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n situ measurement of gas diffusion propertiesf polymeric seals used in MEMS packagesy optical gas leak testing

hangsoo Jangrindam Goswamiongtae Hanniversity of Marylandollege Park, Maryland 20742-mail: [email protected]

uk-Jin Hamamsung Electro-Mechanicsuwonouth Korea

Abstract. A novel inverse approach is proposed for in situ measure-ment of gas diffusion properties of polymeric seals used in microelectro-mechanical systems �MEMS� packages. The cavity pressure evolution ofa polymer-sealed MEMS package subjected to a constant bombing pres-sure is documented as a function of time using classical interferometry,and the diffusion properties of the polymeric seal are subsequently de-termined from the measured pressure history. A comprehensive numeri-cal procedure for the inverse analysis is established considering threediffusion regimes that characterize the leak behavior through a polymericseal. The method is implemented to determine the helium diffusivity andsolubility of a polymeric seal. © 2009 Society of Photo-Optical Instrumentation En-gineers. �DOI: 10.1117/1.3227904�

Subject terms: hermeticity; gas leakage; diffusion properties; optical leak test.

Paper 09072R received Apr. 11, 2009; revised manuscript received Jul. 21, 2009;accepted for publication Aug. 5, 2009; published online Oct. 2, 2009.

Introduction

olymers have been broadly used as a sealing material forarious microelectromechanical systems �MEMS� devicesncluding micro-optoelectromechanical systems1 and RF-

EMS devices2 due to their advantages over conventionaletallic seals in terms of cost and manufacturability. Gasolecules can permeate through bulk polymeric seals due

o the inherent absorbent and diffusive characteristic ofolymers. The gas leakage is a measure of hermetic perfor-ance for polymer-sealed packages.3

The gas diffusion properties of sealing polymers are re-uired to characterize the gas leakage behavior of polymer-ealed packages. Oxygen is of particular interest because itan oxidize metallic surfaces and cause corrosion. The dif-usion properties of film-type specimens can be measuredhrough transient gas transmission testing using MOCONquipment4,5 or through a combination of steady-state gasransmission test �so-called the MOCON test� for perme-bility and a direct measurement technique for oxygen con-ent or solubility �e.g., Fourier transform infraredpectrometry.6� Because of the limitations of the MOCONethod, however, the measurement of oxygen diffusion

roperties cannot be performed at temperatures higher than0°C,7 which is much lower than the temperature range ofonventional accelerated tests �85–121°C�.8,9

More importantly, polymer properties are sensitive toanufacturing processes and, thus, their diffusion proper-

ies can vary significantly; the diffusion properties obtainedrom the film-type specimens may not always representhose of the actual seals used in packages. This warrants ann situ measurement of gas diffusion properties for accuratessessment of gas leakage in polymer-sealed MEMS pack-ges.

932-5150/2009/$25.00 © 2009 SPIE

. Micro/Nanolith. MEMS MOEMS 043025-

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In this study, we utilize the optical leak test method10–12

to measure the gas diffusion properties of a sealing poly-mer. The theoretical basis for gas diffusion is described,and the procedure to determine the diffusion propertiesfrom experimentally obtained gas leak data is proposed.

This paper is complementary to the authors’ precedingpublication,3 which has provided the theoretical basis of thegas diffusion mechanism inside polymer-sealed MEMSpackages. The current paper concerns an experimental pro-cedure for diffusion property measurement while the previ-ous paper has focused on the fundamentals of diffusionmechanism and its modeling implementation. Because of acomplementary nature of modeling and experiments �e.g.,validation of the model through an experimental measure-ment and property measurement through an inverse methodbased on numerical modeling�, some figures and data plotsare excerpted from the previous paper.

