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B. HanDepartment of Mechanical Engineering,

University of Maryland,College Partk, MD 20742

Mem. ASME

Warpage Measurement onDielectric Rough Surfaces ofMicroelectronics Devices by FarInfrared Fizeau Interferometry1

Far infrared Fizeau interferometry is developed and it is proposed as a tool for warpmeasurement of microelectronics devices. The method provides a whole-field msurface topography with a basic measurement sensitivity of 5.31mm per fringe contour.The method is implemented by a compact apparatus using a computer controlledronmental chamber for real-time measurement. The method retains the simplicity ofsical interferometry while providing wide applicability to dielectric rough surfaceRoughness tolerance is achieved by utilizing a far infrared light (l510.6 mm). Thedetailed optical and mechanical configuration is described and selected applicationpresented to demonstrate the applicability. The unique advantages of the methodiscussed.@S1043-7398~00!01303-7#

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IntroductionMicroelectronics devices are comprised of various metal c

ductors separated by insulating materials. As a result of a mmatch of coefficient of thermal expansion~CTE!, the deviceswarp and distort during thermal excursions encountered in mafacturing process and actual operating conditions. Several whfield optical methods have been utilized for warpage measuremof electronics components~Han et al.@1#, Yeh et al.@2#, Guo @3#,Stitler et al.@4#, Han and Guo@5#!. They include Twyman/Greeninterferometry, holographic interferometry, and shadow mo´.The first two provides sub-micron sensitivity and the third tycally provides a sensitivity of 25 to 50 microns. As a result of tlimited sensitivity range, the applications of the first two tecniques were limited to a small out-of-plane deformation of silicdie and the third to a relatively large deformation of printed circboard~PCB!.

The immediate motivation of this work was to document thmally induced warpage of silicon chip and substrate in a flip-cplastic ball grid array~FC-PBGA! package. The warpage of thsilicon chip and substrate is an important design parameteroptimum mechanical/thermal solution for high performance FPBGA packages. The measurement sensitivity in the range ofcrons is sought and relaxation of specimen surface preparatiorequired. The deformations are to be measured as a functiotemperature while heating and cooling the components insideenvironmental chamber.

In this paper, a far infrared Fizeau interferometer is introdufor real-time warpage measurement of rough surfaces. It retthe simplicity of classical interferometry while providing a widapplicability to dielectric rough surfaces. The detailed techniconsiderations are presented and the unique advantages oproposed method are discussed.

Background: Fizeau InterferometryFizeau interferometry is a classical interferometry for meas

ing surface topography of a slightly warped specular~mirror-like!

1Part of this paper was presented at the 1998 ASME Annual Winter MeeAnaheim, CA, November, 1998.

Contributed by the Electrical and Electronic Packaging Division for publicationthe JOURNAL OF ELECTRONIC PACKAGING. Manuscript received by the EEPDApril 13, 1999; revised manuscript received December 20, 1999. Associate Tecal Editor: A. Tay.

Copyright © 2Journal of Electronic Packaging

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surface~Post et al.@6#!. A practical optical setup using a smainclined incidence is illustrated in Fig. 1. In the setup, a partiareflective optical flat is placed near a specimen surface. A diveing beam from a monochromatic light source is collimated anilluminates the optical flat. A portion of the light is reflected frothe back surface of the optical flat. The other portion is transmted and it is reflected from the specimen surface. The beamflected from the specimen undergoes multiple reflections betwthe optical flat and the specimen. After reflection, the beamscollected by an imaging system. Note that some portion of lighreflected from the top surface of the optical flat and it can interfwith the beams to produce undesired ghost patterns. This caavoided by using a wedge as shown in Fig. 1 or by coating thesurface with an anti-reflection coating.

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Far Infrared Fizeau InterferometryAlthough simple, the application of Fizeau interferometry w

visible light is limited since it requires a specular surface ofspecimen. In addition, the corresponding measurement sensiis a fraction of micron, which is usually too sensitive for typicwarpage of microelectronics devices. Far infrared Fizeau interometry ~FIFI! was developed to cope with these problems.

