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Present Problems in Coordinate Metrology for Nano and Micro Scale Measurements

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Present Problems in Coordinate Metrology for Nanoand Micro Scale Measurements

KIYOSHI TAKAMASUDepartment of Precision Engineering, The University of Tokyo

Hongo 7-3-1, Bunkyo-Ku, Tokyo 113-8656, Japane-mail: [email protected]

[Received: 25.02.2011 ; Revised: 03.03.2011 ; Accepted: 05.03.2011]

AbstractFrom macro scale to nano scale measurements, the relationship between measuring range and measuringaccuracy is a key parameter for measuring abilities. When measuring targets are three-dimensional(3D) and include complex geometrical features, high-accuracy cannot be achieved by conventionalmeasuring methods. In this article, we discuss the limitations of 3D metrology in micro and nano scaleprofile measurements. For nano and micro scale measurements, we have to develop three key technologiesas intelligent measuring methods, in-process measurements and high-accuracy standards.

© Metrology Society of India, All rights reserved 2011.

1. Indroduction

From macro scale to nano scale measurements,the relationship between measuring range andmeasuring accuracy is a key parameter for measuringabilities. Table 1 shows sample measuring targets,measuring range and measuring accuracy for macro,micro and nano scale measurements [1-2]. In thisexample of macro scale measurement, the measuringtargets are automobiles and their parts in automobilemanufacturing, and sub millimeter accuracy isrequired in the 1-meter measuring range. Theseclassifications are simple and limited to one-dimensional (1D) size measurement. Therefore, whenmeasuring targets are 3D and include complexgeometrical features, these levels of accuracy cannotbe achieved. In this article, we discuss the limitationsof 3D metrology in micro and nano scale profilemeasurements.

2. Scale Factor and Scale Interface

The relationship between the measuring range andmeasuring accuracy can be defined as a scale factor overa scale interface. Figure 1 illustrates ability areas wherethe measuring methods can be applied along thehorizontal axis indicating the measuring range and thevertical axis indicating the measuring accuracy. The scalefactor is the ratio between measuring range and accuracy,and it is 10-4 in precision measurement and 10-5 to 10-6 inultra-precision measurement. The concept of the scaleinterface is a continuous ability of measurement in thesemeasuring ranges. From macro to micro scale, the scaleinterface is established by conventional measuringmethods, while the gap between nano and micro scalemeasurements exists in the scale interface. This gap iscaused by the following quantum effects in nanometer-resolution measurements;

i) Wave length of light ii) Thermal noise iii) Non-linearity of laser interferometer iv) Size of atom

MAPAN - Journal of Metrology Society of India, Vol. 26, No. 1, 2011; pp. 3-14REVIEW ARTICLE

Kiyoshi Takamasu

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Furthermore, the following factors in dimensionalmetrology should be considered for workshopmeasurements;

i) Not only size but also form in three dimensionsii) Complex workpiece profileiii) Environmental conditions

For nano and micro scale measurements, there areintelligent measuring methods, in-process measurementsand standards to consider.

3. Limitations of Length Measurement in Microand Nano Scale Measurements

3.1 Conditions of Precision Length Measurement

The precision length measurement is

established for the limited conditions illustrated inFig. 2 and in Table 2. Under these conditions, theprecision length measurement is carried out ascomparison measurements with gauge blocks in atemperature-controlled room. The comparisonmeasurement is carried out as follows;

i) Temperatures of the workpiece to be measuredand the gauge blocks are stabilized in atemperature-controlled room.

ii) A high-resolution sensor such as a linear variabledifferential transformer or an optical sensor isaligned using Abbe's principle, as the sensor'sscale and measured length are on a same line.

iii) The sensor magnification is calibrated using twogauge blocks.

iv) The comparison measurement is performed bymeasuring the workpiece and the gauge block.

Using this method, precision length measurementcan be easily done by anyone. Therefore, thetemperature control room, gauge blocks and Abbe'sprinciple are key technologies for precision lengthmeasurement. However, in dimensional metrology,these conditions are not satisfied, and we considerthis situation in the following section.

3.2 Influence of the Profile of the Workpiece Being Measured

There are large differences between lengthmeasurement and profile measurements for complexworkpieces. Figure 3 shows an example of pitchstandard and step standard in nano scale [3-4].

