micro 3d measurement method using sem - metrology society of india

Micro 3D Measurement Method Using SEM

69


YASUHIKO ARAI*, MASAKI ANDO, SHO KANAMEISHI and SHUNSUKE YOKOZEKI1

Department of Mechanical Engineering, Kansai University3-3-35 Yamate-cho, Suita, Osaka, Japan, 564-8680

1Jyouko Applied Optics Laboratory2-32-1 Izumigaoka, Munakata, Fukuoka, Japan, 811-4142

*e-mail: [email protected]

[Received: 22.09.2010 ; Revised: 12.11.2010 ; Accepted: 15.11.2010]

AbstractThree diamensional (3D) measurement method by Scanning Electron Microscope (SEM) has alreadybeen proposed by using the principle of shadow moiré. In the method, the image of original grid inshadow moiré image must be clearly removed in fringe analysis process in order to perform highresolution analysis. A new method based on the principle of projection moiré is proposed to solve thetrouble concerning the grid. In this paper, the mechanism of producing some shadows of grid on thesurface of the object by back scattering electron beam in the new method is discussed. Fringe image asshadow of grid is analyzed by Wavelet transform. The precise 3D measurement is realized by using thephenomenon of shadows of grid. Furthermore, a 3D micro structure on the head of a hard disk ismeasured. From the comparison of results obtained by Atomic Force Microscope (AFM), it is confirmedthat the proposed method has high-resolution power(about 20nm).

© Metrology Society of India, All rights reserved 2011.

1. Indroduction

In the development of the continously improvingtechnology, the demand of precise 3D measurementof micro products is increasing year by year.Generally, such measurements are performed byoptical measurement system and/or SPM (ScanningProbe Microscope) technology [1]. However, eachmeasurement method has its own problems andlimitations. For example, when we use ordinaryoptical measurement methods are generally difficultto measure with a spatial high resolution except aspecial optical system based on near-field opticsbecause there are some problems by the diffraction ofbeam. Furthermore, in the optical measurement, theresolution of the measurement in the direction of the

optical axis is very high. The measurement in nm orderresolution are performed using some fringe scanningmethods [2] in the direction of the optical axis by theoptical methods. However, the lateral resolution ofthe measurement is very poor in comparison to 3Dmeasurement. There is an imbalance in themeasurement resolution power of 3D.

In this paper, a novel 3D measurement methodfor micro size products is proposed by using theWavelet transform and the electron-beam of SEM[3-6].

The 3D measurement method using SEM hasalready been proposed by using the principle ofshadow moiré[7-8]. However, the method based onshadow moiré by SEM has also problems[9]. Forexample, when the fringe image by shadow moiré asshown in Fig. 1 is analyzed, the image of the original

MAPAN - Journal of Metrology Society of India, Vol. 26, No. 1, 2011; pp. 69-78ORIGINAL ARTICLE

Yasuhiko Arai, Masaki Ando, Sho Kanameishi and Shunsuke Yokozeki

70

grid must be clearly removed in fringe analysisprocessing in order to perform a high resolutionanalysis [9]. In the same manner of the ordinaryshadow moiré of optical system [10-13], this problemplayed an important role of error sources of fringeanalysis. In the shadow moiré using SEM, it is usuallydifficult to remove this error source. To solve thistrouble, a new measurement method based on theprinciple of projection moiré [2] is discussed in thispaper.

In order to perform 3D measurement by theprinciple of projection moiré without fail, themechanism of producing some shadows of the gridon the surface of the object by back scattering electronbeam is firstly discussed in this paper. Then, themechanism of producing shadows of grid in thevacuum chamber of SEM is applied to 3D measurementby projection moiré.