Interferometry for Rough Surface. It has been known thathe specular component of the reflected light increases aswavelength or the angle of incidence increases~Beckmann andSpizzichino@7#!. Consequently, with a longer wavelength, a suface regarded as optically rough under visible light can be treaas a specular surface~Munnerlyn and Latta@8#; Kwon @9#; Kwonet al. @10#; Lewandowski et al.@11#; Lewandowski et al.@12#;Sinha and Tippur@13#!. The increase of specular reflection canexplained qualitatively by using the relationship known as ‘‘Raleigh criterion’’

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whereh is height of the surface irregularities,l is the wavelength,u is the angle of incidence~Beckmann and Spizzichino@7#; Sinhaand Tippur@13#!. The Rayleigh criterion can be used as a measof effective surface roughness. Theoretically, a surface willcome perfectly smooth whenh/l approaches zero oru ap-proaches 90 deg.

In FIFI, a far infrared light is employed to increase the wavlength of light. Consideringl510.6mm of CO2 laser, the relativeroughness is reduced by a factor of 20 at normal incidence~u50deg!, compared with a wavelength in the middle of visible spetrum ~green light with 0.5mm!. Consequently, optically roughsurfaces such as the ground surface of silicon, organic subsetc., can be tested without any specimen preparation.

Intensity Distribution: Basic Sensitivity. Fizeau interferom-etry does not produce a pure two-beam interference. Multipleflections occur between the specimen surface and the opticalIn classical Fizeau interferometry with a visible light, the multipreflections are often ignored since the reflectivity of the refereflat is low ~typically 4 percent! ~Post et al.@6#!. In FIFI, however,the optical flat employed in the system has a high refractive inand produces a reference beam with much larger intensity.example, ZnSe has a refractive index of 2.4208 atl510.6mm andreflectivity at normal incidence is nearly 17 percent. Conquently, the multiple reflections become significant and mustconsidered for the intensity distribution of interference patteAnother important factor to be considered for the intensity disbution isroughnessof the specimen surface. Roughness can athe intensity distribution significantly since the specular portionthe light reflected from the specimen is inversely proportionathe height of surface irregularities~Beckmann and Spizzichino@7#; Kwon @9#; Sinha and Tippur@13#!.

Based on the geometrical parameters illustrated in Fig. 2~a!, themathematical expression of the intensity distribution^I & can bewritten as

^I &5I 0RFR21r2~t22R2!

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l 5 wavelength of lighta 5 angle between the reference flat and the specimen surw 5 distance between the reference flat and the specim

surfaceu1 5 angle of incidence

r 5 reflection coefficient of the reference flatt 5 transmission coefficient of the reference flat

r s 5 reflection coefficient of the specimenI 0 5 intensity of the incident beams 5 rms roughness

Equation~1! was based on the intensity distribution of classicFizeau interferometry for specular surfaces~Meyer @14#!. To ac-count for the effect of surface roughness, the specimen surwas treated as a surface containing a Gaussian distribution orms roughnesss ~Stover@15#!. Equation~1! was solved numeri-cally to determine the basic measurement sensitivity~or contourinterval! of the technique. The intensity distributions for a widrange of reflectivity and roughness were calculated as the gap~w!between the reference flat and the specimen surface increaFigure 2~b! illustrates the intensity distribution as a function ofw,obtained for the specimen surface with various reflectivities.

The contour interval of a fringe pattern is the displacembetween two neighboring dark fringes~loci of points with mini-mum intensity!. The distance between the adjacent intensity mimum was determined by solving the first derivative of Eq.~1!

Fig. 2 „a… Optical path in Fizeau interferometry and „b… inten-sity distribution for the surfaces with various values of reflec-tivity

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numerically for w values. The results indicated that the out-oplane displacement required to produce the next intensity mmum wasl/2 cosu1 and it remained unchanged regardlessreflectivity and roughness, while the distribution of the intensand the location of intensity minimum changed with reflectivand roughness as seen in Fig. 2~b!.

