Measurement System for Low Force and Small ... - Stanford University

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 13, NO. 2, APRIL 2004

Measurement System for Low Force and Small Displacement Contacts Beth L. Pruitt, Member, IEEE, Member, ASME, Woo-Tae Park, and Thomas W. Kenny, Member, ASME

Abstract—To support the continued miniaturization of electrical contacts in multichip systems, three-dimensional (3-D) systems, wafer probe cards, and MEMS relays, there is a need for combined measurements of electrical and mechanical phenomena during contact formation. We have carried out a study of electrical contacts in the nN-mN force range for future generation probe cards and novel electronic packaging. One critical phenomenon in the contact formation process is nm-scale deformation of the material layers. To directly study this contact displacement, we have designed a measurement system comprised of a piezoresistive cantilever and an optical interferometer. Together, this system simultaneously measures contact resistance (mOhm to kOhm), ). These measureforce (nN to mN), and displacement (nmments allow the first direct observation of contact mechanical behavior in this important application range. These measurements show that asperities at the contact surface dominate the behavior of the contacts, causing deviations from the Hertzian model of elastic contacts. This paper describes the design and construction of this apparatus, and the operation in a contact mechanics experiment. [915]

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Index Terms—Force measurement, displacement measurement, microelectrodes, microelectromechanical devices, piezoresistance, piezoresistive devices.

I. INTRODUCTION

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HE rapid development of integrated circuits requires denser packaging for higher integration. As interconnect line width and pitch shrink, the area required to transition to off-chip connections and packaging size must also decrease. For these reasons, the electronics packaging and testing industry is developing new methods to decrease the size and force required to make temporary electrical contacts. One approach includes flexible interconnects for probing and packaging, [1]–[5] such as the MicroSpring interconnect developed by Formfactor, Inc. and shown in Fig. 1(a). MicroSprings are used in probe cards for testing or are integrated directly on the wafer to act as both the first and second level interconnect for packaging as shown in Fig. 1(b). To design these pressure-mated low force interconnects for performance and reliability, more complete data for electrical and mechanical properties of contacts made with thin-film metallization are required. This paper presents the integration of force and electrical measurements with interferometric displacement measurement in one system. Manuscript received August 1, 2002; revised August 28, 2003. This work was supported by FormFactor, the National Nanofabrication Users Network facilities funded by the National Science Foundation under award ECS-9731294, and the National Science Foundation Instrumentation for Materials Research Program (DMR 9504099). Subject Editor S. D. Senturia. The authors are with the Department of Mechanical Engineering, Stanford University, CA 94305-4040 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/JMEMS.2003.820266

(b) Fig. 1. (a) FormFactor MicroSprings, the diameter of the spherical tip is about 100 . (b) Memory module uses pressure mated MicroSprings as the flip-chip interconnect between the silicon and printed circuit board. The spacer aligns the die and limits spring travel.

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Several previous experiments have shown that the properties of thin film electrical contacts depart from bulk material properties [6]–[8], mostly indicating that the apparent film hardness exceeds model predictions. Experiments performed with MEMS relays are usually confined to a single choice of materials and geometry, and add somewhat to the data available [9]–[15]. Characterization of electrical contacts at forces below have mostly been carried out on bulk material samples 10 and without continuous data acquisition during the formation

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PRUITT et al.: MEASUREMENT SYSTEM FOR LOW FORCE AND SMALL DISPLACEMENT CONTACTS

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Fig. 2. Measurement system incorporates a customized piezoresistive cantilever to measure force, PolytecP-731 2-axis nanopositioner and E515 closed loop controller with capacitive feedback to apply displacements, and a free space Michelson interferometer for measuring contact displacement. The end of cantilever is aligned to the sphere under a microscope. The interferometer consists of a Hitachi HL6312G 635 nm laser diode (LD) with Melles-Griot 06DLD163 controller, Thorlabs PDA500 amplified GaAsP photo diode (PD), a prism beam splitter, and a polished Si mirror, to measure fine displacement of the surface of the Si cantilever over the first several microns of contact. Beyond this deflection, the angular misalignment is too large to maintain interferometer alignment.