In this new 3D measurement system, the gratingwhich is produced on a silicon-wafer by the silicon-process is used as a physical rigid grid. Fringe imageas a shadow of grid is analyzed by the Wavelettransform. Wavelet transform [14-15] can analyze asignal simultaneously in space and scaling from onlyone sheet of image. The transform is employed to thesignal and image processing as the application well[16]. Recently, some kinds of DWT(discrete wavelettransform) algorithms are supplied on commercial

base. In this experiment, such a commercial DWT [17]is used. The period of fringe image is detected, as aresult, 3D measurement can be realized by using thephenomenon of shadows of grid by back scatteringelectrons. The validity of the measurement principleis discussed by the experiment of measurement of aflat plane. A FE-SEM (Field Emission ScanningElectron Microscope) is employed in the experimentsof the confirmation of the principle. For grating, thepitch of 4 μm is used.

In the experiment, for an application of the newsystem, a very small 3D structure as the parts of ahard disk head, is located at the near-point of the tipof slider of a hard disk and is measured by theproposed method. The measurement result iscompared with the measured result of AFM. From theresult, the 3D measuring accuracy of this method canbe estimated at about 20 nm by comparing the resultswith results obtained using AFM. It is confirmed thatthe very high resolution measurement can beperformed by using the new proposed method.

2. Principle of Measurement

2.1 Production of the Shadows of the Grid

A SEM image taken with a secondary electronbeam is shown in Fig. 2(a). In this case, the structureof a micro cantilever can be observed by SEM.Generally, an object shape can be observed by asecondary electron beam in SEM. Now, when thecantilever is observed by back scattering electrons, theshadow of the cantilever exists on the bottom floor asshown in Fig. 2(b). Then, the shadow cannot be seenin the image shown in Fig. 2(a) taken using asecondary electron beam. This phenomenon is thecharacteristics of an image taken by back scatteringelectron beam.

Using this phenomenon, the 3D measurementmethod based on shadow moiré can be performed [9].However, the method has also some problems. Theimage of the original grid must be clearly removed infringe analysis process in order to perform a highresolution analysis. In this paper, the mechanism ofproducing some shadows of the original grid on thesurface of an object by back scattering electron beamis discussed in detail to develop the 3D measurementmethod based on projection moiré.Fig. 1. Shadow moiré image by SEM


71

In this new system, the grating produced of asilicon-wafer under the silicon-process is used as aphysical rigid grid. The schematic of the system isshown in Fig. 3(a). Then, the grating is set verticallyas shown in Fig. 3(a) in order to remove the image ofthe grid from the fringe image.

As shown in Fig. 3(a), a part of electrons from thegun can pass through the grating at the space of grid.On the other hand, some electrons are intercepted bythe rigid grid. Then, electrons that can pass throughthe grid and that arrive at the detector would producea light region of fringe (Fig. 3(b)). At the same time,some of electrons that cannot pass through the gridwould also make a dark region of the fringe. In thisphenomenon, it can be thought that the electrons canproduce the shadow of the grid in the image of SEM.From this shadow-phenomenon in SEM image,measurement system by SEM can be constructed as ameasurement system corresponding to the opticalmeasurement system.

In the ordinary optical system, the light beam isintercepted by grids before arriving at the object, then,the shadow can be observed. However, in themeasurement system by SEM as shown in Fig. 3, theelectrons that are reflected on the object are shut off bythe rigid part of the grid. Then, the shadows in fringe

image can be observed. The process of production ofshadows is different from the concept of ordinaryoptical system. Therefore, in the measurement systemby SEM, it can be thought that the position of a detectorcorresponds to the position of a light source of theoptical system (Shadow moiré system), and that theposition of a gun also corresponds to the position of aphoto sensor. Due to this reason, it can be thoughtthat SEM system and optical system are completelyopposite concerning the positions of light sourceand detector under the phenomenon of the productionof shadows of grids. Furthermore, there is the peculiarsituation of the measurement system by SEM underthis idea. Therefore, only electron-gun has the two-dimensional (2D) measurement coordinate system byscanning electrons on the object. The sensor-system(detector) has no 2D coordinate-system. As a result,the fringe analysis is very confusing due to thischaracteristic of the SEM system.

