以吸附電壓量測微懸臂樑之殘留應力之改進

Abstract

微機電懸浮結構在製程中容易因殘留應力的影響而導致變形。而利用吸附電壓來量測殘留應力具有可在產線上直接量測的潛力，因此受到重視。而以往利用吸附電壓量測殘留應力的相關文獻中，並未考慮懸臂樑之旋轉角變形量的影響。本篇論文提出一修正之變形之函數，除了考慮了梯度應力造成之懸臂樑翹曲外,並包含了軸向應力造成之懸臂樑固定端的旋轉，進而推導出變形懸臂樑之吸附電壓的解析解。 在製作方面，本篇論文利用多晶矽製作出多組測試結構，每組測試結構包含三個長度分別為256□m、300□m以及330□m的懸臂樑，以白光干涉儀量測微懸臂樑之表面輪廓以及曲率半徑，得到變形函數之參數，並實際量得各懸臂之吸附電壓後，再與利用解析解得到之吸附電壓值進行比對。 由比對結果得知，有考慮旋轉角時，推算出的吸附電壓與實驗值相比，誤差範圍在-4.44%至5.26%之間，而未考慮旋轉角的吸附電壓與實驗值相比之誤差範圍則在6.02%至15.20%之間。此結果可證實本篇論文所提出之變形函數能有效降低吸附電壓理論值與量測值之誤差。

Residual stress due to the fabrication process might cause the deformation of MEMS devices. Using pull-in voltage to determine residual stress is possible to directly detect residual stress on MEMS fabrication process. In previous studies using pull-in voltage to detect residual stress, the tilting effect of cantilever beam was not been taken into consideration. This study proposed a modified deformation function, which considered both curl and tilt deformation caused by gradient stress and mean stress. And this proposed deformation function was used to evaluate the pull-in voltage of the cantilever beam. In test experiment, the cantilever is made of poly-silicon, with three different lengths, 256um, 300um and 330um. The tilt angle and radius of curvature can be determined by white light interferometer (WLI). By comparing the analytical result with measurement results on pull-in voltages, it is found that without considering tilting effect, the average mismatch between analytical solutions and experimental results on pull-in voltage is in a range of 6.02% to 15.20%. On the other hand, when tilting effect is considered, this mismatch is reduced to a range of -4.44% to 5.26% which verifies the improvement of the proposed analytical solution.