Nano-indentation-bending method to identify the residual stresses of MEMS films
J.H. Kim, J.G. Kim, J.H. Hahn, H.Y. Lee, Y.H. Kim
Seoul National University, KR
Keywords: residual stress, nano-indent, MEMS, thin films, surface micromachining
Surface micro-machined MEMS frequently suffer from the residual stress which might significantly decrease the performance and reliability of micro devices. It is important to accurately measure the residual stresses at manufacturing step. The Stoney’s equation has been widely adopted for the measurement of the residual stresses. However, only average stresses over entire wafer or specimen die is obtained although local residual stresses may differ from the average stress. Numerous approaches have been tried to increase the accuracy of residual stress measurement, for example, the XRD test , the vibration method , and so on .
The present study proposes an in-situ measurement method to identify local residual stresses of MEMS thin films. The present method makes use of the phenomenon that residual stress changes the stiffness of micro bridges. Zhang reported similar method to accurately measure residual stress in MEMS films . However, Zhang’s model deals with only tensile residual stress, therefore, it can’t be applicable to general case.
In the present study, general analytic model will be presented that can applied to measure tensile residual stress as well as compressive residual stress. Tensile residual stress stiffens micro bridges but conversely compressive residual stress softens them. Nano-indenter is utilized to assess the stiffness of micro bridges by applying tiny load to the center of micro bridges and recording the load-displacement relationship. Figure 1 shows the analytic model for the residual stress in micro bridge. Note that the analytic model is different by the sign of the residual stress in the bridge (compressive or tensile). Figure 2 demonstrate that the present analytic model shows good agreement with the FEA (Finite Element Analysis) results. Nonlinear effect by large deformation may cause deviation between the analytic model and FEA as shown in the figure. The experiment will be performed in linear range to avoid the nonlinear effect.
Figure 3 shows 2.33 um poly-silicon bridges fabricated for the measurement. Figure 4 shows experimental results of the nano-indentation-bending test that reveals the residual stress of the poly-silicon film is 132.4 MPa.
The present method is capable of measuring local compressive as well as tensile residual stresses in MEMS films with high accuracy. The method needs no additional electric components such as electrodes and insulating layer. The measurement can be performed in-situly in the middle of the conventional surface micromachining process. In the conference site, comprehensive experimental results will be presented to demonstrate the reliability and the convenience of the present method.
NSTI Nanotech 2003 Conference Technical Program Abstract