Constitutive modeling of intrinsic silicon monocrystals in easy glide

Abstract

Articles you may be interested inLithiation-induced tensile stress and surface cracking in silicon thin film anode for rechargeable lithium battery Finite element modeling of indentation-induced superelastic effect using a three-dimensional constitutive model for shape memory materials with plasticity Elastic moduli, strength, and fracture initiation at sharp notches in etched single crystal silicon microstructures Constitutive modeling of silicon materials is currently restricted to the very early stage of deformation. Uniaxial tensile testing of monocrystals oriented for single glide is traditionally simulated by a scalar model relying on the so-called machine equation. The present work uses a crystal plasticity framework to identify the role of secondary slip systems in the yield region. A three-dimensional finite element model of a tensile apparatus is validated by comparison of its outputs to the results yielded by a scalar formulation. Best fits of the constitutive model of Alexander and Haasen to experimental data reveal strong variations in its parameters with temperature. An improved constitutive model for intrinsic silicon monocrystals deformed in single slip is described. Its parameters are identified as analytical functions of temperature. We show its excellent agreement with the observed steady state of deformation in stage I.

Constitutive Relations for Modeling Single Crystal GaN at Elevated Temperatures

“…Specifically, the [1120] (1100) slip system was inclined by 45 deg from the com pression axis. (16) and (18), we obtain relations for the applied compressive plastic strain rate and stress in terms of the shear strain rate and resolved shear stress |«22| = |fs22| =^|y | (26) |t | = |S22ff22| = -| cr221 (27) Figure 2 shows plots of the data reported in Yonenaga and Motoki [9], where the bottom and left scale are apparent shear strain, yapp, and resolved shear stress, t, respectively. The authors report an applied macroscopic shear strain rate of 4.5 x 10 4 s 1.…”

“…The authors report an applied macroscopic shear strain rate of 4.5 x 10 4 s 1. (26) and (27), where the apparent applied compres sive strain is equated to the plastic compressive strain assuming negligible elastic strains [42], The stress-strain curves at all * 2 temperatures are characterized by an apparent elastic increase in the stress, a smooth yield behavior, and a subsequent gradual increase in the stress with strain. Figure 1 shows a diagram of the oriented crystal sample, where the lattice coordinates x\ and X2 are aligned with the slip direction [1120] and opposite the slip plane normal direction (1100).…”

“…Yonenaga and coworkers have used a modified form of the original Alexander and Haasen model to describe the single slip plastic behavior of elemental semicon ductors [21], III-V compounds [22], and GaN [9]. Crystal plasticity models that extend the single slip models to con sider multislip in cubic crystal semiconductors have been devel oped by Moosbrugger [24] for CdTe, by Kalan and Maniatty [25] for InP, and by Zhang and coworkers [26] for Si. Crystal plasticity models that extend the single slip models to con sider multislip in cubic crystal semiconductors have been devel oped by Moosbrugger [24] for CdTe, by Kalan and Maniatty [25] for InP, and by Zhang and coworkers [26] for Si.…”

Silicon bulk growth for solar cells: Science and technology

“…In most reported works concerning the dislocation density in silicon crystals, [55][56][57] thermal stress is regarded as the main cause of dislocations because it drives the multiplication of dislocations in crystals. However, dislocation multiplication and dislocation nucleation are completely different phenomena.…”

“…The values of K, K + , and r c have been reported elsewhere to be as follows: 57) KðTÞ ¼ 7:6 Â 10 À1 e À0:72=k b T ðm=NÞ; ð14Þ is the stress required to overcome short-range obstacles, and ðÞ b is the internal long-range elastic stress generated by mobile dislocations.…”