2 Physics of Gas Diffusion

2.1 Governing EquationsGas flux through a polymeric material is governed byFick’s first law, which is expressed as

J = D � C , �1�

where J is the gas flux �in kilograms per meters squared persecond�, D is the gas diffusivity �meters squared per sec-ond�, � is the gradient operator, and C is the gas concen-tration �in kilograms per cubic meter�. By introducing Hen-ry’s law �C=Sp�, Eq. �1� for isothermal problems can beexpressed as

J = D � �Sp� = DS � p = P � p , �2�

where S is the solubility �in seconds squared per metersquare�, p is the gas pressure �in Pascal� and P is the gas

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ermeability �in seconds�. Fick’s second law is derivedrom the principle of mass continuity for an infinitesimalolume as

p = D�2p . �3�

By assuming that the gas obeys the ideal gas law, theavity pressure at time t1, produced by the gas diffusionhrough the seal, is obtained as

pc�t1� = pc�0� +R0T

MVc�

t1

�Ac

Jc�t� · dAdt , �4�

here pc is the cavity pressure, R0 is the gas constant8.3145 J/molK�, T is the temperature �in Kelvin�, M is theas molar mass �in kilograms per molecule�, Vc is the cav-ty volume �m3�, Ac is the cavity wall area, Jc is the fluxector at the cavity wall.

Three diffusion properties �D, S, and P� appear in Eqs.1�–�4�. Only two properties have to be determined experi-entally because a simple linear relationship exists among

he properties �P=DS�.

.2 Diffusion Regimes

ang et al.3 have reported that the gas diffusion through aolymeric seal can be categorized into three regimes, de-ending on the parameter RS, which is defined as

Fig. 1 Illustration of optimum D-S combinations.

ig. 2 Schematic illustration of optical leak test. �a� initial MEMS paubjected to a leak test, cap surface topography deformed by a preshe test.



RS �Sp�ro

2 − ri2�

Scri2 , �5�

where Sp is the solubility of the polymeric seal, Sc is theeffective solubility of the cavity �refer to Eq. �8� for itsdefinition�, ri is the �effective� inner radius of the seal �inmeters� and ro is the �effective� outer diameter of the seal�in meters�.

The three regimes are �i� permeability-dominant regimefor RS�0.01, �ii� transition regime for 0.01�RS�500, and�iii� diffusivity-dominant regime for RS�500. In the twodominant regimes, the cavity pressure is governed by onlyone parameter �i.e., permeability and diffusivity in the per-meability and diffusivity-dominant regimes, respectively�.Thus, when diffusion properties that produce a certain cav-ity pressure evolution are searched, optimum D-S combina-tions appear as straight lines in a log-scale D-S plot for thetwo regimes as shown in Fig. 1; those for the diffusivity-dominant regime form a horizontal line �D=const� whilethose for the permeability-dominant regime form a linewith a certain slope that represents DS= P=const �orlog�D�+log�S�=const�. In the case of the transition regime,the optimum D-S combination should be located as a dotbecause each D-S combination in the transition regime willideally produce a unique curve. In a real experiment, how-ever, measurement uncertainties will make the optimumcombination lines broader and the dot extended in a par-ticular direction in between the two lines for the other tworegimes as illustrated in Fig. 1.

3 Proposed MethodThe proposed method is an inverse approach using a re-gression analysis. In the method, an optical leak test is usedfirst to determine experimentally the internal cavity pres-sure increase of a polymer-sealed package, subjected to aconstant external pressure, as a function of time. Then, thegas diffusion-based governing equation is solved numeri-cally to simulate the optical leak test with various gas dif-fusion properties of the seal. The simulation results are ana-lyzed systematically by a regression scheme; the schemedetermines an optimum set of properties by minimizing anobjective function, i.e., the difference between the experi-mental data and the numerical predictions.

3.1 Optical Leak TestThe optical leak test10–12 infers the amount of leaked gasfrom the deflection changes of a MEMS package cap or

specimen under an atmospheric condition, �b� when the package isifferential is documented, and �c� reflatten cap surface at the end of

ckagesure d

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ubstrate, produced by the gas pressure differential betweenMEMS cavity and an ambient �Fig. 2�. The pressure dif-

erential is generated by subjecting the package to either aressurized or vacuum environment. If the package iseaky, the deflection is continuously altered by the changef pressure differential until the cavity pressure reaches am-ient pressure.

