the measurement system for particle size on surface … · lyzing the sizes and types of particles,...

284 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.9, NO.2 August 2011

The Measurement System for Particle Size onSurface of Hard Disk Drive based on

Experimental Light Scattering of BRDFSimulation

Mongkol Wannaprapa1 ,

Narongpun Rungcharoen2 , and Wanchai Pijitrojana3 , Non-members

ABSTRACTThis work aims to obtain the perfectly measure-

ment system for 200-600 nanometer of particle size,type of SiO2 on surface of Lubricant (n20

D ) recordingmedia of hard disk drive, at 448 and 635 nm of inci-dent wavelength. This system uses an incident andreflective angles equally, 89o, based on the principleof Mie scattering theory. Moreover, the system is ap-plied to compare an intensity value of scattered lightbetween of BRDFpart simulation model and of exper-iment result of David W. Hahn light scattering. Forthe conclusion, this system could measure the particlesizes and types accurately and efficiently.

Keywords: Scattering Intensity, BRDFpart Simu-lation Model, Mie Scattering Theory, Particle Sizes,Particle Types

1. INTRODUCTION

Although a hard disk drive has been nowadays de-veloped to smaller size, it is low efficiency and causesdamage to the inner components of hard disk drivebecause of contaminated small particle during pro-duction process. As a result, ones are interested instudying to use the scattering technologies for ana-lyzing the sizes and types of particles, which are in-dicated at level of nanometer (nm) scale.

For example, Yuzo MORI and his team studied on“A New Apparatus for Measuring Particle Sizes of theOrder of Nanometer”. They innovated the measure-ment system on Silicon (Si) wafer surface of refractiveindex at 1.5 within particle sizes of 1-30 nm, includ-ing five types of Ag, Au, SiC, Al2O3 and SiO2 whichrespectively contain the refractive index of particle at0.23, 1.46, 2.46, 1.76 and 1.45 [1], with the incidentlight at 448 nm of wavelength.

The result based on Rayleigh Scattering Theory[8], the average measurement of scattering intensity

Manuscript received on August 1, 2010 ; revised on January11, 2011.

1,2,3 The authors are with Department of Electrical En-gineering, Faculty of Engineering, Thammasat UniversityRangsit CampusKlong Luang, Pathumthani 12120, Thailand.,E-mail:w [email protected], [email protected] [email protected]

for five particle types, comparing with 1-30 nm ofparticle size which is consequent to particle types andsizes. The result and diagram of the measurementsystem are shown in fig.1 and fig.2.

Fig.1: Yuzo MORIs experimental result based onRayleigh scattering theory [6]

Fig.2: Yuzo MORIs measurement of particles onthe Si wafer surface [7]

The Measurement System for Particle Size on Surface of Hard Disk Drive based on Experimental Light Scattering of BRDF Simulation285

Besides, David W. Hahn [5] had researched on lightscattering based on Mie Scattering Theory [3]. Hisexperiment used scattered light at 1.7 micrometer ofspherical particle with refractive index of 1.4 and 0o-180o of incident angles vertically at particular areawith wavelength of 532 nm and 90o of θi angle, asshown in fig. 3.

Fig.3: David W. Hahns light scattering at 1.7 mbase on Mie scattering theory [5]

In this work, we use the principle of Bidirec-tional Reflectance Distribution Function (BRDF) [4]to model and design the system using Modeled In-tegrated Scattering Tool program (MIST) [11]. Inorder to study the characteristics of scattered lightfrom particle on surfaces, the BRDFpart simulationmodel based on Rayleigh and Mie scattering theoriesare specified patterns. Then, the results of the sim-ulations are compared to the experimental result ofYuzo MORI [6] using Rayleigh scattering theory andDavid W. Hahn [5] using Mie scattering theory. It isconfirmed that the simulation model and designing ofthe system are well-defined and lead to implementa-tion of the real measurement system for both size andtype of particle, size ranged from 200 to 600 nm andtype of SiO2, on surface of Lubricant (n20

D ) recordingmedia of hard disk drive [2].

2. PRINCIPLES AND THEORIES

2.1 Scattering Principle

The light scattering is the alteration of the direc-tion and intensity of a light beam that strikes an ob-ject, the alteration is due to the combined effects ofreflection, refraction, and diffraction [3] as shown infig. 4.

