Characterization and Control of Residual Stressand Curvature in Anodically Bonded Devicesand Substrates with Etched Features

R.A. Inzinga & T.-W. Lin & M. Yadav & H.T. Johnson &

G.P. Horn

Received: 23 August 2010 /Accepted: 12 July 2011 /Published online: 5 August 2011# Society for Experimental Mechanics 2011

Abstract While anodic bonding is commonly used in avariety of microelectromechanical systems (MEMS) appli-cations, devices and substrates that incorporate this pro-cessing technique are often subjected to significant residualstress and curvature that create post-processing and reli-ability issues. Here, using an anisothermal anodic bondingprocedure, residual stresses and the resulting wafer curva-ture in these structures are controlled by varying the initialbond temperatures of the silicon and Pyrex wafersindependently. Residual stresses are quantified by measur-ing bulk wafer curvature and, locally, stress concentrationsare measured using infrared photoelasticity accompanied by3-D thermomechanical finite element analysis. Based onthe good agreement between numerical predictions andexperimental results, this process can be used to determinethe bulk post-bond wafer curvature and to reduce thelikelihood of structural failure at these sites, by changingthe residual stresses from tensile in nature, which may driveinitiation and growth of cracks, to compressive, which cansuppress such failures.

Keywords Residual stress .MEMS . Anodic bonding .

Infrared photoelastic stress analysis . Silicon inspection

Introduction

Anodic bonding is one of the most commonly used waferbonding techniques in the MEMS industry as it allows the

formation of a reliable hermetic seal between silicon andglass wafers at relatively low temperatures. The techniqueis commonly used in the fabrication of microfluidic devices[1, 2], pressure sensors [3], accelerometers [4, 5] andMEMS power devices [6] among other applications [1].Anodic bonding is performed using substrates with mirrorpolished surfaces that are placed in close contact at elevatedtemperatures. Bonding is initiated by the application of adirect current (DC) potential across the glass and siliconwafers.

One well known problem with anodic bonding is theunwanted curvature of the bonded structure resulting fromthe relaxation of residual stresses that form in the bondedwafer pair upon cooling. As anodic bonding requires thejoining of two dissimilar materials at elevated temperatures,the very slight mismatch in coefficient of thermal expansion(CTE) between the glass and silicon wafers results inresidual curvature and localized stresses in nearly everyprocess currently used in industry and academia. Severaltypes of borosilicate glass wafers, including the widely usedCorning Pyrex 7740, are manufactured to have CTE thatrelatively closely match that of silicon up to high temper-atures. However, at temperatures above about 315°C, theCTE of silicon is larger than that of Pyrex 7740, whichresults in wafer curvature due to residual tension in thesilicon when the wafer pair cools to room temperature [7–10]. Bond strength is shown to depend directly on bondtemperature; in most applications bond temperatures rangefrom 350 to 450°C. At 400°C, the difference in CTEbetween the two wafers is about 7%, which creates asignificant wafer curvature with deflections on the order oftens to hundreds of microns over a 100 mm wafer [8, 9].For equally thick bonded silicon and Pyrex wafers, theresidual stress in the silicon is tensile if bonding is initiatedabove 315°C, and compressive if initiated below this

R.A. Inzinga : T.-W. Lin (SEM member) :M. Yadav :H.T. Johnson :G.P. Horn (*, SEM member)University of Illinois at Urbana-Champaign,1206 W. Green St.,Urbana, IL 61801, USAe-mail: ghorn@illinois.edu

Experimental Mechanics (2012) 52:637–648DOI 10.1007/s11340-011-9528-6

temperature [10]. At the same time, the temperaturedistribution across a wafer pair during bonding can varygreatly due to local capacitive heating caused by nonuni-form local contact between the wafers; this effect can bepartially controlled by current limited anodic bonding [11].We have shown that as a result of these nonuniformities,local residual stress variations can be significant duringanodic bonding [12].

The characterization and manipulation of residual stressand curvature in anodically bonded structures are useful inboth the production and physical protection of MEMSdevices. For example, in many applications wafer curvaturemust be minimized for post-processing reasons, particularlyif high resolution lithography is required. To minimize postbond curvature, the bond recipe must eliminate residualstresses at room temperature. In resonant sensor devices,residual stresses of any orientation must be avoided asinduced stresses effectively alter the resonant frequency ofthe device [11]. On the other hand, compressive stresses ina pressure sensor membrane can cause the membrane tobuckle, degrading its functionality [13]. In this case, it issometimes beneficial to use a conventional isothermalbonding process that leaves the silicon in tension in orderto reduce the likelihood that buckling occurs. Finally, inapplications where etched features are present at the bondinterface, such as in microfluidic devices, light guides andmany common sensors, cracks have been found to growfrom areas of high stress concentration in the silicon [12,14, 15]. Processing to introduce compressive stress in thesilicon wafers with these structures may provide protectionfrom crack initiation and growth. A similar strategy toincrease crack resistance in ceramic materials was first usedto mitigate surface flaws introduced during machining [16,17] and then expanded to other applications such ascontrolling crack growth in glass [18]. However, failurehas also been noted in the Pyrex layer of these devices dueto overpressurization of the channels [2], so residualcompressive stresses in this layer may be useful in otherapplications. In short, for different devices, it can proveuseful to understand the magnitude of residual stresses nearetched features and potentially to control residual stress andwafer curvature during processing.

