测量微悬臂梁曲率的相移显微干涉法

Curvature measurement of micro cantilever based on phase-stepping microscopic interferometry

提出了一种基于显微干涉和有限差分法在微悬臂梁上实现曲率精确测量的方法。该方法将使用相移显微干涉法测得的微悬臂梁表面弯曲信息与用有限差分法解析的弯曲量进行对比,再运用拟牛顿算法或最小二乘法得到曲率的最佳匹配值。实验结果表明:使用该方法可获得弯曲量测量值和解析值之间的均方根差值在1.5 nm以内的精确曲率值,并且一定的像素偏移带来的误差对曲率测量的结果影响很小。由于方法保留了光学干涉法高分辨率及高精度等优点,并考虑了非理想边界条件的影响,在MEMS残余应力和应力梯度测量中具有较大实用价值。

A curvature measurement method based on microscopic interferometry and finite difference method is proposed to extract the curvature of micro cantilevers accurately. In comparison of the measured vertical height data obtained via microscopic interferometry with the modeled data from finite difference method, the best fitted value of curvature is obtained employing quasi-Newton search algorithm or least square method. The experimental results show that precise curvature value can be obtained within rms 1.5 nm, and if measurement is not taken at the actual beginning of the beam but with pixels of offset in the direction of the beam length, the result of curvature is hardly influenced. Experimental results also show the method is very practical in MEMS measurement of residual stress and stress gradient using microscopic interferometry to provide high resolution and accuracy and nonzero boundary condition to refine the beam model.