This phenomenon is based on Rayleigh and Miescattering theories, which α value classifies the type ofscattered light. The formula is defined by the particlesize and reciprocal wavelength of the incident light [1].

α =πD

λ(1)

D is the diameter of particleλ is the wavelength of incident light

Fig.4: Phenomenon of scattering particle [3]

Where α ¿ 1 [Based on Rayleigh Scattering Theory]α À 1 [Based on Mie Scattering Theory]

2.2 Rayleigh Scattering Theory

Fig.5: Rayleigh scattering [9]

According to fig. 5, the incident light on small par-ticle with α ¿ 1 value, which the intensity of scat-tered light equal to the intensity of light scatteringoccurs all around area, which is called Rayleigh scat-tering theory as following formula (2).

IRay = I01 + cos2 θ

2R2

(2π

λ

)(D

2

)6 (n2 − 1n2 + 2

)2

(2)

I0 is incident light intensityθ is the scattering angleR is distance of scatteredn is refractive index of particle

2.3 Mie Scattering Theory

Fig.6: Mie scattering theory [9]

Refer to fig. 6, the incident light on particle withα À 1 value, which the intensity of scattered light


has high scattering intensity in the inverse directionof incident light, which is called Mie scattering theoryas following formula (3).

IMie = Io1

2R2

(2π

λ

)4 (D

2

)6

(i⊥ + i‖) (3)

Where i⊥, i‖ are the intensity function of computationfrom the infinite series.

2.4 Principle of Bidirectional Reflection Dis-tribution Function (BRDF)

BRDF is property of the incident light on mate-rial obtained from optical interaction with three char-acterizations; Reflected light, Transmitted light, andAbsorbed light, which is called Energy conservation[10], as shown in fig. 7.

Fig.7: BRDFs light reaction [10]

Incident light = Reflected light + Transmitted light+ Absorbed light

BRDF is considered by the ratio of reflected lightsignal and incident light signal, as referred to formula(4).

BRDF =OutputSignal

InputSignal=

Lr

Ei(4)

Lr is quantity of light reflected in direction ωr

Ei is quantity of light arriving in direction ωi

ωi is incoming light directionωr is outgoing reflected directionDue to formula (4), it can be considered by the

incident light angle and reflected light angle as fol-lowing formula (5).

BRDF (θi, φi, θr), φr =dLr

dEi

(θi, φi, θr)(θi, φi)

(5)

θi is the zenith angle of incident lightφi is the azimuth angle of incident lightθr is the zenith angle of reflected lightφris the azimuth angle of reflected light

To obtain the incident light angle and the reflectedlight angle under BRDF principle, it can be describedas geometric structure as shown in fig.8.

Fig.8: Geometric structure on BRDF surface

Refer to fig. 8, the incident light angle of Li iscorrelated to Solid Angle : dω which contains the in-cident light angle of θi and Azimuth angle of incidentlight angle φi on xy plane in an area of dAi. If so,the reflected light angle of direction Lr is correlatedto solid angle θr, φr on xy plane. Thus, BRDF canshow geometric structure on half sphere as referredto fig. 9.

Fig.9: BRDFs geometric structure on half sphere

Due to the spherical solid angle tariff (fig. 8), dωand dEi triangle defined as follows:

dω = (height)(width) = (dθ)(sin θdφ)= sin θdθdφ (6)

and dEi = Li cos θidωi (7)

Thus, formulas (6) and (7) are defined small areaon spherical surface, as shown in fig 10, of solid anglein BRDF direction between reflected light angle andincident light angle.

Fig.10: Tariff of spherical solid angle


Therefore, formulas (4) and (5) of BRDF takeplace by formulas (6) and (7) on incident angle oflight as formula (8).

BRDF (θi, φi, θr, φr) =Lr

Li cos θidωi(8)

Refer to above principle of BRDF, BRDFpart sim-ulation model on MIST program will be analyzed par-ticle on surface as following (9).

