А.R. Bestugin - Dr.Sc. (Eng.), Professor, Director, JSC «Institute of Radio Engineering, Electronics and Communications» (St. Petersburg) L.V. Belova - Post-graduate Student, JSC «Institute of Radio Engineering, Electronics and Communications» (St. Petersburg) E-mail: belova-lilia@rambler.ru

Modern wireless communication system, have a high demands on the quality factor, dynamic range and phase noise RF multi-channel filter and voltage controlled oscillator, and require the introduction of new features, including a micro-miniature storage devices and microphones. In this connection, high-Q micromechanical silicon (MEMS) resonators fabricated in a single chip with a chip have emerged as a key element in the realization of the filters and oscillators. MEMS resonators can operate in different modes: bending, torsion, bulk [1]. A bulk mode MEMS resonator is preferred for high fre-quency generation because of the greater rigidity of the structure as compared with other modes. A common example of a bulk-mode device is a circular-disk resonator which can vibrate in two distinct modes. In the article the two-port disc resonator operating mode radial circuit (disk shape expands and contracts equally over the entire surface. To describe the geometry disc resonator using a cylindrical coordinate system. Its resonant frequency for radial contour bulk vibration derived in terms of Bessel functions [2-5]. The dependence of the resonance frequency of the thickness of the disc for the first four modes of vibration has been estimated. Disk resonator are outlined the equivalent mechanical lumped-element model. For this model are found: the effective mass, spring constant and viscous-damping coefficient. In connection with the formal similarity integral-differential equations, we constructed an electric model with lumped parameters for disk micromechanical resonator, where strength, displacement and speed similar to the voltage, the charge and the current accordingly [6]. Thus, the parallel arrangement in the mechanical field appears in series in an equivalent circuit, and vice versa. Its parameters are capacitance, inductance and induced resistance. MEMS resonators convert electrical energy into mechanical energy, by means of two electromechanical transducers at the input and the output. The principal and the equivalent circuit of the electrostatic transducer cross were also built. Values of the system parameters were derived through a transfer equation [7]. The value of induced resistance by the electromechanical transducer is realized in a particular design of the resonator and is important. This parameter has been obtained dependent on the distance between the electrodes and the thickness of the disk radius for multiple values. Theoretical modeling and the resulting dependence have shown that in order to reduce the equivalent resistance MEMS resonator technology design should allow to achieve the distance between the electrodes to the submicron level. Moreover, the thickness of the structural layer for a MEMS resonators should be large enough to increase the area of transduction and power output of the resonator. Also, substantial research should be directed to the development of the respective CMOS-MEMS process for the solution of various problems of integration of MEMS [8]. It requires strict control of size of elements and quality of materials.

 

1. Bestugin A.R., Filonov O.M., Kirshina I.A. Mikro- i nanoehlektromekhanicheskie rezonatory ? funkcionalnye komponenty perspektivnykh sistem obrabotki i peredachi signalov // Uspekhi sovremennojj radioehlektroniki. 2014. № 12. S. 42-44.
2. Wang J, Ren Z, Nguyen CTC. 156-GHz self-aligned vibrating micromechanical disk resonator // IEEE Trans. Ultrason Ferroelectr Freq Control. 2004. № 51. P. 1607-1628.
3. Joydeep B., Tarun K.B. Microelectromechanical resonators for radio frequency communication applications // Microsystem Technologies. 2011. № 17. P. 1557-1580.
4. Clark JR, Hsu WT, Abdelmoneum MA, Nguyen CTC. High-Q UHF micromechanical radial-contour mode disk resonators // Microelectromech Syst. 2005. № 14 (6). P. 1298-1310
5. Libov D.JU., Meleshko V.V. Vysokochastotnye kolebanija konechnykh uprugikh diskov // Akusticheskijj vestnik. 2011. T. 14. № 3. S. 12-22.
6. Schmidt MA, Howe RT. Silicon resonant microsensors // Proceedings of Ceramic Engineering and Science: John Wiley & Sons; New York. 2008. P. 1019-1034.
7. Dolja V.K., Mitko V.N. Obshhaja teorija ehlektromekhanicheskikh preobrazovatelejj. Ucheb. posobie. Rostov-na-Donu. 2009.
8. Fedchenko V.G., Plotjanskaja M.A., Belova L.V. Teoreticheskie osnovy proektirovanija mikromekhanicheskikh sistem s ponizhennojj chuvstvitelnostju k izmeneniju temperatury // Nauka i obrazovanie: tendencii i perspektivy. 2015. № 1(2). S. 54-60.