Acousto-Diffusive Waves in a Piezoelectric-Semiconductor-Piezoelectric Sandwich Structure

ABSTRACT

The propagation of acoustic waves in a homogeneous isotropic semiconducting layer sandwiched between two homogeneous transversely isotropic piezoelectric halfspaces has been investigated. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equation in piezoelectric material and electron diffusion equation in semiconductor along with the boundary conditions to be satisfied at the piezoelectric-semiconductor interfaces. The secular equations describing the symmetric and asymmetric modes of wave propagation have been derived in compact form after obtaining the analytical expressions for various field quantities that govern the wave motion. The complex secular equation has been solved numerically using functional interaction method along with irreducible cardano method. The computer simulated results are obtained with the help of MATLAB software for 6 mm cadmium selenide (*CdSe*) piezoelectric material and n-type silicon (*Si*) semiconductor in respect of dispersion curve, attenuation and specific loss factor of energy dissipation for symmetric (sym) and asymmetric (asym) modes of wave propagation. The study may find applications in non-destructive testing, resonators, waveguides etc.

The propagation of acoustic waves in a homogeneous isotropic semiconducting layer sandwiched between two homogeneous transversely isotropic piezoelectric halfspaces has been investigated. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equation in piezoelectric material and electron diffusion equation in semiconductor along with the boundary conditions to be satisfied at the piezoelectric-semiconductor interfaces. The secular equations describing the symmetric and asymmetric modes of wave propagation have been derived in compact form after obtaining the analytical expressions for various field quantities that govern the wave motion. The complex secular equation has been solved numerically using functional interaction method along with irreducible cardano method. The computer simulated results are obtained with the help of MATLAB software for 6 mm cadmium selenide (

Cite this paper

nullJ. Sharma, K. Sharma and A. Kumar, "Acousto-Diffusive Waves in a Piezoelectric-Semiconductor-Piezoelectric Sandwich Structure,"*World Journal of Mechanics*, Vol. 1 No. 5, 2011, pp. 247-255. doi: 10.4236/wjm.2011.15031.

nullJ. Sharma, K. Sharma and A. Kumar, "Acousto-Diffusive Waves in a Piezoelectric-Semiconductor-Piezoelectric Sandwich Structure,"

References

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[2] A. E. H. Love, “Some Problems of Geodynamics,” London Cambridge University Press, 1911, pp. 19-26.

[3] J. L. Bleustein, “A New Surface Wave in Piezoelectric Materials,” Applied Physics Letter, Vol. 13, 1968, p. 414. doi:10.1063/1.1652495

[4] Y. V. Gulyaev, “Electroacoustic Surface Waves in Solids,” Soviet Physics JETP, Vol. 9, 1969, pp. 37-38.

[5] D. L. White, “Amplification of Ultrasonic Waves in Piezoelectric Semiconductors,” Journal of Applied Physics, Vol. 33, 1962, pp. 2547-2554. doi:10.1063/1.1729015

[6] J. H. Collins, K. M. Lakin, C. F. Quate and H. J. Shaw, “Amplification of Acoustic Surface Waves with Adjacent Semiconductor and Piezoelectric Crystals,” Applied Physics Letter, Vol. 13, 1968, pp. 314-316. doi:10.1063/1.1652628

[7] D. R. Dietz, L. J. Busse and M. J. Fife, “Acoustoelectric Detection of Ultrasound Power with Composite Piezoelectric and Semiconductor Devices,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 35, No. 2, 1988, pp. 146-151. doi:10.1109/58.4164

[8] V. D. Kagan, “Propagation of a Surface Acoustic Wave in a Layered System Containing a Two Dimensional Conducting Layer,” Semiconductors, Vol. 31, No. 4, 1997, pp. 407-410. doi:10.1134/1.1187321