BRDFpart=1

cos θr cos θi

NF

A×

∣∣∣qpartij · e

∣∣∣2(2π

λ

)4(D

1

)6(n2

sph−1

n2sph+2

)2

(9)

N/A is density of scatters within the illuminatedarea

F is structure factor that depends upon thecorrelation between different scatteringcenters.

nsph is refractive index of particlee is a unit vector parallel to the incident

electric field.qij is Jones scattering matrix value

3. RESULTS AND DISCUSSIONS

3.1 Results of BRDFpart Simulation ModelComparing between Incident Angle andReflected Angle for Suitable ScatteringIntensity

To create BRDFpart simulation model by definingthe incident angle and reflected angle, the conditionsare the laser source with 532 nm wavelength and theincident light direction Li that affects the reflectedlight direction Lr at θi and θr angles as shown in fig.11. BRDFpart value will be defined as formula (9) bythe incident light on particle with the size of 10 and100 micrometer, the spherical shape of Polystyrene la-tex (PSL) at refractive index of 1.59 [1] on Lubricant(n20

D ) recording media of hard disk drive as shown infig. 11.

Fig.11: BRDFs geometric structure on PSL parti-cle, surface of Lubricant recording media of hard diskdrive

As the results of BRDFpart simulation model com-paring between incident and reflected angles at 1o,

45o and 89o under 10 and 100 micrometer, both inci-dent and reflected angles at 89o contain the highestBRDFpart value. We could conclude that the anglefor accurate and suitable measuring at 10 and 100micrometer of particle size is 89o angle as shown infig. 12 and 13.

Fig.12: Comparison between incident angle at (1o,45o, 89o) and reflective angle at (1o, 45o, 89o) on 10micrometer of particle

Fig.13: Comparison between incident angle at (1o,45o, 89o) and reflective angle at (1o, 45o, 89o) on 100micrometer of particle

From the incident and reflected angle at 89o, weuse it to compare the results of this paper to BRDFsimulation of Rayleigh and Mie scattering theory.

3.2 Yuzo MORIs Result compare with theResults of BRDFpart Simulation Model tobased on Rayleigh Scattering Theory

Comparison between Yuzo MORIs experimentalresult and the results of BRDFpart simulation modelbased on Rayleigh scattering theory are used to definethe number of angles measuring scattering intensityat 360 points, incident and reflected angle at 89o un-der the same as other conditions and variables, andalso is used to find the average scattering intensities.The conclusion results of simulation correlated withYuzo MORIs real experiment. Because the increas-ing ratio of light scattering intensity is associated tothe increasing particle size in ranged from 1 to 30nm which the slope and linear with all five types are


shown in fig. 14. Thus, the results of this compar-ison relates to the principle of BRDFpart simulationmodel.

Fig.14: Results of BRDFpart simulation model at89o incident and reflective angle under conditions ofYuzo MORIs experiment

According to above results, the number of particlesizes has increased from 1-30 nm to 1-600 nm on sur-face of Ag, Au, SiC, Al2O3 and SiO2 types in orderto consider the correlation between sizes and averageof light scattering intensities as shown in fig. 15.

Fig.15: Results of BRDFpart simulation model at1600 nm on Si wafer surface

Fig. 15 shows the relationship between the parti-cle sizes continuously increasing in ranged from 100to 600 nm and the intensity of scattered light linearlyincreasing. Thus, we are able to apply BRDFpartsimulation model to define the average of light scat-tering from 100 to 600 nm particle sizes on surfacesof Ag, Au, SiC, Al2O3 and SiO2 types as shown infig. 16.

From the experiment, we measure three particletypes of TiO2, Al2O3 and SiO2. Si wafer is used inthe experiment instead of Lubricant recording mediaof hard disk drive in order to observe the linearity ofscattering intensity.

Particle sizes in ranged from 100 to 600 nm andtype of particle: TiO2, Al2O3 and SiO2 relate to theintensity of scattered light as shown in fig. 17. Ob-viously, the intensity of scattering is directly changedwith the particle sizes in the pattern of linearity.

Fig.16: Resulst of BRDFpart simulation model onsurfaces of Ag, Au, SiC, Al2O3 and SiO2 particleranged from 100 - 600 nm on Si wafer surface

Fig.17: Results of BRDFpart simulation model withTiO2, Al2O3 and SiO2 particle at 100600 nm on Lu-bricant recording media of hard disk drive

3.3 David W. Hahns Result compare withResults of BRDFpart Simulation Modelbased on Mie Scattering Theory

In this case, it is similar to the results in section3.2. The comparison between David W. Hahns ex-perimental result and the results of BRDFpart simu-lation model based on Mie scattering theory is usedto define the number of angles for measuring scatter-ing intensity at 180 points. This results of simulationcorrelates with the result of David W. Hahns experi-ment. Consequently, the results of comparison relateto the principle of BRDFpart simulation model theoryas shown in fig. 18.