In order to determine the cavity pressure, the cap orubstrate deflections should be accurately correlated withhe pressure differentials between the cavity and the envi-onment. A calibration process is required to obtain such aorrelation. Within an elastic range, the deflection is lin-arly proportional to the pressure differential. The calibra-ion curve can be obtained by measuring the deflections of

fresh package at linearly varying pressure differentials,hich can be obtained by changing the ambient pressure.

.2 Twyman/Green Interferometryeasurement of the cap or substrate surface deflection is an

ssential element of the optical leak test. In this studywyman/Green interferometry is employed to visualize theurface topography of the package cap. The technique isimple and ideally suited for MEMS packages because theackage surface is specular, which is a critical requirementor the method. The principle of Twyman/Green interfer-metry is illustrated in Fig. 3.13 An expanded laser beam isollimated by a collimating lens. The collimated light isplit into two—one directed toward the specimen and thether toward the reference mirror �an optical flat�. The re-ected wavefronts recombine and interfere to form an in-

erferogram �or fringe pattern�. The interferogram provides

ig. 3 Schematic illustration of Twyman Green interferometry andn interferogram �or fringe pattern�.

ig. 4 Illustration of FFT analysis: �a� Original fringe pattern, �b� modnverse Fourier transform, and �e� 3-D plot. The cavity location is in



a contour map of the surface topography. An example of afringe pattern captured by a camera is shown in Fig. 3.

The deformation, W�x ,y�, at any point on the specimenis given by

W�x,y� =�

2N�x,y� , �6�

where N�x ,y� is the fringe order at a point �x ,y� and � isthe wavelength of the laser. The basic contour interval ofthis arrangement is defined as �/2. When a helium-neonlaser �� 632.9 nm� is employed in the setup, it providesthe basic contour interval of 316.5 nm/fringe order.

The accuracy of deflection measurement is directly re-lated to the accuracy of the cavity pressure measurement.The measurement accuracy can be enhanced by employingan automatic fringe analysis method based on digitalimage-processing techniques. A small fraction of a fringeorder can be accurately determined through techniques,such as phase shifting and fast Fourier transform �FFT�method.14,15

3.3 Digital Image Processing for ResolutionEnhancement

The FFT method was utilized for an automatic fringeanalysis because the region of interest does not contain anyboundaries and the deformation of the package surface var-ies smoothly. An added benefit of the FFT method is thatthe inherent high-frequency random noise can be elimi-nated effectively during the inverse FFT process. The FFTmethod is illustrated using the actual package below. Amore detailed mathematical description of the method canbe found in Ref. 14.

The original fringe pattern of the specimen before pres-surization is shown in Fig. 4�a�. A carrier pattern of con-stant displacement gradient is added to the original patternby a small rigid body rotation of the specimen; the numberof carrier fringes over the cavity was �20, which wasequivalent to 6.3 µm. The modulated pattern is shown inFig. 4�b�. After the two-dimensional FFT, the real harmonicis isolated in the frequency domain �Fig. 4�c��. The centerof the spectrum is moved to the origin of the frequency axisto remove the carrier frequency in the frequency domain.Then, the inverse Fourier transform is performed to restorethe original phase map �Fig. 4�d��. Unwrapping of thisphase map yields a fractional fringe orders with high fidel-ity at every point. This information is used to generate a3-D deformation map shown in Fig. 4�e�.

pattern with carrier fringes, �c� Fourier spectra, �d� phase map afterby the dotted box.

