Application of the finite element method for calculating the surface acoustic wave parameters and devices

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A series of models based on the finite element method (FEM) for analyzing the parameters of surface acoustic waves (SAW) and devices based on them are described. The computer method for generating models in the COMSOL Multiphysics is described. Three main studies in the COMSOL are described and graphically illustrated: stationary, eigenfrequency, frequency domain. The properties of Rayleigh waves and leaky SAW are analyzed. A visualization of a number of characteristics is presented. The analysis of such parameters as phase velocity of the wave, electromechanical coupling coefficient, and static capacitance of transducer is considered. The examples consider an equidistant transducer, a transducer with split electrodes, and a unidirectional transducer of the DART type. Methods for analyzing SAW harmonics and the waveguide effect are proposed. It is shown that the model is valid for both single-crystal substrates and layered structures. The analysis of the temperature coefficient of frequency for such structures as TCSAW and I.H.P.SAW is considered. A model for calculating the amplitude-frequency responses of devices is presented. It is shown that the data obtained as a result of numerical analysis correspond to experimental data and known literature sources.

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Sobre autores

A. Koigerov

St. Petersburg State Electrotechnical University “LETI” Saint Petersburg Electrotechnical University

Autor responsável pela correspondência
Email: a.koigerov@gmail.com
Rússia, St. Petersburg

Bibliografia

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2. Fig. 1. The IDTs considered in the work: a — equidistant with electrodes of width λ/4; b — with split electrodes of width λ/8; c — unidirectional DART type; d — principle of transition to MPP. Designations: λ — wavelength; p — electrode repetition period; w — electrode width.

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3. Fig. 2. Test cells for single-crystal piezoelectric substrates: a — free surface; b — example of a grid; c — pattern of mechanical displacements of the Rayleigh wave for a 128° Y — X LiNbO3 substrate for one of the natural frequencies; d — pattern of mechanical displacements for a surfactant for 36° Y — X LiTaO3 for one of the natural frequencies. Features of the model: 1 — piezoelectric crystal; 2 — perfectly matched layer; λ — wavelength.

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4. Fig. 3. Admittance and mechanical displacement patterns for the test electrode structure on a 36° Y – X LiTaO₃ substrate.

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5. Fig. 4. Admittance for test electrode structures with a period p = λ / 2 for different metallization thicknesses and h / λ ratios on substrates: a — 36° Y — X LiTaO₃; b — 42° Y — X LiTaO₃; h / λ: 1 – 1%; 2 – 3%; 3 – 5%; 4 – 7%.

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6. Fig. 5. Result of static analysis for a unidirectional DART-type transducer in the form of surface potential distribution.

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7. Fig. 6. Test electrode cell for 128° Y — X LiNbO₃ substrate with period p = λ / 4 and electrode width λ / 8 for analysis in the region of natural frequencies and the pattern of mechanical displacements of the Rayleigh wave: a — cell geometry; b — fundamental harmonic; c — 3rd harmonic; d — 5th harmonic.

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8. Fig. 7. Result of calculating the conductivity (Y11) of the converter for a 128° Y — X LiNbO₃ substrate with a period p = λ / 4 and an electrode width of λ / 8 (frequency domain analysis): 1 — real part of the conductivity; 2 — imaginary part of the conductivity; * — fundamental harmonic; ** — parasitic BAW; *** — 3rd harmonic.

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9. Fig. 8. Test cell for the AlN/diamond layered structure: a – cell geometry; b – pattern of mechanical displacements of the Rayleigh wave; c – pattern of mechanical displacements of the Sezawa wave. Features of the model: 1 – piezoelectric film of aluminum nitride; 2 – diamond substrate.

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10. Fig. 9. Dependence of the phase velocity (a) of acoustic waves and KEMS (b) on the thickness of the aluminum nitride film: 1 - Rayleigh wave; 2 - Sezawa wave.

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11. Fig. 10. TCC: 1 — traditional single-crystal substrate 36° Y — X LiTaO₃; 2 — dependence on the SiO₂ film thickness for the TC-SAW structure; 3 — dependence on the thickness of the piezoelectric material layer 36° Y — X LiTaO₃ at a constant film thickness HSiO₂ = 30% for the I.H.P. structure.

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12. Fig. 11. The principle of taking into account waveguide modes: a — calculated frequency response of one filter element on transverse modes; b — test structure and pictures of mechanical displacements of transverse modes: 1 — geometry of a cell with a period p = λ / 2; 2 — symmetric mode S₀; 3 — antisymmetric mode S₁; 4 — symmetric mode S₂; 5 — antisymmetric mode S₃.

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13. Fig. 12. Model of the filter on unidirectional DART-type converters for FEM calculation in COMSOL: a — conditional view of the filter with connected electrical ports in the “normal” connection; b — “reverse” connection; c — DART geometry; d — results of calculating the total mechanical displacement for one frequency point; d — calculated frequency response: 1 — “normal” connection without matching; 2 — “normal” connection with matching; 3 — “reverse” connection. Designations: F — “forward” — direction of maximum SAW radiation; R — “reverse” — direction of minimum wave radiation.

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14. Fig. 13. 3D model of a split-transducer filter with apodization according to the Hamming function in COMSOL: a – Hamming function; b – fragment of the filter with an input IDT; c – general view of the filter geometry.

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15. Fig. 14. Comparison of the calculated (1) and experimental (2) frequency response of the filter.

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