Mechanics and Tribology of MEMS Materials - prod.sandia.gov ...

More documents

Recommendations

Info

the polycrystal, with maximum and minimum stress location, indicated on the figure, at or near boundary triple point junctions. The wide variation in predicted stress is caused by the variable constraints imposed within and between grains caused by the different anisotropic response imparted by their neighbors. Inspection of the stress-distribution indicates that boundary triple point junctions act as stress-concentrating features in the simulations. In the absence of other geometric discontinuities, i.e. corners, notches or surface roughness, these junctions are the only stress concentrating features, thus they serve as fracture initiation sites within the simulation. A primary goal of this short article is to model the statistical variation in fracture strength of polysilicon cause by stress concentrations induced by microstructure features. Fig. 3.3. (a-b) Distribution of stress after 1% tensile strain in a simulation using EBSD derived polysilicon microstructure templetes. Boundary conditions applied to the simulations are illustrated in (a). A series of 100 identical tensile test simulations to 1% strain were performed on the poly12 and poly3 meshed microstructure templates. In each simulation, different crystallographic orientations were assigned to the grains in the templates, but the microstructure morphology defined by the templates remained the same. Fig. 3.4 illustrates the location of maximum stress after 1% strain from each simulation on both templates. Maximum stress values often occurred more than once at the same locations. In these cases, the number of times a maximum stress value occurred at a specific location is labeled. As expected, nearly all maximum stress locations are located at or near boundary triple junctions, many near triple junctions containing free-surface boundaries. In the poly12 template results, a large number of maximum stress locations are also located near the boundary separating the two polysilicon layers. Another characterisitic of the maximum stress locations is that one of the boundaries forming the triple junctions where the maximum stress is located is parallel to the applied tensile 36
direction. Also, maximum stress locations are denser in regions where the grain sizes are smaller, simply because the density of boundary triple junctions is higher in these regions. These regions are near the bottom of the poly3 template and the bottom layer in the poly12 template. Fig. 3.4. (a-b) Maximum stress locations from 100 simulations to 1% tensile strain. Each simulation used the same polycrystal templates with different crystallographic orientations assigned to the grains. The maximum stress values obtained from the 100 simulations to 1% strain are statistically distributed and can be plotted using a Weibull analysis, as described in the previous section. A large value of maximum local stress in a simulated polycrystal corresponds to a sample that would fail at a correspondingly small globally applied stress. Thus, to distribute the data for Weibull analysis in a manner comparable to the experimental results presented in the previous section, the maximum stress data is ranked in reverse order. By using the probability estimator, given in the previous section, then plotting the data against the natural log of the inverse of the maximum stress values, a Weibull plot comparable to the experimentally determined plots given in the previous sections is generated. Fig. 3.5 illustrates the plot. In Fig. 3.5 the poly12 distribution lies to the right of the poly3 distribution. This is caused by the presence of the interlayer boundary oriented parallel to the tensile direction in the poly12 section. This boundary increases the number of critical flaws, slightly increasing the possibility of larger maximum stress values after 1% strain and shifting the poly12 distribution to the right in Fig. 3.5. This shift corresponds to a lower average global failure strength in the poly12 ligaments. The spread of both distributions , which defines the Weibull modulus, is nearly indentical. Estimates of the Weibull modulus based on the plot in Fig. 3.5 are m ≈ 35, indicating 37
Page 1 and 2: SANDIA REPORT SAND2004-1319 Unlimit
Page 3 and 4: SAND2004-1319 Unlimited Release Pri
Page 5 and 6: Contents ACKNOWLEDGEMENTS..........
Page 7 and 8: 6.5 Summary........................
Page 9 and 10: List of Figures Figure 1.1 SEM micr
Page 11 and 12: Figure 6.2 Contact between an elast
Page 13 and 14: Preface Our team was involved in a
Page 15 and 16: strength. The subsequent chapter di
Page 17 and 18: Fig. 1.3. SEM image of cylindrical
Page 19 and 20: Fig. 1.5. Schematic of primary feat
Page 21 and 22: Fig 1.7 Double-hinged pull-tab tens
Page 23 and 24: Fig 1.10. SEM image of optical forc
Page 25 and 26: 2 Strength Distributions in SUMMiT
Page 27 and 28: 2.2 Critical Flaw Size Evaluation T
Page 29 and 30: Fig. 2.5. SEM micrograph of pull-ta
Page 31 and 32: (1) Differences in surface roughnes
Page 33 and 34: 3 The Role Of Microstructure In SUM
Page 35: crystallographic orientation of a g
Page 39 and 40: 3.4 References 3.1 Randle, V., Micr
Page 41 and 42: has the advantage of distributing t
Page 43 and 44: and servovalve at a strain rate of
Page 45 and 46: 4.6 References 4.1. TJ Garino, AM M
Page 47 and 48: microscopy studies. As a first step
Page 49 and 50: Fig. 5.2. Orientation imaging of a
Page 51 and 52: Fig. 5.5. Orientation imaging of a
Page 53 and 54: 6 Novel Techniques for Measurement
Page 55 and 56: of adhesion, and, (iv) a smaller co
Page 57 and 58: Force (mN) Fig. 6.5. Typical load-d
Page 59 and 60: 7 Impact of Silane Degradation Due
Page 61 and 62: All samples were coated with alkyls
Page 63 and 64: the friction structure and the cali
Page 65 and 66: 7.4 RESULTS 7.4.1 Simulation of dos
Page 67 and 68: Dose (MeV/g) Fig. 7.4. Results of X
Page 69 and 70: heating on contact angle for PFTS.
Page 71 and 72: the C-C backbone of the PFTS molecu
Page 73 and 74: The increase in static friction for
Page 75 and 76: 8 Friction and Wear of Selective Tu
Page 77 and 78: During processing of microelectrome
Page 79 and 80: actuator. After unloading, the devi
Page 81 and 82: 9 Conclusions and Recommendations T
Page 83: 10 Distribution 3 MS 0889 M.T. Dugg

Mechanics and Tribology of MEMS Materials - prod.sandia.gov ...

Create successful ePaper yourself

Delete template?

Save as template?