Observation, analysis, and simulation of the hysteresis of silicon using ultra-micro-indentation with spherical indenter
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J. S. Field Department of Mechanical Engineering, University of Sydney, New South Wales 2006, Australia
M. V. Swain CSIRO Division of Applied Physics, Lindfield, New South Wales 2070 and Department of Mechanical Engineering, University of Sydney, New South Wales 2006, Australia (Received 21 August 1992; accepted 14 December 1992)
The recently reported hysteretic behavior of silicon under indentation (Clarke et al.1 and Pharr et al.2~5) is investigated using an ultra-micro-indentation system with an 8.5 /urn spherical-tipped indenter. The onset of "plastic" behavior during loading and hysteresis during unloading was readily observed at loads in excess of 70 mN. Cracking about the residual impression was observed only at loads of 350 mN and higher. An analysis of the data is presented that estimates the following: (1) the initial onset of deformation occurs at a mean pressure of 11.8 ± 0.6 GPa, (2) the mean pressure at higher loads is 11.3 ± 1.3 GPa, and (3) the hysteretic transition on unloading occurs at mean pressures between 7.5 and 9.1 GPa. These values are in good agreement with the accepted literature values for the known silicon transformation pressures. A simulation of the force-displacement data based on the analysis and model is presented and is found to fit the observations very well.
I. INTRODUCTION 1
In a series of recent papers, Clarke et al., Pharr et al.,2~5 and Page et al.6 have studied the indentation of silicon with pointed diamond (Berkovich triangular pyramid) indenters. They argue that the hardness of this material is dictated by a pressure-induced phase transformation from its familiar diamond cubic form [Si(i), after Pharr5] to a denser /3-tin structure [Si(ll)]. This phase change involves a 22% reduction in volume and occurs under a hydrostatic pressure of =11.3 GPa, although it does not usually proceed to completion until a pressure of 12.5 GPa is applied.4 Upon release of the pressure, Hu et a/.7'8 report reversion to another form [Si(ili)] with a bcc structure. This phase has a density intermediate between Si(i) and Si(n) with approximately an 8% reduction in volume over Si(i).7 This reverse transformation is proposed to occur at a pressure of 8.5 to 10.8 GPa and, as argued by Pharr et al.,2~5 is responsible for the observed hysteresis in the low-load indentation (
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