Strength Distributions in Polycrystalline Silicon MEMS - IEEE Xplore

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 2, APRIL 2007

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Strength Distributions in Polycrystalline Silicon MEMS Brad L. Boyce, J. Mark Grazier, Thomas E. Buchheit, and Michael J. Shaw

Abstract—Safe and reliable design of MEMS components requires a statistical description of the material properties that are associated with failure. To this end, a series of microscale tensile tests was performed on polysilicon MEMS structures fabricated using Sandia National Laboratories’ SUMMiT V™ process. Tensile bars were fabricated from each of the four freestanding polysilicon layers, with gage lengths ranging from 30 to 3750 . A two-parameter Weibull distribution appeared to adequately characterize the observed tensile strength distributions. The strength distribution was found to be dependent on the length of the tensile structures, as expected by the Weibull size effect, and unexpectedly strongly dependent on the layer from which the tensile bar was constructed. Specifically, the topmost polysilicon layer in the deposition process (poly4) was more than twice the strength of the bottom freestanding polysilicon layer (poly1). The mechanistic source of this layer-dependent strength appears to originate, at least in part, from process-dependent surface roughness, although other factors such as layer-dependent variations in microstructure, residual stress, and doping are also considered. A fracture mechanics analysis of the strength distributions suggests that the size of the critical flaws is in the vicinity from 50 to 150 nm. Fractography revealed crack origins along the sidewalls, corners, and top surfaces. Weibull strength distributions were also established at elevated temperatures: 200, 400, 600, and 800 C in air and nitrogen environments. These results revealed the onset of ductility and reduction in strength at elevated temperatures: at 600 C strength was less than 40% of the room temperature value. Most of the strength was regained if the material was tested at room temperature after a high-temperature exposure. In the discussion, we briefly review concepts for incorporating these observed strength distributions into probabilistic safe design of MEMS components. [1756]

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Index Terms—Fracture, microelectromechanical (MEMS), silicon, statistics, strength, Weibull.

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I. INTRODUCTION ANY early microelectromechanical systems (MEMS) designs utilized low force on-chip actuation such as provided by electrostatic comb drives, where forces and corresponding maximum stresses were small, i.e., often 500 MPa, and other more pressing reliability issues existed, such as tribological wear and stiction. Proliferation of high-force actuators

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Manuscript received January 22, 2006; revised July 17, 2006. This work of authorship was prepared as an account of work sponsored by an agency of the United States Government. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. Subject Editor S. M. Spearing. The authors are with the Materials and Process Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185 USA (e-mail: blboyce@sandia. gov). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2007.892794

such as chevron thermal actuators, and possible use of MEMS devices in high-risk applications have elevated concern over the statistical probability of failure and the proximity of design stresses to allowable failure limits. MEMS components often produce substantial device stresses which must be compared to fundamental material properties in a statistical way to evaluate probabilistic structural reliability. For brittle MEMS materials, characterization of strength distributions is not only expected to provide probabilistic design guidance, but also to provide insight into the origin of failure-critical flaws, thereby guiding improvements in processing and design. There have been several studies on the strength of microfabricated polysilicon, e.g., [1]–[10]. While there have been appeals for statistical approaches to polysilicon failure [9]–[12], many existing datasets have only limited observations or draw from data collected using multiple test methods. In this study, we apply a tensile test technique that is amenable to collecting a large, multivariate statistical database of strength values. Statistical strength distributions can be used to establish several important design considerations: 1) failure probabilities, 2) description of the “typical” strength, 3) dispersion of strength values, 4) the presence of multiple failure sources, and 5) the existence of a cut-off or strength threshold below which no failures occur. Moreover, with a thorough statistical description of strength, subtle changes such as those induced by process modifications can be distinguished from statistical scatter. There are several factors that can influence the strength distribution of brittle MEMS materials including process conditions, component size, test temperature, and test environment. Process conditions affect strength by controlling the size, density, orientation, and morphology of critical flaws. In brittle materials, component size can influence the strength through the Weibull size effect [9]: smaller component sizes have a lower probability of containing large flaws and are expected to have higher strengths. Temperature can affect strength by activating diffusion and deformation mechanisms, thereby accommodating pre-existing flaws. Temperature in concert with the environment, can adjust the thermodynamics and kinetics of chemical interactions at the crack tip, such as in the case of stress corrosion cracking. The current work sets forth to assess the roles of these factors on the strength distributions of SUMMiT V™ polysilicon. Specific questions that were addressed in this work include: 1) what are the typical statistical strength distributions for SUMMiT V™ polysilicon, 2) is there a size-effect on the strength of polysilicon, 3) how does temperature and environment affect the strength of polysilicon, 4) does the strength vary from layer to layer in the SUMMiT V™ process, and 5) what are the critical flaws produced by this process?

U.S. Government work not protected by U.S. copyright.

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Fig. 1. Cross section of a notional multilayer cantilever fabricated using Sandia’s SUMMiT V™ process, showing the five polysilicon layers (poly0-poly4): (a) encapsulated in sacrificial oxide and (b) after the sacrificial oxide is etched away to leave the cantilever structures. The schematic, generated with Sandia’s SUMMiT V™ process visualization tool, is proportionally accurate and the thickness of each polysilicon layer is noted.

II. METHOD A. Material Tensile structures were fabricated from polysilicon using the Sandia Ultraplanar Multilevel Microsystems Technology (SUMMiT V™). In this process, five layers of polysilicon and four interlayers of sacrificial oxide are deposited and lithographically patterned. A schematic showing a cross section of a multilayer cantilever structure formed by the SUMMiT V™ process is shown in Fig. 1. The substrate for the SUMMiT V™ n-type silicon with process consists of a 6-inch wafer of coating of thermal oxide and a 0.80coating a 0.63of low stress silicon nitride. The first deposit of polysilicon, poly0, is a 0.30- -thick electrical ground plane directly attached to the substrate thereby providing the structural footing for subsequent layers. The four freestanding structural layers are identified as poly1 – poly4 according to their deposition order. In device design, the poly1 and poly2 layers are often used as a composite layer, which is referred to here as poly21. More details of the process and parametric monitoring can be found elsewhere [13], [14]. All test structures for this paper were fabricated from module 8 of reticle set 374 in Sandia’s SAMPLES runs. After release and super-critical drying, a vapor-deposited self-assembled monolayer (VSAM) anti-stiction coating was applied to all exposed silicon surfaces. The particular VSAM coating used in this study was tridecafluoro-(1,1,2,2-tetrahydrooctyl)tris(dimethy, otherwise lamino)silane, known as FOTAS [15]. B. Tensile Method A method for evaluating the tensile strength of surface micromachined structures was developed based on a rectangular dog-bone tensile geometry [16]–[19]. The so-called “pull-tab” tensile test structure consists of a constant-width gage section

