2 NeedsofSomeKeyIndustriesinDimensional
BlocksSince1901............... 4 Metrology.............................. 11
1.2.2 SomeNISTContributionstotheDimensional 2.2.2.1 AircraftIndustry................. 11
MetrologySince1901.................... 4 2.2.2.2 AutomotiveIndustry.............. 12
1.3 IndustrialDriverforLowerUncertaintiesinStandards: 2.2.2.3 ComputerIndustry............... 12
TighteningTolerances.......................... 5 2.2.2.4 MicroelectronicsIndustry.......... 12
1.3.1 NISTUncertaintyRelativetoIndustry 2.3 CurrentWork ................................ 12
Tolerances.............................. 5 2.3.1 Large-ScaleCoordinateMetrology.......... 12
1.3.2 TheTrendofTighteningTolerances......... 5 2.3.2 Dilatometry............................ 13
2. DimensionalMetrologyatNISTToday................ 5 2.3.3 ComplexFormMetrology................. 13
2.1 TheStateofNISTDimensionalMeasurement 2.3.4 MicroformMetrology .................... 13
ServicesProvided............................. 6 2.3.5 SurfaceFinishMetrology ................. 13
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Journal of Research of the National Institute of Standards and Technology
2.3.6 Two-DimensionalMetrology............... 14 distancebetweentwolinesruledonaplatinum-iridium
2.3.7 OpticalMetrology....................... 14 bar carefully preserved in a special vault at the
2.3.8 SEMMetrology......................... 14
International Bureau of Weights and Measures (BIPM)
2.3.9 Scanned-Probe-MicroscopeMetrology....... 14
near Paris [1]. With its founding, NBS became the
2.3.10Atom-BasedArtifactStandards ............ 14
2.3.11Atomic-ScaleDisplacementMetrology....... 15 keeper of a duplicate of this bar, Meter No. 27, which
3. TheFuture....................................... 15 then served as the U.S. national standard of length for
3.1 Limits:Ultimate,Standards-Based,andPractical.... 15 60 years. At the end of that period, the meter as the
3.1.1 UltimateTheoreticalLimits ............... 15
international standard of length underwent the first of
3.1.1.1 QuantizationofSpace............. 15
two fundamental re-definitions.
3.1.1.2 HeisenbergUncertaintyPrinciple ... 16
3.1.1.3 JohnsonkTNoise................ 16
3.1.2 LimitsfromPrimaryReferenceStandards.... 16 1.1.1 The Re-Definitions of the Meter
3.1.2.1 PrimaryReferenceStandardsforthe
SecondandtheMeter............. 16 In 1960, the meter was re-defined by the General
3.1.2.2 TemperatureStandardandLengthof Conference on Weights and Measures (CGPM) to be
MaterialObjects................. 16 1659763.73 vacuum wavelengths of light resulting
3.1.3 PracticalLimits......................... 16
from the unperturbed atomic energy level transition
3.1.3.1 DisplacementInterferometry....... 17
2p –5d ofthekryptonisotopehavingarelativeatomic
3.1.3.2 ProbeLimitations................ 17 10 5
3.1.3.3 Temperature..................... 17 mass of 86 [2].
3.2 IndustryTrends............................... 18 In1983,themeterwasre-definedagaintotheonein
3.2.1 EmergenceoftheNewTraceability......... 19 effect today, namely: “The meter is the length of path
3.2.2 IncreasingDemandforCalibratedArtifacts... 19
traveled by light in vacuum during the interval of
3.2.3 DevelopmentofGPSChainofStandards..... 19
1/299792.458 of a second” [3]. (Among the effects of
3.3 TheEvolvingNISTResponse ................... 19
3.3.1 Atom-BasedArtifactsStandards ........... 19 thedefinitionisthatitfixesthespeedoflightinvacuum
3.3.2 UseofOtherGovernmentCapabilities ...... 19 to be exactly 299792.458meters per second). At that
3.3.3 UseofIndustryCapabilities............... 20 time, the International Committee on Weights and
3.3.4 ShopFloorasNMI...................... 20
Measures (CIPM) gave three basic methods for the
4. Conclusion ...................................... 21
practical realization of the meter: time-of-flight, using
5. References....................................... 21
timeintervals,andinterferometry,usingwavelengthsor
frequencies. CIPM gave five recommended radiations
1. Introduction with assigned frequencies, wavelengths, and uncertain-
ties.Oftherecommendedradiations,thatoftheiodine-
One of the most venerable, commonly encountered, stabilizedhelium-neonlaseristhemostwidelyusedfor
scientifically fundamental, and economically important practical realization of the meter. It has a wavelength
units of measure is length. It is one of the fundamental of (cid:2)HeNe=632.99139822nm, with a relative standard
measurement quantities in physics, commerce, and uncertainty ur of 2.5(cid:1)10–11 [4].