Table 1Comparisons of measuring targets, range and accuracy in macro, micro and nano scale measurements [1-2]

Scale Macro Micro NanoMeasuring targets (example) Automobiles Precision machines SemiconductorsMeasuring range 1 m 10 mm 100 μmMeasuring precision 100 μm 1 μm 10 nmAccuracy measurement 10-4

ultra precision 10 μm~ 100 nm~ 1 nm~measurement 10-5~

Fig. 1. Scale factor over scale interface [1]


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The step height of the sample is 50 nm, and its flatnessis 0.5 nm. The flatness of a 50-mm gauge block is 0.05μm according to the K class ISO standard [5].Comparing the nano step standard and K class gaugeblock, the ratio of size and flatness are 10-6 for thegauge block and 10-2 for the nano step standard. Thiscase shod standards are vital f that the geometricalaccuracy of the nano standard profile is 104 worsethan the micro or macro scale standard such as thegauge block. Therefore, good standards are vital fornano scale measurement, or novel measuring methodsshould be developed using novel data processingmethods.

3.3 Influence of Temperature Effects

The relationship between thermal correction andthermal drift in precision measurements is usually

Table 2Conditions of precision length measurement [1-2]

Abbe's principle E. Abbe, Germany (1890)Gauge block C.E. Johannson, Sweden (1896)Temperature-controlled room NBS, USA (1924)Sensor stability for short time, linearity over short rangeMeasuring workpiece simple profile, high-accuracy profileMeasuring time short, no drift

Fig. 3. Pitch standard and step height standard [3-4]

(a) Pitch standard of 100 nm (b) Step height standard of 50 nm

Fig. 2. Methods of precision length measurement witha temperature-controlled room, gauge blocksand Abbe's principle [1-2]

gauge blocks displacementsensor

temperaturecontrolled room

workpiece

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not clear. This is because thermal drift does notinfluence into the measuring results in the conditionsof Table 1. On the other hand, measurements in aworkshop have the drawbacks that dimensionalmeasurements for complex workpieces take a longtime and the effects of thermal drift are large [6-7].

Figure 4 shows the thermal drift model for lengthmeasurement. First, the zero point of the scale, ls1, isset at time m1, and then the position of the workpiece,ls2, is measured at time m2. The length of the workpiece,lw, is calculated as ls2 - ls1. In this calculation, the COEs(coefficients of thermal expansion) of the scale, base,guide and workpiece are defined as, ab, ag and awrespectively. The differences of temperature aredefined as dtz, dtb, dtg and dtw, respectively, at time m1and m2.

If the differences of temperature is ignored, Eq. (1)defines the temperature correction withouttemperature drift. Equation (2) defines the effect ofthermal drift. In the equation, thermal drift, ldrift,indicates the effects from temperature variation, sizeof each factor and COE of each factor. Therefore, theestimation of thermal drift is difficult because ofuncertainty regarding the COEs and temperaturemeasurement.

+ −= − + − + + −w w w2

s2 s1 s s2 s1 s s b b b g g g

(1 ( 20))( )(1 ( 20))

l a tl l a t l a dt l a dt l a dt (1)

ldrift=ls1asdts+lbabdtb-lgagdtg (2)

4. Problems of Nanometer-Dimensional Metrology

4.1 Problems of CMM (Coordinate Measuring Machines)

The problems of nanometer-dimensionalmetrology by CMM are as follows [8-10];

i. Lack of accuracy of the guidelines; the measuringprinciple of a CMM does not satisfy Abbe'sprinciple, and therefore, the kinematic errors ofguide ways have to be calibrated. Highrepeatability of the guidelines is required.

ii. The need for a high-accuracy probing system.There are many problems in the development ofan accurate nanometer probing system.

iii. The need for high-accuracy standards: nanometeraccuracy and geometrical deviation for length andgeometrical standard is required for calibrationof a CMM.

Fig. 4. Thermal drift model of length measurement [6]

(a) Zero point (at time m1) (b) Length measurement (at time m2)


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4.2 Abbe's Principle in a CMM

Abbe's principle provides a fundamental methodfor precision measurement. The 1D size measurementeasily satisfies Abbe's principle, as shown in Fig. 2,but dimensional metrology and the CMM have greatdifficulty satisfying Abbe's principle. Figure 5 showsa 3D version of Abbe's principle in dimensionalmetrology. In the 3D Abbe's principle, the metrology

frame, which has three laser interferometers, measuresthe position of the three mirrors of the moving table. Ahigh-accuracy CMM and AFM (atomic forcemicroscope) were developed using the 3D Abbe'sprinciple (Fig. 6). However, flexibility ofmeasurements such as direction change of the probingsystem and measuring positions on the workpiece islimited using the 3D Abbe's principle.