ulateddicated

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.4 Numerical Analysis

he cavity pressure development was simulated numeri-ally to determine the diffusion properties of the sealingolymer. A finite element model was built using a commer-ial software package �ANSYS�. The majority of commer-ial software packages including ANSYS do not supportas diffusion analysis. Various thermal-moisture analogychemes, utilizing the thermal diffusion module in variousoftware packages, have been proposed and utilized toolve gas diffusion problems.16,17 In this study, the normal-zed analogy scheme16 is used to handle material interfaces.he normalized analogy scheme uses the following math-matical analogy:

as pressure: p � T ,

iffusivity: D �k

�cp,

olubility: S � �cp, �7�

here T is the temperature, k is the thermal conductivity �inatts per milliKelvin�, � is the density �in kilograms per

ubic meter� and cp is the specific heat �in Joules per kilo-rams per degreeKelvin�.

The gas diffusion in a MEMS package is not a standardiffusion problem because a cavity is involved in theodel. A user-defined subroutine is required to perform a

ransient analysis �Eq. �4��; the internal cavity pressure,hich is the boundary condition at the cavity inner surface,

s to be determined as a function of time. Jang et al.3 pro-osed an effective scheme to solve the problem without aser-defined subroutine, where the cavity was treated as anffective volume with predefined solubility and infinite dif-usivity. In this “effective volume” scheme, the effectiveolubility of the cavity is determined as

c =C

p=

�

nR0T/V=

M

R0T. �8�

he effective diffusivity of the cavity is set to be severalrders of magnitude higher than that of the sealing polymero ensure the uniform pressure within the cavity. The detailsf the effective volume scheme can be found in Ref. 3.

.5 Inverse Approach to Determine DiffusionProperties

he diffusion properties of polymeric seals can be deter-ined from optical leak testing by an inverse approach.he goal of the analysis is to find the D-S combination thatroduces the most accurate cavity pressure prediction. Theredictability of a D-S combination is assessed by utilizinghe conventional coefficient of determination �R2� thatuantifies the degree of coincidence between experimentalnd simulated data. This metric is expressed as



R2 = 1 −�n�pexp,n − psim,n�2

�n�pexp,n − pexp�2 , �9�

where pexp,n is the n’th experimental data point, psim,n is then’th simulation data point, and pexp is the average value ofall the experimental data points.

An insight into the diffusion regimes �Sec. 2.2 and Fig.1� gives an idea how to effectively search the D-S combi-nation that produces the best match between the simulationand experiment. In the case of diffusivity or permeability-dominant regime, there can be an infinite number of opti-mum D-S combinations. Although any “search-style” opti-mization method may determine accurately D or P foreither regime, it cannot provide any information about thediffusion regime to which the case under study belongs.This warrants at least one rough matrix �a plot similar toFig. 1� of R2 by sweeping a sufficiently wide range of Dand S. Once a regime is confirmed, variables for the nextstep can be decided: D or P for the diffusivity orpermeability-dominant regime, and D and S for the transi-tion regime.

In the initial sweeping evaluation, a 2-D 11 � 11 matrixis populated with diffusivity and solubility values, whichare chosen uniformly �in the logarithmic scale� in such away that they could encompass all potential values of thoseproperties. The range of values was: D=10−7–10−5 mm2 /s and S=10−14–10−12 s2 /mm2. The 121D-S combinations obtained from the matrix are used asinputs to the finite element model to generate 121 sets ofsimulated data and corresponding R2 values.

A D-S combination that yields the highest R2 value inthe sweeping is used as an initial design set for the follow-ing step in which the final property values are searched. Inthis study, the first order optimization method18 is em-ployed. It utilizes gradient information to search for opti-mal variables �x= �D ,S� that minimize an objective func-tion �f =1−R2�. At each iteration step a search vector �d� iscalculated from the gradient of the objective function and anew design set for the next iteration is determined using thesearch vector, which is mathematically expressed as

x j+1 = x j + sjdj, where d j = − �f�x j� . �10�

The line search parameter sj corresponds to the minimumvalue of the objective function f in the direction of d j. Theiteration continues until the convergence criteria are met,which is given by

f j − f j−1 � � and f j − fb � � , �11�

where fb is the objective function from the best design setand � is the objective function tolerance. The built-in firstorder optimization algorithm of ANSYS is utilized for theimplementation of the method with a tolerance value �� of1�10−6.

