Analysis of the electro-elastic properties of custom quartz tuning forks for optoacoustic gas sensing

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Highlights

  • We designed and realized a set of four custom tuning forks.

  • We investigated the Quartz tuning forks (QTFs) electrical performance.

  • We determined the dependence of QTFs main physical parameters on their dimensions.

  • We identified in quality factor and conductance the figures of merit for sensing.

  • We provided guidelines to design tuning forks for photoacoustic spectroscopy.

Abstract

We report a detailed experimental and theoretical analysis of the influence of quartz tuning fork (QTF) dimensions on the main physical parameters controlling the QTF performance, namely, the quality factor Q, the resonance frequency, the fork stiffness, the spring constant, and the electrical resistance. Two different gold contact patterns were also compared. As a general trend, the QTF performance in terms of Q and electrical conductance values improves at increasing both the crystal thickness T and prong thickness w, while decreasing the prongs length Lp. However, since the QTF resonance frequency f0 is proportional to T/Lp2, a trade-off should be found in order to keep f0 < 40 kHz, i.e., well below the typical values of non-radiative relaxation rate of a targeted gas absorption lines.

Introduction

Since the 1960s, the quartz crystal tuning fork (QTF) has become a central component for timing and frequency measurements, due to its high stability, precision, and low power consumption. Today, these high quality-factor resonators are the most commonly used electronic component when a stable frequency reference is required for mass produced digital electronic devices such as clocks, smartphones, or telecommunication components. Recently, the use of QTFs for other applications, i.e., sensors in atomic force (AFM) [1], [2], [3], [4], [5] and near-field optical microscopy [6]; optoacoustic gas sensing [7], [8]; gas pressure, density and viscosity determination [9]; high-resolution measurements of acceleration and velocity for accelerometers and gyroscopes [10] have been reported. These applications rely on different QTF parameters (e.g., quality factor, resonance frequency, fork stiffness and spring constant). Since time measurements were originally the main application, the QTFs geometry and crystal cut were optimized to maintain a selected resonance frequency (typically 215  32.7 KHz) in a wide temperature range.

With the aim of determining the dependence of the QTF parameters and performance on their relevant dimensions and identify the optimal design for optoacoustic gas sensing, we designed a set of QTFs with different values of spacing between the prongs, their length and thickness, and crystal thickness. We also used two designs for the gold contact pattern in order to test different piezoelectric charge collection schemes. In the following sections, we will first provide a theoretical model of the QTF resonator, followed by a description of QTF samples supplied by a commercial vendor based on our design. We describe the experimental setup used to determine the electro-elastic properties of custom QTFs, as well as a real world application, i.e., QTF based optoacoustic gas sensor system, identifying the main figures of merit.

Section snippets

Theoretical model of a quartz tuning fork

QTF acoustic resonators consist of two prongs (or tines) connected at one end. Their resonance frequencies are determined by the elastic properties (Young modulus) of the constituent material (i.e., quartz) and their shape and sizes. The symmetry of the structure limits the number of allowed modes having a high quality factor. Since quartz is a piezoelectric material, a mechanical stress can be converted to an electrical signal and vice versa. In terms of elastic modeling, each prong can be

Quartz tuning fork resonators

The schematics of the designed QTFs are shown in Fig. 1(b) together with a standard QTF.

A z-cut quartz wafer with a 2° rotation along the x-axis, which provides stable frequency at room temperature, was selected for the realization of the custom QTFs. The z-cut is the dominant low frequency (up to 50 KHz) crystal-cut, which provides thermally stable flexural vibrational modes frequencies. Standard photolithographic techniques were used to etch the QTFs. Cr and Au patterns are

Quartz tuning forks characterization

Experimental measurements were performed using the setup depicted in Fig. 3.

A function generator (Tektronix model AFG3102) with a resolution of 2 mHz was used to provide a sinusoidal voltage to the QTFs. The in-phase (Ia) and out-of-phase (Ib) components of the current pass through a current-to-voltage converter using an operational amplifier. The output voltage is measured by a lock-in amplifier (Stanford Research Model SR830). To determine the resonance properties of the QTFs, the frequency of

Quartz tuning forks for quartz-enhanced photoacoustic spectroscopy

Apart from timing and frequency applications, one of the most successful implementation of QTF crystals is quartz-enhanced photoacoustic spectroscopy (QEPAS), an optical trace-gas sensing technique based on photoacoustic detection [18]. QEPAS utilizes QTFs as sharply resonant acoustic transducers to detect weak photoacoustic excitation generated by the surrounding target gas [7], [8]. When laser radiation at a specific wavelength is absorbed by the gas sample, the excited molecules will

Conclusions

In this manuscript, we reported an extensive investigation of the electro-elastic properties of QTFs with different shapes and sizes. We assessed the dependence of the Q-factor, the resonance frequency, the fork stiffness, the spring constant, and the electrical resistance from the QTF dimensions. We also identified the optoacoustic gas sensing figures of merit and studied their dependence from the QTFs relevant dimensions. For QEPAS applications, our results show that R should be kept low and

Acknowledgments

The authors from Dipartimento Interateneo di Fisica di Bari acknowledge financial support from Italian research projects PON02 00675 and PON02 00576 and PON03 “SISTEMA”. L. Dong acknowledges support by the National Natural Science Foundation of China (grant #s 61575113 & 61275213). F.K. Tittel acknowledges support by the Robert Welch Foundation (grant C-0586) and a NSF ERC MIRTHE award.

