Effect of Die-Bonding Process on MEMS Device Performance: System-Level Modeling and Experimental Verification

This paper presents a distributed nodal method (DNM) for compact modeling of the package-device interaction of microelectromechanical systems (MEMS). MEMS devices have movable structures that are sensitive to structural stresses and easily influenced by package structures and environmental parameters. Hence, it is necessary to include the packaged behavior of MEMS into a compact simulation tool with acceptable precision. The conventional nodal method is therefore modified to achieve this purpose. A node with distributed nodal quantities is defined to describe the distributed interactions among the device, package, and environmental temperature. Based on the definition, the related processes of element partition, nodal matrix formation, and element assembly have been demonstrated. The case of a die-bonded microbridge has been used as an example, since the microbridge is not only a typical MEMS structure but also is influenced easily by structural stresses. The DNM model is validated first by a finite-element method (FEM) simulation, then by two individual experiments, including the measurement of die warpage using a digital image correlation system and the detection of shifted natural frequencies of surface-micromachined bridges using a laser Doppler vibrometer system, both after die bonding. The FEM and test results agree with those evaluated by the model with a relative error of less than 10%. Stress alleviation of the test structure has been unintentionally achieved by die bonding, leading to relative shifts of 12%-26% and 19%-26% of the first and third natural frequencies of the microbridges. The packaged behavior also exhibits an evident distributed feature along the die surface as expected. Although, at current stage, the application of the DNM is still limited to static domain, it shows potential in developing hierarchical models of MEMS devices including the package.