Simple nanoindentation-based method for determining linear thermal expansion coefficients of micro-scale materials
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Simple nanoindentation-based method for determining linear thermal expansion coefficients of microscale materials Yuanbin Qin1 , Zhiyu Nie1, Chao Ma2, Longchao Huang1, Yueqing Yang1, Qinqin Fu1, Weifeng He3, Degang Xie1,a) 1 Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, P.R. China 2 Center for High Resolution Electron Microscopy, College of Materials Science and Engineering, Hunan University, Changsha 410082, P.R. China 3 Science and Technology on Plasma Dynamics Laboratory, Air Force Engineering University, Xi’an 710038, P.R. China a) Address all correspondence to this author. e-mail: [email protected]
Received: 17 August 2020; accepted: 29 October 2020
The thermal expansion coefficient (CTE) is a vital design parameter for reducing the thermal-stress-induced structural failure of electronic chips/devices. At the micro- and nano-scale, the typical size range of the components in chips/devices, the CTEs are probably different from that of the bulk materials, but an easy and accurate measurement method is still lacking. In this paper, we present a simple but effective method for determining linear CTEs of micro-scale materials only using the prevalent nanoindentation system equipped with a heating stage for precise temperature control. By holding a constant force on the sample surface, while heating the sample at a constant rate, we measure two height–temperature curves at two positions, respectively, which are close to each other but at different heights. The linear CTE is obtained by analyzing the difference of height change during heating. This method can be applied to study the size effect or surface effect of CTE of embedded micro-scale structures, aiding the failure analysis and structural design in the semiconductor industry.
Introduction With the development of micro-nano fabrication techniques, the size of semiconductor devices has been reduced rapidly and the application of micro- and nano-scale materials is more and more extensive, such as large-scale integrated circuits (IC), microelectromechanical systems (MEMS), light-emitting device, and electronics packaging [1]. One of critical factors that threatens the reliability of these chips/devices/systems is the mismatch of thermal expansion coefficient (CTE) between unit structures made of different materials, which introduces residual strain to not only affect the performance of devices but also cause deformation or even structural failure. On the other hand, many thermally driven MEMS devices depend significantly on the linear CTEs [2, 3]. Therefore, the accurate measurement of linear CTEs of micro- and nano-scale materials is vital for optimizing device structure, improving thermal stability and service life of devices. However, many studies show that the linear CTEs of micro- and nano-scale materials are not necessarily the same as that of the bulk materials.
Taking TiN thin films with thickness of several micrometers as an example,
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