Effects of Sample Geometry on Micro-Mechanical Property of Single Crystal Gold for Applications in Microelectronics
Authors: Fujita Kazuya , Suzuki Kosuke , Chen Chun-Yi , Chang Tso-Fu Mark , Ito Hiroyuki , Machida Katsuyuki , Masu Kazuya , Sone Masato 
Published: December 2020

This study reports mechanical properties of single-crystal pure gold toward for applications as movable components in micro-electrical-mechanical system (MEMS) inertial sensors requiring high sensitivity. Gold is commonly applied in electronic devices because of the excellent corrosion resistance, chemical stability, and conductivity. Recently, MEMS inertial sensors utilizing gold materials are reported to have low Brownian noise and high sensitivity while keeping the dimensions small by taking advantage of gold’s high mass density [1]. For design of electronic device, mechanical property characterization of the constituent material is essential. In general, mechanical strengths of metallic materials are governed by movement of the dislocation, and the dislocation movement is affected by the crystal orientation, grain boundaries, texture, impurities, etc. In addition to these, mechanical properties of metallic materials are affected by size of the sample used in the evaluation when the sample size is reduced to micro or sub-micro scale, which is known as the sample size effect [2]. This sample size effect would cause mechanical properties of micro-scale metallic materials to differ from those of bulk-size materials. Therefore, in order to make contribution to design of MEMS devices, the mechanical property characterization must be conducted using specimens having dimensions and deformation system alike components used in MEMS.
Micro-bending test is suggested to be the most suitable micro-mechanical property characterization method toward MEMS devices since movable components in a MEMS device would experience both compressive and tensile stresses during operation. Regarding the sample size effect, the strength has a power-law relationship with cross-sectional area of the specimen [2]. In bending test, the loading direction is perpendicular to the cantilever’s width direction and parallel to the thickness direction. Because of this, the width and the thickness are expected to affect the sample size effect differently. On the other hand, the dislocation movable is also highly affected by the grain boundary and eventually the sample size effect [3]. Hence, single crystalline specimen is often used to examine the sample size effect to eliminate influences from the grain boundary.
In this study, micro-cantilevers composed of single-crystal pure gold were fabricated using focus ion beam (FIB). All micro-cantilevers were ensured to have the loading direction parallel to the [1-10] orientation and the neutral plane parallel to the [110] orientation. Lengths of the micro-cantilevers were fixed at 50 μm. The thicknesses and widths were varied between 5 to 15 μm. The bending test was performed using a machine specially designed for micro-specimens developed in our group as shown in Fig. 1. The strain rate was fixed at 0.125 %/sec. Fig. 2 shows scanning electron microscope (SEM) images of the 50×9.7×10.5 μm3 micro-cantilever before and after the micro-bending test. From these images, slip lines and necking were observed at the base of the cantilever where stress and deformation were concentrated after the bending test. This slip lines indicated the active slip plane according to the Schmid’s law. The engineering stresses, σ, were calculated utilizing the Euler-Bernoulli beam theory [4]. The engineering strains are calculated from ratio of the d/y [5], where d is displacement of tip of the indenter. Fig. 3 shows engineering stress-engineering strain curves of the five micro-cantilevers. Yield stresses of the 6.9, 10.5, and 15.1 μm thick micro-cantilevers were 195, 175, and 128 MPa, respectively. Yield stress of the 4.7, 9.7, and 15.1μm width micro-cantilevers were 177, 175, and 183 MPa, respectively. These yield stresses were all lager than the value of bulk-size pure gold, which were results of the sample size effect. In addition, the yield stress increased as the thickness decreased, whereas it does not change much with the width reduction. This result suggested the sample size effect was only observed when changing the thickness, but not the width. These findings confirmed mechanical properties of micro-cantilevers were affected by the sample geometry, which is named as the sample geometry effect.
[1] D. Yamane, T. Konishi, T. Matsushima, K. Machida, H. Toshiyoshi, and K. Masu, Appl. Phys. Lett. 104 (2014) 074102
[2] J.R. Greer, W.C. Oliver, W.D. Nix, Acta. Mater. 53 (2005) 1821-1830.
[3] J.R. Greer and J.Th.M. De Hosson, Prog. Mater. Sci. 56 (2011) 654-724 (2011).
[4] K. Asano, T.F.M. Chang, H.C. Tang, T. Nagoshi, C.Y. Chen, D. Yamane, H. Ito, K. Machida, K. Masu, M. Sone, ECS J. Solid State Sci. Technol., 8 (2019) P412-P415.
[5] E. Demir, D. Raabe, F. Roters, Acta. Mater. 58 (2010) 1876-1886.

Figure 1