everyday life. The international standard of length is The effect of the re-definitions and advances in
the meter, one of the seven base units of the modern measurement of the frequencies of recommended
International System of Units (SI) and one of the two radiations was to decrease the relative uncertainty
original units of the international system of standards attainable in realization of the meter by five orders of
upon which the SI is based. Both the meter as the unit magnitude
of length and dimensional measurements based on the • from an estimated 2(cid:1)10–6 (this paper’s estimate of
meterhaveundergonesubstantialchangesoverthelife-
the reproducibility with which the first transfer
timeoftheNationalBureauofStandardsanditssucces-
could be made from the prototype meter bar) [5],
sor,theNationalInstituteofStandardsandTechnology.
• through 7(cid:1)10–8 (the relative uncertainty for the
wavelengthemittedbycadmiumdischargelamps,a
1.1 The Evolution of the Meter Since 1901
secondary standard of length),
Three different definitions of the international
• through 4(cid:1)10–9 (the relative uncertainty for the
standardoflengthhavebeenineffectduringthelifetime
wavelengthemittedbykrypton-86dischargelamps),
of NBS-NIST. At the time of the founding of the
NationalBureauofStandardsin1901,theinternational • to 2.5(cid:1)10–11 (the CIPM specified uncertainty for
standard of length was the International Prototype the visible wavelength of the iodine-stabilized
Meter. The meter was defined at that time as the helium-neon laser today) [4].
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1.1.2 NIST Contributions to the Re-definitions of to the SI unit of length through material artifacts
the Unit of Length calibratedasdimensionalstandards.NISThasplayeda
key role for the United States as provider of the link
Theunitoflengthhasevolvedfromadefinitionbased
between the Platonic length of the laboratory and the
onaphysicalprototypethroughonebasedonaspecific
physical length of material objects through its practice
wavelengthoflighttoonebasedonanelectromagnetic
of dimensional metrology.
wavepropagatinginfreespace.NISThasmadesubstan-
tial contributions to this evolution. These contributions
1.2.1 Two Historical Dimensional Measurements
include:
Two mainstays of NIST dimensional metrology over
• Production in 1947 of isotopically pure mercury-
the lifetime of NBS-NIST have been measurements of
198, measurement of its spectral linewidth and
linescales and gage blocks.
proposalofitswavelengthforadoptionastheinter-
national standard of length [6];
1.2.1.1 Measurement of Linescales Since 1901
• Measurement in 1971 of the spectral linewidth and
The lowest uncertainty attained in dimensional
frequencyofanemissionlineofahelium-neonlaser
measurementofamaterialobjectoccursinthecalibra-
corresponding closely to an absorption line of
tion of linescales. The dimensional feature of interest
iodine, then a candidate for a recommended radia-
in a linescale is the distance between parallel lines
tionforthere-definitionofthemetertoreplacethat
inscribed on a substrate.
of krypton-86, the standard for definition of the
By 1904, NBS was providing calibrations of
meter at the time [7];
linescales relative to the U.S. prototype meter bar for
• Measurementin1976oftheratioofthewavelength scalesfrom100mmto50minlengthwithsubdivisions
of an iodine-stabilized HeNe laser to that of a downto0.1mm[6].Today,NISTprovidescalibrations
methane-stabilized He-Ne laser, providing a provi- of linescales relative to first-principles realizations of
sionalextensionofthefrequencyscalebasedonthe the meter using displacement interferometry. These
cesium oscillator into the visible spectrum [8]; calibrations range from scales as small as 10(cid:3)m in
length (with subdivisions down to 1(cid:3)m) to as long as
• Development in 1980 of a portable iodine-absorp-
50m (with subdivisions down to 0.1mm) [11].
tion-stabilized helium-neon laser for use in inter-
Changes have occurred over the century in how
national metrology [9];
NBS-NISThasstateditsestimateoftheclosenessofthe
• Measurement in 1983 of the frequencies of visible- value of the quantity being measured to the result of a
light lasers, including that of the iodine-stabilized measurement—fromnostatement,tothatofmaximum
laser, directly against that of the cesium-beam likely error, to accuracy, and now to uncertainty. As a
atomic clock, the primary standard of time [10]. result, it is not possible to estimate the standard uncer-
taintyofmeasurementresultsforthosereportedoverthe
1.2 The Evolution of Dimensional Metrology period. However, a reasonable characterization is that:
Since 1901
• For the period from 1904-1960, the reproducibility
The definition of the meter—whether in terms of a of measurements against the U.S. prototype meter
prototype meter bar, a wavelength of light, or the bar is estimated to be of the order of 0.25(cid:3)m, in
propagationofanelectromagneticwaveinanintervalof relative terms, 2.5(cid:1)10–7 at 1m, with the legibility
time—hasprovidedthebasisforthelowest-uncertainty of the lines on the bar the major limitation [5].