[9] J. Jin, Q. Wang and S. T. Quek, “Lamb Wave Propagation in a Metallic Semi-Infinite Medium Covered with Piezoelectric Layer,” International Journal of Solids Structures, Vol. 39, No. 9, 2002, pp. 2547-2556. doi:10.1016/S0020-7683(02)00091-4

[10] J. N. Sharma and M. Pal, “Propagation of Lamb Waves in a Transversely Isotropic Piezothermoelastic Plates,” Jour nal of Sound and Vibration, Vol. 270, No. 4-5, 2004, pp. 587-610. doi:10.1016/S0022-460X(03)00093-2

[11] J. N. Sharma, K. K. Sharma and A. Kumar, “Surface Waves in a Piezoelectric-Semiconductor Composite Stru- ctures,” International Journal of Solids and Structures, Vol. 47, No. 6, 2010, pp. 816-826. doi:10.1016/j.ijsolstr.2009.11.016

[12] J. Wu and Z. Zhu, “The Propagation of Lamb Waves in a Plate Bordered with Layers of a Liquid,” Journal of the Acoustical Society of America, Vol. 91, 1992, pp. 861- 867. doi:10.1121/1.402491

[13] J. N. Sharma and Vijayata Pathania, “Generalized Thermoelastic Waves in Anisotropic Plates Sandwiched between Liquid Layers,” Journal of Sound and Vibration, Vol. 278, No. 1-2, 2006, pp. 383-411. doi:10.1016/j.jsv.2003.10.010

[14] J. N. Sharma and Satish Kumar, “Lamb Waves in Micropolar Thermoelastic Solid Plates Immersed in Liquid with Varying Temperature,” Meccanica, Vol. 44, No. 3, 2009, pp. 305-319. doi:10.1007/s11012-008-9170-2

[15] S. V. Sorokin, “Analysis of Propagation of Waves of Purely Shear Deformation in a Sandwich Plate,” Journal of Sound and Vibration, Vol. 291, No. 3-5, 2006, pp. 1208-1220. doi:10.1016/j.jsv.2005.06.023

[16] G. Y. Qiang, C. W. Qiu and Z. Y. Liang, “Guided Wave Propagation in Multilayer Piezoelectric Structures,” Science in China Series G: Physics, Mechanics and Astronomy, Vol. 52, No. 7, 2009, pp. 1094-1104. doi:10.1007/s11433-009-0130-1

[17] H. P. Hu, Z. G. Chen, J. S. Yang and Y. T. Hu, “An Exact Analysis of Forced Thickness-Twist Vibrations of Multi-Layered Piezoelectric Plates,” Acta Mechanica Solida Sinica, Vol. 20, No. 3, 2007, pp. 211-218.

[18] L. Liu and K. Bhattacharya, “Wave Propagation in a Sandwich Structure,” International Journal of Solids and Structures, Vol. 46, No. 17, 2009, pp. 3290-3300. doi:10.1016/j.ijsolstr.2009.04.023

[19] H. Kolsky, “Stress Waves in Solids,” Dover Press, New York, 1963.

[1] L. Rayleigh, “On Waves Propagated along the Plane Surface of Elastic Solids,” Proceedings of the London Mathematical Society, Vol. 17, No. 1, 1885, pp. 4-11. doi:10.1112/plms/s1-17.1.4

[2] A. E. H. Love, “Some Problems of Geodynamics,” London Cambridge University Press, 1911, pp. 19-26.

[3] J. L. Bleustein, “A New Surface Wave in Piezoelectric Materials,” Applied Physics Letter, Vol. 13, 1968, p. 414. doi:10.1063/1.1652495

[4] Y. V. Gulyaev, “Electroacoustic Surface Waves in Solids,” Soviet Physics JETP, Vol. 9, 1969, pp. 37-38.