Methods to control residual stresses and curvature inwafer level anodic bonding have been studied for severalyears with only modest success. Various glass chemistrieshave been investigated for different applications, butprocess limitations such as compositional gradients andelectrolysis effects limit the possible choices for use inanodic bonding [7, 8]. Another approach to reduce residualstress in the silicon wafer is to add an annealing step afterbonding to induce relaxation in the glass [10]. For thisapproach to be useful temperatures typically must reach500°C and/or be held for multiple hours, limiting applica-

tions due to cycle time. In another recent study, a current-limited anodic bonding approach is utilized. The anodicbonding current is limited to 8 mA throughout the bondingprocess and the curvature of the bonded wafer pairs isreduced, though the results show that the silicon is still inresidual tension [11]. We have recently determined theprocess requirements for anisothermal anodic bondingprofiles that can introduce a controlled average residualcurvature in anodically bonded wafers [19]. Simple modelsof anisothermal extensions of the conventional anodicbonding process suggest that introducing temperaturedifferentials as small as 40°C between the bonding chuckscan lead to a residual curvature that is opposite to thetraditional isothermal bond process with a nominal 400°Cbonding temperature.

Considering the significant effect of residual stresses onanodically bonded structures and the large variations due tolocalized heating, the ability to quantify local residual stresswith a rapid inspection tool can improve quality control andcan enable the development of processes such as aniso-thermal anodic bonding. While several inspection toolshave been used in microelectronic device processing, onlyx-ray topography and infrared photoelasticity can quantifyresidual stresses; only the latter can do so rapidly andinexpensively for either laboratory or processing line use[20]. While infrared photoelasticity has been appliedbroadly for measuring residual stresses in microelectronics,quantification of stress in certain configurations remains achallenge. In general, photoelastic stress analysis has beenused for years on geometries with uniform through-samplestress states, but inspection of samples with through-thickness variation in stress state and/or material propertiesintroduces significant difficulties in quantifying the residualstress state. One method for interpreting experimentalresidual stress images from photoelasticity in these casesis to combine data with a process based model of thesample under inspection.

The purpose of this paper is to characterize global andlocal residual stresses associated with conventional andanisothermal anodic bonding and to present a model basedinterpretation of infrared photoelastic images collected fromanodically bonded wafers containing etched cavities. At thesame time, we present experimental verification of arelatively simple modification to the standard bondingprocess as a means to control the average residual stressin anodically bonded samples.

Infrared Photoelasticity

The Infrared Grey-Field Polariscope (IR-GFP; StressPhotonics, Madison, Wisconsin, USA) is a full-fieldinfrared photoelastic stress analysis system that measures

638 Exp Mech (2012) 52:637–648

optical interference generated by stress-induced birefrin-gence [21]. The IR-GFP illuminates a sample withcircularly polarized infrared light and measures the trans-mitted light intensity with an infrared camera fitted with apolarizer mounted in a rotating stage. Circularly polarizedlight traveling along the slow axis in the vicinity of stressedbirefringent material (such as silicon) suffers a greaterphase-shift than the wave traveling along the fast axis, andemerges from the material retarded by a physical distance δcompared with the fast-axis wave. The shifted distancealong the two optical axes is called linear retardation and isdefined by:

d ¼ dðn1 � n2Þ ð1Þwhere d is the material thickness, n1 and n2 are refractiveindices along each optical axes.

This measure of retardation is the actual value quantifiedby polariscope systems, although it is accomplished in variousways by different systems. With the IR-GFP, the retardation ismeasured by quantifying the transmitted light intensitymodulation as the analyzing polarizer rotates. If both thestress magnitude and the material properties are constantthrough the sample thickness, the retardation of the circularlypolarized light can be simply converted to shear stress with thestress optic coefficient, C, so that

d ¼ Cd s1 � s2ð Þ ð2ÞFor the geometry of interest in this experiment, the

residual stress is nonuniform through the thickness of thesample due to the presence of the etched cavity, and theresults are further complicated by the unique stress opticcoefficients of silicon and Pyrex, so equation (2) becomes

d ¼ CSi

Z

Si

s12ðzÞdzþ CPyrex

Z

Pyrex

s12ðzÞdz ð3Þ

While photoelastic imaging provides measurement of thein-plane retardation integrated through the sample thicknesswith high resolution, it provides no information regardingthe through thickness stress distribution. However, inversemethods can be applied to interpret the results of thesephotoelastic images in terms of traditional failure analysisframework if a valid model of through thickness stressescan be interpreted using equation (3). In this paper, all dataare presented in terms of linear retardation and compared tointegrated three-dimensional stress fields from ABAQUSfinite element analyses.