realization of the unit. A primary economic driver for
• For the period from 1960-2000, the expanded
reduced uncertainty with which the meter could be
uncertainty U (coverage factor k=2) for measure-
realized has been demands for reduced uncertainty in
ments of one-meter linescales by interferometry
measurementsmadeincommerce,especiallybymanu-
againstawavelengthoflightdecreasedprogressively
facturers using leading-edge technology in the produc-
from0.25(cid:3)min1960to0.08(cid:3)m(8(cid:1)10–8at1m)
tion of goods. These measurements are not of the
today, due to improvements in measuring machine
“Platonic length” of wavelengths of light propagating
geometry, light sources, and temperature measure-
in free space but of the physical lengths of material
ment and control [11].
objects, from aircraft wings and automobile engine
parts to microelectronic devices. Measurements of Figure 1 shows the NIST Line Scale Interferometer
dimensionsofmaterialgoodsaremostoftenreferenced System,firstintroducedin1965,asitappearedin1971.
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
Fig.1. TheNISTlinescaleinterferometersystemasitappearedstartingin1971[11].Itwasfirstintroducedintoservicein1965.
1.2.1.2 Measurement of Precision Gage Blocks other improvements, especially improvement of the
Since 1901 geometry and material-stability of the blocks in 1960
[6], the limiting expanded uncertainty (coverage factor
One of the most industrially important length- k=2) for short blocks today is 0.008(cid:3)m (8(cid:1)10–6 at
measurement standards, particularly for machine-tool- 1mm) [12], an improvement of two orders of magni-
basedmanufacturing,isprecisiongageblocks.Consist- tude over the lifetime of NBS-NIST.
ing of blocks of metal, usually steel, having two oppo-
site faces that are plane, parallel, and a specified 1.2.2 Some NIST Contributions to Dimensional
distance apart, they are used in manufacturing as size Metrology Since 1901
blocks for precise mechanical work and for checking
NBShasmadefundamentalcontributionstotheevo-
precise mechanical work.
lution of dimensional measurements over the period
Priorto1917,NBSisreportedtohavebeencalibrat-
since the founding of NBS to the era of current work,
ing precision gage blocks with mechanical-contact
whichreachesbacktothebeginningofthelastdecade
comparatorsagainstendstandardscalibratedbyvisual-
of the twentieth century. These fundamental contribu-
microscope comparison to linescales calibrated by
tions include:
visual-microscope comparison to the U.S. prototype
meter bar. Based on the “error” in the process then • Introduction in 1922 of interferometric measure-
reported, today’s estimate of the uncertainty of those ments of precision gage blocks [13]
earliest NBS calibrations of precision gage blocks is
• Development in 1961 of high-stability precision
0.75(cid:3)m (7.5(cid:1)10–4 at 1mm).
gage blocks [6]
In 1922, NBS introduced its first interferometric
measurements of gage blocks, reducing the estimated • Creationin1968ofthefirstscannedprobetopogra-
uncertainty by an order of magnitude to 0.075(cid:3)m phy measuring instrument, a field-emission device
(7.5(cid:1)10–5 at 1mm). In 1935, NBS reportedly gained that was the precursor of the scanning tunneling
another factor of three improvement to an estimated microscope and that was cited in the Nobel Prize
uncertainty of 0.025(cid:3)m (2.5(cid:1)10–5 at 1mm). With award for that device [14]
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
• Development in 1976 of the technique for the low- was deemed to be of the order of 1/100 of the more
uncertainty optical-microscope measurement of demanding part tolerances of the day.
