2014: Disk-shaped high-Q mechanical resonators employing surface vibrational modes with large azimuthal indexes

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Researchers from the Faculty of Physics, Lomonosov Moscow State University (Prof. Valery Mitrofanov, Junior Research Fellow Artemiy Dmitriev, and student Dmitry Gritsenko) studied both theoretically and experimentally various vibrational modes in the disk-shaped mechanical resonators with large azimuthal indexes and developed a novel method of how significantly enhance the coupling between mechanical and electrical subsystems in electromechanical systems.

Microelectromechanical systems based on micromechanical oscillators coupled with transducers which transform mechanical motion into electrical signal find wide applications in industry, instrument engineering, science and technology. In the near future scientists hope to realize quantum states of micromechanical oscillators when their behavior is controlled by lows of quantum mechanics. The quality factor of the mechanical element is a key parameter. It determines the performance and merit of an electromechanical system, therefore reduction of mechanical losses in micromechanical systems is very important. But it is more convenient to study and to check mechanisms of the losses and methods of their reduction by using mechanical resonators with macroscopic sizes.

The researchers from the Faculty of Physics, Lomonosov Moscow State University (Professor Valery Mitrofanov, Junior Research Fellow Artemiy Dmitriev, student Dmitry Gritsenko) have carried out theoretical and experimental investigation of various vibrational modes in disk-shaped mechanical resonators. The research was focused on modes with large azimuthal indexes. Such modes have the advantage because the elastic deformations concentrate in the circumferential area of the disk. This allows one to reduce significantly the losses associated with leakage of the energy to the disk clamping structure. On the other hand, the mode frequency and quality factor become very sensitive to the surface condition of the disk. It is important for development of various sensors. High-Q disk-shaped resonators fabricated from single crystal silicon allowed exploration of different loss mechanisms using various vibrational modes of the same resonator. These resonators demonstrate nonlinear behavior of mainly geometrical origin at large amplitudes. Nonlinearity originates coupling between vibrational modes which can be used for various applications.

It is very important for the electromechanical systems to provide maximal coupling between the mechanical and the electrical subsystems. Such a coupled system was developed and realized experimentally in the version based on the silicon disk-shaped mechanical resonator parametrically coupled in the manner of a capacitive transducer with two resonant radio-frequency (RF) circuits. The interaction between the circuits could be regulated. This three-mode electromechanical system have allowed enhancement of the electromechanical coupling particularly in the resolved sideband regime when the mechanical resonator‘s frequency is larger than the radio frequency circuits’ bandwidths. Additional regeneration or damping of the mechanical resonator was realized by using tuning of the RF circuits.

Results of the research have been published in articles: A.V. Dmitriev, D.S. Gritsenko, V.P. Mitrofanov, “Surface vibrational modes in disk-shaped resonators”, Ultrasonics 54, 905 (2014), A.V. Dmitriev, D.S. Gritsenko, V.P. Mitrofanov, Non-axisymmetric flexural vibrations of free-edge circular silicon wafers, Phys. Lett. A378, 673 (2014), A.V. Dmitriev, V.P. Mitrofanov, Enhanced interaction between a mechanical oscillator and two coupled resonant electrical circuits, Rev. Sci. Instr. 85, 085005 (2014).