4.3 Probing System

It is challenging to develop a nanometer-accuracyprobing system for a CMM for nano scalemeasurement. A probing system to measure a 3Dcomplex workpiece should have a small ball tipprobing system with high resolution. There areprobing systems that were developed using MEMS(Micro-Electro-Mechanical Systems) technology,ultrasonic vibration and the like. The measurementaccuracy of these systems is over 10 nm at present.The difficulties in calibrating and evaluating probingsystems are great. Figure 7 shows some examples ofthe high-accuracy probing systems.

4.4 Calibration of CMM

Conventional CMM that do not satisfy Abbe'sprinciple need to calibrate three translation errors inthe X, Y and Z directions and three rotation errorsaround three axes, as shown in Fig. 8 [14-15].Furthermore, three perpendicular errors among thethree axes, for a total of 21 types of errors, have been

(a) High-accuracy CMM, ISARA 400 [11] (b) Critical dimension AFM [3]

Fig. 6. High-accuracy CMM and AFM using the 3D Abbe's principle

Fig. 5. 3D Abbe's principle for dimensional metrology

probing system

moving tablethree mirrors

laser interferometer

workpiece

Kiyoshi Takamasu

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calibrated by special devices such as ball plates, holeplates and double ball bars, and laser interferometers.Figure 9 shows the calibration method using the ballplate. The ball positions on the ball plate are calibratedtwo-dimensionally. From six measurements (1 - 6 inFig. 9), the geometrical parameters of the CMM can beestimated. When guidelines with high repeatabilityare built in, a position can be calculated with highaccuracy using these geometrical parameters.

5. ISO Standards for CMM

5.1 Activities of ISO/TC 213/WG 10

ISO/TC 213/WG 10 is a working group for thedevelopment of ISO standards for CMM. In theworking group, three series of ISO standards havebeen developed, as follows [16]:

i) ISO 10360 Geometrical Product Specifications(GPS) - Acceptance and reverification tests forCMM

ii) ISO 15530 Geometrical Product Specifications(GPS) - Techniques for determining theuncertainty of CMM measurements

iii) ISO 23165 Geometrical Product Specifications(GPS) - Guidelines for the evaluation of CMM testuncertainty

The ISO 10360 series defines evaluation methodsof acceptance tests for CMM, and ISO 23165 uses theseuncertainty evaluation methods in the acceptance test

defined by ISO 10360. The ISO 15530 series indicatesthe techniques for determining the uncertainty ofmeasurement using CMM.

5.2 Acceptance Tests for CMM

ISO 10360 has 6 parts, as follows:

Part 1: VocabularyPart 2: CMM used for measuring linear dimensions[17]Part 3: CMM with the axis of a rotary table as thefourth axisPart 4: CMM used in scanning measuring modePart 5: CMM using single and multiple styluscontacting probing systemsPart 6: Estimation of errors in computing Gaussianassociated features [18].

Figure 10 illustrates the evaluation methods forsize measurements in ISO 10360 part 2. In the methods,a step gauge or gauge blocks are measured at differentpositions and directions, and then the deviations ofsize measurements are compared with maximumpermissible errors. Figure 11 shows the evaluationmethods for probing errors for 25 measuring positionson the reference sphere in ISO 10360 part 5. Thevariation and deviation of size and profile of thesphere are compared with maximum permissibleerrors.

(a) Ultrasonic vibration UMAP [12] (b) Probing system for F25 [13] (c) Probing system for ISARA [11]

Fig. 7. Examples of small and high-accuracy probing systems


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Fig. 8. Twenty-one geometrical errors on a CMM [14-15]

Fig. 9. Calibration of 21 geometrical errors using a ball plate: 6 measurements at 4 positions of the ball plate

(b) Three translation errors and three rotation errorson the X axis

(a) Configuration of three scales and probing systemin a CMM

X axis scale

Z axis scale

Y axis scale

probing system

workpiece

Z axis

Y axis

XYZ rotationerrors

XYZtranslationerrors

X axis

probedirection

ball plate

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5.3 Uncertainty Estimation of Dimensional Measurement

For the next generation production system, the3D complex machine parts with high accuracy andhigh function will be used to perform the high-functionmachining and as part of the nano-based mechanicalsystem. There are three key technologies in intelligentmeasurements for the next generation productionsystem, as follows [19-20];

i) Uncertainty of measurement will be utilized todecide proving conformance in industry,

ii) 3D complex machine parts will be the keys to highaccuracy and high function.

iii) Uncertainty in coordinate metrology will presentlarge difficulties.

