Elasticity, plasticity and cracking at indentations in single-crystal silicon

Abstract

Indentation mechanics has been a useful tool in the analysis of hardness measurements and of the resistance to fracture [1-5]. Several types of shaped indentors have been used to determine the relative hardness and cracking resistance of essentially brittle materials. A recent study of silicon indentation results [6] demonstrated a correlation between measurements obtained with variously shaped indentor geometries and showed that plastic or inelastic deformation played an important role in determining the nature of cracking at the indentation sites, as well as the magnitude of the corresponding hardness values. An important result from that study was that plastic flow initiated in the indentation process, even for a brittle material such as single-crystal silicon at room temperature, contributes to easier cracking than should occur for cracking following on from totally elastic behaviour. This relates to the use of indentation fracture mechanics to explain Auerbach's law that the ratio of load to (indentor) ball radius is constant for the onset of cone cracking. For a fixed indentor shape a fully developed crack length proportional to the two-thirds power of the load is generally obtained. The purpose of this letter is to clarify further the role of plastic deformation for silicon in the development of the hardness impression [6] and the follow-on extent of cracking [5-7]. A combination of previous independently reported results [6, 7] is presented here, together with new {0 0 1} surface results for the indentation load dependence of the diameter or diagonal lengths, measuring the elastic, plastic and cracking responses of individual crystals. Fig. 1 shows a comparison of experimental indentation and cracking measurements on an extended load-scale basis [6]. The graph of force-dependent ball elastic contact diameters (d), plastic pyramid diagonal lengths (di) and tip-to-tip crack diagonal lengths (do) provides a basis for interpreting the progressive indentation loading behaviour. For example, on the log-log scale of Fig. 1, elastic Hertzian behaviour results in a slope of 3.0 for the theoretical relationship