with a freestanding ring on one end for gripping and load application. On the other end, the gage section is attached to the substrate via a free-rotating hub. Gage dimensions of the pull-tab structures were chosen to be similar to the critical dimensions of actual components. The nominal width of the polysilicon tensile . The nominal thickness of the gage section structures was 2 depended on the layer being tested, as defined by the SUMMiT for poly1, 1.5 for poly2, 2.5 for poly V™ process: 1 21, and 2.25 for poly3 and poly4. Four gage lengths were . evaluated: 30, 150, 750, and 3750 The free-rotating pivot Fig. 2(a) incorporated in the design allows self-alignment to minimize bending errors associated with off-axis loading. Without the ability to self-align, a 1 displacement offset between the centerline of the specimen and the applied displacement vector can result in a significant bending moment that induces a threefold increase in the maximum bending stress compared to the homogeneous stress of perfect alignment.1 Early test methodology [16]–[18] utilized a nanoindenter with lateral force sensing capability coupled to a cylindrical tip to engage the ring end of the “pull-tab”. In this early method, the tip was dragged along the substrate during lateral testing resulting in the superposition of elastic tensile forces and substrate friction forces. The friction effects were found to produce anomalously high strength measurements [8]. To overcome these effects, the present study utilized a custom-built mechanical probe station. The probe station, schematically illustrated in Fig. 2(b), is centered on the MEMS test structure, typically die, affixed to an aluminum work surface a using a vacuum chuck. The aluminum work surface is secured to a Compumotor 2-axis stage. The 2-axis stage allows the work surface and specimen to be moved in the horizontal plane with respect to the fixed optics column. The optics column suspends long working-distance lenses above the work surface. resolution An independent Newport 3-axis stage with 0.1 1This finite element error estimate is based on a gage section that has a cross section of 2 m 2 m and a gage length of 150 m.

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in a positive-pressure of the MEMS devices to over 800 environmental chamber. All probe station functionality is controlled via a custom-programmed Labview-based software platform, including 5-axis motion control, pre-amp arbitrary function generation for driving electrostatic actuators, and data recording/scaling of the force and linear encoder signals. The raw data collected is force from the load cell and displacement of the 3-axis stage that supports the load cell Fig. 2(d). Only the maximum force at failure is used for evaluating the tensile strength of the brittle polysilicon. Ultimate strength is obtained by dividing the maximum force by the nominal cross-sectional area. Measurement of the actual cross-sectional area of each tensile specimen was prohibitively time consuming. Instead, we consider the variability in actual cross-sectional area as a process characteristic that contributes to the overall scatter in the observed strengths. Device designers likewise typically design based on nominal dimensions, and not on the actual dimensions of individual processed components. and is discussed Dimensional variation was typically further in Section IV-B3. While the strain values were not of interest for brittle strength determination, other researchers have used image correlation routines on AFM images of the deforming surface to quantify local strains for measurement of elastic properties, especially in the presence of strain-concentrating features such as holes or cracks [5]–[7], [20], [21]. C. Statistical Analysis Fast fracture in brittle materials is typically driven by pre-existing flaws. In such a case, there is a distribution of flaws within the material, and variability in critical flaws from sample to sample results in a distribution in failure strengths. Such strength variability in brittle materials is often described by the Weibull distribution. The two-parameter Weibull distribution can be expressed by the following cumulative distribution function:

(1) Fig. 2. (a) Scanning electron micrograph (SEM) of the pull-tab tensile structure fabricated in Sandia’s SUMMiT V™ technology. (b) schematic of mechanical probe station, (c) scanning electron micrograph of focused-ion beam machined tungsten tip with a 35 m tip diameter used to hook and pull the ring end of the pull-tab structures, (d) typical raw load-displacement traces corresponding to tensile tests at room temperature and 800 C.

linear encoders is used to position the load cell and associated probe tip with respect to the work surface and specimen; and is used as the drive actuator during mechanical testing. A Transducer Techniques 10 g load cell in conjunction with a Vishay signal conditioning amplifier with a 100 Hz low pass . Attached to the filter provides a force resolution of load cell is a tungsten probe tip Fig. 2(c), machined into a cylindrical geometry using a Focused Ion Beam (FIB) tool to engage the free ring of the “pull-tab” structure. The Newport actuator was used to hold the flat end of the cylindrical probe above the substrate during testing to avoid frictips tion effects. The probe station was further modified to include a resistance coil die heater capable of heating the active surface

where represents the probability of failure, and represents the applied stress. The characteristic strength or scale paramis the stress value at which there is a 63% probability eter is a of failure and the Weibull modulus or shape parameter measure of the breadth of the distribution, with lower values corresponding to a wider distribution of strengths. A mathematical manipulation of the previous equation yields the following relationship:

(2) From this equation, a linear fit to experimental data can be used to evaluate the Weibull nature of the distribution and extract values for the characteristic strength and Weibull modulus. A three-parameter Weibull distribution adds an additional location parameter to account for the possibility of a nonzero cutoff stress, i.e., a stress below which no failures occur. In cases where

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is less scatter in the flaw distribution, or less scatter from test method artifacts. B. Effect of Size and Process Layer

Fig. 3. The failure probability (inset) and Weibull transform observed for a unimodal strength distribution of the 150 m long poly3 tensile structures.