Modeling of Anisothermal Anodic Bonding

Standard anodic bonding processes use an isothermal bondrecipe, with bonding carried out when both the silicon and

glass wafers are at the same temperature, often between 350and 450°C, resulting in a bonded structure with the silicondevice wafer in residual tension. However, with anisother-mal anodic bonding, the initial temperatures of the bondedwafers are controlled with full consideration of the smalltemperature-dependent differential thermal expansion be-tween single crystal (100) silicon wafers and Pyrex 7740wafers. The theoretical process requirements for anisother-mal bonding to enable control over residual wafer curvaturecan be determined using a simple thermomechanical finiteelement model [19]. In this model the silicon and Pyrexwafers are joined at their interfacial nodes, with a uniformelevated wafer bonding temperature. The model includesthe full temperature dependence of the thermal expansioncoefficients of both silicon and Pyrex, and can account fornonuniformity in the wafer geometry. The wafers are cooledto room temperature and the resulting bulk wafer deforma-tion field due only to the CTE mismatch is obtained. It isassumed that the silicon and Pyrex wafers are at spatiallyuniform temperatures prior to bonding.

In the case of an isothermal bond procedure where bothPyrex and silicon wafers are initially at 400°C, with the waferthicknesses and material properties assumed here and inagreement with experimental parameters and the best avail-able CTE data [22, 23], the resulting average wafer radius ofcurvature is roughly −9.1 m. The silicon temperature canthen be reduced in the calculation until a roughly oppositecurvature is predicted. When the Pyrex wafer is maintainedat 400°C and the pre-bond silicon wafer temperature isreduced to 360°C, the model predicts an average curvature ofroughly 8.5 m. Consideration of the full range of temperaturedifferentials in between allows the selection of a curvature-free anisothermal bonding recipe with Pyrex/silicon temper-atures of approximately 400/377°C (giving a predicted waferradius of curvature of greater than 1 km). This modelassumes uniform temperature in each wafer at bonding andinstantaneous bonding at these temperatures and thusneglects the complicated interaction of thermal conductionand the development of bond strength, both of which aretime dependent. As such, this model provides an expectedupper bound for residual wafer curvature. In the followingsections, we compare the experimentally determined residualcurvatures with those predicted by this simple model.

We then extend this model by introducing 100 μm deepcavities into the silicon portion of the 3D model geometry.The shear stress data from the ABAQUS model are thenintegrated through the thickness using equation (3) and theretardation measured by the IR-GFP can be directlycompared with the integrated numerical solution. ABAQUSalso provides prediction of maximum normal stresses thatare associated with these geometries at the given processingcondition. Thus, comparing the integrated residual shearstress map with the measured IR-GFP image, we obtain

Exp Mech (2012) 52:637–648 639

results that can be interpreted in the context of traditionalfailure analysis theories commonly applied to brittlematerials such as silicon.

Experimental Samples and Preparation

Silicon substrates are processed from Prime grade 100 mmdiameter, 525 μm thick, p-doped (100) single crystal doubleside polished wafers and are bonded to 525 μm thick PyrexCorning 7740 glass wafers. Wafer processing is carried outin a class 100 clean area and bonding is done in a class 10room. Square features with varying cavity corner radius (5,25, 60, 120 μm) are etched in various positions around thewafer via standard photolithography techniques to study theeffect of residual stresses in the vicinity of these features.All features are etched to a depth of approximately 100 μmin the silicon handle wafer and each feature presented inthis study is distributed at a distance from other patternedgeometry such that the stress fields do not interactsignificantly with any other stress concentrations. To patternthe interfacial features in a virgin silicon wafer a positivephotoresist is spun prior to exposure through a photomask.After developing the photoresist, the silicon etching processis completed in an ICP-DRIE etching system using theBosch process. The Bosch process combines an etchingstep using SF6 gas to etch the exposed silicon surface witha C4F8 passivation step that produces vertical sidewalls.The dry etching process also allows better control of thecavity corner geometry than does wet etch processes.

Prior to bonding, the patterned silicon wafer firstundergoes a modified RCA-1 clean to strip organicmaterials and dust particles from the surface of the waferwith minimal wafer surface roughening [24, 25]. An RCA-2 solution is then used to remove any metals left on thesurface from earlier processing and cleaning [26]. ThePyrex 7740 wafers are cleaned using a Piranha solutionconsisting of a sulfuric acid and hydrogen peroxide in a 5:1ratio [27]. The wafers are bonded in an EVG 501 vacuumbonding system. Bond platens in contact with each waferare individually controlled to achieve the required temper-ature at the non-bonding surface of the wafers. A potentialof 400 V is applied across the wafer pair in conjunctionwith an applied force of 80 N. The voltage and force areheld constant for 25 min to ensure that bonding is complete.