The result of the numerical analysis defined the contour inteof the technique as 5.31mm per fringe order. The displacemenmeasurement sensitivity can be defined as the number of frinper unit displacement; it is 1.88 fringe lines per 10mm displace-ment. The detailed mathematical derivation of the intensity disbution, including the effect of reflectivity and roughness, canfound elsewhere~Verma and Han@16#!.

Optical and Mechanical Configuration. A mechanical con-figuration for real-time warpage measurement is illustrated scmatically in Fig. 3~a!. An air-cooled CO2 laser ~Synrad: Model48-I! with continuous 10 W output power was used as a cohelight source. It produces a highly stable TEM00 single longitudinalmode. The light has a linear polarization in the vertical directand a beam diameter was 4 mm. The output power of the lwas controlled by a D/A converter installed in a PC throughuniversal controller~Synrad: Model UC-1000!. The minimumstable laser power was about 0.5 W and air-cooling becameessary when the power exceeded 2 W.

An expanded beam illuminates the optical flat and the collimtor mounted on a specially designed port of an environmechamber. The chamber is equipped with an RS232 interface awas controlled by the PC through its serial port. The chambera heating/cooling rate of 0.5°C/s and its operating temperarange is240°C to 300°C. The imaging system is comprised of

Fig. 3 „a… Mechanical and „b… optical configuration of the farinfrared Fizeau interferometer for real-time measurement

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imaging lens and an infrared CCD camera~Electrophysics: Model5500!. The imaging lens was mounted on a translation stagetraveled along a rail to provide a desired magnification factorvarious sizes of specimens. The image was displayed on a moand the output from the monitor was digitized by a frame grabfor image processing.

A detailed optical arrangement is explained in Fig. 3~b!. Thebeam from the laser was first divided by a partial reflector~10percent transmission and 90 percent reflection! to reduce the in-tensity of the laser. The reflected light was absorbed by a grapblock attached to the laser diode assembly. The transmittedwas redirected by a silicon mirror and it was expanded by a placonvex lens. The expanded beam was collimated by a 2-in. dieter plano-convex lens. An optical flat was placed next tocollimating lens. One side of the optical flat closer to the lens wcoated with an anti-reflection coating to avoid the ghost patteThe optical axis of the collimating lens was perpendicular tooptical flat and the angle of incidence was 2 deg, as shown in3~a!. A portion of collimated beam was reflected from a referensurface while the transmitted beam was reflected from the spmen surface. The reflected beams were collected by the infrCCD camera.

All the optical elements described above were fabricated frZnSe. Its transmission spectrum is 0.54 to 18.2mm. Since theinfrared light was not visible, a visible laser diode~l5670 nm!was used for initial alignment of the optical elements. A speciadesigned laser diode assembly was mounted on the head oCO2 laser. The position of the laser diode was adjusted untilbeams of the laser diode and the CO2 laser had the identical pathA fluorescent plate was used to observe the beam of the CO2 laser.After the initial alignment, the CO2 laser was operated. Thfringes were visible on the TV monitor at this stage and fiadjustments were made while observing the fringe patterns.

Fig. 4 Tilt stage assembly

Fig. 5 Infrared Fizeau fringes on a ground glass

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The specimen was mounted on an L shape fixture, as illustrain Fig. 4. The fixture was mounted on a translation stage, whichturn was mounted on a tilting stage for angular adjustments.adjusting screws~T1, T2, and T3 in Fig. 4! were connected tohigh torque flexible shafts. The shafts were extended to theside of the chamber to allow remote adjustments while operathe chamber.

Figure 5 illustrates a fringe pattern obtained from the setup. Tspecimen was a float glass ground by a 600 grit grinding paThe specimen was adjusted until its surface became parallel tooptical flat. The specimen was then rotated with respect toz-axis ~Fig. 4! and the fringe pattern was recorded. The straigfringes shown in Fig. 5 represent linear out-of-plane displaments caused by rotating the specimen. In spite of rough surand low reflectivity of the ground glass, excellent fringe contrawith high signal-to-noise ratio was achieved. Note that the flglass has a refractive index of 1.5 and its reflectivity is only ab4 percent at a normal incidence~Post et al.@6#!.