From the above items, we conclude that theuncertainty estimation in coordinate metrology willbe a key technology.

Figure 12 shows an example of the uncertaintyestimation in coordinate metrology. In this figure, theangle (88.52 arc-degrees) between the axis of thecylinder and the normal vector of the plane can beeasily measured and calculated by a CMM. However,the uncertainty of the angle (0.25 arc-degree) isdifficult to estimate, because the uncertaintyestimation method evaluates the uncertaintycontributors from the uncertainty of each coordinate,

(a) Twenty-five measuring positions on reference sphere (b) Definition of probing error P

Fig. 11. Evaluation of probing error using the reference sphere in ISO 10360 part 5 [18]

Fig. 10. Evaluation of size measuring errors using astep gauge in ISO 10360 part 2 [17]

(a) (b)


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effects of form deviations, effects of environmentalconditions and so on. In addition, the relationshipbetween uncertainty and strategy of measurement isvery complex. Figure 13 shows the positionaldeviation of the center coordinate of a measured circle.The positional deviation is determined by the numberand the positions of measured points.

5.4 Methods to Estimate Uncertainty in ISO 15530

The ISO 15530 series defined "Techniques fordetermining the uncertainty of measurement" by 4parts, as follows;

Part 1: Overview and general issuesPart 2: Use of multiple measurement strategies [21]Part 3: Use of calibrated workpieces or standards [22]Part 4: Evaluation of task-specific measurementuncertainty using simulation [23].

Figure 14 illustrates the example of multiplemeasurements in ISO DTS 15530 part 2. The artifact ismeasured in 4 orientations, which the user accepts as"natural positions," i.e. in which no bigger oradditional uncertainty sources are present. Fivedifferent randomly selected point distributions areused in each orientation.

Figure 15 shows the procedure of substitutionmeasurement by a measuring cycle (ISO TS 15530 part3). In the substitution method, uncertainties from thecalibration of the calibrated workpiece, measurementprocedure (repeatability) and variations due to theexpansion coefficient, form errors and roughness areevaluated. The measured object and the standard aremeasured by the same measuring strategy and thegeometrical features, form deviations, surfaceroughness and material are similar due to thefunctional properties.

The main and flexible method for determining theuncertainty is the computer simulation method (ISOTS 15530 part 4).

Figure 16 illustrates the computer simulationmethod "Virtual CMM," which is proposed by PTB(the German standards laboratory). Using VirtualCMM, we created a virtual uncertainty model of CMMin the computer system. The measurement was thendone using Monte Carlo simulation, and theuncertainty of measurement was estimated [24-26].

Fig. 13. Uncertainty estimation in coordinate metrology for the center position of circle measurement

Fig. 12. Uncertainty estimation in coordinatemetrology for angle measurement

Fig. 14. Multiple measurements in ISO DTS 15530 part2 [21]

Variation and uncertaintiesof measuring opints

Uncertainty ofcenter position

88.52° ± 0.25°

Kiyoshi Takamasu

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Fig. 15. Substitution measurement by a measuring cycle (ISO TS 15530 part 3) [22]

Fig. 16. Concept of virtual CMM method for ISO TS 15530 part 4 [24-26]

Working standard

Workpiece

Working standard handling

Working standard measurement

Workpiece handling

Workpiece measurement


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6 Conclusion

First, we described the relationship betweenmeasuring range and measuring accuracy is a keyparameter for measuring abilities from macro scale tonano scale measurements. When measuring targetsare three-dimensional and include complexgeometrical features, high-accuracy cannot beachieved by conventional measuring methods. In thisarticle, we discuss the limitations of 3D metrology inmicro and nano scale profile measurements. Weintroduced that the scale factor is the ratio betweenmeasuring range and accuracy and the concept of thescale interface is a continuous ability of measurementin these measuring ranges. From macro to micro scale,the scale interface is established by conventionalmeasuring methods, while the gap between nano andmicro scale measurements exists in the scale interface.Therefore, for nano and micro scale measurements,we have to develop three key technologies as intelligentmeasuring methods, in-process measurements andhigh-accuracy standards.

References

[1] K. Takamasu, Mesoscale Profile MeasurementImproved by Intelligent MeasurementTechnology, Journal of JSPE, 74 2008, 213-216.

[2] K. Takamasu, Macro, Meso and Nano ScaleDimensional Profile Measurement, Optical andElectro-Optical Engineering Contact, 49, 2011.