two different flaw populations drive failure, the result is typically a bimodal strength distribution, which can be evaluated using the maximum likelihood estimation method for a censored dataset as described in ASTM C 1239 [22]. III. RESULTS The “pull-tab” tensile test method was used to quantify the fracture strength distributions of each of the freestanding structural layers of Sandia’s SUMMiT polysilicon of various ) and over a range of temperatures gage lengths (30–3750 (25–800 ) in air and dry nitrogen environments. A. Weibull Results of a Single Poly Layer As a baseline set of tests to evaluate the statistical nature of failure, a series of 37 strength measurements was performed on tensile bars from the poly3 structural layer with a gage length at room temperature in air. The nominal gage width of 150 and the thickness of the poly3 layer was 2.25 , was 2 . The 37 thereby yielding a gage surface area of 1290 through in ascending strength values were ranked order, and a probability was assigned to each of the strengths [22]. In this way, each layer according to could be assessed in terms of a probability of failure as a function of applied stress. The two-parameter Weibull transform of these data, shown in the primary graph of Fig. 3, appears to reasonably capture the unimodal distribution of strengths. Based on a linear regression of these data, the estimated Weibull modulus is 16.7 and the estimated characteristic strength is 2.43 GPa. The Weibull modulus of 16.7 observed for this current dataset is somewhat higher than the values of measured by Bagdahn and Sharpe on polysilicon from the Multi User MEMS Process (MUMPs) [1] and by China’s National Tribology Laboratory for a low pressure chemical vapor deposited (LPCVD) polysilicon2[3], indicating that there 2In both of these existing Weibull modulus measurements, the gauge width of the tensile specimens ( 20 m) was at least an order of magnitude wider than the gage width used in the current study (2 m).

A total of 30 strength tests were performed on each of the four freestanding structural layers and the poly21 composite layer: 6–8 tests for each of the four gage lengths (30, 150, ). A semi-log plot of strength as a function 750, and 3750 of gage surface area (total area of all four gage surfaces) is shown in Fig. 4. This plot clearly shows that the layer ranking from weakest to strongest is poly1, poly2, poly21, poly3, and poly4. Also, for each layer there is a decrease in strength associated with increasing gage area, as expected due to an area-dependent flaw probability, i.e., the Weibull size effect. In many studies on the Weibull size effect, e.g., [3], specimens of various surface-area-to-volume ratios are evaluated to decipher whether the effect is driven by surface or volumetric defects. The present study, confined by the dimensions of the SUMMiT V™ process, was not designed to delineate between these potential sources. A plot of failure strength as a function of volume would look nearly identical to the plot as a function of surface-area shown in Fig. 4. However, fractographic evidence presented in Section III-E does indicate that the failure-controlling flaw population is surface-based: sidewall, corner, and top/bottom-surface defects have all been observed. The slopes in Fig. 4 can be analyzed to assess the statistical significance of the size effect. Linear regression of the data in Fig. 4 yields slopes of 0.146, 0.142, 0.140, 0.218, 0.302 for poly1, poly2, poly21, poly3, and poly4 respectively. A statistical t-test on the slopes confirmed that they are statistically distinguished from zero-slope with better than 99% confidence. In other words, the size-effect does exist and is statistically significant. The trends in decreasing strength with increasing surface area can also be used to estimate associated Weibull moduli. Manipulation of the two-parameter Weibull equation yields a wellknown relationship for the ratio of strength of two components of differing surface area

(3) From this equation, the negative reciprocal of the slope from a linear regression of the log-area versus log-strength data yields an estimate for the modulus. Using this analysis on the data were estimated to be plotted in Fig. 4, the Weibull moduli 20.9, 25.1, 30.0, 24.9, and 19.3, for poly1, poly2, poly21, poly3, and poly4, respectively. One should note that the exponent in , is small ( 0.05), which reiterates that the size effect is (3), subtle: only when component sizes span several orders of magnitude can a size effect be clearly distinguished. C. Weibull Strength Distributions The strength data described in the previous section can also be analyzed with respect to the probability of failure. For each of the four freestanding structural layers and the poly21 composite layer, a distribution of failure strengths is plotted in


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Fig. 4. Failure stress plotted as a function of gage surface area for each of the 5 polysilicon layers. Each layer shows decreasing strength with increasing surface area as expected from a Weibull size effect.

Fig. 5(a). These data are plotted according to a Weibull distribution; however, the dataset is inherently convoluted by grouping various gage lengths into individual poly layer distributions: it is only done here to show how strength varies from layer to layer and not to determine fundamental Weibull parameters. One way to remove this gage length convolution is to use the observed fracture strengths at various gage lengths to estimate the corresponding strengths at a standard gage size, thereby normalizing all of the data. Here, we chose a standard gage , and invoked (3) to estimate these surface area of 1000 normalized strength values, as plotted in Fig. 5(b). A linear regression of each normalized dataset can be used to estimate the layer’s characteristic strength. The estimated characteristic strengths, are 1.39, 1.68, 1.99, 2.48, and 2.99 GPa for poly1, poly2, poly21, poly3, and poly4 respectively. Strength variation from layer to layer is quite dramatic: the strength of the poly4 layer is more than twice that of the poly1 layer! This large difference in strength from layer to layer gives insight into a potential source for the wide variation in reported polysilicon strength levels between studies [10]. Linear regressions of the data in Fig. 5(b) can also be used to estimate the Weibull modulus. The estimated moduli are 9.7, 8.1, 10.1, 15.5, and 9.4 for poly1, poly2, poly21, poly3, and poly4 respectively. The characteristic strength and Weibull modulus for poly3 from this normalized heterogeneous dataset , ) are similar to the values reported ( in Section III-A obtained directly from a homogeneous dataset ( , with a constant gage surface area of 1290 ). This suggests that the normalization process produces reasonable estimates of the true strength distributions. Also, all five of these Weibull moduli obtained from linear regression of the normalized Weibull data are somewhat smaller than the moduli obtained from linear regression of the size effect in Section III-B. While the source of this discrepancy