of the contact [8], [11], [16]–[18]. Simultaneous measurements of resistance, displacement and force have not been carried out, and are needed to understand the contact formation process. When metal electrodes are brought into contact under load, mechanical deformation takes place at the contacting surface. This deformation results in an increase of the contact area and a corresponding reduction in the contact resistance [11], [19]. The amount of deformation is dependent on the mechanical properties and surface roughness of the metal films. In order to build a comprehensive model for electrical contact behavior, it is critical to measure the mechanical forces and the electrical properties, and also to determine the contact deformation independently. Without this simultaneous measurement of contact displacement, the roles played by film morphology and roughness cannot be independently determined. Contact displacement is not easily extracted by external means. Under the loads applied in these studies, the displacement of the contact is less than 10 nm in many cases. At the same time, the displacement of the cantilever base may be as . Measurement of the cantilever stress as a much as 100 function of the displacement of the base would yield contact displacement, but only if the stress measurement is accurate to 1 ppm—a degree of absolute accuracy that is very difficult to achieve with piezoresistive sensors. We developed an interferometer-based measurement for this experiment because interferometers are well-known for the ability to measure nm displacements with absolute accuracy, and because the interferometer would not disturb the other measurements being carried out in our experiment. This paper presents a measurement system, as shown schematically in Fig. 2, for evaluating thin film contacts and allowing easy variation of load, displacement, and current during the test. Contact forces are measured with a piezoresistive cantilever [20], while the resistance of the contact is measured electrically. Contact displacement is directly measured with an interferometer whose design and operation is also described in

this paper. The materials tested in the initial experiments were thin films of evaporated gold with varied thickness [21]. II. BACKGROUND A. Contact Mechanics When a spherical electrode is brought into contact with a flat surface, the electrical resistance is expected to start at a large value, and rapidly decrease as mechanical forces at the contact cause elastic and plastic deformation, which increases the contact area. A detailed model can be constructed based on the known properties of the materials on both electrodes and the mechanical forces and deformation behavior of those materials. The Hertzian model of elastic contact is the most commonly used model to describe the behavior of such contacts [11], [19]. The “ -spot” contact area radius, , for a Hertz elastic contact between materials 1 and 2 is [19]:

(1) where load (N); Young’s modulus of material on either side of the contact (Pa); Poisson’s ratio; radius of curvature of the contact sphere (m). The properties used for the materials in this work are given in Table I. The substrate properties are given for bulk gold as well as for polystyrene, silicon and glass substrates, as they are found to have significant effect on the mechanical behavior of the contact. The gold films are generally taken to have modulus and Poisson’s ratio similar to those in bulk, though yield and hardness will differ.

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TABLE I BULK PROPERTIES OF SUBSTRATE MATERIALS

B. Contact Displacement The key missing piece of information in these contact resistance measurements is the displacement of the contact during the applied load. If the actual displacement is much less than predicted by a Hertzian model, the discrepancy can be explained primarily by increased hardness and material behavior of the thin films. The displacement may then be related to a more complicated model of film mechanical properties, as measured by nanoindenter. In the case where measured displacement exceeds that predicted by a Hertzian model, more complicated models of the asperity deformation and relationships to the surface roughness, as measured by AFM, and improved quantitative models can be created. Existing contact models which incorporate surface roughness are primarily developed for flat-on-flat geometries, e.g., Greenwood and Williamson’s modifications to Hertzian assumptions [22], [23]. The models which address surface roughness are formulated empirically from applied loads and indirect observations of contact area, typically via contact resistance, and large scale displacements resulting in gross plastic deformation. Contact mechanics models have not been evaluated with contact area/resistance in this force regime previously. “Contact displacement,” , is the amount of the total deformation of the tip, film, and the cantilever surface when force is applied to the contact pair. The actual displacement ought to be larger than that predicted by a Hertzian model if there is plastic deformation, and the total elastic and plastic displacement will vary with increased hardness and material behavior of the thin films as well as the presence of asperities. The displacement due to film deformation may be related to a more complicated model of film mechanical properties, e.g., as measured by nanoindenter. Several cases are depicted in Fig. 3: Case (1) films with near bulk properties on smooth, hard substrates should follow Hertz theory and deform elastically; Case (2) elastic-plastic behavior in films with reduced hardness (e.g., a thick film or as an effect of a soft substrate) would have excessive displacement and low resistance relative to Hertz theory; Case (3) elastic-plastic behavior in thin films on hard substrates results in smaller displacement and increased resistance from Hertz theory; Case (4) films on hard substrates with persistent asperities cause larger displacement and higher resistance relative to Hertz theory, and asperities on soft substrates should cause even larger displacements but still somewhat higher resistance relative to Hertz theory. Force and contact resistance alone are not enough to determine the role of the soft substrate or the asperities, but the parallel measurement of displacement enables construction of more realistic models of the contacts in these experiments.