4 Implementation Using Helium Gas

4.1 Test PackageFigure 5�a� shows schematically the structure of the pack-age used in this study. An epoxy-based photosensitive ad-hesive was used as a sealing material. A cavity was definedthrough a lithography process after the adhesive layer was

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ispensed over the silicon substrate. The package cap,ade of a glass plate, was placed. Then, the packaging

rocess was completed by curing the adhesive. A nitrogennvironment �0.9 bar� was maintained throughout the pack-ging process. The overall dimensions of the package are.6�4.5 mm, and the cavity dimension is 2.22�2.86 mm.he thicknesses of the glass cap, the polymer seal, and theilicon substrate are 120, 46, and 500 µm, respectively. Thenternal cavity volume is 2.92�10−4 cc.

A quarter-symmetry finite element model of the packages shown in Fig. 5�b�. The 3-D structure was reduced to a-D model because the top and bottom surfaces are imper-ious to gases. The effective volume scheme was employedn the model so the cavity was modeled as an effectiveolymeric volume.

.2 Experimental Setuphere are two major parts in the experimental setup: �i� anptical setup for deformation measurement and �ii� a pres-ure chamber with a high-precision pressure regulation sys-em. The optical/mechanical configuration is shown sche-

atically in Fig. 6�a�. The specimen is held inside aylindrical stainless steel pressure vessel, which is providedith a window for direct viewing. Both the vessel and theindow are designed to withstand pressures up to 50 atm.he pressure vessel is mounted on a heavy duty stage torevent vibrations caused by the vessel’s gas supply tubing.his stage offers x-y translation and rotational adjustmentf the vessel and hence, the specimen inside it as desired.he fringe pattern is captured by a high-resolution cameraith a 1 in. CCD format �Pulnix TM-1040� through an

maging lens.Any high-pressure gas tank can be used as the source of

as. A mechanical regulator located on the tank reduces theas pressure from the tank pressure value ��70 atm� to 7tm. This lower pressure gas is then supplied to aroportional–integral–derivative �PID� controllerTESCOM ER3000�. The PID controller has an internalensor, which is used in conjunction with PID logic andser-defined PID parameters to reduce gas pressure to theesired pressurization value. An additional pressure sensorTESCOM 200-1000-2527� is screwed into the pressureessel in order to read the pressure inside the chamber,hich can detect any large leakage of gas due to an acci-ental failure/rupture of the chamber gaskets and seals. Thencertainty of measurement using this pressure regulationetup is 0.02 atm �0.3 psi�.

ig. 5 �a� Schematic illustration of test specimen �excerpted fromef. 3� and �b� mesh setup of the quarter-symmetry finite elementodel.



It should be noted that light reflected from the front andback surfaces of the window can interfere with each otherand also with light reflected by the specimen, and therebycontributes to noise in the recorded interferogram. Asshown in Fig. 6�b�, the specimen surface was positionedwith an angle �approximately by 8 deg� with respect to thewindow. In this way, only the light reflected from the speci-men surface was collected by the camera. This arrangementensures that the light beams reflected from the window sur-faces are not collected by the camera.

4.3 Calibration: Pressure Differential versus CapWarpage

The desired deformation value is the relative deformationbetween the center of the cavity O, and any one of thecorners: A, B, C, and D �Fig. 5�a��. In order to account forany rigid body rotation, the desired deformation value wasdetermined by averaging the four relative deformations atthe corners. The initial deformation induced by the fabrica-tion process was first measured �1017 nm�, and then thetrue deflection corresponding to each pressure value wasdetermined by subtracting the initial deformation from themeasured deformation.