Fringe images are shown in Figs. 4 (a) and (b),when the measured objects are set as a plane and asphere, respectively. In each fringe image, the opaquepart of gratingthe (A-B) correspond to the part (D-C)of the object. However, because detector has no 2Dcoordinate system, the coordinate shown as the part(F-E) is detected as the shadow of the opaque part of

100µm

50µm

(b) By backscattered electrons (a) By secondary electrons

electron

Fig. 2. SEM images

electron

(b) by backscattered electrons(a) by secondary electrons


72

grating(A-B) practically. This is the characteristics ofthe SEM coordinate system. When the fringe imagesby SEM are analyzed, it is very important for theoperator to understand this phenomenon in detail.

When the measured-object is a flat plane (Fig. 4(a)),the detected fringes are straight lines. On the otherhand, when the sphere (Fig. 4(b)) is a measured object,the shadows of grids are curved. It is confirmed thatfringe patterns, which depend on the shape of theobject, happen as shown in Fig. 4. In this paper, the3D shape of object can be measured using thisphenomenon.

2.2 Measurement Principle Based on the Production of Shadows of the Grid

As shown in Fig. 5, the principle of measurementof this method can be explained using the principle ofthe production of shadows by electrons in SEM. Inthe chamber of SEM, the electrons, which are emittedfrom the electron gun(G-point), reflect on the surfaceof the object. Then, the back scattering electrons areemitted from the surface of the object. When the backscattering electrons pass through the grid and arriveat the detector, the reflecting point where the electronscan pass through the grid is observed as a light pointof fringe image. On the other hand, the electrons,which cannot pass through the grid, are interceptedby the grid of the grating. Then, the point, where theelectrons cannot pass through the grid, is observed asa dark point of fringe image as shown above.

On the assumption that the profile; I(y) of thegrating(O-y1-y2) as shown Fig. 5 is the sinusoidaltransmittance distribution as shown in Eq.(1), theintensity distribution of the fringe on the surface ofthe object can be assumed as the intensity of theshadow (O-P1-P2) of the grating shown as the dottedline in Fig. 5. However, then, the detector of electronsin SEM does not have any 2D coordinate system asshown above. That is, because only the electron gunof SEM has the 2D coordinate system, the grid profileon the object (O-P1-P2) is recorded as the fringe profilewhich is the thin line (O-x1-x2) under thecharacteristics of the SEM coordinate system.

( ) cos(2 ) πω= +I y A B y (1)

where, A is bias, B is amplitude, and ω is spatialfrequency of grid.

Here, the points on the grating y1 and y2 are thepoints where the phase of the fringe profile are π and2π rad, respectively. Then, the points P1 and P2 on theobject would correspond to the points y1 and y2 on thefringe. Finally, these points correspond geometricallyto the points x1 and x2 as the fringe image of SEM.

Because the coordinate of point-D and point-y1are known, the line(D-y1) that can be defined by thesetwo points( point-D and point-y1) can be confirmeddefinitely. Furthermore, the coordinate of point-G andpoint-x1 are also known. So, the line (G-x1) that can bedefined by these two points(point-G and point-x1) canbe confirmed uniquely. Then, the intersection of these

Fig. 3. Shadow of grid

Dark region Light region

Dark region Light region

(b) Fringe image(a) Optical system

de tec to r

gun

gra ting

ob jec t


73

lines(D-y1 and G-x1) can be defined as the point-P1.The coordinate of this point can be measured as theresult of the 3D measurement method.

In the same manner as the calculating process ofthe coordinate of the point P1, the cross point betweenthe line(D-y2) and line(G-x2) can be defined as thepoint-P2, at the point-y2 which corresponds to 2π radof the fringe profile. When the concept of thiscalculating process is expanded to general points, thecoordinate of points which doesn't correspond to πand 2π rad of the grid profile can be also defined, asfollows;

As shown above, in this measuring principle, itis assumed that the electrons that reflect at themeasured point on the surface of the measured objecttravel in the straight line to detector directly. That is,in this experiment, it is assumed that the phase of thepoint-y3 shown in Fig. 5 is same as the phase of thepoint-x3 as the shadow of the grid. Under thisassumption, the measurement is performed. Therefore,when the phase at point-x3 is x3, the coordinate of y3is given as Eq.(2).

