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.