REGISTRATION OF SURFACE ACOUSTIC WAVES in Z-SECTIONS of PIEZOELECTRIC SINGLE CRYSTALS ZnO and CdS
Abstract
Subject and Purpose. The subjects of this research are the internal electric field and the electric polarization vector, both existing in the volume of a deformed piezoelectric crystal. The work has been aimed at determining the dynamic electric polarization within the Z-section of a class 6 mm piezoelectric single crystal, deformed by surface acoustic waves (SAW), and estimating the sensitivity of the electrode pair of the inter-digit transducer in the mode of recording surface acoustic waves in Z-sections of the piezoelectric crystals.
Methods and Methodology. The analysis proceeds from construction of a mathematical model for the SAW detector, through the use of an appropriate set of differential equations. It is taken into account that the electric charge on an electrode is determined by the vector of dynamic electric polarization and the the electric field distribution along the electrode. The effects of cross-sectional dimensions of the electrodes, the scattered electric field, and of the harmonic electrical polarization vector are taken into account.
Results. Mathematical models have been constructed for a long electrode of finite cross-sectional dimensions, intended for surface acoustic wave (SAW) excitation in Z-sections of piezoelectric crystals of crystallographic class 6mm. The problem of calculating the electric charge distributions along the electrodes of the inter-digit transducer which operates in the SAW detector mode has been solved with account of the effects owing to the scattered electric field and harmonic wave motion of the electric polarization vector. Numerical values have been determined for the sensitivity of the inter-digit transducer operated in the receiving mode. In the case of ZnO and CdS single crystals the figures are 7.73·1010 and, 3.08·1010 V/m, respectively.
Conclusions. A general solution to the boundary value problem of the internal electric field in the volume of a deformed piezoelectric has been obtained. The dynamic electric polarization has been determined within a Z-section plane of the single-crystal piezoelectric of class 6mm in the process of its interaction with a SAW. A mathematical model has been developed for a SAW detector, taking into account the effect of the electrodes’ cross-section size. The operating sensitivity of a pair of electrodes of the inter-digit transducer has been estimated for the SAW registration mode.
Keywords: piezoelectric; surface acoustic waves; single crystal
Manuscript submitted 22.01.2025
Radio phys. radio astron. 2025, 30(2): 129-140
REFERENCES
1. Caliendo, C., Hamidullah, M., 2019. Guided acoustic wave sensors for liquid environments. J. Phys. D: Appl. Phys.,
52(15), 153001. DOI: 10.1088/1361-6463/aafd0b
2. Poveda, A.C., Buhler, D.D., Saez, A.C., Santos, P.V., de Lima, M.M., 2019. Semiconductor optical waveguide devices mod- ulated by surface acoustic waves. J. Phys. D Appl. Phys., 52(25), 253001. DOI: 10.1088/1361-6463/ab1464
3. Weiß, M., Krenner, H.J., 2018. Interfacing quantum emitters with propagating surface acoustic waves. J. Phys. D Appl. Phys., 51(37), P. 373001. DOI: 10.1088/1361-6463/aace3c