3 3 /2xy pφ π= (2)

where, p is the pitch of the grid

When the phase of the arbitrary point in the fringeimage of SEM can be detected exactly, the coordinateof the point can be detected by using the relationshipbetween the phase of the detected point in the fringeimage of SEM image and the phase of the grid underthe geometric measurement principle. Under aboveidea, the high resolution 3D measurement with highspatial resolution can be performed in this paper, asfollows;

The fringe's period distribution T(xn) of the point-xn can be detected from the SEM fringe image by usingthe Wavelet transform. The fringe's period distributionT(xn) of the point-xn, which is an arbitrary point onthe fringe image, can be detected with only one sheetof fringe image by using Wavelet transform. Then, thephase( φxn) of the point-xn is defined as Eq. (3).

( )n n n2 / x x T xφ π= (3)

The point-yn on the grating which corresponds tothe phase of the point-xn is defined by using therelationship of the phase of points (xn and yn). In thiscalculation of the measurement results, the measuredresult of the point should be calculated within therange of every period of the grid. In the example shownin Fig. 5, the calculating method for the range(O-y2) of

y

x

detector grating

gun

Measured object

o

A B C D

E F

Fringe images without any Image of grid

y

x

detector grating

gun

Measured object

o

A B C D

E F

(a) plane (b) sphere Fig. 4. Shadow of plane and sphere

(a) plane (b) sphere


74

the first period of the grid profile; I(y) is shown as Eq. (1).So, when the measurement of the range of the secondperiod is performed, the information of gridprofile(from y2 to y4) shown in Fig. 5 should be usedas a matter of course.

2.3 Calibration of the Measurement System Based on SEM

As the new 3D measurement using SEM is a highresolution measurement method for a very smallobject, the high accuracy of the measurement isrequired. In this method, the calibration ofmeasurement system is performed as the operation of

deciding the precise coordinate of the electron gunand the detector of the system.

Under the principle of this method, the correctcoordinate of the detector and the gun should beknown as exact values. In this experiment, these valuesare defined analytically and geometrically by usingtwo kinds of planes.

Firstly, the first-plane, of which the inclined angleis known, is set as the first reference plate as shown inFig. 6. The equation of this first reference plane is alsoknown naturally. In this case, the points y1 and y2 onthe grating correspond to P11 and P21 on the object,

α

D

G

O x1 x2

y4

Surface of object

Grating

T1

y1

y2

P1

P2

(Detector)

(Gun)

y3 P3

x3

Fig. 5 Principle of measurement

y

x

detector grating

gun Reference plate-1

o

y1 y2

P11 P21

P22 P12

x21 x22 x11 x12

D(xd, yd)

G(xg, yg)

α β

Reference plate-2

Fig. 6. Coordinate of gun and detector


75

respectively. The point-y1 and -y2 also correspond tox11 and x21, respectively on the SEM image.

Now, the equations of two straight lines G-x21 andG-x11 are expressed using the coordinate of G(xg, yg) asparameters. The cross points between these straightlines (G-x11 and G-x21) and the first reference plane aredetected as P11 and P21. Consequently, the equations(f11 and f21) of two lines of y1-P11 and y2-P21 are defined,respectively.

f11 : y ={tanβ (1+(y1xg-y1x11)/ygx11)-y1/x11}x+y1

f21 : y ={tanβ (1+(y2xg-y2x21)/ygx21)-y2/x21}x+y2 (4)

Similarly, the expressions for f12 and f22 of twolines of y1-P12 and y2-P22 are given by using the secondreference plane, respectively, as follows;

f12 : y ={tanα (1+(y1xg-y1x12)/ygx12)-y1/x12}x+y1

f22 : y ={tanα(1+(y2xg-y2x22)/ygx22)-y2/x22}x+y2 (5)

Then, the simultaneous equations concerning xgand yg by using the conditions that f11 corresponds tof12 and that f21 corresponds to f22 are given analytically.The coordinate of electron Gun(xg, yg) can be resolved.Furthermore, two straight lines y1-P12 and y2-P22 canbe given by using the coordinate of electron Gun(xg,yg). Then, the coordinate of the cross point of theselines corresponds to D(xd, yd).