microelectronic photomask linewidths [15] Nowacommonmachiningtoleranceofthetimewas
reportedly (cid:4)50(cid:3)m [18] and the uncertainty of NBS
• Developmentin1977ofthetechniqueofcomputer-
calibrationsofgageblockspriorto1917was0.5(cid:3)mto
based real-time correction of systematic errors in
1.0(cid:3)m[13].ThusthelowerendoftheNBSuncertainty
positioning of coordinate measuring machines [16]
was smaller by the requisite factor of 100 than the
• Development in 1981 of the technique for laser- commonly called-for tolerance (presumably a high-
interferometer-based scanning-electron-microscope accuracy tolerance for an earlier decade). By 1917,
measurement of microelectronic photomask line- however, the tolerance of a high-accuracy part was
widths [17] (cid:4)6.25(cid:3)m[18],and,tolerancesof(cid:4)2.5(cid:3)mwerebeing
sought[13].Inordertoprovidecalibrationsafactorof
1.3 The Industrial Driver for Lower Uncertainties 100 better than that latter tolerance, NBS advanced its
in Standards: Tightening Tolerances measurementcapabilitiestoprovidecalibrationsofgage
blocks with an uncertainty of the required (cid:4)0.025(cid:3)m
The need for reduced uncertainty in the “primary
[13].
standard” aspect of length, that is, in its definition and
realization,andinthe“secondarystandard”aspect,that
1.3.2 The Trend of Tightening Tolerances
is,initstransferanddisseminationthroughdimensional
metrology,islinkedstronglytotighteningtolerancesin Thetrendoftighteningtolerancesandtheconsequent
industrial manufacturing. need for lower uncertainties at NBS-NIST as first
suggested in 1922 [13] have continued unabated
1.3.1 NIST Uncertainty Relative to Industry throughout the lifetime of NBS-NIST. According to an
Tolerances 1980 academic analysis of industrial trends in ultra-
precision machining over the central decades of the
ThebasiclogicisthatmeasurementsmadebyNBS-
twentieth century, achievable machining tolerances for
NISTasthenationalmetrologyinstituteresponsiblefor
particularclassesofprocesseshasdecreasedatarateof
realization and dissemination of the SI unit of length
approximatelyanorderofmagnitudeeverytwentyyears
need to be at levels of uncertainty that are small
[19].Bythisaccount,thetolerancesachievablebywhat
fractionsofthetightesttolerancesachievedinmanufac-
is described as normal precision machining have
turer’s use of leading-edge technology. NBS length
decreased from the order of 10(cid:3)m in the period 1920
metrologists’ explicitly used this line of reasoning
to 1940 to less than 1(cid:3)m in the period 1980 to today.
within two decades of NBS’ founding [13]. It is still
The analysis also indicated an evolution of a parallel,
valid today.
ultra-precision machining regime—which includes
In order to assess with confidence the conformance
atomic-, molecular-, and ion-beam milling and semi-
of parts to tolerances, the uncertainty associated with
conductor-lithography processes—that has tolerances
thegagesemployedwasrequiredtobesomefractionof
anorderofmagnitudesmallerthanthoseofthenormal
the tolerance on the dimensions of the part being
precision regime. In this ultra-precision regime,
measured. In other words, the uncertainty associated
attainable tolerances have decreased from the order of
withmeasurementsmadewiththegagewasrequiredto
1(cid:3)mintheperiod1920to1940totheorderof1nmto
be equal to the value of the tolerance divided by some
10nm today.
factor.Ina1918treatiseonindustrialmeasurementand
inspection,thegageuncertaintywasrequiredtobeless
than the part tolerance by a factor of four (or five, 2. Dimensional Metrology at NIST Today
dependinguponround-offtothenearesthalf-digit)[18].
Bythesamereasoning,theuncertaintyoftheprocessof Today, the NIST division responsible for the realiza-
calibration of the gage was required to be a second tion and dissemination of the SI unit of length serves a
factoroffoursmallerthanthedesiredgageuncertainty. range of industries, from aircraft and automotive to
According to a 1922 NBS paper on interferometric computers and microelectronics. It provides fourteen
measurement of gage blocks [13], NBS’ calibration of majortypesoflengthmeasurementservicestoapproxi-
thetestinglaboratory’sstandardswas,inturn,required mately 120 different fee-paying institutional customers
tobeathirdfactorsmallerthanthatofthegageuncer- per year. Each measurement service begins with a
tainty.Asaresultofthesethreesuccessivereductionsby first-principles realization of the SI unit of length via
factors of four or five (less round-off at various levels), frequency-stabilized lasers and displacement inter-
theuncertaintyrequiredofNBScalibrationsatthattime ferometry. The measurement technologies employed
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
include laser-ranging devices, theodolites, large-scale Representing the lowest uncertainty of linescale
coordinate measuring machines(CMMs), optical- and measurementsisthatonthe1(cid:3)msubdivisionofascale
ultraviolet-light microscopes, scanning electron micro- of 10(cid:3)m in overall length. The attainable expanded
scopes(SEMs),atomicforcemicroscopes(AFMs),and uncertainty (coverage factor k=2) for these short
scanning tunneling microscopes (STMs). linescales is 1nm [11]. According to the NIST bench-
marking study, this is also the lowest absolute uncer-
taintyofalinescalemeasurementprovidedbyanyofthe
2.1 The State of NIST Dimensional Measurement
world’s NMIs [20].
