Influence of eccentric nanoindentation on the top surface of silicon micropillar arrays

Silicon micro- and nanopillars have been widely used in various scientific and industrial fields including environmental monitoring and energy harvesting. Reliable application of these low-dimensional materials demands quantitative characterization of the mechanical properties of silicon pillars. Based upon the nanoindentation technique, one of the typical techniques for material testing at nanoscale, the department 5.1 has developed a verified methodology for quantitative nanomechanical characterization and evaluation of silicon pillars with high-aspect ratios and nearly perfect 3D forms, in which typical nanoindentation tests have been performed at the center of micro- and nanopillars. [1,2].

In practice, however, it becomes evident that eccentric nanoindentation on micro and nano-pillars will appear due to in-plane drift, especially in the case of long-time measurement of pillar arrays. Furthermore, nanoindentation at the center of pillars becomes rarely realizable, especially for silicon pillars with imperfect 3D form. In both cases, noticeable measurement deviation has been found. To determine and thereafter model the measurement deviations as a function of eccentricity of nanoindentations on pillars (as shown in Fig. 1(a)), comprehensive experimental investigation has been carried out.

As illustrated in Fig. 1(b), a series of depth-controlled indentations with a diamond Berkovich indenter were performed on the top surfaces of Si micropillars with variable eccentricity. The measured mechanical properties of Si pillars (i.e. indentation hardness HIT and reduced moduli Er ) are directly interpreted from nanoindentation curves with the standard Oliver and Pharr model.
First measurement results illustrated in Fig. 1(b) indicate that EIT on the micropillar shows smaller values compared to the bulk substrate and follows a parabolic dependence on the eccentricity, i.e., the distance of indentation from the center point. After 320 nm from the center, the indentation result exhibited a deviation of 10 percent from the measured EIT at the center. However, HIT remains nearly unchanged even when the eccentricity of nanoindentation rises to nearly 90%.

Detailed measurement data analysis indicates that EIT is following a parabolic dependence on the eccentricity, as shown in Fig. 1(b). It is worthwhile to mention that similar phenomena have also been found for silicon samples with different crystal orientations, e.g. Si<110> and Si<111>. It has been anticipated that the aforementioned experimental investigations can help to further improve the measurement accuracy of nanomechanical characterization of micro- and nano-pillars.

Abb. 1(a) Schema der zentrischen und exzentrischen Nanoindentationstests von Mikrosäulen.	Abb. 1(b) Indentationsmodul und Härte von Si <100> Mikrosäulen über dem radialen Abstand vom Zentrum.

Literature
[1] Z. Li, S. Gao, F. Pohlenz, U. Brand, L. Koenders, E. Peiner, “Determination of the mechanical properties of nano-pillars using the nanoindentation technique”, Nanotechnology and Precision Engineering 3 (2014), pp 182 – 188.
[2] G. Hamdana, P. Puranto, J. Langfahl-Klabes, Z. Li, F. Pohlenz, M. Xu, T. Granz, M. Bertke, H. S. Wasisto, U. Brand, E. Peiner, “Nanoindentation of crystalline silicon pillars fabricated by soft UV nanoimprint lithography and cryogenic deep reactive ion etching”, Sensors and Actuators A 283 (2018) pp 65–78; doi.org/10.1016/j.sna.2018.09.035.
[3] W.C. Oliver, G.M. Pharr: J. Mat. Res. 7, 1564, (1992)