is unclear, possibilities include: 1) the gage surface area does not adequately estimate the defect population sampling size, 2) the size effect is somewhat suppressed, leading to low apparent Weibull moduli, or 3) the large degree of scatter in Fig. 4 confounds accurate determination of the Weibull moduli from the size effect. D. Effect of Temperature and Environment Elevated temperature tensile strength measurements were long poly3 test structure at temperaperformed on the 150 tures up to 800 using a resistance heater placed beneath the die with feedback temperature control from a grounded-sheath ) placed directly on the thermocouple (sheath diameter 250 micromachined surface in the vicinity of the test structures. The entire apparatus was contained in a positive-pressure envi. Tensile strengths were ronmental chamber backfilled with using the measured at temperatures ranging from 22 to 800 same method as at room temperature. At temperatures up to , the observed force-displacement curves were linear 600 there was some noticeable curvature until failure. At 800 in the load-displacement curve Fig. 2(d), although the plastic , i.e., less than 0.66% of the displacements were less than 1 gage length. Neither resultant load-displacement curves nor post-test inspection of the failed tensile bars revealed any evidence of necking. These observations are similar to previously reported observations in larger silicon structures at 540 and [23]. 770 The resulting strength distributions are shown in Fig. 6. The in the nitrogen environment were characteristic strengths 2.72, 2.68, 1.66, 1.02, and 0.96 GPa at temperatures of 22, 200, respectively. The corresponding Weibull 400, 600, and 800 moduli were 10.8, 10.1, 20.2 15.4, and 16.6, respectively. These room temperature tests in nitrogen exhibited a slightly higher , characteristic strength and less scatter (

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Fig. 5. (a) Weibull failure probability plot for each of the five polysilicon layers confounded by intermixing various gage lengths. (b) same data with the tensile strengths normalized using (3) to a gage surface area of 1000 .

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) than the corresponding dataset in air from Section III-A ( , ). As expected, tensile tests at performed nearly identically to room temperature tests. 200 and above, the characAs the temperature increased to 400 teristic strength decreased. Specifically, at 600 , the polysilicon retained less than 40% of the room temperature tensile strength. The observed decrease in strength with increasing temperature was consistent with previous observations [23]. Howwas someever, the apparent transition in the vicinity of 400

what surprising: the onset of dislocation activity and the ductile-to-brittle transition in single crystal silicon is typically taken [24], although the transition temperature to be around 500 [24]–[26], depending on straincan range from 500 to 900 rate [27], [28] and dopant levels [29]. The somewhat lower temperature observed here could be due to the spatial inaccuracy diameter wire resting on the of the thermocouple: the 250 surface may not accurately detect the actual temperature of the test structure. For accurate determination of the temperature


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Fig. 6. Weibull plot of failure distributions at temperatures ranging from room temperature (RT) to 800 C in nitrogen. For comparison, a series of tests at 800 in air and at room temperature after a 1 hr. exposure at 800 C are also plotted. All strength tests were performed on the 150 m long poly3 tensile structure.

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of the 2 wide test structure, advanced techniques such as micro-Raman temperature measurements may be necessary. To assess the role of environment on this thermally-induced tests were performed both in strength change, the 800 and air, resulting in essentially identical behavior. The strength change is largely reversible: as shown in Fig. 6, after a 1 hr. exposure at 800 , subsequent room temperature tests recovered most of their strength. Both of these observations indicate that the thermally induced strength change is intrinsic to the material as would be expected from a dislocation mechanism associated with a ductile-to-brittle transition. E. Fractographic Observations In many brittle materials, fractographic observations lead to definitive evidence of the source for failure-inducing flaws. Signature features, such as mirror, mist, and hackle zones [30] are used in conventional ceramics to identify failure origins, estimate failure stresses, and understand the fracture process. There are some examples where researchers are able to identify similar features in microscale applications [9], [16], [31], [32]. However, in the polycrystalline silicon MEMS structures in this – ) study, the coarse microstructure (grain widths relative to the scale of the fracture surface and flaw size complicated the fractographic analysis. Nevertheless, in some cases, the apparent flaws can be located, as shown in Fig. 7. In these cases, the most characteristic features are a mirror-like region at the failure origin surrounded by so-called twist hackle or twist boundaries [30]. These hackle lines appear to emanate away from the origin of fracture and are likely caused by the vertical step connecting parallel facet planes that are at slightly

Fig. 7. Fracture surfaces from poly21 (a) and (b), and poly2 (c) and (d) showing apparent evidence of failure origins [arrows] at sidewalls (c), top surfaces (a), and corners (b) and (d). Many other fractographs had no clearly identifiable fracture origin.

different heights. Fracture experiments on SUMMiT V™ microcompact-tension specimens revealed similar twist hackle features near the fracture origin at the notch tip. At room temperature, it was not possible to obtain complimentary fracture surfaces from mating surfaces: the gage section always broke in multiple locations, presumably due to the transient elastic wave interactions during dynamic fracture. While the multiple failures were always confined to the gage section, sometimes the entire gage section from the fillet on the ring

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side to fillet on the hub side was missing after fracture. For this reason, the observed failure surfaces may not always reveal the original critical flaw. Nevertheless, from the collection of apparently identifiable fracture origins, the fractures appear to always initiate at the sidewall surface, the top surface, or the corners. The limited number of observations prevented a quantitative assessment of the relative prevalence of the various surface locations for crack initiation. Also, no clear distinction in failure origins was identified between the various poly layers. Nevertheless, there were no failures that showed definitive evidence of internal flaws. Presuming that the failure origins are identified correctly in Fig. 7, a large mirror-like plane is often found at the origin of the hackle lines, as shown most clearly in (a) and (c). This feature could be a single-grain cleavage plane, indicating that the grain closest to the origin is often quite large and occupies a significant fraction of the cross section.

Fig. 8. Histograms of apparent flaw size distributions estimated from fracture mechanics analysis of the observed strength distributions. The two distinct histograms are based on the same dataset of 37 tests, using different values of the geometry factor F for analysis. The analysis was based on the 37 room temperature 150 long poly3 tests described in Section III-A.