Fig. 6 Cross-sectional view of the FC-PBGA module andassembly

Fig. 7 Warpage contours of FC-PBGA module, where contourinterval is 5.31 mm per fringe order

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Applications

Flip-Chip Plastic Ball Grid Array Package. In a FC-PBGApackage~or module!, a silicon chip is mounted on an organsubstrate using flip-chip solder bumps; the gap between the buis filled with an epoxy underfill. The package is then mounteda PCB using an eutectic solder ball array to form an assemThe underfill significantly reduces the strains in the bumps cauby the CTE mismatch between the chip and the substrate, wthe increased coupling through a high strength underfill produa large bending of the module. The bending of the moduleconstrained after it is mounted on a PCB. The real-time FIFI wemployed to document the effect of the PCB constraints onwarpage of the module. The cross sectional views of the modand the assembly investigated in the study are illustrated in Fiwith relevant dimensions. In the module, a square chip~7 mm37mm! was mounted on a BT based substrate. The moduleconnected to a FR4 based PCB by 19316 array of eutectic soldeballs.

The test specimens were installed in the environmental chber. Initially, they were heated to the underfill curing temperat~140°C!. Then, the deformations of the top surface of the spemens were documented while cooling the specimens to240°C.The resultant fringe patterns at various temperatures are showFig. 7 for the module and Fig. 8 for the assembly, wherecontour interval is 5.31mm per fringe order. Note that the fringpatterns from the chip and the substrate were recorded frosingle experiment, although the surfaces of the silicon andsubstrate were not located in the same plane. In addition, thesignal-to-noise ratio provided by the fringes on the rough grousurface of the chip clearly indicates the highly effective roughntolerance of the method. The bending displacements of the

Fig. 8 Warpage contours of FC-PBGA package assembly,where contour interval is 5.31 mm per fringe order

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were extracted along its diagonal line~AA8! and they are plottedin Fig. 9. As expected, chip was nearly flat at the underfill curtemperature and the warpage of the chip increased as temperdecreased. The chip bending displacements of the modulenearly the same as those of the assembly until the temperareached room temperature. At240°C, however, the chip bendindisplacements of the module became larger than that of thesembly. It was ascribed to the increased coupling betweenmodule and the PCB through the solder balls at cryogenic tperatures.

More striking results were obtained in the substrate warpaThe out-of-plane displacements of the substrate of the mo

Fig. 9 W displacements of the silicon chip at various tempera-tures

Fig. 10 W displacements of the substrate of the module as afunction of temperature

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were extracted from the patterns in Fig. 7. The total displacemalong BB8 are plotted in Fig. 10. The warpage of the substratethe module increased as temperature decreased. The asymseen in Fig. 10 was ascribed to the nonuniform thickness ofsolder resist mask applied on the top surface of the substratecan be seen in Fig. 8, however, the warpage of the substrate oassembly was nearly zero at 140°C and it remained unchanduring the entire cooling process. In the assembly, the subsunder the chip warped due to the high coupling between the cand the substrate through the underfill layer, but the rest ofsubstrate was constrained by the PCB through the couplingsolder balls. In order to quantify the effect of the PCB constraduring cooling, the change in the substrate warpage from 140°240°C is plotted in Fig. 11. The inflection point at the edge of tchip is evident for the assembly. This sudden change of the sstrate curvature produces a large nominal strain within the soball located at the edge of the chip. The effect of the PCB cstraints on the solder ball reliability is beyond the scope of tpaper and will be reported elsewhere~Han et al.@17#!.