Services
Representingthelowestrelativeuncertaintyofanend
Table 1 describes a number of the types of length standard is that of the 1m step on a CMM step gage
measurements provided by NIST today. Shown in the [12]. According to the NIST benchmarking study, with
table for each type are: range; expanded uncertainty; itsrelativeexpandeduncertainty(coveragefactork=2)
relativeexpandeduncertaintiesatrespectiveendsofthe of7(cid:1)10–7,NISTistiedwithoneotherNMIinprovid-
range; and an assessment of where the uncertainty ing this level of uncertainty [20].
stands relative to the best provided by other national Representing the state-of-the-art of precision gage
metrology institutes (NMIs). block calibration is the expanded uncertainty of 10nm
Representing the largest dimensions that NIST cali- to 30nm on gage blocks of 10mm to 1000mm in
brates are surveyor’s measuring tapes, one type of length [12]. According to the NIST benchmarking
linescale. The 50m length of such measuring tapes study,theNISTuncertaintyisthatattainedbythegroup
canbecalibratedtoanexpandeduncertainty(coverage of the leading NMIs of the world [20].
factor k=2) of 500(cid:3)m or, fractionally, 1(cid:1)10–5 at Representingthelowestuncertaintyofend-standard-
50m.AccordingtoabenchmarkingofNISTmeasure- typemeasurementsinthemicroscopicregimeisthatof
ment services against those of eleven other NMIs, sub-micrometerandmicrometerlinewidthsoftheNIST
includingallofthemajorindustrializedcountries,these photomask linewidth standards, with an expanded
uncertaintiestieNISTwithoneotherNMIforproviding uncertainty of 36nm over the range of lines from
the lowest uncertainty [20]. 0.5(cid:3)m to 30(cid:3)m width [23]. According to the NIST
Representingthelowestrelativeuncertainty(U/L)of benchmarking study, NIST is the first provider of such
dimensionalmeasurementsprovidedinaNISTcalibra- standards and provides the lowest uncertainty [20].
tionisthatofthelengthofa1mlinescale.Inthiscase, Finally, representing the lowest reported uncertainty
the relative expanded uncertainty (coverage factor ever attained in an SI-traceable dimensional measure-
k=2) is 7(cid:1)10–8 at 1m [11]. According to the mentofanindividualmaterialfeatureisthatofthestep
NIST benchmarking study cited, this is also the height of fabricated single-atom steps of silicon (111).
lowest uncertainty of a dimensional measurement The expanded uncertainty (coverage factor k=2) of
of a material artifact provided by any of the world’s measurement of the 304picometer (pm) step height is
NMIs [20]. 8pm [24, 25].
Table1. RangesanduncertaintiesofselectedNISTdimensionalmeasurementcapabilities
Measurement Range UncertaintyU U/L U/L Relativetoleading
min max
types (L to L ) (k=2) NMI
min max
Linescales
Measuringtapes[20] 1mto50m 60(cid:3)mto500(cid:3)m 6(cid:1)10–5 1(cid:1)10–5 Tiedwithleader
Linescales(“long”)[11] 10(cid:3)mto1m 1nmto70nm 1(cid:1)10–3 7(cid:1)10–8 Leader
Linescales(“short”)[11] 1(cid:3)mto10(cid:3)m 1nm 1(cid:1)10–3 1(cid:1)10–4 Leader
Endstandards
CMMstepgages[21] 100mmto1m 0.4(cid:3)mto0.7(cid:3)m 4(cid:1)10–6 7(cid:1)10–7 Tiedwithleader
Gageblocks[22] 1mmto100mm 10nmto30nm 1(cid:1)10–5 3(cid:1)10–7 Same as leading NMIs
ICphotomasklinewidth[23] 0.5(cid:3)mto30(cid:3)m 36nm 7(cid:1)10–2 1.2(cid:1)10–3 Leader
Stepheight[24,25] 300pmto75(cid:3)m 8pmto0.4(cid:3)m 2.5(cid:1)10–2 5(cid:1)10–3 Leader
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
2.2 Research and Development in Dimensional • Inordertoachieveacriticalfunctionofabusiness-
Metrology at NIST Today criticalproduct,acompany(inthisscenario,onein
an economically important industry) designs a part
Given the trend to tightening tolerances in precision
to a tight dimensional tolerance.
machining and the goal of a factor of 100 for NIST to
surpass the tightest tolerances in the manufacturing it • Amanufacturerproducesthecriticallydimensioned
supports,NISTwouldbeexpectedtoprovidemeasure- part.
ments with uncertainties of the order of tens of nano-
• Inordertoachievethetighttolerance,themanufac-
meters to support what has been called the “normal
turer uses a manufacturing process that produces
precisionmachining”regimeandoftheorderoftensof
parts to high precision with high reproducibility.
picometers to support the “ultra-precision” regime.