Fig. 3. Illustration of contact displacement, , and contact radius, a, for four cases. (1) The Hertzian model contact, in which elastic deformation leads to compression of the contact electrode pair with increasing load, and a gradual increase in contact area. (2) Film deformation includes plasticity, and displacement and area grow beyond the elastic Hertz case, hardness = H2. (3) Another case with elastic and plastic behavior, but the hardness H3 > H2, possibly due to thin film effects. Here, the contact displacement and the radius of contact are reduced, leading to larger contact resistance for harder films. (4) Asperities on the surface lead to early initial contact and larger total displacement at any given force. Asperities inhibit contact area growth, leading to a contact area reduced below that predicted by Hertz theory and increased contact resistance. By measuring resistance, force and displacement simultaneously, it is possible to distinguish these cases.

III. EXPERIMENT A. Design and Characterization of Cantilevers Piezoresistive cantilevers were fabricated to measure force and contact resistance simultaneously. Cantilever geometry (the most sensitive devices have length 6 millimeters, width 400 , and thickness 25 ) and doping density and arrangement were optimized to measure the desired force range (nanoNewtons to milliNewtons). The sensor and the spherical contact “tip” are metallized with plated, sputtered and evaporated gold of varied thickness. Two aluminum traces on the cantilever along with the two electrical leads at the tip enable four-wire contact resistance measurement


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Fig. 4. Contact tests on 25 radius spherical polystyrene electrodes on silicon cantilevers with evaporated gold films of 0.18 , 0.5 , and 1.2 thickness. The solid line represents the loading data and the dotted line unloading-adhesion of the contacts is apparent from the negative or pull-off forces on unloading. The dashed curves are the Maxwell spreading resistance predicted from Hertz theory (1) for the contact area over the loading range only. Bulk properties for gold are used for the calculation assuming gold film properties dominate in the curve labeled Hertz A. Bulk properties for silicon and polystyrene are used for the calculation assuming substrate properties dominate in the curve labeled Hertz B.

when the sensor makes contact with the tip. The resonant frequency, effective spring constant, and calibration factor for voltage to force transformation is derived by mechanically resonating the cantilever and measuring tip displacement and piezoresistor voltage. The transformations are made using linear beam theory. Details of cantilever design and fabrication are discussed in a previous paper [24]. The contact geometry investigated is a sphere on flat because it is easily modeled, controlled, and characterized. The spherical contact electrodes are SEM calibration spheres of glass or polystyrene from Duke Scientific, Palo Alto, CA, with dimensional and shape control dia. glass) to 9.1% (100 dia. certified within 3.2% (100 polystyrene) of nominal diameter. The spheres are mounted on a wafer in thick photoresist and metallized with gold films identical to those on the cantilevers. Fig. 4 shows an example of contact resistance measurements for 25 micron radius spherical polystyrene electrodes with evap. The mating orated gold films of thickness 0.18, 0.5, and 1.2 electrode on the silicon cantilever is of the same film composition and thickness as that of the spherical electrode. For comparison, the data are plotted along with a Hertzian model using bulk properties from Table I. It is clear that there is poor agreement with the predicted and measured contact resistance in the larger load regimes; the data suggest a more rapid flattening of the contact resistance behavior. Whether film or substrate properties dominate, gold-gold film contacts

are expected to behave similarly to glass-silicon substrates. However, a Hertz model applied with polystyrene-silicon substrate properties predicts very different behavior from the case where film properties dominate , and we investigate this case. For reference, Hertz theory is only appropriately applied for materials which will not experience any plasticity under these test conditions (e.g., glass and silicon). B. Film Characterization The discrepancy between model and measurement can be attributed to a number of factors. In this data, we have a case in which the measured contact resistance exceeds the modeled values over the range of forces explored in this experiment. Looking at Fig. 3, possible explanations include cases (3) and (4). Case 3 arises when the elastic-plastic behavior of the thin films on hard substrates gives rise to larger than expected hardness. While the modulus of thin films is generally reported to be similar to that of bulk materials, we believe that the Hertz model may fail to describe this situation because of onset of plasticity and hardening in the films for these small contact areas. Hardness and roughness may be better descriptors of contacts in this scale and configuration. The mechanical properties of thin metal films can be expected to depart from the properties of bulk material. Fig. 5 shows a series of nanoindentation

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Fig. 5. Hardness of evaporated gold films, inferred from nanoindentation and the Oliver and Pharr method [25], also varies with thickness and is measured at about 10% indentation depth. Hardness of a 0.18 film is H 2:3 GPa, a 0.66 m film is H 1:6, and a 1.2 m film is H 1:0. Hardness of bulk gold is around 0.6 GPa. Film hardness is also a function of process parameters, but is consistently correlated with the gold film thickness.

