Ž . Sensors and Actuators 84 2000 310–314 www.elsevier.nlrlocatersna On the thermal expansion coefficients of thin films Weileun Fang ) , Chun-Yen Lo Power Mechanical Engineering Department, National Tsing Hua UniÕersity, Hsinchu 30043, Taiwan Received 9 July 1999; received in revised form 15 November 1999; accepted 21 December 1999 Abstract Ž . The coefficient of thermal expansion CTE is an important mechanical property for thin film materials. There are several problems that arise from the thermal expansion effect; for example, the mismatch of thermal expansion between the thin films and the underlying substrate may lead to residual stresses in the thin films. On the other hand, the thermal expansion effect can be exploited to drive microactuators. The CTEs of Al and Ti thin films were determined in the present study using the bilayer microcatilever technique. The contribution of this paper is to demonstrate the variation of the thin film CTE with the film thickness. The CTE of the Al thin film changes from 18.23 =10 y6 r8C to 29.97 =10 y6 r8C, when the film thickness increases from 0.3 to 1.7 mm. The CTE of the Ti thin film changes from 21.21 =10 y6 r8C to 9.04 =10 y6 r8C, when the film thickness increases from 0.1 to 0.3 mm. Further, the concept that thin film CTE may be influenced by the defects in thin film materials is proposed. Thus, a desired thin film CTE can be obtained by tuning the film thickness as well as the deposition conditions. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Thermal expansion coefficients; Thin film 1. Introduction Thermal expansion is an important mechanical behavior in the areas of microelectronics and microelectromechani- Ž . cal systems MEMS . There are several problems that arose from the thermal expansion effect, for instance, the mismatch of thermal expansion between the thin films and the substrate may lead to residual stresses in the thin films wx 1 . Thus, the electronic devices as well as the microma- chined structures will be damaged or deformed by this effect. On the other hand, the thermal expansion effect can w x be exploited to drive microactuators 2,3 . In order to design micromachined components as well as microelec- tronics devices properly, it is necessary to characterize the Ž . coefficient of thermal expansion CTE for thin film mate- rials. There are several available techniques used to mea- w x sure the CTE of bulk materials 4–7 . However, the thick- ness of the films are too small to be determined using the w x conventional optical techniques 4–7 . Although the X-ray ) Corresponding author. Tel.: q 886-3-574-2923; fax: q 886-3-572- 2840. Ž . E-mail address: fang@pme.nthu.edu.tw W. Fang . diffraction method can be used to measure the CTE of thin film materials, it is only appropriate for crystalline struc- w x tures 8–10 . The idea of determining thin film CTE with w x an ellipsometer was available 11 . However, the variations in thickness induced by factors other than thermal expan- w x sion were not considered. In Ref. 12 , the thermal expan- sion coefficient of thin film materials was determined Ž using the deformation of micromachined cantilever micro- . cantilever . Thus, the thermal expansion of the film with a very small thickness can be determined accurately in this manner. It is obtained that the mechanical properties of thin wx films, such as the residual stresses 1 and the elastic w x constants 13 , may not be the same as those of the bulk materials. The mechanical properties of thin films can even depend upon the film thickness and the fabrication pro- w x cesses used 14 . Hence, it is more reliable to directly characterize the mechanical properties from the thin film to be determined. In this study, the approach presented in w x Ref. 12 is exploited to determine the CTEs of the alu- minum and titanium films. The variation of the CTEs of Al and Ti films with their film thickness is also discussed. According to the experimental results, the difference of the CTE between the bulk and thin film materials is signifi- 0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0924-4247 00 00311-3