For one particular standard for each regime, NIST can • To assure conformity of the part to the customer-
beviewedasmeetingthoseprojections.Forthenormal specified tolerance, the manufacturer makes mea-
machiningregime,NISTprovidescalibrationsofpreci- surements of the part’s critical dimension with a
sion gage blocks with a state-of-the-art expanded high-resolutionmeasuringinstrument,oftenthebest
uncertainty (coverage factor k=2) of 10nm. In the commercially available.
“ultra-precision machining” regime, NIST can perform
• The customer also makes measurements of the
measurements of single-atom steps in silicon with an
part’s dimension, with a comparable or identical
expandeduncertaintyof8pm.Atthesametime,NIST
measuring instrument.
is carrying out extensive research and development to
addressanticipatedU.S.industryneedsfornewtypesof • Theresultsofthemanufacturer’smeasurementsand
dimensional measurements and reduced uncertainties. of the customer’s measurements are of high preci-
sion and high reproducibility.
2.2.1 The First-Principles Method of NIST
• Theresultsofthemanufacturer’smeasurementsin-
Dimensional Measurements
dicate that the part dimension is within specified
Today,possiblymoresothanatanytimeinitshistory, tolerance.
NIST is called upon to meet extraordinary demands of
• In contrast, the results of the customer’s measure-
U.S. manufacturing industries in their use of leading-
mentsindicatethatthepartdimensionisoutoftoler-
edge technologies with state-of-the-art dimensional
ance.
tolerances. These extraordinary demands include:
• Tothemanufacturer,thepartconformstospecifica-
(1)uncertainties for dimensional measurements on
tion and is acceptable.
production devices that are beyond the world state-
of-the-art in measurement capability [26]; and • Tothecustomer,thepartfailstoconformtospecifi-
cation and is unacceptable.
(2)traceability to a measurement by an NMI of a
“primary standard” of the particular dimensional • The discrepancy in the measurement results cannot
featureoftheirdiscrete-partproduct,thatis,whatis be accounted for by the manufacturer and the
now being called measurement-task-specific trace- customer.
ability [27]; and, in some cases.
Insum,thesituationisamarket-transactiondisagree-
(3)bothstate-of-the-artuncertaintyandNMItraceabil-
ment between sets of results of high-precision, high-
ity in the same measurement.
reproducibility measurements made with state-of-the-
Demands from industry for NIST to develop low- artmeasuringinstrumentsonpartswithstate-ofthe-art-
uncertainty, task-specific, “primary-standard” mea- tolerances.
surements often arise when there is an unresolved For NIST to contribute to the resolution of such dis-
discrepancy between different, highly reproducible agreements requires that NIST fundamentally advance
resultsofmeasurementsmaderespectivelybyproducers thestateoftheartofmeasurementscienceandtechnol-
of and customers for economically important products ogy. Prototypical results of NIST to resolve such
with state-of-the-art dimensional tolerances. The discrepancies are its photomask linewidth Standard
circumstances of such an unresolved discrepancy in ReferenceMaterials(SRMs)anditsgear-formcalibra-
measurement results are frequently as follows: tion services.
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
Over the last two decades, NIST has developed a once again in its use for calibration of a user’s instru-
family of photomask linewidth standards covering a ment. As a result, the variations in the features are
range of linewidths measured by optical [15] or scan- required to be substantially smaller than the measure-
ning electron microscopes [28] from 30(cid:3)m down to mentuncertaintyrequiredofNIST.Ideally,variationsin
0.25(cid:3)m.Morerecently,NISThasdevelopedcalibration features would be so small as to contribute insignifi-
services for the dimensions and geometrical forms of cantly to the measurement uncertainty NIST delivers.
involute gears that are critical parts of transmission By the same token, these variations should be substan-
power trains of aircraft, heavy equipment, and auto- tially smaller than the variations of the manufactured
mobiles [29]. partinquestion.Sincetheproductistheresultofstate-
The prototypical solution to the problem of system- of-the-art manufacturing processes, the artifact often
atic differences in measurement results of dimensions needstobeofadegreeofgeometricperfectionbeyond
produced by different dimensional measuring instru- the current state of the art.