In order to obtain the calibration curve, the applied pres-sure in the chamber was increased to 4 atm �gauge� in stepsof 0.25 atm, and the surface deformation was recorded ateach step. The deformation-induced deflections are plottedas a function of the applied external pressure and bombingtime in Fig. 7�a�. Three data points marked by a dottedcircle were obtained from the representative fringe patternsand the corresponding 3-D maps shown in Fig. 7�b�. Fromthis plot, the following linear relationship between pressure

Fig. 6 Schematic diagrams of �a� the experimental setup3 and �b�the arrangement for mitigation of optical noise.

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ifferential, ∆p, and the maximum deflection, Wmax, of thepecimen was obtained

max = 309.58�p� , �12�

here the units for pressure and deformation are atmo-phere and nanometers, respectively.

The total measurement time for obtaining the calibrationurve was �300 s, and on the basis of the subsequent ex-erimental observations, it was safe to assume that the ef-ect of diffusion of helium into the cavity during the cali-ration experiment was negligible.

The repeatability of the deformation measurement wasstimated by repeating measurements in an unpressurizedtate. For each measurement the specimen was taken off the

ig. 7 �a� Calibration curve �the encircled values correspond to theringes in �b��3 and �b� representative fringe patterns and 3-D defor-ation maps obtained during the calibration process �the units in the

cale are microns�. The cavity location is indicated by the dottedox.



fixture and then remounted to simulate independent mea-surements. The results of 10 independent measurements areshown in Fig. 8. The standard deviation, �, of the measure-ments was 5 nm. For a 99.7% confidence interval, the un-certainty in deformation is given by the 3� range and isequal to 15 nm.

It is evident from Eq. �12� that the 15 nm uncertaintyin deformation measurement corresponds to an uncertaintyof 0.048 atm in the calculation of the corresponding pres-sure value. In addition, the accuracy of pressure control is0.02 atm as mentioned earlier. The uncertainty in pres-sure measurement depends on the accuracy of both theseparameters. Considering sequential perturbation, the uncer-tainty estimate at 95% confidence level, ue, can be givenby19

Ue�atm� = ��Udm�2 + �Upc�2, �13�

where Udm �� 0.048 atm�, and Upc �0.02 atm� are theuncertainty associated with the errors in deformation mea-surement and pressure control, respectively. From Eq. �13�the uncertainty in the measurement of cavity pressure is0.052 atm.

4.4 Optical Leak Test ResultAfter the calibration curve was obtained, the package wassubjected to a constant bombing pressure of 4 atm �gauge�and the deflections were measured as a function of time.The bombing pressure was maintained for 600 h after

Fig. 9 History of effective chip surface deflections and correspond-ing internal cavity pressure evolution during the bombing stages.

Fig. 8 Repeatability of the measurement; the data points are scat-tered around the average value �solid black line�.

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hich there was no noticeable deflection change, indicatinghat the cavity pressure at that stage was equal to the bomb-ng pressure.

The effective deflections obtained from fringe analysesre plotted in Fig. 9, along with the corresponding cavityressure history. Fringe images obtained from the experi-ents can be found in Ref. 3. Using the calibration curve

Eq. �7��, the deflection values during the bombing stagesere converted into pressure differential values. The inter-al cavity pressure was then calculated by subtracting thesealues from the known external pressure �4 atm whileombing and 0 atm during release�.

.5 Determination of Diffusion Propertieshe diffusion properties were calculated through the in-erse approach described in Sec. 3.5. The experimental pro-edure was simulated using the finite element model �Fig.�b��. Figure 10 illustrates a typical simulation result ofavity pressure history and gas pressure distributions withinhe polymeric seal.

ig. 10 Typical gas diffusion simulation results of �a� gas pressureistory and �b� gas pressure distributions inside the seal. Close cir-ular dots in the graph correspond to distribution contours and num-ers in parenthesis of contour plots indicate the cavity pressures.



