Self-calibration for microelectromechanical systems (MEMS) with comb drives: Measurement of flexure width, gap, displacement, force, and stiffness

Fengyuan Li, Purdue University

Abstract

In the first part of this dissertation, we present the first experimental validation process of EMM for measuring the performance-based flexure width of a pair of MEMS devices through capacitance sensing. We define the performance-based flexure width as the width that the model must have such that the performance of the model matches the performance of the true device. We validate EMM’s practicality, precision, repeatability, and ability to create experimentally accurate models. We create the first EMM test and validation process. The capacitance measurement uncertainty of our capacitance metering system is about 20 aF. Our present design and equipment prototype setup yields a width measurement uncertainty on the order of 1nm, which is about an order of magnitude better than what we are able to achieve using SEM. The ultimate of EMM uncertainty has yet to be explored. EMM theory suggests that uncertainty can be further improved by increasing deflection, improving the precision of applied voltage, reducing parasitic capacitance, improving the precision of capacitance, reducing the overall size of the device, or optimizing the design parameters. Our validation procedure includes using the conventional SEM to visually measure the width of flexures having coarse sidewalls at various axial locations. Human error and subjectivity are associated with each SEM measurement in determining the edge location of the coarse sidewalls. In fact, every time SEM measurements are made, the result varies. SEM measurements are good for inspecting local geometry details. However, SEM cannot be used to measure the performance-based width. That is, the average width obtained by SEM cannot be used for bending models because stiffness is nonlinear in width. Moreover, width varies along the thickness of the flexure, which cannot be measured by SEM. Since there are no standards for measuring width and since SEM does not provide complete validation, we instead use SEM as a bounding validation method. That is, the direction and magnitude of the measurements are comparable. For example, if the width measured by SEM is larger than layout width, then the performance-based width measured by EMM is larger as well, and about the same order of magnitude. In addition, the performance-based width measured by EMM lies within the estimated bounded range of minimum and maximum width measured by SEM. In the second part of this dissertation, we modify the original EMM theory for geometry from measuring flexure width (EMM1) to measuring gap stop (EMM2). We present the first experimental validation process of EMM2. Compared to EMM1, EMM2 reduces the number of devices to one, reduces thermal vibrations through contact, and eliminates the sensitivities to non-ideal geometries and compliant bulk material. Our results validate the EMM2 in terms of its practicality, precision, and repeatability, and also suggest its accuracy though bounding analysis from SEM measurements. The capacitance measurement uncertainties of the probing and wire bonding capacitance metering systems are about 20aF and 80 aF, respectively. With our current design and system configuration, we achieve a gap measurement uncertainty on the order of 1nm and 10nm, respectively. Our results are better than what we were able to achieve using our available SEM. The ultimate of EMM2 uncertainty has yet to be explored. EMM2 theory suggests that uncertainty can be further improved by reducing parasitic capacitance, improving the precision of capacitance, or optimizing design parameters. In the third part of this dissertation, we present how to extend the results of EMM2 measurements of gap to immediately extract measurements of displacement, force, and stiffness without any further calibration efforts. Measurements of displacement, force, and stiffness are based on accepted first principles: the comb drive’s linear relationship between capacitance and displacement, the relationship between stored potential energy and electrostatic force, and the linear force-displacement for folded flexure with small deflection. Our results validate EMM2’s practicality, precision, and repeatability for measuring displacement, force, and stiffness, and also suggest its ability to create experimentally accurate models. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Clark, Purdue University.

Subject Area

Electrical engineering|Mechanical engineering|Nanotechnology

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