3.4 Results of BRDFpart Simulation Modelbase on Rayleigh and Mie Scattering The-ories

According to fig. 19 and 20, the results of Rayleighand Mie scattering theories are different. We cancombine these two scattering theories to consider thecorrelation of sizes ranged from 1 - 100 nm and from200 - 600 nm.

The first range of sizes of particle is 1-100 nm withα ¿ 1 value based on Rayleigh scattering theory asshown in table 1. Firstly, the smallest particle size,1 nm. , shown as the first inner-circle gives the low-


Fig.18: BRDFpart simulation model on particle at1.7 µm (m =1.4-0i) with wavelength at 532 nm com-parison with David W. Hahns

Fig.19: Rayleigh and Mie scattering theories withwavelength at 448 nm on SiO2 particle sizing 1-600nm on (n20

D ) surface

est intensity of scattered light. Secondly, the particlesize, 100 nm. , shown as the ninth circle gives thehighest intensity of scattered light. Finally, the otherparticle sizes give the proportion of intensity of scat-tered light. The second range of sizes of particle is200-600 nm with α À 1 value based on Mie scatter-ing theory. Similarly, the increasing of scattered lightintensity directly change according to the increasingof particle sizes. The scattered light intensities of theparticle sizes ranged from 200-600 nm are higher thanof the particle sizes ranged from 1-100 nm.

Table 1 shows, the calculation of parameters ofα values according to the particle size of 1-600 nmwith λ are 448 and 635 nm. For instance, α = (3.14)(7×10−9)/ (448×10−9) = 0.049 (α ¿ 1) shows thatscattering theory is based on Rayleigh. Similarly, α= (3.14) (400× 10−9)/ (635× 10−9) = 1.978 (α À 1)shows that scattering theory is based on Mie. Fromthe calculations, we obtain the suitable patterns of

Fig.20: Rayleigh and Mie scattering theories at 635nm wavelength on the particle type of SiO2, sizing1-600 nm on (n20

D ) surface

Table 1: α value presents the relation between Dparticle sizing 1-600 nm and 448, 635 nm wavelengths

scattered light intensities.Clearly, fig. 21-22 and 23-24 show separately

for Rayleigh and Mie scattering theories with wave-lengths at 448 nm and 635 nm.

Firstly, BRDFpart simulation model is under con-dition of α ¿ 1 in table 1 on particle size of 1-100 nmat 448, 635 nm wavelengths as shown in fig. 21 and22. The innermost circle: particle size of 1 nm at twowavelengths gives the lowest light scattering inten-sity and the outermost circle: particle size of 100 nmat two wavelengths gives the highest light scatteringintensity respectively. Clearly, the results obtainedagree with Rayleigh scattering theory. Because thepattern of these light scattering intensities are thesame pattern of Rayleigh scattering theory, i.e. thereare light scattering intensities all directions equally.

Secondly, BRDFpart simulation mode is undercondition of α À 1 in table 1 on particle size of 200-600 nm at 448, 635 nm wavelengths as shown in fig.23 and 24. Similarly, both of the particle size of 200


Fig.21: Rayleigh scattering theory at 448 nm on Fig. 22: Rayleigh scattering theory at 635 nm onSiO2 particle sizing of 1-100 nm on (n20

d ) surface SiO2 particle sizing of 1-100 nm on (n20D ) surface

Fig.23: Mie scattering theory at 448 nm on SiO2 Fig. 24: Mie scattering theory at 635 nm on SiO2

particle sizing of 200-600 nm on (n20D ) surface particle sizing of 200-600 nm on (n20

D ) surface

and 600 nm, at two wavelengths, give the increasingof scattered light intensity directly changed accord-ing to the increasing of particle sizes and give thesame pattern of Mie scattering theory, i.e. the lightscattering intensities are the highest in the oppositedirection to the incident light. Clearly, the resultsobtained agree with Mie scattering theory.

Finally, This BRDFpart simulation model is un-der the same conditions and factors. For instance,the incident and reflected angle are equal to 89o with

SiO2 particle at refractive index of 1.45 on Lubricantrecording media surface of hard disk drive at the samerefractive index of 1.5. Therefore, this leads to theconclusion that BRDFpart simulation model can beused to design and construct the system to measuresizes and types of particle on Lubricant recording me-dia surface base on Rayleigh or Mie scattering theory.For this paper, the particle size is defined between200-600 nm at parameter equal to α À 1 accordingto Mie scattering theory.


