Using capacitance to quantify planar geometry variances for micro electro mechanical systems structures

Joo Lien Chee, Purdue University

Abstract

I present the first quantification of planar geometry variance, between layout and fabrication, of a Micro Electro Mechanical System (MEMS) structure by performing differential capacitance and capacitive ratio measurement. Differential capacitance measurement is the difference between two capacitance measurements of the same MEMS structure, while capacitive ratio is the ratio of two differential capacitance values of two different MEMS structures. This work is motivated by the limited number of quality control standards within the MEMS industry. Geometrical and material properties are critical to the performance of most MEMS structures. Small changes in geometry due to process variations could yield stiffness that are several times larger or smaller when compared to design. The same concern can be applied to material properties especially when within the stiffness expression, Young's modulus is a variable. Conventionally, geometries of a MEMS structure are most often measured by visual inspection tools such as optical microscopy, electron microscopy, or interferometry. However, the magnitude of microfabrication process-caused geometry variance is often in the same order of magnitude as the theoretical resolution limit of optical microscopy at 0.2 μm. For electron microscopy, the ability to resolve smaller dimensions come at the high cost to purchase and maintain, the high level of technical training and expertise needed, and the long inspection turn-around time. Interferometry is a popular tool used for scanning and quantifying planar geometries for structures fabricated en masse on a wafer but the geometrical characterization is limited to pre-packaged structures. Essentially these three visual measurement methods are either expensive, requires long measurement turn-around time from a batch characterization perspective, and/or limited to pre-packaged structures. Capacitance measurement is electronic-based which requires the structure under test be probed and the parameters of the measurement can be automated. This leads to the possibility that the time taken, uncertainty, expertise required, and cost be significantly reduced. In addition, since capacitance measurements can be performed with on-chip or off-chip electronics, our method can be automated for batch measurement. The goal of this investigation is to provide a foundation on which future work can be built upon where built-in on-chip sensors for MEMS characterization can be incorporated into packaged applications. In this investigation, I had used the planar geometry quantification technique theorized by Electro Micro Metrology (EMM). EMM is a set of theoretical measurement concepts which suggest that up to three dozen MEMS geometry, material, and dynamic properties can be determined from differential capacitance, capacitive ratio, differential voltage, and frequency measurements. I test the EMM concept by using a low-cost and off-chip capacitance sensor on a Tang resonator comb drive MEMS structure. The EMM planar geometry variance measurement technique was able to quantify planar geometry variance, Δw, between layout and fabrication, of ∼2.5 μm for the Tang resonator structure microfabricated using a 30 μm-thick photoresist patterning process. In the course of this investigation, a repeatability measurement was used to determine the accuracy of our capacitance measurement testbed which had an uncertainty of ∼1 fF. The EMM method translates the measured capacitive uncertainty into the uncertainty of the planar geometry variance, δ w, which for our testbed is ∼62 nm. We compared the planar geometry variance obtained from our method against results obtained using optical microscopy, electron microscopy, and COMSOL finite element analysis (FEA) modeling. The comparison showed that EMM determined planar geometry variance results has comparable accuracy to the three comparison method, and better uncertainty than optical microscopy. To demonstrate the fast turn around of this method, we repeated the EMM measurement for 24 pairs of structures which were fabricated on a 7.5 cm diameter wafer. For comparison purposes, the same structures were inspected by electron microscopy and the largest difference between the two methods for the same structure was 0.12 μm. Noise contributions from equipment, thermal effects, environment, and their effects on the low-capacitance measurement testbed were discussed and modeled.

Degree

Ph.D.

Advisors

Clark, Purdue University.

Subject Area

Electrical engineering

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