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IV. DISCUSSION

A. An Estimate of the Critical Flaw Size Distribution

B. Potential Origins for the Layer Dependence on Strength

A critical flaw size distribution can be estimated from the strength distribution using linear elastic fracture mechanics, (see, for example, [18]). The flaw size is related to the failure by the fracture toughness and the geometry strength factor :

As shown in Section III-B, there is a distinct change in strength from one layer to the next in the SUMMiT V™ process. This layer-dependent strength is almost certainly caused by differences induced by the fabrication process, such as by the different annealing times for the various layers (i.e., poly1 is exposed to more annealing cycles than the subsequent layers). There are several possible process-induced layer-by-layer material differences that could be considered as a potential contributor to this effect: surface topography, microstructure, doping condition, actual beam dimensions, residual stress, process-induced damage or flaws, and grain boundary chemistry. Each of these potential mechanisms for layer-dependent strength changes are considered here to evaluate their likelihood and significance. 1) Surface Topography: Some previous strength studies on other silicon MEMS materials have noted a dependence of the strength on process-induced surface topography, and inferred surface roughness as the critical flaws (see, for example [6], [35]). To explore this possibility, a Park Scientific atomic force microscope (AFM) was used to scan the sidewalls of SUMMiT V™ polysilicon structures for layer-dependent differences in surface topography. To expose the silicon sidewalls to the AFM tip, special structures were designed to lay flat on their sides region was scanned for process upon release. An layers poly21, poly3, and poly4, revealing the etch-induced sidewall topography, Fig. 9. From these measurements, a notable trend exists in the average and root-mean-squared (RMS) roughness, as shown in Table II: specifically the strongest layer, poly4, also has the lowest roughness, the intermediate strength poly3 has an intermediate roughness, and the lower strength poly21 has the highest roughness, consistent with notions of a critical-flaw associated with sidewall roughness. It is also interesting to note that in this very limited scan of sidewall area, the AFM revealed that the worst-case sidewall features

(4) The maximum geometry factor for a semi-elliptical half-penny shaped surface flaw contained in a semi-infinite body under whereas a homogeneous far-field stress is quarter-penny corner flaw under homogeneous far-field stress has a maximum geometry factor of 1.112 [33]. Since the actual tensile bars are not semi-infinite, these geometry factors should be considered as lower-bound estimates. Previously measured fracture toughness values for polysilicon are typically in the (e.g., [31], [34]). We can use vicinity of 1.0–1.2 numbers in this range to estimate flaw sizes. The dataset of long poly3 37 room temperature tests conducted on 150 structures (described in Section III-A) is used here as the input distribution, since all tests were conducted under nominally identical conditions. From this strength distribution (Fig. 3), the calculated flaw distribution is shown in Fig. 8 for two different choices of geometry factor. While the predicted flaw size distribution is dependent on the specific choice of the fracture toughness and geometry factor, the typical flaw size is likely between 50 and 150 nm. This calculation can only be used as a rough guide to the flaw sizes since real flaws in these very small tensile specimens do not have the idealized half-penny shape or quarter-penny shape and are contained in microstructural inhomogeneities that can not be described accurately with fracture mechanics.


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TABLE I LAYER-DEPENDENT RESITIVITY CHANGES

TABLE II SIDEWALL ROUGHNESS OF POLYSILICON MEASURED BY AFM

Fig. 9. AFM scans of the sidewall trenches aligned along the deposition direction, orthogonal to the tensile axis. Grayscale in AFM images are for reference only and the scales are not identical for each image. Corresponding characteristic roughness values are shown in Table II.

can be as deep as 90 nm (Fig. 9), consistent with the fracture mechanics estimates of flaw size in Section IV-A. 2) Microstructure: The crystallographic elastic anisotropy in polycrystalline aggregates result in elastic mismatch-induced stress concentrations at grain boundaries and triple points that could drive failure. Annealing treatments are known to grow grains and therefore alter the distribution of microstructural inhomogeneities driving local stress concentrations. Polycrystal elasticity modeling has been used on simulated representative silicon microstructures to estimate the potential differences in strength induced by layer-by-layer microstructural differences [36]. Using Monte Carlo methods, this modeling has confirmed that when an external force is applied to a polycrystalline microstructure, there are specific types of grain boundary triple points that tend to produce the maximum local stress in the component. However, polycrystal elastic analysis of the various polysilicon microstructures, shows that this effect only accounts for small layer dependent strength changes less than 0.1 GPa, and does not account for the broad scatter in the observed strength values for particular layers.

3) Doping Condition: Son et al. [37] have shown that doping type and process can affect strength. Specifically, knock-on damage from ion-implanted dopants result in lower strengths than diffusion-driven dopants. Also, boron implanted films have been shown to have slightly lower strengths than phosphorous implanted films. In the current study, The SUMMiT V™ polysilicon layers all utilize a phosphorous dopant and the layers are all doped by the same method. However, there are some layer-dependent differences in dopant levels, which result in layer-dependent resistivity differences (see Table I). Yet this layer-dependent resistivity trend does not appear to be commensurate with the layer-dependent strength trend. 4) Actual Beam Dimensions: As described in Section II-B, the nominal beam width and thickness were used for all stress calculations. If the process induces a systematic layer dependent error in the beam width and/or thickness, then this could result in an apparent strength difference. However, for poly1 to be half as strong as poly4, the cross-sectional area error would have to be 50%. While parametric monitoring of width and thickness has shown some layer-dependent systematic bias, the levels (typ) are not sufficient to account for the dramatic ically, changes in strength, nor does the observed trend from layer to layer scale in the same way as the layer-dependent strength trend. 5) Residual Stress: The superposition of tensile residual stress along the axis of loading is known to lower the apparent failure stress, while compressive stresses elevate the apparent failure stress [38]. Residual film stresses are affected by annealing treatment [38] and hence are expected to be layer dependent. However, in the SUMMiT V™ process, annealing treatments maintain minimal residual stresses in the vicinity of 10 MPa, as required for a 5-layer process. Within these very low levels of residual stresses, there does exist a layer-depenhigher stress than poly3 or poly4. dence: poly1 has Nevertheless, the small magnitude of layer-dependent changes in residual stress do not account for the very large differences between poly1 and poly4. in strength, e.g., 6) Grain Boundary Chemistry: The combination of different thermal anneal exposures for the polysilicon layers and the different doping levels could result in layer-by-layer differences in

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the homogeneity or boundary-segregation of dopants. In turn, this could result in a layer-dependent strength effect. The semiconductor single-crystal silicon literature provides several examples of thermally-driven Phosphorus dopant segregation to interfaces [39]–[41], although less appears to be known Si/ about the segregation to grain boundaries in polycrystals. Preliminary Auger spectroscopy on the polysilicon fracture surfaces does show an apparent trend: the poly1 fracture surface contains 0.3 at% whereas the poly4 fracture surface contains 0.5 at% . Here again, a parametric study on the effect of dopant levels and annealing cycles on resulting fracture strength would be necessary to quantify this contribution. Summarizing these various potential material factors driving failure: variations in microstructure, doping condition, actual beam dimensions and residual stress are all expected to have ) either a small or negligible effect on the substantial ( layer-dependent differences in failure stress. Instead, evidence suggests that the surface topography may be a significant source of the layer-dependence in strength: the trend in average roughness approximately scales with the observed strength changes, and the deepest trenches found in the etch-grooved sidewall surface roughness, are deep enough (50–90 nm) to be the failurecritical flaws. Finally, too little is known about grain boundary chemistry to completely assess its potential role on the layer-dependent strength effect.

