Electro Micro-Metrology (EMM) is a novel methodology for precision metrology, sensing, and actuation at the micro- and nano-scale. EMM is well-suited for tiny technology because it leverages off the electromechanical benefits of the scale. EMM is the method of using micro- or nano-scale devices to measure and characterize themselves, other devices, or whatever the devices subsequently interact with. By electronically measuring the change in capacitance, change in voltage, and/or resonant frequency of just a few simple test structures, a multitude of geometric, dynamic, and material properties may be extracted with a much higher precision than conventional methods. In essence, EMM is a new and powerful measurement tool for the tiny technologists.
Although microsystem technology is becoming a well-established industry, testing standards for their properties are still under development. There are several problem areas associated with conventional metrological techniques. Some of the typical issues are: 1) the measurements require highly specialized equipment; 2) the equipment is costly and not readily accessible to most researchers in the field; 3) the properties obtained are averaged over a large area of the wafer; 4) a large amount of chip real estate or a chip’s worth of test structures are required; 5) the setup and data collection process is time consuming; 6) the methods require highly specialized training; 7) the measured property depends on other properties that are not well-known; 8) results containing uncharacterized dependencies are often open to misinterpretation; 9) the testing methods are not standardized, yielding arguable results; 10) each technique extracts only about one property; 11) the accuracy is poor1; 12) the precision is poor, often only providing one or two significant digits; 13) the methods are difficult to automate and require human interaction; 14) the testing apparatus is usually not portable and orders of magnitude larger than the device being tested; 15) some test methods are destructive; 16) the methods are not well-suited for batch fabricated testing; and 17) conventional metrology techniques are not designed to be performed outside of the laboratory, in the field, or after the device is packaged. These issues are compounded at the nanoscale.
The methods described herein do not suffer from any of the above issues. We present novel methods which conform well at the micro- and nano-scale by utilizing the beneficial aspects of the scale such as the precise sensing and actuation capabilities of micro electromechanical systems. Moreover, all measurements are based on the actual performance of the device. This is important because it is the performance of the device that system designers and users care about most. We present techniques that differ from conventional techniques in practicality and that none of the geometric, dynamic, or material property values of the fabricated devices are presumed. Only on- or off-chip, capacitively-based measurements are required.
In this dissertation we describe the methods and application of Electro Micro-Metrology. We derive analytical extraction formulas and we analyze the precision and limits of application. The methods cover the extraction of over two dozen fundamental properties. The geometric, dynamic, and material properties are classified as follows. Geometric properties include the extraction of beam widths, beam lengths, gap spacing, etch hole size, plate area, sidewall angle, and layer thickness. Dynamic properties include comb drive force, minimum gap closing voltage, fringing field factor, displacement, system stiffness, displacement resonance, velocity resonance, natural frequency, damping factor, time constant, mass, and damping. Material properties include system Young’s modulus, quality factor, beam stiffness, material Young’s modulus, Poisson’s ratio, shear modulus, residual strain, residual stress, and comb drive asymmetry.
We also show that the errors due to both our modeling assumptions and microfabrication assumptions are smaller than the errors due to electrical measurands, as long as the measurements performed on the test structure are within their prescribed operating range. We examine fabrication issues such as deposition, proximity, lithography, etchants, and residual stress. We examine nonideal modeling issues such as nonlinear dynamics, electrostatic fields, the capacitance and stiffness of coarse sidewalls, and deflection-induced moments.
Finally, we conclude by summarizing our results and examining future research directions and applications of Electro Micro-Metrology to measure more complex phenomena and its application to computer aided engineering and design.
December 31, 2005
Clark, J. V. (2005). Electro Micro-metrology. United States: University of California, Berkeley.