Quantum 1/f effect in resonant biochemical piezoelectric and MEMS sensors

Abstract

Piezoelectric sensors used for the detection of chemical agents and as electronic nose instruments are based on bulk and surface acoustic wave resonators. Adsorption of gas molecules on the surface of the polymer coating is detected by a reduction of the resonance frequency of the quartz disk, subject also to fundamental quantum 1/f frequency fluctuations.The quantum 1/f limit of detection is given by the quantum 1/f formula for quartz resonators. Therefore, for quantum 1/f optimization and for calculation and improvement of the fundamental sensitivity limits, we must avoid closeness of the crystal size to the phonon coherence length, which corresponds to the maximum error and minimal sensitivity situation, as shown here. Adsorbed masses below the pg range can be detected.Microelectromechanical system (MEMS) resonators have provided a possibility for the nanominiaturization of these sensors. Essential for integrated nanotechnology, these resonant silicon bars (fingers) are excited magnetically or electrically through external applied forces, since they are not piezoelectric or magnetostrictive. The application of the quantum 1/f theory to these systems is published here for the first time. It provides simple formulas that yield much lower quantum 1/f frequency fluctuations for magnetic excitation, in comparison with electrostatically driven MEMS resonators.

Some considerations on acoustic resonator phase noise modeling and recent short-term stability experimental results

“…P. H. Handel proposes in [9] a summary of his 1/f quantum noise theory. According to him, the general origin of the intrinsic 1/f noise is due to a quantum self-interference process caused by very small spontaneous bremsstrahlung energy losses.…”

Volume dependence in handel's model of quartz crystal resonator noise

“…It has been applied to several physically different systems by P. Handel (see e.g. [6], [13][14][15][16][17][18][19]), among which quartz crystal resonators. In the case of Bulk Acoustic Wave (BAW) quartz resonators at their turn-over temperature (~350 K), the fluctuations are mostly caused by the three-phonons process corresponding to the interaction of a phonon from the main resonator mode with a thermal phonon.…”