Indentation-induced phase transformations in silicon as a function of history of unloading
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A crystalline silicon surface, loaded by a Berkovich indenter to a constant maximum load, was unloaded using three unload functions, each consisting of five linear segments of equal time period. The first function had an exponentially decaying unload rate and was found to promote a pop-out event more readily than the second function, having a linear unload rate, or the third case with its unload rate increasing with time. Statistical analyses of experimental data suggest that the unload rate within 20%–30% of the maximum load, when the mean contact pressure in the indent volume is roughly 5 to 6 GPa, is the most dominant factor influencing the probabilistic occurrence of a pop-out event. Unload rates at higher load levels were shown to have a much less significant effect on the probability of pop-out occurrence.
I. INTRODUCTION
Pressure-induced phase transformations in crystalline silicon (c-Si) have been of considerable scientific interest and more recently of technological interest as a result of potential applications. High-pressure experiments using a diamond-anvil cell have shown that the diamond cubic Si-I phase transforms to a metallic Si-II phase when the isostatic pressure reaches ∼11 GPa.1,2 Decompression from this pressure range causes the Si-II phase to further transform first to a crystalline high-pressure phase SiXII, which then partially transforms to another crystalline high-pressure phase Si-III on further pressure release. This process results in a mixture of Si-XII and Si-III phases subsequent to full pressure release.3,4 In the case of indentation, despite the absence of in situ diffraction data, there have been a number of studies that serve as evidence for the Si-I to Si-II transformation on indentation loading.5 Upon indentation unloading, Si-II transforms either to an amorphous phase (a-Si) or to a mixture of Si-XII and Si-III phases.6–10 An abrupt drop in indentation displacement or a so-called “pop-out event” that occurs during unloading has been shown to coincide with the formation of Si-XII/Si-III phases in the residual indent, as identified by post-indentation Raman microspectroscopy.7,9 In the absence of a pop-out event during unloading, the unloaded material was found to become predominantly amorphous as determined by Raman mi-
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0322 J. Mater. Res., Vol. 23, No. 10, Oct 2008
crospectroscopy and transmission electron microscopy measurements.6,10 The Si-II to Si-XII/Si-III transformation is a probabilistic event that requires nucleation of the end crystalline phases. A higher probability is obtained when a large volume of the transformable Si-II material is unloaded at a slow unload rate,6,8,11 consistent with a process that is kinetically limited by the nucleation of Si-XII/Si-III phases from Si-II. In this study, a crystalline silicon sample (diamond cubic Si-I) is loaded to a constant maximum load using the same loading history to keep the volume of Si-II constant prior to unload
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