Size and Temperature Dependent Behavior

In Situ Study of Size and Temperature Dependent Brittle-to-Ductile Transition in Single Crystal Silicon

Silicon based micro and nano scale devices operating at various temperatures are ubiquitous today. However, thermo-mechanical properties of silicon at small scale and their underlying mechanisms remain elusive. Brittle to ductile transition (BDT) is one of such properties relevant to these devises. Materials can be brittle or ductile depending on temperature. BDT happens over a small range of temperature. For bulk silicon, BDT is within a few degrees of 545degreeC. It is speculated that BDT temperature of silicon may decrease with size at nanoscale. However, recent experimental and computational studies have provided inconclusive evidence, and are often contradictory to each other. Potential reason for the controversy might originate from the lack of an in situ methodology that allows to vary both temperature and sample size. Here we resolve the controversy by carrying out in situ thermo-mechanical bending tests on SCS samples with concurrent control of these two key parameters. We unambiguously show that BDT temperature reduces with sample size. For example, BDT temperature decreases to 293degreeC for sample size 720nm. We propose a mechanism based model to interrupt the experimental observations [1].Size Dependent Yield Strength in Single Crystal Silicon

In this work, I have developed an isotropic elastic continuum based model to explore size dependent plasticity in single crystal silicon (SCS) under the influence of stress gradient. The model accounts for dislocation interactions under strong influence of free surface and stress gradient associated with sample size, and their effect on the onset of plasticity in SCS. The model predicts that stress concentration factor due to dislocation pile-up decreases by up to 82% with increase in stress gradient. This result indicates that material yield is intrinsically coupled with stress gradient. For a SCS sample subjected to a pure bending moment, stress gradient for a given maximum bending stress at surface is inversely proportional to sample size and hence effective yield strength increases as sample size decreases. In addition, the model predicts that size dependence becomes more important for materials with large Peierls stress, e.g., SCS and SiC due to covalent atomic bonds. We validate the theoretical predictions by experimentally carrying out in situ thermo-mechanical testing with nano to micro scale SCS samples. As predicted by our model, experimental data show increase in yield with decrease in sample size, for example, about 260% increase in yield strength with sample size reduction from 8.7μm to 720nm [2].

Reference

1. W. Kang and T. Saif, Size and Temperature Effect on Brittle-to-Ductile Transition in Single Crystal Silicon, 23(6), 713-719, Advanced Functional Material, 2013.
2. W. Kang and T. Saif, Size Effect on Yield Strength of Single Crystal Silicon, Journal of the Mechanics and Physics of Solids, 2015 (in preparation).