Acoustic Modes in Chalcogenide Layer As2s3 on Rotated 1280 Y-Cut of Lithium Niobate

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Acoustic Modes in Chalcogenide Layer As2S3 on rotated 1280 Y-cut of Lithium Niobate

Substrate

Rinat M. Taziev

Abstract—By means of effective permittivity function for layered system the frequency dependence of excitation of various acoustic modes in a chalcogenide film As2S3 on rotated 1280Y-cut lithium niobate is investigated..

Index Terms—surface acoustic wave, lithium niobate, chalcogenide, layered structure

I.INTRODUCTION

aveguide structure similar to thin layer of chalcogenide As2S3 (or As2Sе3 ) over surface of lithium niobate substrate allows to improve acoustooptic interaction characteristics in comparison with a usual waveguide on LiNbO3, preparing by diffusion method [1-4]. However, the structure of the acoustic modes excited by a linear point charge source in a such layered structure, practically is not studied. The aim of the present paper is numerically to study characteristics of the acoustic modes launched by linear point charge source, located on the layer-substrate interface by effective permittivity method. For its derivation usually one uses a method of transfer matrix [5], which essence is to transfer the amplitudes of acoustic fields from one layer to another, satisfying boundary conditions on interfaces of layers.

A. Computation method

Let us consider briefly the derivation of effective permittivityfunction for computation of excitation characteristics of acoustic modes in layered system: a thin film ofchalcogenide As2S3-YZ-cut of lithium niobate. It can be derived if we solve system of the wave equations with corresponding boundary conditions on interfaces of every section of these layered structure [5].

The acoustic fields in the medium (see Fig. 1) are described by the wave equations [6]:

(1)

andmaterial constitutive relations

(2)

where Cijkl , eikl и ik are the elastic, piezoelectric and dielectric material constants; Di, Ui are the electrical and elastic displacements, respectively; , Tij are the electrical potential and elastic stress tensor, respectively;  is the density of medium.

Assuming that the normal vector n to the surface of medium coincides with the axes x3, and the axes x1 is directed along to the wave vector k (see Fig.1), we seek the solution of (1) in the following way:

a) for piezoelectric lithium niobate

,j=1..3 (3)

b) for chalcogenide As2S3

,j=1..3 (4)

Fig.1. Chalcogenide layer As2S3– Y+1280,X-cut of lithium niobate.

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Fig.2а. Phase velocities of acoustic modes in layered system As2S3/Y+1280,X-cut of LiNbO3. / Fig.2b. Electromechanical coupling coefficients for acoustic modes in layered system As2S3/Y+1280,X-cut of LiNbO3.

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here, pn and (uj, )n are the eigenvalues and eigenvectors of wave equations (1) for every region of layered medium, V is the phase velocity, Cn is the unknown constants, determined from the boundary conditions for solutions (3)-(4). Elastic, piezoelectric and dielectric constants for chalcogenide and lithium niobate were taken from [7], [8] and [9], respectively.

If we denote the vectors U=(u3,u2,u1,) and T=(T33,T32,T31,D3), then, the vector y=(T/ik,U) for acoustic fields on bottom and top interfaces of layer can be presented as:

(5)

After some manipulations, excluding the unknowns Cj in (5), we can derive relation y(h)=M(h)M(0)-1y(0), where the matrix M(h)M(0)-1 is the transfer matrix of dimension (8x8), which consists of the matrices M(h)=[y1exp(ikhp1),…,y8exp(ikhp8)] and M(0)=[y1,…,y8]. From the relation y(h)=M(h)M(0)-1y(0) one can derive the Green’s function G for linear charge source q at the interface of layered system: U(0)=G(V,kh)T(0), which leads to the effective permittivity function at interface of layered system:

(6)

where and are the normal components of electric displacement on the surface of substrate and bottom surface of chalcogenide layer As2S3 at x3=0 (see Fig.1), respectively.

B. Numerical results

Fig.2 shows acoustic modes in the layered structure As2S3/Y+1280,X-cut LiNbO3 for thickness h=0.8  of chalcogenide film. Several acoustic modes are observed in the layered structure: besides the Rayleigh wave, the guided modes such as Love and Sezawa waves, which arisewhen the

sound velocity in the chalcogenide layer is lower than one in the substrate. It should benoted, that leaky wave modes may also appear in a such structure. The main mode is a surface acoustic wave (Rayleigh wave) mode, propagating without attenuation in the layered structure for arbitrary As2S3 film thickness. Other acoustic modes propagates without attenuation only for appropriate thickness h of As2S3 film and frequency f0. For other values of thickness and frequency they are the leaky modes or skimming surface bulk acoustic waves with a strong or weak attenuation along propagation direction. These modes may be interpreted as Lamb waves in chalcogenide layer, perturbed by the presence of lithium niobate substrate. The first such nonsymmetric Lamb wave mode is known as a Sezawa wave [10]. One can see from Fig.2, the magnitude of electromechanical coefficient (K2/2) of Rayleigh wave has maxima around the frequency of 780 MHz for chalcogenide film thickness of 0.8 . Sezawa wave has a lower value of K2/2, than that for Rayleigh wave. At frequency of 375 MHz there is a strong interaction of Rayleigh and Love wave modes, and, as a result, they are transformed into each other without crossing their dispersion curves. Nevertheless, to observe in details the excitation properties of these modes it is necessary numerically investigate the effective permittivity function for layered structure As2S3/Y+1280,X-cut LiNbO3. Fig.3 displays the effective permittivity function as a function of slowness for different values of frequencies with its discrete step of 50 MHz. The sharp peaks (residues) on these curves belong to propagating modes without attenuation, which is described approximately by function /(s-s0), where  is proportional to the value of electromechanical coupling coefficient of wave. The greater the value, the broader the resonanse peak in Fig.3. From Fig.3 one can see Sezawa wave emergence. For frequency range of f0=100550 MHz this wave is a leaky wave, which attenuation magnitude depends on the frequency of source. The broader and smaller peak, thelarger attenuation of wave. The leaky wave in the range of frequency f0=400550 MHz has small attenuation andmay be

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Fig.3. Effective permittivity function as a function of frequency on layered structure As2S3/Y+1280,X-LiNbO3. Solid and dashed lines are the real and imaginary parts of the effective permittivity function, respectively.

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considered as a pure propagating mode in the layered structure. With increasing the excitation frequency its strong attenuation appears again, and at frequency of 600 MHz it transforms to undamping Sezawa wave mode.

References

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Manuscript received May 10, 2011.

R. M. Taziev is with the Institute of Semiconductor Physics of Siberian Branch of Russian Academy of Sciences, Acad. Lavrentjev Avenu, 13, Novosibirsk, Russia, 630090 ( e-mail: taziev@ thermo.isp.nsc.ru).