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Fig. 6. Focused ion beam (FIB) sections of typical 0.5 m and 1.2 m thick as-evaporated gold films. The grain size increases over this range of thickness. Surface roughness is measured from AFM scans though changes little with increasing thickness.

measurements on these films, with values of hardness, derived using the Oliver–Pharr method [25], that are larger than bulk and also showing that the derived hardness of the film is not constant as the indentation evolves because of substrate effects. The film hardness is generally taken as the value at ten percent evapindentation depth for a hardness of 2.3 GPa in a 0.18 orated film (250 titianium, 250 platinum, 1300 gold), hardness of 1.6 GPa in 0.66 m film, and of 1 GPa in a 1.2 film. Hardness of bulk gold is around 0.6 GPa [26]. Focused ion and 0.5 evaporated films, beam sections of typical 1.2 shown inFig. 6, help explain the difference in hardness. The mi-

crostructure of thin films varies with thickness with grain sizes increasing over several microns of increasing film thickness. Smaller grain size implies more grain boundary surfaces to accumulate and pin dislocations and higher stress levels and loads needed to produce strains similar to a film with larger grains. When the grain size approaches the mean free path of an electron (reported as approximately 40 nm in gold [27]), the resistivity of the film may also be increased. The films studied in this . work have nominal thicknesses of 150 nm, 500 nm, and 1 Grain size is on the order of the film thickness in the 150 nm films and increases with increasing thickness as in Fig. 6.


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Fig. 7. (a) 20 20 AFM scans of 100 diameter glass sphere: surface roughness, = 601 A, peak to valley roughness = 0:737 m, average roughness = 380 A. The z -axis is magnified 50 times. (b) 500 optical image of another 100 m diameter glass sphere, taken using differential interference = 559A, peak to valley roughness contrast (DIC) microscopy. (c) 30 m 30 m AFM scan of 100 m diameter polystyrene sphere: surface roughness, = 0:901 m, average roughness = 311 A. The bulging asperity at the edge of this sphere is about 1 m in height and 2 m diameter. (d) 500 optical image a typical polystyrene sphere. Polystyrene spheres generally exhibited larger asperities but a lower average roughness.

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Therefore, our contact resistance data and our independent measurements of film hardness and morphology are consistent with the Case (3) explanation—that thin film morphology and substrate hardness contribute to an increased effective hardness for these films, giving rise to smaller contact area and larger contact resistance. Alternatively, Case (4) arises when asperities on one or both surfaces give rise to very small electrical contacts which do not appreciably grow in area as the asperities are deformed. These asperities might be modeled as Hertzian contacts with very small radii, and would exhibit excess resistance consistent with the experimental observations. The topography of a typical diameter glass sphere is characterized from an AFM 100 scan and is rendered in Fig. 7(a). The roughness and presence of dominant asperities on the uncoated spheres are obvious with optical inspection as well, as in Fig. 7(b). Each of these two cases are expected to exhibit excess contact resistance, just as observed. If we rely only on resistance versus force measurements, we cannot distinguish these 2 cases. However, if we can independently measure the contact displacement, we would observe very small displacement in case 3, and very large displacement in case 4. C. Contact Displacement Measurement In order to directly measure contact displacement, a Michelson interferometer is incorporated into the existing measurement system [28]. The configuration of the interferometer