[5] D. L. White, “Amplification of Ultrasonic Waves in Piezoelectric Semiconductors,” Journal of Applied Physics, Vol. 33, 1962, pp. 2547-2554. doi:10.1063/1.1729015

[6] J. H. Collins, K. M. Lakin, C. F. Quate and H. J. Shaw, “Amplification of Acoustic Surface Waves with Adjacent Semiconductor and Piezoelectric Crystals,” Applied Physics Letter, Vol. 13, 1968, pp. 314-316. doi:10.1063/1.1652628

[7] D. R. Dietz, L. J. Busse and M. J. Fife, “Acoustoelectric Detection of Ultrasound Power with Composite Piezoelectric and Semiconductor Devices,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 35, No. 2, 1988, pp. 146-151. doi:10.1109/58.4164

[8] V. D. Kagan, “Propagation of a Surface Acoustic Wave in a Layered System Containing a Two Dimensional Conducting Layer,” Semiconductors, Vol. 31, No. 4, 1997, pp. 407-410. doi:10.1134/1.1187321

[9] J. Jin, Q. Wang and S. T. Quek, “Lamb Wave Propagation in a Metallic Semi-Infinite Medium Covered with Piezoelectric Layer,” International Journal of Solids Structures, Vol. 39, No. 9, 2002, pp. 2547-2556. doi:10.1016/S0020-7683(02)00091-4

[10] J. N. Sharma and M. Pal, “Propagation of Lamb Waves in a Transversely Isotropic Piezothermoelastic Plates,” Jour nal of Sound and Vibration, Vol. 270, No. 4-5, 2004, pp. 587-610. doi:10.1016/S0022-460X(03)00093-2

[11] J. N. Sharma, K. K. Sharma and A. Kumar, “Surface Waves in a Piezoelectric-Semiconductor Composite Stru- ctures,” International Journal of Solids and Structures, Vol. 47, No. 6, 2010, pp. 816-826. doi:10.1016/j.ijsolstr.2009.11.016

[12] J. Wu and Z. Zhu, “The Propagation of Lamb Waves in a Plate Bordered with Layers of a Liquid,” Journal of the Acoustical Society of America, Vol. 91, 1992, pp. 861- 867. doi:10.1121/1.402491

[13] J. N. Sharma and Vijayata Pathania, “Generalized Thermoelastic Waves in Anisotropic Plates Sandwiched between Liquid Layers,” Journal of Sound and Vibration, Vol. 278, No. 1-2, 2006, pp. 383-411. doi:10.1016/j.jsv.2003.10.010

[14] J. N. Sharma and Satish Kumar, “Lamb Waves in Micropolar Thermoelastic Solid Plates Immersed in Liquid with Varying Temperature,” Meccanica, Vol. 44, No. 3, 2009, pp. 305-319. doi:10.1007/s11012-008-9170-2

[15] S. V. Sorokin, “Analysis of Propagation of Waves of Purely Shear Deformation in a Sandwich Plate,” Journal of Sound and Vibration, Vol. 291, No. 3-5, 2006, pp. 1208-1220. doi:10.1016/j.jsv.2005.06.023

[16] G. Y. Qiang, C. W. Qiu and Z. Y. Liang, “Guided Wave Propagation in Multilayer Piezoelectric Structures,” Science in China Series G: Physics, Mechanics and Astronomy, Vol. 52, No. 7, 2009, pp. 1094-1104. doi:10.1007/s11433-009-0130-1

[17] H. P. Hu, Z. G. Chen, J. S. Yang and Y. T. Hu, “An Exact Analysis of Forced Thickness-Twist Vibrations of Multi-Layered Piezoelectric Plates,” Acta Mechanica Solida Sinica, Vol. 20, No. 3, 2007, pp. 211-218.

[18] L. Liu and K. Bhattacharya, “Wave Propagation in a Sandwich Structure,” International Journal of Solids and Structures, Vol. 46, No. 17, 2009, pp. 3290-3300. doi:10.1016/j.ijsolstr.2009.04.023

[19] H. Kolsky, “Stress Waves in Solids,” Dover Press, New York, 1963.