A plot of R2 obtained from the initial sweeping is shownin Fig. 11. It is evident that there is a D-S combination thatyields a high R2 value �yellow regions�. This is a clearindication of the transition regime �Fig. 1�. The D-S com-bination at the center of the yellow region was taken as theinitial set for a subsequent optimization process; they were3.98�10−6 m2 /s and 6.31�10−13 s2 /mm2. The final diffu-sivity and solubility values were 4.11�10−6 m2 /s and6.41�10−13 s2 /mm2, and the corresponding R2 value was0.9997. The cavity pressure curve obtained using theseproperties is plotted in Fig. 12 along with the experimentaldata. The numerical result agrees very well with the experi-mental data, confirming the efficacy of the inverse method.

5 DiscussionA diffusion regime of helium diffusion inside the packagecan be determined from the package dimensions and thesolubility determined above. The two effective diameters ofthe package under study can be approximated by equatingthe area of cavity and package rectangles to the area ofeffective circles, which is expressed as3

ri,e = �Ai/� and ro,e = �Ao/� . �14�

The inner and outer radii are calculated to be 1.42 and 2.56

Fig. 11 Plot of R 2 obtained from the initial sweeping.

Fig. 12 Experimental data of the cavity pressure evolution duringthe bombing process are compared to numerical predictions usingthe best D-S combinations obtained from the inverse method

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m, respectively. For the test condition �T � 298 K�, Eq.5� then can be reduced to

S = 1.39 � 106Sp. �15�

he value of Rs for the present helium leak test is 0.76,hich falls within the transition regime �0.01�Rs�500�

s it was expected earlier.In order to examine the trend of curve fitting, two more

teps of sweeping were carried out by zooming in to theest combination areas in matrix plots and a matrix plot ofhe last step is shown in Fig. 13. It shows that beyond aertain point it is meaningless to continue refining the ma-rix for the “very best” D-S combination because all suchefinements result in virtually the same R2 value. Physi-ally, this means that discrepancies among the curves ob-ained by different D-S combinations—albeit within a lim-ted range—are smaller than the resolution of thexperimental technique.

The best set obtained from the first-order method is lo-ated at the right-bottom corner of the optimum line seg-ent �Fig. 13�. The final result of the optimization process

hould be dependent on the initial set due to the distributionf pseudo-local minima along the optimum line segmenti.e., negligible gradients in the tangential direction�. Anyombination within this optimum line segment producesirtually the same gas diffusion predictions.

In order to confirm the above statement, three represen-ative combinations obtained from the third matrix �Fig. 13�ere used to predict the pressure release behavior of the

ame “bombed” package. During the experiment, the pres-ure release started right after the end of the bombing stagey subjecting the package to an atmospheric environmentnd the cavity pressure was also documented during theelease stage. A comparison to the experimental data ishown in Fig. 14. The excellent agreement for all threeases confirms that the finite set of optimum D-S combina-ions within the optimum line segment can accurately pre-ict the cavity pressure evolution of polymer-sealed MEMSackages, and thus, that the initial set-dependency of theptimization method will not significantly affect the accu-acy of the property measurement.

Fig. 13 Plot of R 2 obtained from the third sweeping.



6 ConclusionsAn optical leak test was utilized to characterize the leakbehavior of a polymer-sealed package and thus to measurethe in situ diffusion properties of the polymeric seal. Aprocedure to determine the properties from experimentaldata through an inverse method was established consider-ing three diffusion regimes that characterize the leak behav-ior of the package. The proposed method was implementedto determine the helium diffusion properties of a polymericseal used in a test MEMS package. The proposed methodoffers a unique advantage over the existing methods: in situmeasurement capability. In addition, high-temperature mea-surements are possible, thus offering the potential to mea-sure the diffusion properties at temperatures much higherthan the limits of exiting methods �e.g., 50°C for the MO-CON method�.