In the experiments using a FE-SEM, values of thecoordinate of Gun(0.005, 8.700) and Detector(-13.400,5.700)[unit is mm] are used concretely. In this

measurement, the coordinates of the gun and thedetector can be defined before the measurement.

3. Experimental Result and Discussion

The experiment is performed in order to confirmthe validity of the measurement principle by usingthe experimental apparatus(see Fig. 7(a)), the gratingas shown in Fig.7(b) (pitch is 4µm and thickness is1µ m), and the measured object (flat plane) which isinclined by 70 degree from a horizontal line.

The apparatus is shown in Fig. 7(a) set in thevacuum chamber of SEM. The magnification of SEMis 5,000. The fringe image of the grid is grabbed asshown in Fig. 8(a). Because the measured object is theflat plate, the fringes are straight and parallel. Theintensity distribution on section (A-A') is shown inFig. 8(b). The period of fringes as shown in Fig. 8(c) iscalculated by Wavelet transform using the profile ofintensity of the fringe. In this experiment, WaveletTransform package[16] is employed for detecting theperiod of fringe signal. It can be seen from Fig.8(c) thatthe period of the intensity distribution(fringes) isalmost constant. Finally, the shape of the plate can bedetected by the measurement principle of this methodas shown in Fig. 8(d). Assuming that this plate as themeasured object is a perfect plane, the standarddeviation of the difference between the result by thismethod and the ideal surface of the perfect plane canbe estimated as 140nm.

From the result of this experiment, it can beconfirmed that the measurement principle of this

(b) Grating (Pitch=4µm)

Grating holder Sample holder

(a) Experimental apparatus

Fig. 7. Measurement apparatus

(a) Experimental apparatus (b) Grating (Pitch =4 µm)


76

method is effective in the measurement of smallstructures.

4. Measurement Results of 3D Structure of HardDisk Head

The new measurement system is applied to themeasurement of a very small 3D structure. Bymeasuring a simple 3D structure, the basic feature ofthe new system is discussed. A very small 3D structurewhich is located at the near point of tip of slider of ahard disk shown in Fig. 9(a) is measured by thismethod. As shown in Fig. 9(b), there are two straightline-structures in the vicinity of the head of the harddisk. The width and the height of the structure areabout 2 μm and 150nm, respectively. These straightline structures are located parallel by separating by10 μm. Now, the part (B-B') of the structure shown inFig. 9(c) is measured. The magnification of SEM is8,000 in this experiment.

The fringe image by FE-SEM is shown in Fig. 10(a). In the image, the fringe pattern and structure areobserved. It can be confirmed that the fringe pattern iscurved by the measured object as shown by the dotline. The intensity profile on the line B-B' is shown inFig. 10 (b). The period distribution of the fringe patternshown in Fig. 10 (b) by using Wavelet transform

analysis is shown in Fig.10 (c). The shape of onesection (B-B') of 3D measured structure is calculatedby using the period of the fringes shown in Fig. 10 (c).The measured shape of the structure is shown in Fig.10 (d) by dotted line. In order to verify the measuredresult, the same structure is measured by AFM. Theresult by AFM is also shown in Fig. 10 (d). It is evidentfrom the results that both results agree well.

In Fig. 8(d), the standard deviation of differencebetween measured results and the ideal plane is 140nm. However, in Fig. 10 (d), it can be seen that thedifference between both results is not larger than20nm. In this experiment, the magnification of SEM is8,000. It can be seen that the high resolutionmeasurement can be performed by setting highmagnification of SEM. It can also be calculated thatthe very high resolution measurement in thisexperiment.