Pietro Patimisco obtained the Master degree in Physics (cum laude) in 2009 and the PhD Degree in Physics in 2013 from the University of Bari. Since 2013, he is a Post-Doctoral Research associate at the University of Bari. He was a visiting scientist in the Laser Science Group at Rice University in 2013 and 2014. Dr. Patimisco’s scientific activity addressed both micro-probe optical characterization of semiconductor optoelectronic devices and optoacoustic gas sensors. Recently, his research

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    Pietro Patimisco obtained the Master degree in Physics (cum laude) in 2009 and the PhD Degree in Physics in 2013 from the University of Bari. Since 2013, he is a Post-Doctoral Research associate at the University of Bari. He was a visiting scientist in the Laser Science Group at Rice University in 2013 and 2014. Dr. Patimisco’s scientific activity addressed both micro-probe optical characterization of semiconductor optoelectronic devices and optoacoustic gas sensors. Recently, his research activities included the study and applications of trace-gas sensors, such as quartz-enhanced photoacoustic spectroscopy and cavity enhanced absorption spectroscopy in the mid infrared and terahertz spectral region, leading to several publications, including a cover paper in Applied Physics Letter of the July 2013 issue.

    Angelo Sampaolo obtained his Master degree in Physics in 2013 from the University of Bari, where he is currently a graduate student earning his PhD in Physics. Since September 2014, he is a Research Associate in the Laser Science Group at Rice University. His research activity has included the study of the thermal properties of heterostructured devices via Raman spectroscopy. Most recently, his research interest has focused on the development of innovative techniques in trace gas sensing, based on Quartz Enhanced Photoacoustic Spectroscopy and covering the full spectral range from near-IR to THz. His achieved results have been acknowledged by a cover paper in Applied Physics Letter of the July 2013 issue.

    Lei Dong received his Ph.D. degree in optics from Shanxi University, China, in 2007. June 2008–December 2011, he worked as a post doctor in Rice University, USA. Now he is an associate professor of Shanxi University. His research interests include optical sensors, trace gas detection, and laser spectroscopy.

    Marilena Giglio received the M.S. degree (cum laude) in Applied Physics from University of Bari, Italy, in 2014, discussing the results obtained during a five months internship at the Academic Medical Center of Amsterdam, The Netherlands. Since 2014, she is pursuing a post-degree master in mechatronics and is currently a PhD student in the Physics Department of the University of Bari. Her research activity has included Optical Coherence Tomography (OCT) as an imaging technique for thin tissues and the analysis of the parameters of speckle distribution in OCT B-scans. Recently, her research activity has focused on the development of gas sensors based on Quartz-Enhanced Photoacoustic Spectroscopy.

    Gaetano Scamarcio received the PhD in physics from the University of Bari, Italy, in 1989. Since 2002, he is full professor of experimental physics at the University of Bari, Italy. From 1989 to 1990 he was a research fellow at the Max-Planck-Institute für Festkörper-forschung, Stuttgart, Germany, and in 1992 a visiting scientist at the Walter-Schottky-Institute, Garching, Germany. In the period 1994–1996, in 2000 and 2001 he was a visiting scientist of Bell Laboratories, Lucent Technologies (formerly AT&T), Murray Hill, NJ (U. S. A.). In 2006, he was an invited professor at the University of Paris 7. His research interests include the development and applications of quantum cascade lasers, optical, vibrational and transport properties of semiconductor structures at the nanoscale, spectroscopic techniques for real-time monitoring of optoelectronic devices, optoelectronic sensors for mechatronics. Gaetano Scamarcio was the recipient of the Award of the Italian Physical Society in 1989, the Firestone Prize for young laureates in 1985 and a NATO-CNR Advanced Fellowship in 1995.

    Frank K Tittel obtained his bachelor, master, and doctorate degrees in physicsfrom the University of Oxford in 1955 and 1959, respectively. From 1959 to 1967, he was a Research Physicist with General Electric Research and Development Center, Schenectady, New York. Since 1967 he has been on the faculty of the Department of Electrical and Computer Engineering and Biomedical Engineering at Rice University in Houston, TX, where he currently an Endowed Chaired Professor. Current research interests include various aspects of quantum electronics, in particular laser spectroscopy and laser applications in environmental monitoring, atmospheric chemistry, industrial process control, and medical diagnostics. Dr. Tittel is a Fellow of the IEEE, Optical Society of America, the American Physical Society and SPIE.

    Vincenzo Spagnolo obtained the PhD in physics, in 1994 from University of Bari. From 1997 to 1999, he worked as researcher of the National Institute of the Physics of Matter (INFM). From 1999 to 2003, he was a Postdoctoral Research Associate at the Physics Department, University of Bari. Since 2015, he is an associate Professor of Physics at the Polytechnic of Bari. His research interests include quantum cascade lasers, spectroscopic techniques for real-time device monitoring, optoacoustic gas sensors. His research activity is documented by more than 130 publications and two filed patents. He has given more than 30 invited presentations at international conferences and workshops. Prof. Spagnolo is senior member of the SPIE.

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