[3] I. Misumi, S. Gonda, T. Kurosawa and K.Takamasu, Uncertainty in Pitch Measurementsof One-Dimensional Grating Standards Usinga Nanometrological Atomic Force Microscope,Meas. Sci. Technol., 14 (2003) 463-471.

[4] I. Misumi, et al., Reliability of Parameters ofAssociated Base Straight Line in Step HeightSamples: Uncertainty Evaluation in Step HeightMeasurements Using Nanometrological AFM,Precision Engineering, 30 (2006) 13-22.

[5] ISO 3650, Geometrical Product Specification(GPS) - Length standards - Gauge blocks.

[6] T. Ohnishi, S. Takase and K. Takamasu, Studyon Improvement Methods of CMM (CoordinateMeasuring Machine) in Workshop Environ-ment - Evaluation and Correction of ThermalDrift-, Journal of JSPE, 73 (2007) 270-274.

[7] ISO 1:2002, Geometrical Product Specifications(GPS) - Standard Reference Temperature forGeometrical Product Specification andVerification.

[8] A. Weckenmann, H. Knauer and H. Kunzmann,Influence of Measurement Strategy on theUncertainty of CMM-Measurements, CIRPAnnals, (1998).

[9] K. Takamasu, S. Koga, S.Takahashi, M. Abbe,R. Furutani and S. Ozono, Evaluation ofUncertainty by Form Deviations of MeasuredWorkpieces in Specified Measuring Strategies,Proc. ISMQC2004, (2004) 535-540.

[10] M. Cox and P. Harris. Measurement Uncertaintyand Traceability. Meas. Sci. Technol., (2006).

[11] ISARA, IBS homepage: http://www.ibspe.com/

[12] M-NanoCoord, Mitutoyo homepage: http://www.mitutoyo.co.jp/products/nmworld/nano.pdf

[13] F25 Mircosystem CMM, Zeiss: http://www.zeiss.de/4125682000247242/Contents-Frame/5b1a8ebc2a5e14b886257154006ae1a3

[14] M. Abbe, K. Takamasu and S. Ozono, Reliabilityon Calibration of CMM, Measurement, 33(2003) 359-368.

[15] K. Takamasu, S. Takahashi, M. Abbe and R.Furutani, Uncertainty Estimation forCoordinate Metrology with Effects ofCalibration and Form Deviation in Strategy ofMeasurement, ISMTII2007, (2007).

[16] ISO TC 213 homepage: http://isotc213.ds.dk/[17] ISO 10360-2: 2009, Geometrical Product Specifi-

cations (GPS) - Acceptance and ReverificationTests for Coordinate Measuring Machines(CMM) - Part 2: CMMs Used for MeasuringLinear Dimensions

[18] ISO 10360-5:2010, Geometrical Product Specifi-cations (GPS) - Acceptance and ReverificationTests for Coordinate Measuring Machines(CMM) - Part 5: CMMs Using Single andMultiple Stylus Contacting Probing Systems.

[19] K. Takamasu, M. Abbe, R. Furutani and S.Ozono, Estimation of Uncertainty in Feature-Based Metrology, Proc. ISMTII2001, (2001).

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[20] K. Takamasu, R. Furutani and S. Ozono, BasicConcept of Feature-Based Metrology.Measurement, 26 (1999) 151-156.

[21] ISO DTS 15530-2:2007, Geometrical ProductSpecifi-cations (GPS) - Coordinate MeasuringMachines (CMM): Technique for Determiningthe Uncertainty of Measurement - Part 2: Use ofMultiple Measuerment Strategies.

[22] ISO TS 15530-3:2004, Geometrical ProductSpecifi-cations (GPS) - Coordinate MeasuringMachines (CMM): Technique for Determiningthe Uncertainty of Measurement - Part 3: Use ofCalibrated Workpices or Standards.

[23] ISO TS 15530-4:2008 Geometrical ProductSpecifications (GPS) - Coordinate MeasuringMachines (CMM): Technique for Determining

the Uncertainty of Measurement - Part 4:Evaluating Task-Specific MeasurementUncertainty Using Simulation.

[24] H. Schwenke, B. Sievert, F. Wäldele and H.Kunzmann, Assessment of Uncertainties inDimensional Metrology by Monte CarloSimulation: Proposal of a Modular and VisualSoftware. CIRP Annals, (2000).

[25] K. Takamasu, et al., NEDO International JointResearch Project Final Research Report,International Standard Development of VirtualCMM (Coordinate Measuring Machine), (2002).

[26] E. Trapet, et al., Traceability of CoordinateMeasurements According to the Method of theVirtual Measuring Machine, PTB-Bericht F-35(1999).

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