The anodic bonder used in this study requires closeproximity to the wafers during the heating phase, with agap between the wafers of less than 1 mm and thin steelspacers in contact with both wafers at three positionsaround the outer edge. As such, it is expected that there aresome thermal gradients within each wafer prior to bonding.The temperatures reported here are those measured at thebonding chuck in contact with the nonbonded surface of

both the Pyrex and silicon wafers. In this study, baselinesamples, representative of typical isothermal bondingrecipes, are bonded with both substrates nominally at390°C. Two anisothermal bonding profiles are utilized inthis study, where the silicon wafer temperature is held atroughly 20°C and 40°C less than the Pyrex wafer prior tobonding. The former condition is expected to result in apost-bond structure that would be near stress-free, while thelatter anisothermal recipe would induce compressive resid-ual stresses in the silicon wafer. For comparison purposes,two additional bond profiles are included that are expected toprovide intermediate curvatures (nearly isothermal 380°C and369°C/337°C anisothermal) In addition to the thermal con-ditions defined by the bonder recipe, temperatures aremeasured using Type K thermocouples in direct contact withthe wafer chuck surfaces when blank wafers are included inthe bonder running the experimental recipes as shown inFig. 1. In most cases, these thermocouple readings varysignificantly from the nominal thermal conditions of eachrecipe and are the temperatures that will be reported here.The expected error in Type K thermocouples is 1.5–1.6°C forClass 1 and 2.5–3.0°C for Class 2 thermocouples in thetemperature range covered in these experiments. In additionto errors in the thermocouples, the measurement system itselfhas an intrinsic error that is often reported to be on the orderof 1–2°C. Thus, the total potential error in the temperaturemeasurement of this system is expected to be up to 3–5°C.

Residual Stress Quantification

To quantify the magnitude of bulk residual stresses inbonded wafer pairs, an Alpha Step IQ Surface Profiler witha spatial scanning capability of 5000 μm sections is used toobtain curvature measurements of the bonded samples atseveral locations 25 mm from the wafer center. It isassumed that the average bulk curvature of the bondedsample is comparable to the local curvature over thesesections. This location is measured because the curvature atthe center of the wafer can be strongly affected by initialcompression from the wafer bond chuck and the outerregion of the sample is more prone to debond defects. Themeasurements are averaged to estimate the wafer curvatureafter bonding. Curvature is estimated using a second-degreepolynomial curve fit to the profilometer results. Theaverage radius of curvature across the wafer can beestimated from

R ¼ l2

2 � hmaxð4Þ

where hmax is the difference in height from the local minimumto a height located a distance l away. The curvature is

640 Exp Mech (2012) 52:637–648

measured at 5 different locations and averaged for each wafer.While equation (4) is commonly used to characterizecurvature of a thick wafer with a thin stressed film, ourgeometry consists of two wafers of nearly the same thickness,which may result in a curvature field that is non-uniformfrom the center to the edge of the wafer. Nevertheless, forconsistency throughout the manuscript, we present thecurvature from the half radius of the wafers as therepresentative “average” curvature of the bonded wafer pair.

To study local residual stress concentrations at the etchedfeatures, full-field residual stress maps are acquired usingthe infrared grey field polariscope. The images shown hereare taken with a 5X optical magnification with a 1600×1200 detector that provides a spatial viewing window ofapproximately 1.8 mm×1.3 mm with a spatial resolution of1.3 μm; data collection takes approximately 20 s. Previousimplementations of the IR-GFP system provide measure-ments of shear stress with a resolution of approximately0.1 MPa for a single wafer thickness [21], whichcorresponds to an optical retardation of approximately0.3 nm. As outlined above, these results are interpretedusing the 3-D ABAQUS finite element model to experi-mentally determine the effects of different anodic bondingrecipes on through-thickness stress distribution in a failureanalysis framework.

Experimental Results and Discussion

Based on the experimental results of the work, we find thatmeasured post-bond wafer curvature of anodically bondedsilicon/Pyrex wafers can be estimated through a relativelysimple model of the initial thermal conditions of the Pyrexand silicon. Furthermore, the residual stresses in the vicinityof etched cavities can be controlled through both thermaland geometric means and the same simple model can beused to interpret infrared photoelastic data of thesegeometries in a manner that is suitable for failure analysis.

