Measurement of Young's Modulus on Microfabricated Structures Using a Surface Profiler

A point-force, load-deflection method using a stylus-type surface profiler to determine the Young's moduli (Ey ) of thinfilm microstructural materials is introduced. In this method both force and deflection in microstructures are measured simultaneously by the profiler to provide a convenient and accurate means to obtain Young's modulus directly. Measurements on two types of micromechanical structures are described: a doubly supported bridge and a bridge-slider (a beam with one fixed end and one end which can slide in a flanged housing). The influence of residual stress in the doubly supported beam is described and accounted for theoretically to interpret measurements made on low-stress silicon-nitride films. For this material Ey is 373 GPa. In the bridge-slider structure, residual strain is relaxed to zero. Measurements on a polycrystalline-silicon bridge slider show a value for Ey of 123 GPa in unannealed material that is doped heavily with phosphorus, and grown at 650°C. L INTRODUCTION Three methods have been identified in previous research as useful to measure the Young's moduli of thin-film materials. The first of these makes use of measured wafer warpage under the stress imposed by coating with the thin-film material. Typically, either a range of coating thicknesses are used [1], or else the temperature is varied [2]. A second method uses measurements made on the deflection of membranes of the thin-film material that are subjected to differential pressures [3,4]. The third technique is based upon measurements of the resonant frequency f, of vibrating structures such as cantilevers or doubly supported bridges [5-7]. Young's modulus is extracted from the theoretical expression for f,. All three of these methods are relatively complicated and painstaking to carry out We report here a straightforward and relatively easy point-force, load-deflection method to obtain Ey which requires only a stylus-type surface profiler, a test machine that is present in most microfabrication laboratories. In this new method, the stylus of the surface profiler scans over a free-standing structure made of the material under test. The profiler records both the stylus force and the vertical position of the free-standing structure under load. A mechanical analysis is used to determine the dependence of the structural deflection in terms of Ey for the material including the effects of residual strain, if any. The measured data is then used to extract a value for the Young's modulus of the material. IL THEORY Figure 1 shows the cross section of an arbitrarily shaped free-standing structure (an example might be a microbridge) which is loaded by a stylus force F. In the linear bending region (small deflection), the height h of the free-standing structure can be related to the loading force F by