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Fig. 3.1. (a) EBSD map of SUMMiT TM polysilicon, grid spacing 0.025µm. (b) 〈001〉 micropole figure from EBSD data. (c) 〈001〉 colorized pole figure depicting crystallographic orientation distribution. 3.2 Simulating the Response of Polycrystalline Silicon 3.2.1 Simulation Procedure To begin investigating the role of specific types of flaws on the failure of polysilicon ligaments, akin to those tested using the “pull tab” test methodology given in the previous section. A model has been implemented into finite element code that explicity captures grainscale interactions known to occur during elastic deformation of polycrystalline materials. [3.6] The fundamental material model used in the finite element simulations is an anisotropic elasticity model based on the cubic crystal structure of single crystal silicon. Single crystal silicon has three elastic constants, defined as C11=166 GPa, C12 = 64 GPa, and C44=80 GPa [3.7]. The elastic response of a grain to an applied local stress in polysilicon is dependent on the orientation of that grain relative to the stress direction, as dictated by the well-known elasticity law defined in equation (1): σ = C ε (1) i In this equation, σ and ε are tensor quantities respectively defining stress and strain in reduced index notation. C is the elastic stiffness tensor. A comprehensive description of anistropic elasticity in silicon within the context of equation (1) is given in [3.7]. Polycrystalline silicon, or polysilicon may be thought of as an agglomerate of single crystallites, or grains. Fig. 3.1 conveys this concept. The fundamental material model defined in equation (1) and the 34 ij j
crystallographic orientation of a grain, or finite element within a grain, determine its response to a local stress condition. Within a simulation, grain boundary intersections act as stressconcentrating flaws and, unless other geometric features are placed into the simulation, they dictate failure. Fig. 3.2. Digitized microstructures mapped by EBSD for finite element analysis. (a) Section of a joined poly1 and poly2 (poly12) layer and (b) section of a poly3 layer. The EBSD map given in Fig. 3.1 was used as a template for generating finite element meshes to be used in the simulations. Sample microstructures representing the poly12 and poly3 layers were digitized using sections of the EBSD map as illustrated in Fig. 3.2. Finite element meshes were paved into these templates; thus, grain boundaries and free surfaces remained straight and sharp. Series of polycrystal elasticity simulations were performed using the meshed templates. The simulations were performed with periodic boundary conditions on the front and back faces; therefore, the simulations represent a microstructure infinite in extent. Top and bottom edges were treated as free surfaces, as they would be in real polysilicon ligaments. Displacement boundary conditions were placed on the left and right edges of the finite element meshes intended to replicate tension on a polysilicon ligament. These boundary conditions are illustrated in Fig. 3.3a. A randomly assigned crystallographic orientation was assigned to each grain within a polycrystal microstructure template prior to performing a simulation. The resultant crystallographic texture of the simulated polycystals was similar to the crystallographic texture of the SUMMiT TM polysilicon given by the EBSD experiment. 3.2.2 Results and Discussion A simulated result, spatially resolved Von-Mises stress distribution in each polycrystal template after 1% tensile strain is given in Fig. 3.3. The stress-distribution varies widely across 35
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: 3 The Role Of Microstructure In SUM
Page 37 and 38: direction. Also, maximum stress loc
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

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