A simple method for determining linear thermal expansion coefficients of thin films

Abstract

In this paper we present a simple method for determining the linear thermal expansion coefficients (LTECs) of thin films using compact micromachined structures and common experimental apparatus. The structures can be fabricated by simple silicon-based micromachining techniques with one mask process and in situ along with active devices on the same chip for monitoring the LTECs of the thin film. An analytical expression is derived to relate the LTECs of thin films with the lateral displacements of microstructures. The displacements can be measured directly under an optical microscope with the specimen placed in a heating stage. The analytical expression is free from any correction factor. Furthermore, the accuracy of LTEC determination is significantly enhanced because the analytical expression is not necessary to know the Young's modulus, the Poisson's ratio and the thickness of the thin film. A finite element model is used herein to support the analytical model and also to perform nonlinear analysis. In this research, experimental results with a heavily phosphorus-doped low-pressure chemical vapour deposition polycrystalline silicon film are used to demonstrate the effectiveness of the proposed method. According to the results, the LTEC is dependent on temperature and increases as the temperature rises. The average value of the obtained LTEC is 2.7 × 10−6 °C−1 from room temperature to 400 °C.

Polysilicon micro beams buckling with temperature-dependent properties

“…It has been reported that Fig. 4 Thermal expansion coefficient versus temperature (Pan 2002) this effect can generates a variation of analytical results about 10%.…”

“…Also, thermal expansion coefficient increase with temperature rise during micro actuator operation. The variation of thermal expansion coefficient for polysilicon is reported by Pan (2002). This report shows that polysilicon thermal expansion coefficient varies significantly over the temperature range of 450°C and higher.…”

“…The data related to the variation of Young's modulus and thermal expansion coefficient (TEC) reported in literature (Sharpe et al 2001;Pan 2002) is applied to the theoretical and numerical models (see Appendix).…”

In-situ determination of the coefficient of thermal expansion of polysilicon thin films using micro-rotating structures

“…The deflection is measured by using the optical interferometric technique. Pan has reported a structure composed of a pair of cantilever beams with different lengths connected by a short tip beam to measure the CTE of the thin film [13]. When the temperature changes, a large displacement of the tip beam induced by different expansions or contractions between the two cantilever beams has been observed and measured with an optical microscope.…”

A novel method for determining Young’s modulus of thin films by micro-strain gauges

“…The structures comprise of a pair of strain gauges with known Young's modulus and a cantilever beam made of the measured film. The strain gauge is similar to author' s previous works [26,27]. The detailed performance of the strain gauge can be found in reference [26].…”