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is shown in Fig. 2. The back of the cantilever sensor replaces one of the mirrors of a typical Michelson interferometer to measure the movement of the cantilever. The movement of the cantilever relative to the interferometer produces a sinusoidal oscillation in the optical signal at the detector. Once the cantilever makes contact with the opposing surface, this sinusoidal signal is disrupted. If the contact were made between a pair of infinitely hard surfaces, we would expect the sinusoidal signal to terminate in a fixed signal at the point of contact. In the case of all our measurements, the tip of the cantilever does not come to a complete stop at the point of contact—the deformation of the electrodes leads to a very small amount of continued motion. We see this as a signal that varies linearly with displacement after the contact is established (this is independently confirmed by the electrical measurements of the contact resistance and the mechanical measurement of force on the cantilever). The tricky aspect of this measurement is that we cannot predict or control the exact position of the contact as we advance the cantilever toward the surface. Therefore, the occurrence of this contact relative to the oscillatory interferometer signal is not controlled or predicted. Furthermore, the relationship between additional contact displacement and the optical signal from the interferometer depends on the placement of the point of contact relative to the sinusoidal signal pattern. If the contact is at the maxima or minima of the sine wave, the sensitivity will be zero. The maximum sensitivity will occur when the signal is halfway

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between maxima and minima, and so in order to achieve maximum sensitivity, the contact must occur in that region. However, it is impossible to predict the contact point at the start of the test, and therefore not every contact test will yield usable interferometer data. To compensate for this, we record the entire sinusoidal signal pattern prior to the point of contact. We fit this signal pattern to a sine wave, and compute the sensitivity (volts/nm) at the instant of contact from the slope of the sine wave. This computed sensitivity is used as a calibration to convert the subsequent signal changes to displacement. This calibration must be carried out for every contact measurement, and is only valid for a limited range of displacements after contact. Fortunately, this calibration data is available in every measurement, and we are only interested in measurements of small displacements in these contact experiments. To reduce mechanical and electrical noise (e.g., acoustic pickup, microscope vibration, piezostage ringing) present at high frequencies, Krohn–Hite low-pass three-pole filters (60 dB roll-off) were used at 10 Hz to filter the interferometer displacement data and at 30 Hz for the piezoresistive force data. The experimental apparatus is controlled through a Labview interface using National Instruments GPIB and data acquisition cards. In a standard test, the compliance of a Keithley 236 source measure unit was set to 10 mA and 20 mV (dry contact specifications [29]), though the effect of varying current compliance was evaluated as well. The cantilevered electrode is advanced toward the spherical electrode with a GPIB commanded Polytec P731/E515 piezoactuator/controller in few nm steps at a rate of 1 to 2 Hz. The sampling algorithm employed introduces some additional filtering and averaging. The data acquisition occurred at high rates but the interval varied with Windows/GPIB overhead delays; therefore in averaging the data, no set time interval could be taken because of the inherent delay in the GPIB bus. To assure the force, displacement, and resistance data are acquired at a single position, the sequence included: a position step change, a delay of 400 ms to assure the step was complete, and data acquisition of 500 measurements within 250 ms which are averaged and stored as a single measurement. This averaging makes use of the speed of the acquisition system to significantly oversample the 10–30 Hz bandwidth of the low-pass filters, guaranteeing that the bandwidth is determined by these filters and not by the acquisition system. Referring to the noise spectra in Figs. 8 and 9, we can estimate the rms noise for a single measurement by integrating over the bandwidth. The entire experiment begins by zeroing the offset before the contact, proceeds by incrementing the position of the cantilever at rate of 1 Hz to 2 Hz, and is finished within 10–20 s of the initiation of the contact for purposes of displacement measurement. If we also consider that each data point is averaged over 250 ms, the effective bandwidth for the noise is no larger than 1 Hz to 30 Hz for the piezoresistor and 1 Hz to 10 Hz for the interferometer. We can then estimate rms noise from Figs. 8 and 9 by integrating the square of the measured noise spectral density in this frequency range, and then taking the square root of the result of the integral. Since the noise spectral density has units of N/rt-Hz for the piezoresistor, the result of the square

Fig. 8. Noise data for piezoresistor are collected on an HP89410A vector signal analyzer. The piezoresistor noise over the frequency range 10 to 10 is dominated by 1/f noise below 1 kHz. For the experimental conditions, noise is integrated over the range of 2–30 Hz.