4. Varlamov, A.V., Lebedev, V.V., Agruzov, P.M., Ilichev, I.V., Shamrai, L.V., Shamrai, A.V., 2019. Acousto-optic frequencyshift modulators with acoustic and optic waveguides on X-cutlithium niobate substrates. J. Phys. Conf. Ser., 1326, 012011. DOI: 10.1088/1742-6596/1326/1/012011
5. Jahanshahi, P., Wei, Q., Jie, Z., Zalnezhad, E., 2018. Designing a Non-invasive Surface Acoustic Resonator for Ultra-high Sensitive Ethanol Detection for an On-the-spot Health Monitoring System. Biotechnol. Bioprocess Eng., 23, pp. 394–404. DOI: 10.1007/s12257-017-0432-5
6. Delsing, P., Cleland, A.N., Schuetz, M.J.A., Knörzer, J., Giedke, G., Cirac, J.I., Srinivasan, K., Wu, M., Balram, K.C., Bäuerle, C., Meunier, T., Ford, C.J.B., Santos, P.V., Cerda-Méndez, E., Wang, H., Krenner, H.J., Nysten, E.D.S., Weiß, M., Nash, G.R., Thevenard, L., Gourdon, C., Rovillain, P., Marangolo, M., Duquesne, J.-Y., Fischerauer, G., Ruile, W., Reiner, A., Paschke, B., Denysenko, D., Volkmer, D., Wixforth, A., Bruus, H., Wiklund, M., Reboud, J., Cooper, J.M., Fu, Y.Q., Brugger, M.S., Rehfeldt, F., and Westerhausen, C., 2019. Surface acoustic waves roadmap Topical Review. J. Phys. D: Appl. Phys., 52(35), 353001. DOI: 10.1088/1361-6463/ab1b04
7. Aleksandrova, M., Badarov, D., 2022. Recent Progress in the Topologies of the Surface Acoustic Wave Sensors and the Corresponding Electronic Processing Circuits. Sensors, 22(13), 4917. DOI: 10.3390/s22134917
8. Ziping, W., Xiqiang, X., Lei, Q., Jiatao, W., Yue, F., and Maoyuan, T., 2021. Review Article Research on the Progress of Interdigital Transducer (IDT) for Structural Damage Monitoring. J. Sens., 2021, 6630658. DOI: 10.1155/2021/6630658
9. Hatfield, A., Zhang, S., Li, Bo, Xu, Tian-Bing, 2022. Finite element modeling for a flexible transparent piezoelectric surface acoustic wave transducer. In: Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil In- frastructure, and Transportation XVI. Proc. of SPIE, 12047, 1204713. DOI: 10.1117/12.2613275
10. Draper, A., Deng, Z., 2022. Multiphysics modeling of printed surface acoustic wave thermometer. In: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. Proc. of SPIE, 12046, 1204608. DOI: 10.1117/12.2613141
11. Wang, T., Green, R., Guldiken, R., Wang, J., Mohapatra, S., Mohapatra, S.S., 2019. Finite Element Analysis for Surface Acoustic Wave Device Characteristic Properties and Sensitivity. Sensors, 19(8), 1749. DOI: 10.3390/s19081749
12. Lepikh, Ya.I., 2023. Determination of the optimal physical and mathematical model and weight functions for calculating the topology of counterpine converters of surface acoustic waves. Sensor Electronics and Мicrosystem Technologies, 20(1), pp. 11—19. DOI:10.18524/1815-7459.2023.1.275943
13. Viktorov, I.A., 1981. Sound surface waves in solids. Moscow: Nauka Publ.
14. Linchevskyi, I.V., 2019. Excitation of Surface Acoustic Waves in a Z-section of Piezoelectric Crystals by the Electric Field of a Long Electrode. Int. J. Appl. Phys., 6(3), pp. 42—50. DOI: 10.14445/23500301/IJAP-V6I3P108
15. Linchevskyi, I.V., Petrischev, O.N., 2020. Surface Acoustic Waves in Z-Sections of Piezoelectric Monocrystals of Hexagonal Syngony. Radioelectronics and Communications Systems, 63(3), pp. 156—170. DOI: 10.20535/S0021347020030048
16. Linchevskyi, I.V., 2021. Excitation Features of Surface Acoustic Waves by Interdigital Transducer in Piezoelectric Crystals.
Radioelectronics and Communications Systems, 64(8), pp. 426—439. DOI: 10.20535/S0021347021080033