In brittle components, fracture mechanics in combination with weakest link theory suggests that monotonic failure occurs when the local flaw-size dependent stress intensity exceeds the mode I fracture toughness. A stochastic analysis based on preexisting strength distributions is used to assess the probability of a large flaw being located in a highly stressed region. Following closely with [46], arbitrary multiaxial stress states can be assessed in Weibull weakest-link theory through the use of 1) Batdorf theory, 2) normal stress averaging, or 3) principle of independent action. The Batdorf theory assesses the probability of the crack being of a critical size and orientation with respect to the far-field equivalent maximum normal stress, integrated over all orientations and locations. A special case of the Batdorf theory, the normal stress averaging method integrates over all normal tensile stresses, ignoring shear components. Finally, the principle of independent action integrates over all principle stresses, with the assumption that the principle stresses are independent of one another. In the principle of independent action method, the Weibull cumulative distribution function for a can be used to assess the total probability for failure surface area of a component subjected to principle stress

C. Implications for Statistically Sound Design of Polysilicon MEMS Components

where the Weibull parameters and are defined by the observed strength distribution for the material. A similar expression can be used for volumetric flaws by integrating over all three principle stresses present in the volume. The success of these types of analysis requires that the active flaw population driving failure in the complexly stressed component is the same flaw population that was used to determine the material’s Weibull parameters. McCarty and Chasiotis [43] have demonstrated this type of analysis for predicting failure induced by perforations in polysilicon microtensile tests based on Weibull parameter estimates from either uniform tensile bars or from a parametric estimate generated with other perforated tensile tests. They found that the predictions based on uniform tensile data were better suited to predict failure in perforations with shallow stress-gradients and less capable in situations where the stress-gradient was steep. These and other similar observations highlight the challenges that remain in the use of uniform tensile data to predict failure in the presence notches or cracks.

The strength distributions presented in this study provide a comparison of relative fracture resistance among different conditions (poly layer, temperature, etc.), and an assessment of the variability of strengths. For example, immediately from the Weibull distribution results and (1), one can estimate the probability of failure associated with a particular stress. Using the Weibull parameters ( , ) obtained in Section III-A for a poly3 tensile structure, the allowable stress for a probability of failure of 1 in 1000 is 1.61 GPa, and the allowable stress for a probability of failure of 1 in 1 000 000 is 1.06 GPa. An important limitation of this simple calculation is that these estimates only apply to a structure with a surface under homogeneous tensile stress. area of 1290 The statistical strength data can become much more powerful when they are extended to assess probability and location of failure for actual MEMS components with complex geometries and multiaxial inhomogeneous stress states. The extension from uniaxial tensile strength data to predictions for complex components is not trivial and a typical approach is described in the following paragraphs and in more detail elsewhere [42]–[46]. This type of analysis relies on Weibull data for specific failure modes. Multiple active failure modes or flaw populations must be treated explicitly for appropriate design interpretation, as described in [47]. In the present dataset, the Weibull distributions appeared to have a reasonably unimodal response and all failures occurred within the tensile gage section. Yet, since our characterization of fracture surfaces was limited, we are forced to assume that there was only one failure mode—a critical assumption when applying such statistics to design.

(5)

V. SUMMARY AND CONCLUSION A series of micro-scale tensile tests was performed on polysilicon MEMS structures fabricated with Sandia National Laboratories’ SUMMiT V™ process to evaluate the statistical strength distributions. A two-parameter Weibull distribution appeared to adequately characterize the tensile strength distribution. This strength was dependent on the size of the tensile structure, as expected by the Weibull size effect [9], and strongly dependent on the individual process layer from the five-layer process. Several factors were considered to assess the mechanistic origin of this layer-dependent strength: 1) surface topography appears to be of sufficient scale and varies as expected from layer-to-


layer, 2) microstructural elastic anisotropy, doping condition, or residual stresses all had small or negligible contributions, and 3) the possible role of grain boundary chemistry merits a more thorough parametric evaluation. Fractographic analysis appears to point towards the critical flaws populated along the exterior surfaces of the silicon structures. The effective size of these critical flaws is expected to be in the vicinity of 50–150 nm based on a simplistic fracture mechanics analysis. Testing at elevated temperature in both air and nitrogen showed a dramatic but rethe strength of silicon versible effect on the strength: at 800 is less than half of its room temperatures strength, with only a very modest amount of temperature-induced ductility. ACKNOWLEDGMENT Accordingly, the United States Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so for United States Government purposes. Neither Sandia Corporation, the United States Government, nor any agency thereof, nor any of their employees makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by Sandia Corporation, the United States Government, or any agency thereof. The views and opinions expressed herein do not necessarily state or reflect those of Sandia Corporation, the United States Government, or any agency thereof. The authors would like to thank C. McCann, J.J. VanDenAvyle, and C. R. Garcia, for their experimental assistance during summer internships that contributed to portions of this work, D. LaVan for early development of the pull-tab method, and B. McKenzie for relentless fractographic characterization in the SEM. B. L. Boyce would also like to thank S. J. Glass, M. T. Dugger, M. P. DeBoer, C. Muhlstein, I. Chasiotis, N. Nemeth, D. Miller, and O. Kraft for useful discussions on this topic. REFERENCES [1] J. Bagdahn and W. N. Sharpe Jr., “Fracture strength of polysilicon at stress concentrations,” J. Microelectromech. Syst., vol. 12, p. 302, 2003. [2] T. Yi and C.-J. Kim, “Measurement of mechanical properties for MEMS materials,” Meas. Sci. Tech., vol. 10, p. 706, 1999. [3] D. Jianning, M. Tonggang, and W. Shizhu, “Scale dependence of tensile strength of micromachined polysilicon MEMS structures due to microstructural and dimensional constraints,” Chin. Sci. Bull., vol. 46, no. 16, p. 1392, 2001. [4] G. C. Johnson, P. T. Jones, and R. T. Howe, “Materials characterization for MEMS – A comparison of uniaxial and bending tests,” Proc. SPIE—Int. Soc. Opt. Eng., vol. 3874, p. 94, 1999. [5] W. G. Knauss, I. Chasiotis, and Y. Huang, “Mechanical measurements at the micron and nanometer scales,” Mech. Mater., vol. 35, p. 217, 2003. [6] I. Chasiotis and W. G. Knauss, “The mechanical strength of polysilicon films: Part 1. The influence of fabrication governed surface conditions,” J. Mech. Phys. Sol., vol. 51, p. 1533, 2003. [7] ——, “The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular performations,” J. Mech. Phys. Sol ., vol. 51, p. 1551, 2003.