Fig. 9. Noise data for interferometer are collected on an HP89410A vector signal analyzer. For the experimental conditions, noise is integrated over the range of 2–10 Hz.

root of the integral has units of N, representing the expected RMS noise between single measurements with this bandwidth. For the piezoresistor, the estimated RMS noise is 0.55 nN; for the interferometer, the estimated RMS noise is 0.16 nm. For both sensors, drift eventually gives rise to larger errors. Fig. 10(a) shows a set of data from a contact of a silicon canon a 100 diameter polystyrene tilever sphere with evaporated gold films. Although the movement of the piezoelectric actuator is not ideal and produces vibration, an accurate measurement is obtained by oversampling and averaging the signals from the various sensors. A sine curve is carefully fitted to the interferometer data as shown in Fig. 10(a). The actual contact point is found by extrapolating the curve from before and after the contact. Differentiating the fitted curve at the contact point produces the sensitivity of the interferometer. In Fig. 10(a), a sensitivity of 9.25 mV/nm was obtained by this method. The last step is to divide the voltage change after the contact by the sensitivity to get the


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(b) Fig. 10. (a) Data from contact of a silicon cantilever (K = 72:1 N=m) and a 100 m polystyrene sphere with 0.5 m evaporated gold films. The sinusoidal trace is the interferometer data with a curve fit, the linear flat to ramp trace is the piezovoltage with gain 1000. (b) Data from a second contact with the same cantilever parameters but different interferometer phase.

displacement at the corresponding force. From this set of data, , the measured contact disit is found that for a force of 5 placement is 4.8 nm. The contact displacement of the polystyrene sphere on a silicon flat surface is predicted from Hertzian elastic theory for the mutual approach of distant points in the solid as

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where = approach of distant points on two sides of the contact (m). Using the properties given in Table I for gold as both material is 0.5 nm, 1 and 2 and (2), the predicted displacement at 5 whereas using the properties of silicon and polystyrene for the two contact materials, the predicted displacement is 4.3 nm. These results suggest that the substrate properties play a dominant role in the contact behavior for these loads and film parameters, most likely due to the real film plasticity as well the properties and asperities of the underlying sphere. In addition to

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considering the influence of the substrate modulus, the discrepancy between Hertz theory and this measurement is attributed to the presence of small asperities on the surface of the contact (as seen in Fig. 7), which create an initial contact and penetrate the opposing surface more readily than a smooth surface would, but eventually limit the engagement of the two surfaces thus decreasing the real contact area and increasing the contact resistance. If this situation is idealized to a single asperity contact, diameter sphere on flat, the displacement modeled as a 1 predicted by Hertz theory for a gold on gold contact is 2.3 nm at , much larger than for an ideal 100 sphere. If the prop5 erties of silicon and polystyrene are then assumed to dominate the contact after initiation, the predicted contact area, , exceeds the asperity radius and therefore is beyond the applicability of Hertz theory. A second data set with the same cantilever and test conditions is shown in Fig. 10(b). From the figure, we extract a contact dis, whereas the predicted placement of 9.7 nm at a force of 3.5 displacement is 3.5 nm. These results are consistent with those in Fig. 10(a) and again appear to be asperity controlled, though the displacement in this case is even larger. We expect that while the contact will engage some number of asperities, the quantity and size distribution will vary. In the contact tests with the 500-nm gold films, we infer that the films effectively smooth the sphere surface by filling between the larger asperities thereby affording less initial gap and less contact displacement under the same load conditions. The displacement is predicted for the cases where substrate moduli dominate, film moduli dominate, and also for the case of an as. This asperity model is particularly ill perity contact of 1 suited for predicting behavior in a polystyrene on silicon contact as the predicted radius of the contact area would exceed the radius of the asperity at these loads. However, the combination of large displacement and high resistance behavior seems to point strongly toward the asperities playing a dominant role in this measurement. If most of the displacement were from polystyrene deformation, the resistance should be closer to that predicted by Hertz theory for at least the elastic portion of the loading cycle. The high resistance strongly indicates that much of the displacement is related to the asperities. The results suggest a better model incorporating roughness and plasticity is needed and will be facilitated by more measurements with this system and further investigation. To increase accuracy of predictions and future models, additional data from pure substrate tests, without gold films, must be taken to create a reference for calculating additional gold deformation. Nanoindentation is presently the preferred method for extracting these material properties, however it does not have the capabilities to measure electrical properties concurrently and provide information on contact initiation and the real contact area. This system provides this aspect and the capability to observe behavior in a current carrying contact. IV. CONCLUSION This new MEMS/Materials characterization system is capable of simultaneous measurement of nm-sized displacements and deformations, forces from a few nN’s to several mN’s, and

