A kinetic study of indentation pop-out in Si

by 1971- Wen, Songqing

The kinetics of the phenomenon of pop-out during nanoindentation of silicon were studied by a variety of mechanical and structural characterization techniques. Popout is commonly viewed to result from the reversal of a unique pressure-induced, volume reducing phase transformation that occurs in silicon and germanium. The mechanical characteristics were examined by standard nanoindentation methods using a number of triangular pyramidal indenters with centerline-to-face angles varying in the range 35°-85°. The load at which pop-out occurs was systematically measured as a function of indenter angle, loading/unloading rate, and maximum load. Nanoindentation tests were conducted both at a constant loading rate and by step unloading to fixed percentages of the maximum load. In the step unload tests, the pop-out occurred after a delay time that was measured for periods up to 30 minutes. A limited number of elevated temperature tests were performed at 45°C to establish the temperature dependence of the rate controlling mechanism. The phases that form during indentation were investigated by micro-Raman spectroscopy, cross-sectional transmission electron microscopy, and high resolution electron microscopy. It was found that the primary transformed phase after unloading at fast rates and low maximum loads is amorphous, with occasional observations of some Si-I (diamond cubic) embedded in the amorphous matrix. These structures correspond to no pop-out during unloading. At slower unloading rates and higher maximum loads, popout is observed, and the structure of the transformed material is a mixture of nanocrystalline phases including Si-XII (rhombohedral), Si-III (body centered cubic), and v Si-I (diamond cubic), along with some amorphous silicon. The volume of the transformed zone depends on the indenter angle, with the sharper indenters tending to produce smaller transformed volumes and extruded material. A kinetic model was developed that accounts for most of the experimental observations based on the assumption that pop-out is a thermally activated process corresponding to the homogeneous nucleation of Si-XII from the high pressure Si-II phase (?-tin structure) followed by rapid growth of metastable nano-crystalline material. If the unloading rate is so fast that there is not enough time for the formation of a nucleus during the unloading period, the material transforms to amorphous via a structural frustration process. Comparison to experimental data shows that the model has reasonable qualitative and semi-quantitative predictive capabilities. vi