Wafer Curvature

The variation in surface height measured by scanningprofilometry of wafers bonded under isothermal and aniso-

thermal conditions is shown in Fig. 2. As expected, thebaseline “isothermal” case (391/394°C– Pyrex/Silicon) resultsin a negative post-bond curvature as the silicon wafercontracts more than the Pyrex wafer after bonding iscomplete. This orientation results in residual tension in thesilicon wafer, while the Pyrex layer is in residual compres-sion. The measured temperature differential between thewafers is within the error of the measurement system (±3–5°C). The measured curvature (inverse of radius of curvature)is significantly reduced when the temperature differential isapproximately 16°C (394/378°C). When the silicon wafertemperature is reduced by approximately 45°C (388/343°C)relative to the Pyrex temperature, the post-bond wafercurvature then changes to a level that is opposite inorientation (and slightly higher in magnitude) from theisothermal case. Additionally, the wafer pair bonded with alower isothermal temperature (380/379°C) had a reducedcurvature compared to the 391/394°C recipe, while in thecase where the silicon wafer temperature is reduced by 32°C(369°C/337°C), the resultant curvature is intermediate be-tween the other anisothermal recipes.

Based on the surface profiles and equation (4), averagelocal radii of curvature from all bonded samples arecomputed and shown in Table 1. The isothermal bondingrecipes lead to negative radii of curvature, which indicatesthat the Pyrex side of the wafer pair is concave. On theother hand, the wafer pair bonded with a 16°C difference

Fig. 1 Location of thermocou-ple measurements during theexperimental analyses of bond-ing conditions

Fig. 2 Representative experimental surface profiles for wafers bondedat five different temperature combinations

Exp Mech (2012) 52:637–648 641

has curvature (inverse of radius of curvature) that isreduced by approximately 600% from the nominal 390°Cisothermal case, with a magnitude that is only slightlyhigher than the curvature of a typical unbonded wafer. Thelack of significant wafer curvature across these samples is aresult of negligible post-bond residual stress. Wafers with apre-bond temperature differential of 32°C and 45°C havewafer curvature that is similar in magnitude, yet opposite insign from the standard isothermal processes with nominaltemperatures of 380°C and 390°C, respectively. Theseexperiments show that it is clearly possible to reverse thepost-bond residual curvature in anodically bonded sub-strates using commercially available bonding systems byindependently controlling the temperature at each bondingplaten. The required temperature differential of only 45°C isrelatively easily accomplished. Most importantly, this changein bonding parameters requires neither additional post-processing nor an increase in processing time. We note thatthe experimental measurements in Table 1 show significantvariations in local curvature, which can be largely attributedto the variation in residual stresses from localized heating[11] that can cause spatial variations of the local curvature[12] and to pre-bond wafer curvature that has been shown tohave a significant effect on wafer bondability and post-bondshape in fusion bonding studies [28, 29].

The results of the 3D thermomechanical finite elementmodel [19] are shown in Table 1 and provide a comparisonbetween the numerically predicted radius of curvature andthe experimental data for each condition. It is apparent thatthe simple model can be used to predict trends in bulk wafercurvature that are verified in experiments. However, theexact post-bond wafer curvature, even within a singlebonded wafer pair, is highly sensitive to process variablessuch as pre-bond curvature and nonuniform heating. Never-theless, the trends are captured well, without exception.

There are several possible explanations for variationsbetween experiment and theory. First, the simple processmodel used here assumes that no conduction has occurredduring bonding and thus that the predicted curvature shouldbe larger than the experimentally determined values, whichis verified in Table 1. Second, errors in thermal measure-ments can result in different anisothermal conditions thanexpected. As noted above, the total potential error in thetemperature measurement of this system is expected to be

as much as 3–5°C. To provide an estimate of the effect of a5°C variation in wafer temperatures, the analysis conductedin reference [19] suggests that with a nominal 390°C meantemperature this level of thermal uncertainty can result inwafer bow variations of approximately 40%.

Additionally, the model used to compare with theseexperiments only accounts for the temperature dependenceof the coefficient of thermal expansion as a means ofintroducing residual stresses, and does not include effects ofother possible mechanisms such as glass shrinkage anddevelopment of a depletion zone, or variations in the initialwafer curvature, all of which could result in more error inthe comparison with experimental data. Previous researchhas shown that Pyrex 7740 is not as likely to be affected bya depletion zone as other glass chemistries [8]. However,holding the bonded wafer pair at 400°C for 25 min mayallow for some relaxation. This relaxation would tend toreduce the wafer curvature for the isothermal case andincrease the curvature for the anisothermal cases presentedhere. The initial shape of the silicon and Pyrex wafers priorto bonding will affect the overall bonded wafer shape as hasbeen shown with fusion bonded structures [28, 29]. Thelatter two mechanisms may be important to consider tomore accurately predict the resulting wafer curvature fromanisothermal bonding conditions. As Table 1 suggests, thecomparison between experiment and theory is best whenthe curvature is large and appears to be dominated by thethermal expansion mismatch between the Pyrex and silicon.However, when the wafer temperatures are controlled suchthat the total thermal expansion mismatch between thewafers is small, these other mechanisms become relativelymore important in predicting the resulting wafer curvature.