contact resistance from mOhms to kOhms. This capability falls in the force regime between typical atomic force microscope (AFM) cantilevers and conventional load cells. When combined with materials data like focused ion beam sections for microstructure, AFM scans for surface roughness, and nanoindentation measurements for hardness, this system enables the understanding of thin film electrical contact behavior in the low force regime. In the experiments presented here, we have shown an example where the measured contact displacement is significantly different from the predicted displacement with and without the presence of gold films. This discrepancy and the deviation from Hertzian contact behavior may be understood by considering surface roughness and asperities. The consistently larger than predicted displacements and contact resistance higher than that predicted from Hertz theory suggest the asperities play a dominant role in this system. V. FUTURE WORK Further measurements of contacts are necessary to collect enough data for improvement of contact-roughness models at this scale. Additionally, identical contact geometries with different film thicknesses and hardness are found to result in drastically different contact resistance behavior. Thinner, harder films on identical contact geometries are consistently found to produce similar trends upon loading but with a higher contact resistance over the same force range. This increased resistance implies a smaller contact area which is attributed to the larger hardness of the thinner films, also discussed above. Work is underway to improve the system for more robust alignment to increase the yield of data sets with measurement of force, resistance, and displacement. In parallel, we are pursuing finite element simulations of microcontacts and nanocontacts with surface asperities and modified film properties to verify the contributions of nonlinear film deformation, surface roughness, and nonlinear contact mechanics, and ultimately, the extraction of nanomechanical material properties. ACKNOWLEDGMENT The first author gratefully acknowledges the support of the Hertz Foundation Fellowship Program during this research. The authors wish to thank D.-H. Choi for help performing many hardness measurements and Professor W. D. Nix for his comments and technical advice. REFERENCES [1] G. L. Mathieu and FormFactor, Inc. et al., “Method of Making and Using Lithographic Contact Springs,” U.S. Pat. 6 268 015, 2001. [2] M. Little and Hughes Electronics, “Integrated Spring Contact Fabrication Methods,” U.S. Pat. 5 665 648, 1997. [3] D. Smith, A. Alimonda, and Xerox Corporation, “Photolithographically Patterned Spring Contact,” U.S. Pat. 5 613 861, 1997. [4] D. Smith and Xerox Corporation et al., “Photolithographically Patterned Spring Contact and Apparatus and Methods for Electrically Contacting Devices,” U.S. Pat. 5 944 537, 1999. [5] Y. Zhang et al., “Thermally actuated mircoprobes for a new wafer probe card,” J. Microelectromech. Syst., vol. 8, pp. 43–49, Mar. 1999. [6] B. Kebabi et al., “Stress and microstructure relationships in gold thin films,” Vacuum, vol. 41, no. 4–6, pp. 1353–1355, 1990.