AcknowledgmentThis work was supported by the Center for Advanced LifeCycle Engineering �CALCE� of the University of Mary-land. This support is acknowledged gratefully.

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clave,” JEDEC, �2000�.9. J-STD-020D, “Moisture/reflow sensitivity classification for nonher-

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Fig. 14 Experimental data of the cavity pressure evolution duringthe pressure release using the three combinations of D-S valuesobtained from the third sweeping matrix �they are marked as dots inthe matrix plot in Fig. 13�.

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Changsoo Jang received his BS, MS, andPhD in mechanical engineering from KoreaAdvanced Institute of Science and Technol-ogy �KAIST� in 1993, 1995, and 2000, re-spectively. Currently, he is an assistant re-search scientist in the Department ofMechanical Engineering at the University ofMaryland. His research areas of interest in-clude multiscale and multiphysics computa-tional mechanics, experimental mechanicsfor model validation and material character-

zation, and design for reliability and manufacturing. He has au-hored over 40 journal and conference papers in the field of micro-lectronics, MEMS, and flexible organic electronics. He holds three. S. Patents on the design criteria and manufacturing processes ofemory packages and radio-frequency identification.

Arindam Goswami received his BE in me-chanical engineering from the University ofPoona, India, in 2001, and MS and PhDalso in mechanical engineering, from theUniversity of Maryland, College Park, in2004 and 2007, respectively. For his doc-toral dissertation, he developed an opticaltechnique for quantitative hermeticity mea-surement of wafer level packages. His ar-eas of interest include product design, solidmechanics, optimization, and electronics

ackaging. Dr. Goswami received the IEEE/CPMT Motorola Fellow-



ship Award at the 56th ECTC in 2006. He was also awarded the AnnG. Wylie Dissertation Fellowship Award in 2007. He is currentlyworking as a reliability engineer �portables� at Apple Inc. in Cuper-tino, California.

Bongtae Han received his BS and MS fromSeoul National University in 1981 and 1983,respectively, and PhD in engineering me-chanics from Virginia Tech in 1991. He iscurrently a professor of the Mechanical En-gineering Department of the University ofMaryland at College Park and is directingthe Laboratory for Optomechanics andMicro/Nano Semiconductor/Photonics Sys-tems �LOMSS�, which is one of the CALCEresearch laboratories. Dr. Han has coau-

thored a textbook entitled. High Sensitivity Moiré: ExperimentalAnalysis for Mechanics and Materials �Springer-Verlag, 1994�. Heedited two books and has published eight book chapters and over150 journal and conference papers in the field of microelectronicsand experimental mechanics. He holds two U.S. Patents and fourinvention disclosures. Dr. Han received the IBM Excellence Awardfor Outstanding Technical Achievements in 1994 and was also arecipient of the 2002 Brewer Award, presented at the Annual Con-ference of the Society for Experimental Mechanic �SEM� in Emerg-ing Technologies. He also received the 2005 Associate Editor of theYear Award from the American Society of Mechanical Engineers�ASME�. He served as an associate technical editor for Experimen-tal Mechanics, from 1999 to 2001, and has been serving as anassociate technical editor for the ASME Journal of Electronic Pack-aging, since 2003. He was elected a Fellow of the SEM and theASME in 2006 and 2007, respectively.

Suk-Jin Ham received his BS, MS, andPhD in mechanical engineering from theKAIST, Daejeon, in 1993, 1995, and 2002,respectively. He joined Samsung AdvancedInstitute of Technology in 2002 and was in-volved in several projects related MEMS de-vice and package design, evaluation, andreliability including physics of failure analy-sis. Currently, he is working at SamsungElectro-Mechanics as a principal re-searcher. His research interests include

system-in-package integration, physics of failure analysis, and ma-terial characterization.

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In situ measurement of gas diffusion properties of ...terpconnect.umd.edu/~bthan/paper/Hermeticity/2009JM3-In situ measurement of gas...in situ measurement of gas diffusion properties

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