mentsiscalibrationoftheinstrumentsagainstthesame The historical prototype of the idealized-geometry
reference standard. The requirement for the standard is physicalartifactasthebasisforlow-uncertaintycalibra-
thatitsmeasurementuncertaintybemuchsmallerthan tions by NBS-NIST is the industrial precision gage
the discrepancies in question. block. Gage blocks were invented and developed by
Historically,theuncertaintyassociatedwithgagesor others between 1910 and 1920 and substantially im-
inspectionmachinesisrequiredtobefactorsof4,5,or proved by a NIST-industry collaboration in the 1950s
even10timessmallerthantolerances.Inturn,theuncer- [13, 6]. Modern counterparts to gage blocks are the
tainty associated with industry reference standards is NIST photomask linewidth standard [23], the NIST
requiredtobefactorsof4to10timessmallerthangage sinusoidal surface-roughness standard [31,32], and the
or inspection machine uncertainty. Finally, the uncer- NIST microelectronic overlay standard [33]. Each of
tainties of NIST dimensional standards are expected to these artifact standards, developed during the last two
befactors4to10timessmalleryetagain[30].Thusthe decades, required advancing the state-of-the-art of
uncertainties of reference measurements or calibrated manufacturing processes for its production.
standardssoughtfromNISTcanbefactorsof64toeven
1000 times smaller than state-of-the-art tolerances. 2.2.1.2 The Measuring Machine
The ability of NIST to provide reference measure-
For a NIST measurement process to be capable of
ments at such levels of uncertainty requires develop-
resolving the discrepancies encountered by industry in
mentsbeyondthecurrentstateoftheartineachofthree
its measurement processes, the NIST measurements
areas:
needtobehighlyreproducibleandfreeofthesystematic
• the physical artifact to be calibrated; errorsimplicitinindustry’sreproduciblebutdiscrepant
• the measuring machine to do the calibration results.
• the theoretical model of the systematic errors in At the heart of each of NIST’s industry-problem-
measurement results arising from the interaction solving measurement processes is an innovative,
of the artifact and the measuring machine in the specialized, first-principles measuring machine. The
calibration process. innovative aspect of the machine is its ability to make
measurements with uncertainty previously unattainable
In addition, the three developments need be tied to- for that specific task. The specialized aspect of the
gether in a measurement procedure that includes inno- machine is its ability to make task-specific measure-
vative measurement algorithms and methods. ments, such as that of photomask linewidth, gear
involute,ormachined-partcylindricity,overaparticular
2.2.1.1 The Artifact
range of feature dimension. The first-principles aspect
The innovative physical artifact that NIST needs to of the machine is its direct realization of the definition
develop in order to provide reference measurements to oftheSIunitoflengthinthetask-specificdimensional
deal with the scenario described above is one that measurementitisdesignedtoperform.Practicalrealiza-
mimics the product features for which industry is tion of the definition of the meter (Sec. 1.1.1) in a
experiencing the discrepant measurement results. This dimensionalmeasurementmostcommonlyimpliesthat
artifact is required to be of a material and a form and one must be able to do three things:
havefeaturesanddimensionssimilartothedimensioned • generate a line in space
partthatisatissueintheindustry.Becausetheartifact
• define the end points of that line
is used in two sets of measurements, variations in its
dimensionedfeaturescontributetoausermeasurement • dividetheintervalofspacebetweentheendpointsof
uncertainty twice: once in its calibration by NIST and that line into appropriate subintervals.
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
To carry out these functions, a measuring machine themechanical-contactofagage-blockcomparator,the
needs to have certain essential elements [34]. reflectedvisiblelightofalinescaleopticalmicroscope,
the scattered electrons of a metrology SEM and the
Frame
quantum-mechanical tunneled electrons of an STM. In
Thefirstelementisthemeansforthephysicaldefini- eachcase,theprobe,ineffect,definestheendpointsof
tion of a line in space. Geometrically, a line is defined thelinesegmentimpliedinthe“lengthofpath”portion
by a direction in space relative to a coordinate system of the definition of the unit of length.