17. Tamm, I.E., 1979. Fundamentals of the Theory of Electricity. Moscow: Mir Publ.
18. Catti, M., Noel, Y., Dovesi, R., 2003. Full Piezoeletric Tensors of Wurtzite and Zinc Blende ZnO and ZnS by First-Principles Calculations. J. Phys. Chem. Sol., 64(11), pp. 2183—190. DOI: 10.1016/S0022-3697(03)00219-1
19. Gorla, C.R., Emanetoglu, N.W., Liang, S., Mayo, W.E., Lu, Y., Wraback, M., and Shen, H., 1999. Structural, optical, and sur- face acoustic wave properties of epitaxial ZnO films grown on (0112) sapphire by metalorganic chemical vapor deposition. J. Appl. Phys., 85(5), pp. 2595—2602. DOI: 10.1063/1.369577
Methods and Methodology. The analysis proceeds from construction of a mathematical model for the SAW detector, through the use of an appropriate set of differential equations. It is taken into account that the electric charge on an electrode is determined by the vector of dynamic electric polarization and the the electric field distribution along the electrode. The effects of cross-sectional dimensions of the electrodes, the scattered electric field, and of the harmonic electrical polarization vector are taken into account.
Results. Mathematical models have been constructed for a long electrode of finite cross-sectional dimensions, intended for surface acoustic wave (SAW) excitation in Z-sections of piezoelectric crystals of crystallographic class 6mm. The problem of calculating the electric charge distributions along the electrodes of the inter-digit transducer which operates in the SAW detector mode has been solved with account of the effects owing to the scattered electric field and harmonic wave motion of the electric polarization vector. Numerical values have been determined for the sensitivity of the inter-digit transducer operated in the receiving mode. In the case of ZnO and CdS single crystals the figures are 7.73·1010 and, 3.08·1010 V/m, respectively.
Conclusions. A general solution to the boundary value problem of the internal electric field in the volume of a deformed piezoelectric has been obtained. The dynamic electric polarization has been determined within a Z-section plane of the single-crystal piezoelectric of class 6mm in the process of its interaction with a SAW. A mathematical model has been developed for a SAW detector, taking into account the effect of the electrodes’ cross-section size. The operating sensitivity of a pair of electrodes of the inter-digit transducer has been estimated for the SAW registration mode.
Keywords: piezoelectric; surface acoustic waves; single crystal
Manuscript submitted 22.01.2025
Radio phys. radio astron. 2025, 30(2): 129-140
REFERENCES
1. Caliendo, C., Hamidullah, M., 2019. Guided acoustic wave sensors for liquid environments. J. Phys. D: Appl. Phys.,
52(15), 153001. DOI: 10.1088/1361-6463/aafd0b
2. Poveda, A.C., Buhler, D.D., Saez, A.C., Santos, P.V., de Lima, M.M., 2019. Semiconductor optical waveguide devices mod- ulated by surface acoustic waves. J. Phys. D Appl. Phys., 52(25), 253001. DOI: 10.1088/1361-6463/ab1464
3. Weiß, M., Krenner, H.J., 2018. Interfacing quantum emitters with propagating surface acoustic waves. J. Phys. D Appl. Phys., 51(37), P. 373001. DOI: 10.1088/1361-6463/aace3c
4. Varlamov, A.V., Lebedev, V.V., Agruzov, P.M., Ilichev, I.V., Shamrai, L.V., Shamrai, A.V., 2019. Acousto-optic frequencyshift modulators with acoustic and optic waveguides on X-cutlithium niobate substrates. J. Phys. Conf. Ser., 1326, 012011. DOI: 10.1088/1742-6596/1326/1/012011
5. Jahanshahi, P., Wei, Q., Jie, Z., Zalnezhad, E., 2018. Designing a Non-invasive Surface Acoustic Resonator for Ultra-high Sensitive Ethanol Detection for an On-the-spot Health Monitoring System. Biotechnol. Bioprocess Eng., 23, pp. 394–404. DOI: 10.1007/s12257-017-0432-5
