Nonlinear effects and applications for piezoelectric materials


  • A. F. Jaramillo Alvarado Electronics Department, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)
  • F. J. de la Hidalga-Wade Electronics Department, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)
  • P. Rosales Electronics Department, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)
  • A. Torres Jacome Electronics Department, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)



Tunable piezoelectric resonators, Nonlinear piezoelectric effects, Lambwave resonators, elastoelectric effect


The requirements of high quality factor, low power consumption, easy design techniques and compatibility with the main standard fabrication processes of integrated circuits (IC) make the tunable piezoelectric resonators a suitable option for the new technologies of fifth generation of telecommunication (5G) and Internet of Things (IoT). In this work the nonlinear state equations for piezoelectric effect are presented. From these equations we may deduce which materials can be used in applications where a hysteresis behavior or resonance frequency tunability are required, additionally, it is shown which crystals have the nonlinear tensor’s symmetry compatible with each application field. A novel model for the tunable piezoelectric devices is shown taking into account the consequences of voltage tuning. Finally, three different ways to design and implement the nonlinear behavior of piezoelectric materials to tune devices are introduced.


J. C. Doll, B. C. Petzold, B. Ninan, R. Mullapudi and B. L. Pruitt, Aluminum nitride on titanium for CMOS compatible piezoelectric transducers, Journal of Micromechanics and Microengineering 20 (2009).

C. Elgaard and L. Sundström, A 491.52 MHz 840 uW crystal oscillator in 28 nm FD-SOI CMOS for 5G applications, ESSCIRC 2017 - 43rd IEEE European Solid State Circuits Conference (2017) 247-250.

Y. Kuo, C. Hsiao and H. Wei, Phase noise analysis of 28 GHz phase-locked oscillator for next generation 5G system, 2017 IEEE 6th Global Conference on Consumer Electronics (GCCE) (2017) 1-2,

P. T. Do, et al., Wideband tunable microwave signal generation in a silicon-micro-ring-based optoelectronic oscillator, Scientific Reports 10 (2020).

A. Siddique, et al., Low-power low-phase noise VCO for 24 GHz applications, Microelectronics Journal, 97 (2020).

F. Ullah et al., A Wideband Tunable Voltage Controlled Oscillator Supporting Non-harmonically-Related Multiple Frequency Bands for Future 5G Applications Using 0.13 µm SiGe BiCMOS Technology, 2018 IEEE 3rd International Conference on Integrated Circuits and Microsystems (ICICM), (2018) 160-163.

R. V. Snyder, A. Mortazawi, I. Hunter, Fellow, Simone Bastioli, Member, Giuseppe Macchiarella and Ke Wu, Fellow, Present and Future Trends in Filters and Multiplexers, IEEE Transactions On Microwave Theory and Techniques, 63 (2016) 3324.

Introducion 5G networks - Characteristics and usages, Gemalto, September 2021 [Online]. Last Check: September 2021. Available:

S. Yost, MMwave: Battle of bands, National Instruments, (June 2020). 10. IoT Signals, Summary of Research Learnings, Microsoft, 2020, [Online]. Last check September 2021. Available: Edition%202 English.pdf

G. Piazza, R. Abdolvand, G. K. Ho, F. Ayaz, Voltage-tunable piezoelectrically-transduced single-crystal silicon micromechanical resonators, Sensors and Actuators A, 111 (2004).

J. Singh, A. Kumar, Tunable Film Bulk Acoustic Wave Resonator Based on Magnetostrictive Fe65Co35 Thin Films, 2018 Asia-Pacific Microwave Conference (APMC), (2018) 800-802.

E.-C. Park et al., Performance Comparison of SGHz VCOs Integrated by CMOS Compatible High Q MEMS Inductors, IEEE MTT-S International Microwave Symposium Digest, 2003, Philadelphia.

J. A. Kusters, The Effect of Static Electric Fields on the Elastic Constants of α-Quartz, 24th Annual Symposium on Frequency Control, (1970) 46-54,

K. Hruska, Non-Linear Equations of State of Second-Order Electromechanical Effects, Czech. Journal of Physics B, 14 309.

O. P. Niraula and N. Nod, Derivation of Material Constants in Non-Linear Electro-Magneto-Thermo-Elasticity, Journal of Thermal Stresses, 33 (2010) 1011.

P. P. Rodriguez-Ramos et al., Variational principles for nonlinear piezoelectric materials, Archive of Applied Mechanics, 74 (2004) 191.

J. Tichy, J. Erhart, E. Kittinger, and J. Prıvratska, Fundamentals of piezoelectric sensorics, (Springer, London, 2010). pp. 55-67.

D. Damjanovic, The Science of Hysteresis, Academic Press, 3 (2006) 337.

Z. Jahromi, and S. Abdolali, Nonlinear Constitutive Modeling of Piezoelectric Materials, (University of Calgary, 2013).

R. Tabrizian and F. Ayazi, Tunable silicon bulk acoustic resonators with multi-face AlN transduction, 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS) Proceedings, 2011, pp. 1-4.

B. A. Auld, Acoustic Fields and Waves in Solids, John Wiley & Sons, New York, 1 (1973) 386.

M. Feldmann and Jeannine Henaff, ´ Surface Acoustic Waves for Signal Processing, Artech House, Norwood, (1989). pp. 29-41,

H. Wu, L. Tang, Y. Yang, and C.K. Soh, A novel two-degreesof-freedom piezoelectric energy harvester. Journal of Intelligent Material Systems and Structures. 2013,

Y. Wang et al., Parasitic analysis and π-type Butterworth-Van Dyke model for complementarymetal-oxide-semiconductor Lamb wave resonator with accurate two-port Yparameter characterizations, Rev. Sci. Instrum. 87

A. F. Jaramillo Alvarado, Modelo General Semiempírico para la Frequencia de Resonancia en Resonadores Piezoelectricos de Contorno (LWR), Instituto Nacional de Astrofísica, Optica y Electrónica, (2018).

B. A. Auld, Acoustic Fields and Waves in Solids, John Wiley & Sons, New York, 1 (1973) 73-82.

E. R. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure, Oxford University Press, (2004) pp. 147-160.

S. Chen and J. Zhao, The Requirements, Challenges, and Technologies for 5G of Terrestrial Mobile Telecommunication, IEEE Communications Magazine, 2014.




How to Cite

A. F. Jaramillo Alvarado, F. J. de la Hidalga Wade, P. Rosales Quintero, and A. Torres Jacome, “Nonlinear effects and applications for piezoelectric materials”, Rev. Mex. Fís., vol. 68, no. 6 Nov-Dec, pp. 061002 1–, Nov. 2022.