Thin Small Outline Package. Thin small outline package~TSOP! is a chip carrier plastic package or module, where

Fig. 11 Change in warpage from 140°C to À40°C along thevertical centerline

Fig. 12 „a… Warpage contours of TSOP, where contour intervalis 5.31 mm per fringe order „b… W displacements along the hori-zontal centerline

SEPTEMBER 2000, Vol. 122 Õ 231

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module has terminal leads emanating from its sides. This packhas been widely used in products that require very thin ovepackage dimensions. The TSOP modules consist of an activecon chip and leaded frame assembly, encapsulated in a thinof plastic. The modules are then surface mounted on a PCB,viding interconnections through the lead frame by means of tycal surface mount process. The CTE values of the chip andlead frame~Alloy 42! are comparable, whereas the plastic moing compound has a much higher CTE. As a result, the packwarps at room temperature after it is cooled from the moldtemperature. The FIFI system was employed to measurewarpage of a TSOP module induced by the manufacturprocess.

The package tested in the study had 28 I/O. The overall paage dimension was 22 mm39.5 mm31 mm and the size of thechip was 6 mm34 mm30.2 mm. The contour map of the tosurface obtained at room temperature is shown in Fig. 12~a!,where the contour interval is 5.31mm/fringe order. Warpage othe package surface is faithfully revealed with excellent visibilalthough the surface is optically opaque and rough under vislight. Figure 12~b! plots the W displacement obtained along thorizontal centerline~CC8!. Sudden change in the slope is evidenear the edge of the chip. It was attributed to out-of-plane dplacements produced at the material discontinuity.

DiscussionsFor the thermally induced warpage measurement of curren

terest, the optical configuration of Fizeau interferometry hasmerous advantages over the configuration of Twyman/Greenterferometry ~Munnerlyn and Latta @8#; Kwon et al. @10#;Lewandowski et al.@11#; Sinha and Tippur@13#!. With Fizeauinterferometry, the reference path and the active path are idenwhereas the active path is perpendicular to the reference paT/G interferometry. Consequently, Fizeau interferometry wmuch easier to tune. This advantage was especially importanan infrared optical system inasmuch as the infrared light wasvisible during normal operation. With the configuration shownFig. 3, the specimen was mounted on the L shape fixture whileoven door was open, and then it was aligned to be parallelside of the oven by visual inspection. The fringes were usuvisible on the monitor with small or no adjustment of the L shafixture as soon as the oven door was closed.

Another important feature is stability of the system. In Fizeinterferometry, the active path~the gap between the optical flaand the specimen surface! can be very small. If the active path iseparated from the reference path and it is kept inside an ovenrapidly moving air current inside the oven would produce nouniform change in the optical path length of the active beam ding real-time observation. The random change of the optical plength would result in rapid movement of the fringe patterns. Wthe tiny gap used in the system, however, the fringes were clevisible and the necessary adjustment of the specimen positionmade while operating the oven. Note that the air current inpath where the active and the reference beam coexist do notthe fringe pattern. In addition, with the current configuration, tspecimen was fixed to the oven, and it moved together withoptical flat. This negated the accidental relative rigid-body mtions between the specimen and the optical flat and providedcellent stability even with mechanical vibration caused by an etrical motor used in the oven.

ConclusionsA far infrared Fizeau interferometer was developed and it w

proposed as a tool for real time warpage measurement of m

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electronics devices. A compact apparatus using a computertrolled environmental chamber was developed to implementmethod. With the method, preparation of a specimen surfacenot required. Roughness tolerance was achieved by employilong wavelength infrared light~l510.6 mm!. The method wasused to document the warpage of a FC-PBGA module and assbly, and a plastic leaded package. The relatively high sensiti~compared to geometric moire´ techniques! and roughness tolerance provided by the method make it ideally suited for warpameasurement of a wide range of dielectric rough surfaces enctered in microelectronic devices.

AcknowledgmentThe first author was the recipient of IBM Cooperative Fello

ship Award. He wishes to thank IBM Corporation for the financsupport and his technical mentor, Dr. S. B. Park at IBM, for ttechnical guidance. The authors wish to thank Intel Corporatfor the financial support. The technical guidance of Drs. R. Mhajan and B. Chandran at Intel is graciously acknowledged.computer program to control the hardware was developed byD. Columbus of Clemson University and his contributions aacknowledged. Helpful suggestions from Dr. J. Sinha of ADCorporation on the infrared laser are also acknowledged.