6. Delsing, P., Cleland, A.N., Schuetz, M.J.A., Knörzer, J., Giedke, G., Cirac, J.I., Srinivasan, K., Wu, M., Balram, K.C., Bäuerle, C., Meunier, T., Ford, C.J.B., Santos, P.V., Cerda-Méndez, E., Wang, H., Krenner, H.J., Nysten, E.D.S., Weiß, M., Nash, G.R., Thevenard, L., Gourdon, C., Rovillain, P., Marangolo, M., Duquesne, J.-Y., Fischerauer, G., Ruile, W., Reiner, A., Paschke, B., Denysenko, D., Volkmer, D., Wixforth, A., Bruus, H., Wiklund, M., Reboud, J., Cooper, J.M., Fu, Y.Q., Brugger, M.S., Rehfeldt, F., and Westerhausen, C., 2019. Surface acoustic waves roadmap Topical Review. J. Phys. D: Appl. Phys., 52(35), 353001. DOI: 10.1088/1361-6463/ab1b04
7. Aleksandrova, M., Badarov, D., 2022. Recent Progress in the Topologies of the Surface Acoustic Wave Sensors and the Corresponding Electronic Processing Circuits. Sensors, 22(13), 4917. DOI: 10.3390/s22134917
8. Ziping, W., Xiqiang, X., Lei, Q., Jiatao, W., Yue, F., and Maoyuan, T., 2021. Review Article Research on the Progress of Interdigital Transducer (IDT) for Structural Damage Monitoring. J. Sens., 2021, 6630658. DOI: 10.1155/2021/6630658
9. Hatfield, A., Zhang, S., Li, Bo, Xu, Tian-Bing, 2022. Finite element modeling for a flexible transparent piezoelectric surface acoustic wave transducer. In: Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil In- frastructure, and Transportation XVI. Proc. of SPIE, 12047, 1204713. DOI: 10.1117/12.2613275
10. Draper, A., Deng, Z., 2022. Multiphysics modeling of printed surface acoustic wave thermometer. In: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. Proc. of SPIE, 12046, 1204608. DOI: 10.1117/12.2613141
11. Wang, T., Green, R., Guldiken, R., Wang, J., Mohapatra, S., Mohapatra, S.S., 2019. Finite Element Analysis for Surface Acoustic Wave Device Characteristic Properties and Sensitivity. Sensors, 19(8), 1749. DOI: 10.3390/s19081749
12. Lepikh, Ya.I., 2023. Determination of the optimal physical and mathematical model and weight functions for calculating the topology of counterpine converters of surface acoustic waves. Sensor Electronics and Мicrosystem Technologies, 20(1), pp. 11—19. DOI:10.18524/1815-7459.2023.1.275943
13. Viktorov, I.A., 1981. Sound surface waves in solids. Moscow: Nauka Publ.
14. Linchevskyi, I.V., 2019. Excitation of Surface Acoustic Waves in a Z-section of Piezoelectric Crystals by the Electric Field of a Long Electrode. Int. J. Appl. Phys., 6(3), pp. 42—50. DOI: 10.14445/23500301/IJAP-V6I3P108
15. Linchevskyi, I.V., Petrischev, O.N., 2020. Surface Acoustic Waves in Z-Sections of Piezoelectric Monocrystals of Hexagonal Syngony. Radioelectronics and Communications Systems, 63(3), pp. 156—170. DOI: 10.20535/S0021347020030048
16. Linchevskyi, I.V., 2021. Excitation Features of Surface Acoustic Waves by Interdigital Transducer in Piezoelectric Crystals.
Radioelectronics and Communications Systems, 64(8), pp. 426—439. DOI: 10.20535/S0021347021080033
17. Tamm, I.E., 1979. Fundamentals of the Theory of Electricity. Moscow: Mir Publ.
18. Catti, M., Noel, Y., Dovesi, R., 2003. Full Piezoeletric Tensors of Wurtzite and Zinc Blende ZnO and ZnS by First-Principles Calculations. J. Phys. Chem. Sol., 64(11), pp. 2183—190. DOI: 10.1016/S0022-3697(03)00219-1
19. Gorla, C.R., Emanetoglu, N.W., Liang, S., Mayo, W.E., Lu, Y., Wraback, M., and Shen, H., 1999. Structural, optical, and sur- face acoustic wave properties of epitaxial ZnO films grown on (0112) sapphire by metalorganic chemical vapor deposition. J. Appl. Phys., 85(5), pp. 2595—2602. DOI: 10.1063/1.369577
Keywords
piezoelectric; surface acoustic waves; single crystal
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