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[8] D. A. LaVan, T. Tsuchiya, G. Coles, W. G. Knauss, I. Chasiotis, and D. Read, “Cross comparison of direct strength testing techniques on polysilicon films,” ASTM Special Tech. Publ., no. 1413, pp. 16–27, 2001. [9] T. Tsuchiya, O. Tabata, J. Sakata, and Y. Taga, “Specimen size effect on tensile strength of surface-micromachined polycrystalline silicon thin films,” J. Microelectromech. Syst., vol. 7, p. 106, 1998. [10] O. M. Jadaan, N. N. Nemeth, J. Bagdahn, and W. N. Sharpe Jr., “Probabilistic Weibull behavior and mechanical properties of MEMS brittle materials,” J. Mater. Sci., vol. 38, no. 20, p. 4087, 2003. [11] P. T. Jones, G. C. Johnson, and R. T. Howe, “Statistical characterization of fracture of brittle MEMS materials,” Proc. SPIE—Int. Soc. Opt. Eng., vol. 3880, p. 20, 1999. [12] K.-S. Chen and K.-S. Ou, “Equivalent strengths for reliability assessment of MEMS structures,” Sens. Actuators A, Phys., vol. 112, p. 163, 2004. [13] J. J. Sniegowski and M. P. de Boer, “IC-compatibile polysilicon surface micromachining,” Annu. Rev. Mater. Sci., vol. 30, p. 299, 2000. [14] A. D. Oliver, D. M. Tanner, S. S. Mani, S. E. Swanson, K. S. Helgesen, and N. F. Smith, “Parametric monitoring for the SUMMiT V™ surfacemicromachining process,” Proc. SPIE—Int. Soc. Opt. Eng., vol. 4558, p. 242, 2001. [15] M. Hankins, P. J. Resnick, P. J. Clews, T. M. Mayer, D. R. Wheeler, D. M. Tanner, and R. A. Plass, “Vapor deposition of amino-functionalized self-assembled monolayers on MEMS,” Proc. SPIE—Int. Soc. Opt. Eng., vol. 4980, p. 238, 2003. [16] S. J. Glass, D. A. LaVan, T. E. Buchheit, and K. Jackson, “Strength testing and fractography of MEMS materials,” in Fractography of Glasses and Ceramics IV, J. R. Varner and G. D. Quinn, Eds. Westerville, OH: American Ceramic Society, 2001, p. 227. [17] D. A. LaVan and T. E. Buchheit, “Strength of polysilicon for MEMS devices,” Proc. SPIE—Int. Soc. Opt. Eng., vol. 3880, p. 40, 1999. [18] D. A. LaVan, K. Jackson, B. McKenzie, S. J. Glass, T. Friedmann, J. P. Sullivan, and T. E. Buchheit, “Direct tension and fracture toughness testing using the lateral force capabilities of a nanomechanical test system,” ASTM Special Techn. Publ., no. 1413, p. 62, 2001. [19] D. A. LaVan, B. L. Boyce, and T. E. Buchheit, “Size and freqeuency of defects in silicon MEMS,” Int. J. Damage Mech., vol. 12, p. 357, 2003. [20] I. Chasitots, S. W. Cho, and K. Jonnalagadda, “Fracture toughness and subcritical crack growth in polycrystalline silicon,” J. Appl. Mech., vol. 73, pp. 1–9, 2006, to be published. [21] S. W. Cho, J. F. Cárdenas-García, and I. Chasiotis, “Nano-displacement based microscopic hole method for determination of thin film properties,” Sens. Actuat. A, vol. 120, p. 163, 2005. [22] Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics American Society for Testing and Materials, West Conshohocken, PA, ASTM C 1239-95, 1995. [23] W. N. Sharpe Jr., J. Bagdahn, K. Jackson, and G. Coles, “Tensile testing of MEMS materials – Recent progress,” J. Mater. Sci., vol. 38, p. 4075, 2003. [24] K. Sumino, “Deformation behavior of silicon,” Metall. Mater. Trans. A, vol. 30A, p. 1465, 1999. [25] G. L. Pearson, W. T. Read, and W. A. L. Feldman, “Deformation and fracture of small silicon crystals,” Acta Metall., vol. 5, p. 181, 1957. [26] J. Samuels and S. G. Roberts, “The brittle-ductile transition in silicon. I. Experiments,” Proc. R. Soc. London A, vol. 421, p. 1, 1989. [27] P. B. Hirsch and S. G. Roberts, “The brittle-ductile transition in silicon,” Philos. Mag. A, vol. 64, no. 1, p. 55, 1991. [28] C. S. John, “The brittle-to-ductile transition in pre-cleaved silicon single crystals,” Philos. Mag., vol. 32, p. 1193, 1975. [29] M. Brede, “The brittle-to-ductile transition in silicon,” Acta Metall. Mater., vol. 41, no. 1, p. 211, 1993. [30] D. Hull, Fractography: Observing, Measuring and Interpreting Fracture Surface Topography. Cambridge, U.K.: Cambridge University Press, 2000, pp. 121–55. [31] I. Chasiotis, S. W. Cho, and K. Jonnalagadda, “Fracture toughness and subcritical crack growth in polycrystalline silicon,” J. App. Mech., vol. 73, p. 1, 2006. [32] T. E. Buchheit, S. J. Glass, J. R. Sullivan, S. S. Mani, D. A. LaVan, T. A. Friedmann, and R. Janek, “Micromechanical testing of MEMS materials,” J. Mater. Sci., vol. 38, p. 4081, 2003. [33] H. Tada, P. Paris, and G. Irwin, The Stress Analysis of Cracks Handbook, Third ed. New York: The American Society of Mechanical Engineers, 2000.

