Observation, analysis, and simulation of the hysteresis of silicon using ultra-micro-indentation with spherical indenters

Abstract

The recently reported hysteretic behavior of silicon under indentation (Clarke et al.1 and Pharret al.2-5) is investigated using an ultra-micro-indentation system with an 8.5 μm 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.

Phase transformations in (111) Si after spherical indentation

“…It is known that hydrostatic stresses cause the transformation of Si-I to Si-II. [26][27][28] The size of this transformation zone developed beneath the indenter tip is approximately $1.25 mm wide and $160 nm deep. Unlike the hemispherical transformation zone observed at low loads on spherical indentation of (100) Si, 1-3 the transformation zone seen in Fig.…”

“…On the other hand, the hydrostatic stresses (s H ) associated with the Hertzian stress fields beneath the indenter are reported to be responsible for phase transformation in the silicon substrate. [26][27][28] Although the accepted value for the transformation of Si-I to Si-II under pure hydrostatic stress is of the order of 11.3-12.5 GPa, 27,28 the presence of shear stresses during indentation has been reported to lower the transformation pressure to 8 GPa. 18,33 Therefore, it can be assumed that values of this order are required for phase transformation.…”

Optical and mechanical properties of plasma-beam-deposited amorphous hydrogenated carbon

“…The results of each batch then are normalized on the literature hardness value of 12 GPa for silicon. 15 The hydrogen and carbon content of the films have been determined with elastic recoil detection analysis ͑ERDA͒ in combination with Rutherford backscattering ͑RBS͒. 16,17 The optical band gap has been obtained with transmission experiments in the range from 400 to 900 nm.…”

Atomic force microscopy study of nanoindentation deformation and indentation size effect in MgO crystals

“…Among the most widely discussed and controversial topics in the area of indentation hardness are (i) the dependence of microhardness on applied load, a phenomenon known as indentation size effect (ISE), [1][2][3][4][5][6][7][8][9][10][11][12] (ii) the nature of deformation beneath and around indentations, 1,11,[13][14][15][16][17][18][19] and (iii) the mechanism responsible for the appearance of hills piled up around indents. 17,19 The earlier investigations dealt with microindentation, but recently papers have also been devoted to the study of nanoindentation deformations, 3,10,17,19,20 comparison of deformation in small volumes with continuum plastic and Hertzian elastic theories, 17,19 and phase transitions 15,16,20,21 and twinning induced by indentation deformation. 11 Moreover, with an increase in load or indentation size both a decrease 9,10,20,22,23 and an increase in microhardness [5][6][7][8]…”