[7] C. Khan et al., “Effect of thermal treatment on the mechanical and structural properties of thin films,” J. Vacuum Sci. Technol., vol. B9, pp. 3329–3332, 1991. [8] W. C. Oliver et al., Measurement of Hardness at Indentation Depths as Low as 20 Nanometers: ASTM Special Technical Publication, 1985. [9] P. M. M. Zavracky, E. Nicol, R. H. Morrison, and D. Potter, “Microswitches and microrelays with a view toward microwave applications,” Int J RF Microwave Comput Aided Eng., vol. 9, no. 4, pp. 338–347, 1999. [10] S. Majumder et al., “Study of contacts in an electrostatically actuated microswitch,” in Proc. Electrical Contacts -1998. Proceedings of the FortyFourth IEEE Holm Conference on Electrical Contacts (Cat.CB36238), 1998, p. XVII+325. [11] R. Holm and E. Holm, Electric Contacts; Theory and Application, 4th ed. Berlin, Germany: Springer-Verlag, 1967. [12] D. Hyman and M. Mehregany, “Contact physics of gold microcontacts for MEMS switches,” in Proc. Electrical Contacts -1998. Proceedings of the Forty-Fourth IEEE Holm Conference on Electrical Contacts (Cat.CB36238), 1998, p. XVII+325. [13] J. Schimkat, “Contact Materials for Microrelays,” in Proc. MEMS 98. IEEE. Eleventh Annual International Workshop on Micro Electro Mechanical Systems. An Investigation of Micro Structures, Sensors, Actuators, Machines and Systems (Cat.CH36176), 1998, p. +666. [14] E. J. J. Kruglick and K. S. J. Pister, “Lateral MEMS microcontact considerations,” J. Microelectromech. Syst., vol. 8, pp. 264–271, Sept. 1999. , “Micronewton contact characterization for MEMS relays,” in [15] Proc. ICEC ’98 19th International Conference on Electric Contact Phenomena, 1998, p. 507. [16] M. Antler, “Tribological properties of gold for electric contacts,” IEEE Trans. Parts, Hybrids and Packaging, vol. PHP-9, pp. 4–14, 1973. [17] M. D. Pashley and J. B. Pethica, “The role of surface forces in metalmetal contacts,” J. Vac. Sci. Technol. A, Vac. Surf. Films (USA), 1985. [18] S. P. Sharma, “Some notes on the physics of contact adhesion,” Insulation/Circuits, vol. 23, no. 11, pp. 41–45, 1977. [19] K. L. Johnson, “Aspects of contact mechanics,” in Proc. IMechE 14, 1987. [20] B. Pruitt et al., “Design of piezoresistive cantilevers for low force electrical contact measurements,” in Proc. IMECE: 2000 International Mechanical Engineering Congress and Exposition, Orlando, FL, 2000. [21] B. L. Pruitt et al., “Low force contact resistance measurements of thin film gold using micromachined piezoresistive cantilevers,” in Proc. MRS Fall Meeting, Boston, MA, 2001. [22] [23] J. A. Greenwood and J. B. P. Williamson, “Contact of nominally flat surfaces,” in Proc. Royal Soc. , vol. A295, London, U.K., 1966, pp. 300–319. [24] B. L. Pruitt and T. W. Kenny, “Piezoresistive cantilevers and measurement system for characterizing low force electrical contacts,” Sens. Actuators, Phys. A, vol. 104, pp. 68–77, 2003. [25] W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” J. Mater. Res., vol. 7, pp. 1564–1583, 1992. [26] R. B. Ross, Ed., Metallic Materials Specification Handbook, Fourth ed. London, U.K.: Chapman and Hall, 1992. [27] J. Beale and R. F. Pease, “Limits of high-density, low-force pressure contacts,” IEEE Trans. Compon., Packag., Manufact. Technol., pt. A, vol. 17, pp. 257–262, 1994. [28] E. Hecht and A. Zajac, Optics. Reading, MA: Addison-Wesley, 1974. [29] B 539 Standard Test Methods for Measuring Contact Resistance of Electrical Connections (Static Contacts), Annual Book of ASTM Standards, 1996.

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Beth L. Pruitt (M’02) received the S.B. degree in mechanical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in 1991, the M.S. degree in manufacturing systems engineering from Stanford University, Stanford, CA, in 1992, and the Ph.D. degree in mechanical engineering from Stanford University in 2002 supported by both the Hertz Foundation Fellowship and the Stanford Future Professors of Manufacturing Program. She served as an officer in the U.S. Navy with tours as an engineering project manager at Naval Reactors, Washington, DC, and as an engineering instructor at the U.S. Naval Academy and is certified as a professional engineer. She worked at EPFL in the Microsystems Laboratory after receiving the Ph.D. degree and recently joined the Faculty of the Mechanical Engineering Department at Stanford University. Her research interests include Microelectromechanical systems (MEMS), materials characterization and associated instrumentation, manufacturing and design for packaging and systems integration, and biomedical devices for biological measurements. Dr. Pruitt is a Member of the American Society of Mechanical Engineer (ASME).

Woo-Tae Park received the B.S. degree in Mechanical Design with Honors from Sungkyunkwan University, Seoul, Korea, in 2000, the M.S. degree from Stanford University, Stanford, CA, in 2002, and is currently working towards the Ph.D. degree in mechanical engineering at Stanford University. His current research interests are wafer level packaging of MEMS devices and design of novel structures for high-frequency micromechanical resonators.

Thomas W. Kenny received the B.S. degree in physics from the University of Minnesota, Minneapolis, in 1983 and the M.S. and Ph.D. degrees in physics from the University of California, Berkeley, in 1987 and 1989, respectively. He has worked at the Jet Propulsion Laboratory, Pasadena, CA, where his research focused on the development of electron-tunneling-based microsensors and instruments. In 1994, he joined the Mechanical Engineering Department at Stanford University and directs MEMS-based research in a variety of areas such as advanced tunneling sensors, cantilever beam forces sensors, wafer-scale packaging, microfluidics, and novel fabrication techniques for micromechanical structures. Recently, he co-founded Cooligy, a venture-funded startup that is developing liquid cooling technology for computers. Dr. Kenny is a Member of the American Society of Mechanical Engineer (ASME).