190


[34] H. Kahn, N. Tayebi, R. Ballarini, R. L. Mullen, and A. H. Heuer, “Fracture toughness of polysilicon MEMS devices,” Sens. Actuators, vol. 82, pp. 274–280, 2000. [35] K.-S. Chen, A. Ayon, and S. M. Spearing, “Controlling and testing the fracture strength of silicon on the mesoscale,” J. Am. Ceram. Soc., vol. 83, p. 1476, 2000. [36] T. E. Buchheit, C. C. Bataille, J. R. Michael, and B. L. Boyce, “Microstructure and reliability of surface micromachined polysilicon used for MEMS,” in Proc. ASME Int. Mech. Eng. Congr. Exhib.. New York: American Society of Mechanical Engineers, Micro-Electromechanical Systems Division Publication, 2003, vol. 5, p. 187. [37] D. Son, J.-J. Kim, T. W. Lim, and D. Kwon, “Evaluation of fracture properties of silicon by combining resonance frequency and microtensile methods,” Thin Solid Films, vol. 468, p. 167, 2004. [38] S. Kamiya, J. Kuypers, A. Trautmann, P. Ruther, and O. Paul, “Annealing temperature dependent strength of polysilicon measured using a novel tensile test structure,” Proc. IEEE International Conference on Micro Electro Mechanical Systems (MEMS), p. 185, 2004. [39] M. J. Chou, T. J. van der Meulen, R. Hammer, and J. Cahil, “Auger and ellipsometric study of phosphorus segregation in oxidized degenerate silicon,” Appl. Phys. Lett., vol. 24, p. 200, 1974. [40] J. S. Johannessen, W. E. Spicer, J. F. Gibbons, J. D. Plummer, and N. J. -Si interface,” Taylor, “Observation of phosphorus pile-up at the J. Appl. Phys., vol. 49, p. 4453, 1978. [41] W. B. Ying, Y. Mizokawa, Y. Kamiura, K. Kawamoto, and W. Y. Yang, “The chemical composition changes of silicon and phosphorus in the process of native oxide formation of heavily phosphorus doped silicon,” Appl. Surf. Sci., vol. 181, p. 1, 2001. [42] J. Büttner, N. Huber, M. Burns, and O. Kraft, “Reliability assessment of a gas microsensor,” IEEE Trans. Device Mater. Rel., vol. 4, no. 3, 2004. [43] A. McCarty and I. Chasiotis, “Prediction of failure of non-uniform MEMS geometries,” Thin Solid Films, 2006, to be published. [44] N. N. Nemeth, L. J. Evans, O. M. Jadaan, W. N. Sharpe Jr., M. A. Trapp, and G. M. Beheim, “Fracture strength of single crystal silicon carbide microspecimens versus weibull size effect predictions,” Thin Solid Films, Feb. 2005, submitted for publication. [45] N. N. Nemeth, O. M. Jadaan, and J. P. Gyekenyesi, Lifetime Reliability Prediction of Ceramic Structures Under Transient Thermomechanical Loads NASA Rep. NASA/TP—2005-212505, 2005. [46] O. M. Jadaan, N. N. Nemeth, J. Bagdahn, and W. N. Sharpe Jr., Probabilistic Weibull Behavior and Mechanical Properties of MEMS Brittle Materials, vol. 38, no. 20, p. 4087, 2003. [47] A. McCarty and I. Chasiotis, “Quantitative failure analysis for MEMS materials with multiple active flaw populations,” Proc. Soc. Exper. Mech., no. 214, p. 1103, 2005.

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Brad L. Boyce received the B.S. degree in metallurgical engineering from Michigan Technological University in 1996 and the M.S. and Ph.D. degrees in materials science and engineering from the University of California at Berkeley in 1998 and 2001, respectively. He is a Principal Member of the Technical Staff at Sandia National Laboratories in Albuquerque, New Mexico. His primary research interests are in mechanical performance and reliability of structural materials and MEMS materials. Dr. Boyce is a Key Reader for Metallurgical Transactions, and a Hertz Fellow.

J. Mark Grazier is a Principal Technologist at Sandia National Laboratories in Albuquerque, NM. He is a key member of the experimental micromechanics laboratory within Sandia’s Materials and Process Sciences Center. Prior to working at Sandia, he spent over 10 years in petroleum industry laboratory environments. He has a broad range of expertise and over 22 years of experience on experimental mechanical behavior studies ranging from the development of novel MEMS mechanical test platforms, to mechanical behavior of solder materials, to geomechanics.

Thomas E. Buchheit received the B.S. degree in mechanical engineering from the New Jersey Institute of Technology, Newark, in 1989 and the M.S. and Ph.D. degrees in materials science and engineering from the University of Virginia, Charlottesville, in 1991 and 1995, respectively. Since 1995, he has been employed as a Postdoctoral appointee and then a Staff Scientist at Sandia National Laboratories, Albuquerque, NM, and is presently a Principal Member of the Technical Staff. His research interests focus on mechanical behavior in small volumes. Dr. Buchheit is a member of MRS, and former chapter chair of ASM.

Michael J. Shaw received the B.S. and M.S. degrees in materials science and engineering from Rensselaer Polytechnic Institute of Troy, NY, in 1999 and 2001, respectively. Since 2001, he has worked as a Member of Technical Staff in the MEMS Science and Technology Organization at Sandia National Laboratories. He is currently a Senior Member of Technical Staff in the MEMS Science and Technology organization with responsibility for Waveguide fabrication technology, SUMMiT V Surface Micromachine technology and several novel DRIE and molded silicon MEMS technologies.