References@1# Han, B., Guo, Y., and Choi, H. C., 1993, ‘‘Out-of-plane Displacement Me

surement of Printed Circuit Board by Shadow Moire´ with Variable Sensitiv-ity,’’ Proceedings of the 1993 ASME International Electronics PackagConference, September, Binghamton.

@2# Yeh, C.-P., Ume, I. C., Fulton, R. E., Wyatt, K. W., and Stafford, J. W., 199‘‘Correlation of Analytical and Experimental Approaches to Determine Thmally Induced PWB,’’ IEEE Trans. Compon. Hybrids, Manuf. Technol.,16,No. 8, pp. 986–995.

@3# Guo, Y., 1995, ‘‘Applications of Shadow Moire´ Method in Determination ofThermal Deformations in Electronic Packaging,’’Proceedings of the 1995SEM Spring Conference, Grand Rapids, MI.

@4# Stiteler, M. R., Ume, I. C., and Leutz, B., 1996, ‘‘In-process Board WarpaMeasurement in a Lab Scale Wave Soldering Oven,’’ IEEE Trans. CompPackag. Manuf. Technol., Part A,19, No. 4, pp. 562–569.

@5# Han, B., and Guo, Y., 1997, ‘‘Photomechanics Tools as Applied to ElectroPackaging Product Development,’’Experimental/Numerical Mechanics inElectronics Packaging, Han, B., Mahajan, R., and Barker, D., eds., Society fExperimental Mechanics, Bethel, CT, Apr., Vol. 1, pp. 1–14.

@6# Post, D., Han, B., and Ifju, P., 1994,High Sensitivity Moire´: ExperimentalAnalysis for Mechanics and Materials, Springer-Verlag, NY.

@7# Beckmann, P., and Spizzichino, A., 1963,The Scattering of ElectromagneticWave from Rough Surface, Macmillan, New York.

@8# Munnerlyn, C. R. and Latta, M., 1968, ‘‘Rough Surface Interferometry UsiCO2 Laser Source,’’ Appl. Opt.,7, No. 9, pp. 1858–1859.

@9# Kwon, O., 1980, ‘‘Infrared Lateral Shearing Interferometers,’’ Appl. Opt.19,No. 8, pp. 1225–1227.

@10# Kwon, O., Wyant, J. C., and Hayslett, C. R., 1980, ‘‘Rough Surface Interfometry at 10.6mm,’’ Appl. Opt., 19, No. 11, pp. 1862–1869.

@11# Lewandowski, J., Mongeau, B., Cormier, M., and Lapierre, J., 1986, ‘‘InfraInterferometers at 10mm,’’ J. Appl. Phys.,60, No. 10, pp. 3407–3413.

@12# Lewandowski, J., Mongeau, B., Cormier, M., and Lapierre, J., 1986, ‘‘InfraHolographic Interferometry,’’ Appl. Opt.,25, No. 18, pp. 3291–3296.

@13# Sinha, J., and Tippur, H., 1998, ‘‘Infrared Interferometry for Rough SurfaMeasurements: Application to Failure Characterization and Flaw DetectioOpt. Eng.,38, No. 8, pp. 2233–2239.

@14# Meyer, Y. H., 1981, ‘‘Fringe Shape with an Interferential Wedge,’’ J. OpSoc. Am.,71, No. 10, pp. 1255–1263.

@15# Stover, J. C., 1995,Optical Scattering, SPIE Press, Bellingham, WA.@16# Verma, K., and Han, B., 2000, ‘‘Far Infrared Fizeau Interferometry,’’ App

Opt. ~submitted for publication!.@17# Han, B., Park, S.-B., Verma, K., and Ackerman, W., 2000, ‘‘On the Des

Parameters of Flip-chip PBGA Package Assembly for Optimum Solder BReliability,’’ IEEE Trans. Compon., Packag., Manuf. Technol., Part A~sub-mitted for publication!.

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