Finally, these experiments show the importance ofcorrectly calibrating and maintaining thermal control ofthe bond systems. Variations between the nominal (“input”)and actual thermal boundary conditions can result insignificant deviations in the residual curvature of the post-bonded wafer pair. If the error in each platen thermocoupleis only 5°C, it is possible that wafers could be bonded at405/395°C or 395/405°C, thus resulting in significantdepartures from the expected curvature. For example, themodel used here predicts a radius of curvature of −9.1 m forthe nominal temperatures of 400/400°C, but −7.3 m for theactual measured conditions of 391/394°C.

Bonding conditions Measured radius of curvature (m) Predicted radius of curvature (m)

391°C/394°C −10.1±3.0 −7.3380°C/379°C −16.0±4.5 −9.6394°C/378°C −58.2±6.6 −29.9369°C/337°C 15.0±4.9 12.4

388°C/343°C 7.5±2.2 7.4

Table 1 Resulting wafer curva-ture as estimated from deflectionprofiles of bonded samples withdifferent pre-bond wafer tem-peratures along with numericalpredictions (Pyrex/silicontemperature)

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Importantly, however, the good agreement betweenpredicted and experimentally measured radii of curvaturesuggests that the simple model provides an acceptabledescription of the residual stresses during bonding, and thatit is reasonable to extend this description to study localizedstresses near etched cavities. As described in the nextsection, the local stress measurement is in some ways morerobust and less subject to some of the error sources towhich the curvature measurement is susceptible.

Etched Features Concentrating Residual Stresses

In many anodically bonded MEMS devices for microfluidicsand sensing, for example, features are etched into the silicon

device layer. These features can provide locations for crackinitiation and resulting growth [12]. Previous studies usingx-ray topography show strain concentrations at the edges ofetched cavities in fusion bonded wafers [30]. Our previousstudies show that infrared photoelastic stress analysis candetect stress concentrations analogous to XRT for trappedparticles and gas bubbles [31], but there have been noprevious applications of infrared photoelasticity to studyingresidual stresses associated with etched cavities in bondedsilicon substrates.

In order to understand the effects of modified bondprotocols on microscale etched features common in micro-fluidic and other MEMS devices, we consider the stressnear several square features patterned at the bond interface

(a) (b) (c)Fig. 3 IR-GFP shear stressimages of a square feature etchedin a silicon wafer anodicallybonded at Pyrex/silicon temper-atures of (a) 391°C/394°C (b)394°C/378°C, and (c) 388°C/343°C

Fig. 5 Calculated shear stress (σxy) field near a square feature etched inthe silicon wafer of an anodically bonded Pyrex/silicon structure for pre-bond wafer temperatures of (a) 391°C/394°C and (b) 388°C/343°C.Units are in Pa

(a)

(b)

Fig. 4 IR-GFP shear stress images of an etched feature in the vicinity oftrapped particles bonded at Pyrex/silicon temperatures of (a) 391°C/394°C(particle in upper left corner) and (b) 388°C/343°C (large particle belowthe etched cavity)

Exp Mech (2012) 52:637–648 643

of the silicon wafers with the nominal 390°C isothermaland anisothermal recipes as described in ExperimentalSamples and Preparation. Figure 3 shows IR-GFP imagesfrom representative square features with cavity corner radiiof 5 μm in each of the three samples. Qualitatively, areas inthese images with low residual stresses display a grey valuehalfway between pure white and pure black. Areas thathave a significant concentration of residual shear stressesappear more strongly white or black. In Fig. 3(a) and (c)there are obvious stress concentrations at each corner of thecavity, though the orientations of the positive shear (white)and negative shear (black) are inverted indicating that thelocal stress fields are of opposite sign. On the other hand,the cavity etched in the 394/378°C anisothermal wafershows a relatively uniform grey level indicating littleresidual stress. It is important to note that the grey scaleintensity in each pixel of these images is directly related tothe retardation, δ, thus providing a full field in-planemeasure of the integrated through-thickness shear stressdistribution.

Figure 4 shows IR-GFP images of etched cavities fromthe isothermal and 388/343°C anisothermal wafer pairswhich have trapped particles in the vicinity to allowcomparison between the local stress fields. The stress fieldin Fig. 4(a) (similar to 3(a)) shows the same orientation asthat typically associated with a trapped particle or gasbubble at a bond interface. The edges of the cavity show astrong concentration of the residual shear stress due to thefree surfaces created by the etching process, particularly atthe corners with two free surfaces. In the small cavity limit,this stress field would be identical to the “bow tie” patternassociated with trapped particles [31] (though with thecenter of the bow tie enlarged and stress-free since there isno bonding at this location).