4. CONCLUSION

Fig.25: The measurement system for spherical par-ticle on smooth surface based on the principle of Miescattering theory

According to the principle of scattering theory andthe results of BRDF simulation model of this work,we can confirm the results of the BRDF compared be-tween Yuzo MORIs Result and David W. Hahns Re-sult are properly and appropriately. We can conclu-sion that the BRDF simulation can be used in orderto measure for 200-600 nm, SiO2 particle on Lubri-cant recording media surface base on Mie scatteringtheory. Besides, the BRDF can measure other par-ticles, other surfaces, base on Mie or Rayleigh scat-tering theory. In the figure 25 shown, the design ofmeasurement system is implemented and tested baseon Mie scattering theory. The system consists of thephoto detector can be moved from 0o to 180o anglesand detects the intensities of light scattering. More-over, the suitable angle of incident and reflected lightis 89o angle and the samples are moveable and con-trollable automatically. The signals of the system areanalyzed by using computer and software. Besides,the system can be developed to measure other parti-cle sizes and types in industry of hard disk drive.

5. ACKNOWLEDGMENT

The author would like to thank the National Elec-tronics and Computer Technology Center of Thailandand I/U CRC in HDD advanced manufacturing for fi-nancial support

References

[1] R. Xu, “Particle characterization light scatteringmethods,” in KLUWER ACADEMIC PUBLISH-ERS, ISBN: 0-792-36300-0, (2002).

[2] http://books.google.com/books?id=GpAO5dGXN60C&pg=PA125&lpg=PA125&dq=lubricant+refractive+index&source.

[3] P. A. Webb, “A primer on particle sizing bystatic laser light scattering,” Micromeritics tech-nical workshop series (2000).

[4] T. A. Germer, “Angular dependence and polariza-tion of out-of-plane optical scattering from partic-ulate contamination subsurface defects and sur-face micro roughness,” SPIE 3275, 8798-8805,(1997).

[5] D. W. Hahn, “Light Scattering Theory,” Depart-ment of Mechnical and Aerospace Engineering(2008).

[6] Y.Mori, H.An, K.Endo, K.Yamauchi and T.Ied“A new apparatus for measuring particle sizes ofthe order of nanometer,” J.JSPE, Sept 1991.

[7] S.SASAKI, H.AN, Y.MORI, T.KATAOKA,K.ENDO “Evaluation of particle on a Si waferbefore and after cleaning using a new laserparticle counter,” IEEE, 317-320, 26-28 Sept.

[8] http://hyperphysics.phyastr.edu/hbase/atmos/blusky.html.28-Feb-2006.

[9] http://commons.wikimedia.org/wiki/Image:Miescattering. svg.

[10] C. Wym “An introduction to BRDF-based light-ing”, NVIDIA Corporation.

[11] Thomas A. Germer “Modeled integrated scattertool (MIST)”, Available free of charge from NIST:http://physics.nist.gov/scatmech (2006).

Mongkol Wannaprapa received hisBachelor of Engineering (B. Eng) andMaster of Engineering (M.Eng) inelectrical engineering from the King’sMongkut Institute of Technology Lad-krabang (KMITL), Thailand.

Narongpun Rungcharoen receivedhis Bachelor of Engineering (B. Eng)in electrical engineering from the King’sMongkut University of Technology Thon-buri (KMUTT), Thailand. He alsoreceived the Master of Engineering(M.Eng) in electrical engineering fromThammasat University (TU), Thai-land.

Wanchai Pijitrojana received theB.Eng. degree in Telecommunica-tion Engineering from King’s MongkutInstitute of Technology, Ladkrabang,Bangkok, Thailand. He also received theM.S. degree in both, Computer Tech-nology and Nonlinear Optics (Electro-physics) from Asian Institute of Tech-nology, Bangkok, Thailand and the Uni-versity of Southern California, Califor-nia, U.S.A., respectively, and the Ph.D.

degree in Optoelectronics from King’s College, University ofLondon, London, England. He is currently a lecturer in theEE Department, Thammasat University, Bangkok, Thailand.His current research interests are Optical Interconnection sys-tems, Optical Design, Optics, Nonlinear Optics, Physical Op-tics, PBG, and Mathematics applied to Optics.

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