Piezoelectrically transduced temperature compensated silicon resonators for timing and frequency reference applications

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto. fi Author Antti Jaakkola Name of the doctoral dissertation Piezoelectrically transduced temperature compensated silicon resonators for timing and frequency reference applications Publisher School of Science Unit Department of Applied Physics Series Aalto University publication series DOCTORAL DISSERTATIONS 6/2016 Field of research Applied Physics Manuscript submitted 11 September 2015 Date of the defence 29 January 2016 Permission to publish granted (date) 2 November 2015 Language English Monograph Article dissertation (summary + original articles) Abstract Reference oscillators are used in a wide range of electronic devices for timing and for providing the frequency reference signals for wireless communications. Typically, an oscillator has to be based on a mechanical resonator, and for many decades, quartz crystals have served for this purpose. With the progress of microelectromechanical system (MEMS) technologies, silicon resonators have been developed for providing similar functionality as quartz. A silicon MEMS resonator can offer several advantages over quartz, such as smaller device size, decreased costs, and integration with other electronics. This work focuses on two challenges in silicon resonators: First, electromechanical transduction of silicon resonators has typically been achieved with electrostatic coupling, which is inherently quite weak and requires DC biasing of the devices and tends to complicate fabrication. Transduction based on a piezoelectric thin film on top of the resonator has been investigated as an alternative. Second, the resonance frequency of a silicon resonator is orders of magnitude more sensitive to temperature variations than that of a quartz crystal. Degenerate doping of silicon can be used to drastically reduce this effect. The first part of the work concentrates on the design, fabrication and characterization of piezoelectrically transduced silicon resonators. An oscillator based on a width extensional resonator operating at a frequency 24 MHz is demonstrated to have a phase noise -128 dBc/Hz at a 1-kHz offset from the carrier. An experimental test is conducted on piezoelectrically transduced square extensional mode resonators, whose dimensions are varied so that the main resonance mode occurs at a frequency range of f = 13 . 30 MHz. As a result, an anchor coupling effect is identified and a subharmonic nonlinear coupling mechanism is discovered. In the second part of the work, the effect of degenerate doping on the elastic parameters of silicon is investigated experimentally, with a focus on temperature compensation. Resonance modes that can be temperature compensated using doping are identified, and design rules for the optimization of the frequency stability are developed. The elastic parameters of silicon are determined as a function of temperature and n-type doping up to a level of n = 7.5x1019cm-3, enabling modelling of the frequency-vs-temperature characteristics of an arbitrary resonator design. Extrapolation from the results yields a prediction of full second order temperature compensation in optimally designed resonators for n-type doping level above 1020cm-3. The prediction is experimentally verified by the demonstration of piezoelectrically transduced resonators with frequency stability within +/10 ppm on a temperature range of T = -40 . +85C, on par with the best quartz crystals.