A particle trapped at the bond interface introduces atensile in-plane residual stress field due to the localizedindentation stresses as described by the well knownBoussinesq problem for a point indentation in an elasticmaterial [32]. Thus the orientation of the stress signaturesurrounding the etched cavity in the isothermal bondedwafer indicates that the residual stress pattern at thesecavities is also in tension. On the other hand, the stress fieldat the etched cavity shown in Fig. 4(b) (similar to 3(c)) hasan orientation that is opposite to that of the trapped particle(noting that the orientation of the stress field surroundingparticles does not change, though this particle is much

larger than that in Fig. 5(a) and the magnitude issignificantly different), indicating that the material at thecavity is in a concentrated residual compressive stress state.These results demonstrate that it is possible to introduce acontrolled local tensile or compressive residual stress fieldin the silicon wafer by patterning mesas or etching cavitiesat the bond interface respectively. This is not possible inconventional isothermal bonding since both positive andnegative features result in tensile residual stresses in thesilicon wafer near the bond interface.

The finite element results for stress near etched features inthe silicon substrate are shown in Fig. 5. There is strongqualitative agreement between the simulation results in Fig. 5(a) and (b) and the experimental results Fig. 3(a) and (c). Theorientation of the predicted positive and negative residual

Bonding conditions Measured retardation (nm) Predicted retardation (nm)

391°C/394°C −19.7±5.6 −32.4394°C/378°C −10.6±8.3 −6.9388°C/343°C 33.4±6.3 29.2

Table 2 Predicted retardationfrom integrated finite elementresults compared to experimen-tal measurements from theIR-GFP

Fig. 6 Calculated through thickness shear stress (σxy) distributionnear cavity corners of anodically bonded Pyrex/silicon wafers for pre-bond wafer temperatures of (a) 391°C/394°C and (b) 388°C/343°C

644 Exp Mech (2012) 52:637–648

shear stresses matches that of the experiments, though theshape of the highly stressed lobes is much more symmetricin the model. This discrepancy is due to the significant localstress variations that are typically seen in anodically bondedstructures due to localized heating and multiple bond frontsinitiating at different locations on the wafer [12].

The finite element stress field is then integrated through thesample thickness using equation (3) to provide a quantitativecomparison with experimental results, as shown in Table 2.Experiment and theory agree quite well for the 388/343°Canisothermal wafer pairs and acceptably well for the 394/378°C anisothermal wafer pairs considering the large rangeof experimentally measured values. However, the measuredretardation for the isothermal wafer pairs is significantlylower than that predicted by simulation. This resultcorresponds well with the bulk wafer curvature, which islower than expected as described in Water Curvature.

In this case, a comparison is made between themaximum integrated values associated with the cavitycorner, based on the through-thickness shear stress distri-bution shown in Fig. 6. Similar comparisons can be madealong a 1-D line scan from the cavity corner or byintegrating the full 3-D image node-by-node to provide a

2-D map that can be correlated with the IR-GFP imagesshown in Fig. 3. The correlation for the point-wisecomparison between experiment and theory is likely to besomewhat poor, as the effects of non-uniform heating,resulting in significant local variations in residual stress, arenot currently included in the model and are difficult topredict prior to bonding. Nevertheless, the proposedmethod can be used in reverse such that the integratedoutput from the ABAQUS simulations is compared with theIR-GFP images and the boundary conditions modified untilthe residual stress fields agree for a given initial thermalcondition.

To understand these results in a failure analysis frame-work, we also consider the calculated maximum normalstresses near the etched cavity. Figure 7 shows themaximum normal stresses at the etched cavity corners afterthe wafers are cooled back to room temperature. For brittlematerials such as silicon, the most common failure criteria,known as the Coulomb or Rankine theories, compare themaximum normal principal stress in the structure to thematerial’s tensile or compressive strength. Alternatively, theWeibull method can be applied using the distribution of

Fig. 7 Calculated maximum principal stresses near a square featureetched in the silicon wafer of an anodically bonded Pyrex/siliconstructure for pre-bond wafer temperatures of (a) 391°C/394°C and (b)388°C/343°C. Units are in Pa

Fig. 8 Calculated through thickness maximum principal stress (σmax,

min) field near cavity corners of anodically bonded Pyrex/siliconwafers for pre-bond wafer temperatures of (a) 391°C/394°C and (b)388°C/343°C

Exp Mech (2012) 52:637–648 645

principal stresses around the etched cavity along with astatistical distribution of silicon and Pyrex failure strengths[33]. Here, we adopt the simplest maximum normal stressapproach and as Fig. 7 shows, the tensile stress fieldassociated with the isothermal recipe is strongly concen-trated near the cavity, thus providing a driving force forcrack initiation and growth. On the other hand, thecompressive normal residual stress obtained by the aniso-thermal recipe may provide protection against brittlefracture [16, 17]. Through-thickness distributions of themaximum normal residual stresses near the cavity cornerare shown in Fig. 8. The magnitude of the maximumnormal stresses in these geometries reach 53 MPa for theisothermal recipe and −48 MPa for the 388/343°Canisothermal recipe. Residual stress concentrations canincrease significantly from these values when the cornersare patterned with a sharper radius or using anisotropic wetetching techniques (which have been shown to increasestress concentrations by an order of magnitude comparedwith cavities produced by dry etching techniques) or whenthe cavities are etched further into or completely throughthe silicon wafer. While etched features in silicon structurescan significantly concentrate stresses locally, they havebeen also shown to drastically reduce the local strength,

which depends strongly on the etching technique [34].Likewise etch depth plays an important factor in modifyingthe local strain energy accumulation during bonding [29].