having axes and an origin. The frame is the set of
Interval and Subintervals
physicalelementsthatdefinephysicalpoints,lines,and
planes to embody, to the degree of perfection required, The last element is the means for determining an
theidealgeometryofthatreferencecoordinatesystem. interval or subintervals of distance in terms of the
Ingeneral,axesaregeneratedbyavarietyofmechani- definitionofthemeter.Themeansistousetheknown
caldevicesthatconstrainmotioninallbutonedirection wavelength of a reference laser and laser displacement
such as v-groove ways, while an origin is generated by interferometry. The reference laser is typically a com-
a well-defined mechanical stop. mercial, frequency-stabilized, HeNe laser calibrated
against an iodine-frequency-stabilized HeNe laser, one
Motion Generator
oftherecommendedradiationsforthepracticalrealiza-
The second element is a set of physical structures, tionofthemeter.Sincethedefinitionofthemeterfixes
suchasamovingstageoranimagescanner,togenerate thespeedoflightinvacuumtobeexactly299792458
reproducible relative motion between the object of meterspersecond,andtherelationofthewavelengthof
measurement and the coordinate frame. This motion anelectromagneticradiationtoitsfrequencyis(cid:2)=c/v,
maybeactualorvirtual.Actualmotionisbymeansof by measuring the frequency of a laser with a given
a physical carriage that translates the object relative to relative uncertainty, one immediately knows its wave-
astationaryframeortranslatestheframerelativetothe length with the same relative uncertainty.
stationary object. Virtual motion may be, for example, Table2describesthetypeofprobe,frame,scalesand
by means of translation of an image of the object length reference for each of six different dimensional
relative to the coordinate frame. measuring machines at NIST, each of which embodies
the elements for the realization of the meter as the SI
Probe unit of length.
The third element is a probe, that is a sensor system
thatsimultaneouslydetectsaboundary,suchasanedge • The NIST coordinate measuring machine(cid:5)CMM)
orsurface,oftheobjecttobemeasuredandlocatesthat for measuring industrial gages uses a mechanical-
detected feature relative to the coordinate system. The contactprobe,anx-yslidewaysstageandz-axisram,
physical principles underlying probes on NIST first- andhelium-neonlaserdisplacementinterferometers
principles dimensional measuring machines include: for each axis [12].
Table2. NISTdimensionalmeasuringmachinesforfirst-principlesmeasurementsofdimensions
Measuringmachine Probe Frame Scales Wavelength reference
CMMa Mechanicalcontact x-ystage x,y&zinterferometers HeNe
z-ram
Gage-blockinterferometer Visiblelight Platen,bridge z(Michelson)interferometer HeNe
Overlaymicroscope Visiblelight x-ystage x,y&zinterferometers HeNe
z-PZT
MetrologySEM Electronbeam x-ystage xinterferometer HeNe
CalibratedAFM Atomicforce x-ystage x&yinterferometers HeNe
z-PZT zinterferometer-calibratedCG
M3 Scanningtunneling x-ystage x&yinterferometers HeNe
z-PZT zinterferometer-calibratedPZT
aCMM: coordinate measuring machine; HeNe: helium-neon laser; PZT: piezo-electric transducer; SEM: scanning electron microscope;
AFM: atomicforcemicroscope;CG: capacitancegauge;M3: MolecularMeasuringMachine.
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Volume106,Number1,January–February2001
Journal of Research of the National Institute of Standards and Technology
• The NIST gage block interferometer for calibration • TheNISTMolecularMeasuringMachine(M3)isa
ofprecisiongageblocksisasinglez-axisMichelson scanning-tunneling-microscope-based system being
interferometerwithabridgeoverafixedplaten[22]. developedfornanometer-uncertaintymeasurements
over a 50mm by 50mm area [36].
• TheNISToverlaymicroscope,showninFig.2,isa
visible-light-microscope system with an x-y stage
2.2.1.3 The Theoretical Model
with moveable z-axis, with helium-neon laser dis-
placement interferometers on each axis for calibra- In addition to artifacts and measuring machines,
tionofmicroelectronicoverlayerrorstandards[33]. NIST measurements to address industry’s most funda-
mental measurement problems require theoretical
• The NIST metrology SEMs are scanning electron
models that advance the state-of-the-art. Such models
microscopes with single-axis stage-interferometers
are most often needed to scientifically understand the
systemforcalibrating250nmphotomasklinewidths
interactionbetweentheartifactandmeasuringmachine
[28]andhigh-accelerating-voltageSEMmagnifica-
in order to eliminate systematic errors in measurement
tion standards [35].
resultsduetothatinteraction.Thesourceofthesystem-
• The NIST Calibrated Atomic Force Microscope atic error is in the physics that governs the interactions
(C-AFM)haslaserdisplacementinterferometerson oftheprobewiththematerialboundaryofthefeatureto
each of its x and y axes and a laser-interfero- be located. Probe-boundary interactions contribute to
meter-calibratedcapacitancegaugeonitszaxis,for errorsinlengthmeasurementsdependinguponthetype
calibration of nanometer-scale step-height, pitch, of length being measured.
and roughness standards [24].
Fig.2. TheNISTopticaloverlaymicroscope,utilizinganinnovativeStewart-platformstructureanddigital-arrayimageprocessing[33]
10