5. Conclusion

In this paper, a novel 3D measurement methodfor a micro size product is proposed by using theWavelet transform and the electron-beam of SEM. Anew measurement method based on the principle ofprojection moiré was discussed. The mechanism ofproducing shadows of the grid on the surface of the

Fig. 8. Measurement result


77

object by back scattering electron beam is alsodiscussed. The 3D measurement was performed byusing these shadows. In this measurement system,the grating which was produced of a silicon-wafer

under the silicon-process based on the semiconductorfabrication technology was used as a physical rigidgrid. Fringe image as shadows of the grid wasanalyzed by Wavelet transform. A flat plate was

Fig. 9. Hard disk -reading and -writing head

(a) Whole of slider (c) Expansion of A-A'

(b) Head

Fig. 10. Measured results of micro structure in hard disk


78

measured in order to confirm the validity of themeasurement principle. It was confirmed that thestandard deviation of the measurement was about140nm, when the grid of period 4 μm was used.

As an application of this method, a very small 3Dstructure of the hard disk was measured by using thegrating of pitch 4 μm. In the measurement of harddisk slider, the results by this method were comparedwith the results of AFM. From the result, the 3Dmeasuring accuracy of this method is estimated as 20nm. It is confirmed that the very high resolution 3Dmeasurement can be performed by using the proposednew method.

References

[1] G. Binning and H. Rohrer, Scanning TunnelingMicroscopy, Helv. Phys. Acta, 55 (1982) 726-735.

[2] D. Malacara, Optical Shop Testing, 2ed; JohnWiley & Sons, New York, (1992) pp. 501-598and pp. 653-685.

[3] J.I. Goldstein, Scanning Electron Microscopyand X-Ray Microanalysis, Plenum press, NewYork, (1981) pp. 1-203.

[4] L. Reimer, Transmission Electron Microscopy;Springer-Verlag, Berlin Heidelberg , (1984) pp.1-133.

[5] T. Suganuma, Measurement of SurfaceTopography Using SEM with Two SecondaryElectron Detectors, J. Electron Microscopy, 34(1985) 328-337.

[6] J.W. Dally and D.T. Read, Electron Beam Moiré,Experimental Mechanics, 33 (1993) 270-277.

[7] D.M. Meadows, Generation of Surface Contoursby Moiré Patterns., Appl. Opt., 9 (1970) 942-947.

[8] H. Takasaki, Moiré Topography, Appl. Opt., 9(1970) 1467-1472.

[9] Y. Arai and S.Yokozeki, Micro 3D ShapeMeasurement Method Based on Shadow MoiréUsing Scanning Electron Microscopy, J. ModernOptics, 53 (2006) 2641-2655.

[10] D. Post, B. Han and P. Ifju, High SensitivityMoiré; Springer-Verlag, New York, (1994) pp.118-131.

[11] Y. Arai, S. Yokozeki and T. Yamada, Fringe-Scanning Method Using a General Function forShadow Moiré, Appl. Opt., 34 (1995) 4877-4882.

[12] Y. Arai and S.Yokozeki, Improvement ofMeasurement Accuracy in Shadow Moiré byConsidering the Influence of Harmonics in theMoiré Profile, Appl. Opt., 38 (1999) 3503-3507.

[13] Y. Arai and S.Yokozeki, Experimental ModalAnalysis for Vibration with Large AmplitudeUsing Moiré Topography, Int. J. Japan Soc. Prec.Eng., 31 (1997) 301-302.

[14] G. Kaiser, A Friendly Guide to Wavelets;Birkhauser, Boston, (1994) pp. 60-77.

[15] G. W. Wornell, Signal Processing with Fractals:a Wavelet-Based Approach; Prentice Hall PTR,Upper Saddle River, (1996) pp. 8-28

[16] W.H. Press, S.A. Teukolsky, W.T. Vetterling andB.P. Flannery, Numerical Recipes in Fortran 772nd Ed., Cambridge Univ. Press, (1992) pp.584-599.

[17] Stephen Wolfram, The Mathematica Book, 4th

ed, Wolfram Media/Cambridge Univ. Press,(1999).

micro 3d measurement method using sem - metrology society of india

Documents