In addition to controlling the sign of the residual stressfield using anisothermal bonding, the magnitude of thestress and the region over which the residual stresses areconcentrated can be influenced by the geometry of the etchedcavity. To quantify the effect of cavity corner radius on theresidual stress field, a series of patterned squares with threedifferent radii of curvature are considered. Figure 9(a) shows aseries of IR-GFP line scans (corresponding to the position ofthe lines in Fig. 9(b)-(d)) from features with radii ofcurvature of 25, 60, and 120 μm. Each of these images istaken from a single wafer pair bonded with a 45°Canisothermal bonding recipe. The scans begin in anunbonded region of the etched cavity and progress at a 45°angle through and then away from the corner of the square.

As shown in Table 3, the retardation values, or shearstress magnitudes, are greatest at corners with small radii.The corners with larger radii have lower relative peakstress, but a larger range of influence. The range ofinfluence is determined by measuring the distance fromthe cavity edge to the location where the stress magnitudediminishes to the local far-field value. Thus, features

Corner radius (μm) Maximum retardation, δ (nm) Distance to background value (μm)

25 40.5±1.4 124±3

60 37.3±1.0 134±3

120 35.4±1.0 144±10

Table 3 Comparison of experi-mentally measured retardationof etched features as a functionof corner radius

Fig. 9 (a) Integrated shearstress profile at the corners ofsquare cavities with varyingradii of curvature and IR-GFPimages showing the paths of theline scans for (b) 25 μm, (c)60 μm and (d) 120 μm cornerradii

646 Exp Mech (2012) 52:637–648

patterned with sharper corners are more likely to sufferfrom cracking if an isothermal bonding recipe is used. Atthe same time, the corner radius can be used to tailor theresidual compressive stress field during anisothermalbonding, to generate a highly concentrated and localizedstress field or a less concentrated stress field that isdistributed over a larger region. It is important to note,however, that the retardation values for these cavities are allsignificantly higher than those reported in Table 1 for thecavities with sharper radius (5 μm), which were located in adifferent area of the bonded wafer pair. All of the threecavities in Fig. 9 come from the same area on the wafer thathas a significantly elevated local residual stress, most likelydue to localized heating in this area [11, 12]. Thus, whilegeometry and bond recipes can be modified to assertcontrol over the bulk residual stress state, a rapid inspectiontechnique that can provide a means of quantifying theactual stress state in the vicinity of the geometry of interestis critical in these applications.

Conclusions

A simple method to control the residual stresses and theresulting wafer curvature in anodically bonded structures bycontrolling the initial bond temperatures of the silicon andPyrex wafers independently has been verified experimen-tally and good agreement is found between experiment andtheory. This process can be carried out using standard waferbonding technology without significantly increasing pro-cess time as is needed with post-bonding annealing treat-ments. The process makes it possible to obtain a range ofresidual stress states in the silicon device layer, including astress-free state, a state of residual compression, or a stateof residual tension, the magnitude of which depends on theanisothermal temperature difference between the wafers. Asa result of this residual stress, the resulting post-bond wafercurvature can likewise be controlled. The stress concen-trations associated with etched features are modifiedthrough this process such that highly tensile stresses nearetched cavities can be completely eliminated, thus reducingthe driving force for crack initiation. The proposed methodcan generate a protective compressive residual stress fieldat these locations in order to actively prevent crack growth.The geometry of this residual compressive stress field canalso be controlled by modifying the corner radii of etchedcavities. We present a quantitative method for experimentalinfrared photoelastic residual stress characterization of thesecavities in order to provide a rapid means for analyzinglikelihood of failure from these cavity corners. Based on thesignificant local variations in residual stresses, such amethod is useful and important for quality and processcontrol for wafer bonded devices of this kind.

Further study in this area is required to understand theeffects of anisothermal conditions on bond strength and torefine the thermomechanical model to include othermechanisms of generating residual stresses in anodicallybonded wafers, particularly that of temperature-dependentglass shrinkage due to microstructural changes and initialwafer bow as well as the time dependent coupling betweenbond strength and heat transfer between the wafers.

Acknowledgements The authors gratefully acknowledge the sup-port of NSF grant # CMMI 07–00704.

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