Surface and quasi-longitudinal acoustic waves in KTiOAsO4 single crystals

Ultrasonics 54 (2014) 425–427

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Short Communication

Surface and quasi-longitudinal acoustic waves in KTiOAsO4 single crystals Rinat M. Taziev ⇑ Institute of Semiconductor Physics SB RAS, Acad. Lavrentjev Avenue, 13, 630090 Novosibirsk, Russian Federation

a r t i c l e

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Article history: Received 4 July 2013 Received in revised form 8 September 2013 Accepted 20 September 2013 Available online 1 October 2013 Keywords: Potassium titanyl arsenate (KTiOAsO4, KTA) Surface acoustic wave Quasi-longitudinal acoustic wave Effective permittivity function

a b s t r a c t Surface and quasi-longitudinal acoustic wave properties have been investigated in potassium titanyl arsenate (KTiOAsO4, KTA) single crystals for the first time. Surface acoustic wave (SAW) velocity, electromechanical coupling coefficient and power flow angle characteristics have been obtained in rotated Y-cut of KTA crystals. High SAW electromechanical coupling coefficient (0.4%) is found in Z-cut of KTA crystals. For high-frequency devices it is promising the resonators on quasi-longitudinal acoustic wave in X-cut of KTA crystals with sharp response in interdigital transducer conductance at resonance frequency. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Potassium titanyl arsenate KTiOAsO4 (KTA) is one of a broad family of isostructural type potassium titanyl phosphate KTiOPO4 (KTP). In comparison with the KTP, KTA has large non-linear optical and electro-optical constants, and much less absorption at 2–5 lm wavelength range [1–3]. They exhibit excellent non-linear optical properties and have been expected as second- and third-harmonic generation devices. Since the KTA belongs to point group mm2 in the orthorhombic crystal system, the single crystals show piezoelectric properties. We then paid attention to the KTA crystal as a new piezoelectric material for SAW devices. For potassium titanyl phosphate, the elastic constants have been measured 20 years ago [4], but for potassium titanyl arsenate, they have been measured recently [5]. The phase velocity of surface acoustic wave (SAW) and shear piezoelectric waves called as Bleustein–Gulyaev waves have been calculated and measured on selected cuts and propagation directions in KTP single crystal [6,7]. However, there is no report on the literature on the detailed theoretical analysis of surface acoustic waves propagation properties for KTA single crystals. In this paper, we report a theoretical study on the SAW properties in Y-rotated cuts and quasi-longitudinal acoustic wave characteristics in X-cut of KTA crystal. For numerical computation of parameters of surface acoustic waves, phase velocity V, electromechanical coupling coefficient, power flow angle, we used the program [8]. The effective permittivity function of crystal and conductance of interdigital ⇑ Tel./fax: +7 (383)3306578. E-mail address: [email protected] 0041-624X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2013.09.019

transducers were calculated by [8]. The orientation of a crystal plane (cut) is defined by the first two Euler angles (a, l), and SAW propagation direction on this plane is defined by the third Euler angle h. Taking into account the symmetry of the crystals, for the fixed value of the Euler angle a = 0° both angles l and h were changed from 0° to 90° with step of 5°. Step size of 5° is chosen because of all SAW parameters are slightly changed within a given step, and to refine it is sufficient to apply a linear or quadratic interpolation to them. 2. Numerical results and discussion 2.1. Surface acoustic waves The SAW propagation in a piezoelectric single crystal is governed by the Christoffel equation with semi-infinite boundary conditions. Due to piezoelectric coupling, the equations of motion for elastic and electromagnetic fields must be solved simultaneously for piezoelectric media [9]. SAW velocities under free boundaries and with metal surface coatings are defined as VS and VM, respectively. For piezoelectric materials, the strength of piezoelectric effect is determined by the electromechanical coupling coefficient k2/2, which can be quantified by the formula: 2

k =2 

ðV S  V M Þ : VS

ð1Þ

The power flow angle (PFA) u is defined as the separation angle between power flow and phase propagation wave vector, it reflects the diffracted intensity of sound wave. The PFA u is given by the following formula:

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80

80

70

3700

70

60

3600

60

50

3500

40

3400

30

3300 3200

20

3100

10 0

0 10 20 30 40 50 60 70 80 90

SAW propagation direction, θ

90 80 70

0.4 0.3

50 40

0.2

30

0.1

20

0.0

10 0

Cut angle, μ

90

Cut angle, μ

Cut angle, μ

426

10

60 50

0

40

-10

30

-20

20 -30

10 0

0 10 20 30 40 50 60 70 80 90

0 10 20 30 40 50 60 70 80 90

SAW propagation direction, θ

SAW propagation direction, θ

(a)

(b)

(c)

Fig. 1. Contour plots: (a) SAW phase velocity (m/s), (b) SAW electromechanical coupling coefficient (%) and (c) SAW power flow angle (degrees) in KTA crystals. Thick (blue) line is a zero value contour line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

tan u ¼

1 dV : V dh

ð2Þ

The contour plots of results of numerical studies of SAW properties in Y-rotated cuts of KTA crystals, defined by Euler angles (a = 0°, l, h), are shown in Fig. 1. There are the following extreme values: (a) The phase velocity changes in the ranges from 3100 m/s to 3700 m/s. (b) The electromechanical coupling coefficient of wave varies in the ranges from 0% to 0.45%. (c) The power flow angle of wave changes in the ranges from 30° to 30°. There are a lot of crystal orientations with sufficiently high electromechanical coupling coefficients for efficient SAW excitation in KTA crystals. They all are located in the region defined by the Euler angles: a = 0°, l  0°–40° and h  10°–70°. There are SAW propagation directions with zero power flow angle. It should be noted that SAW power flow angles are small in the defined region (less than 7°). High electromechanical coupling coefficients of SAW in KTA crystals occupy an intermediate position between those for alpha-quartz and lithium tantalate. Extreme values of SAW electromechanical coupling coefficients are in Z-cut (l = 0°) of KTA crystals (see Fig. 1b). For SAW propagation direction along h = 30° away from the X-axis, the electromechanical coupling coefficient is about 9 times larger than those in well-known ST-cut of a-quartz. For these orientations it is equal to 0.40% for KTA crystals. It is promising for use in SAW devices, because of absence the excitation of bulk acoustic waves.

(a)

2.2. Quasi-longitudinal acoustic waves The effective permittivity, which are presented in Fig. 2a, shows that in X-cut of KTA crystals both the longitudinal bulk and surface acoustic waves are excited along Z-axis propagation direction. But the shear bulk acoustic wave is not excited along this direction. Sharp resonance behavior of effective permittivity near quasilongitudinal acoustic wave excitation has leaky wave properties in KTA crystals. Fig. 2b shows the dependence of the conductance as a function of frequency of electric potential difference between adjacent electrodes for interdigital transducer (IDT), which consists of periodic structure of 101 electrodes with width of 5 lm. Changing the thickness of the aluminum electrodes (see Fig. 2b), one can control the coherence interference of quasi-longitudinal acoustic wave in the periodic electrode structure. For electrode thickness of h/k  5%, the resonance on conductance behavior occurs in the structure. The quality factor Q is a measure of the propagation attenuation of quasi-longitudinal waves in the electrode structure [10]. At resonance frequency fr  318 MHz it equals to Qr  2120 and at antiresonance frequency far  328 MHz it equals to Qar  410 for electrode thickness of h/k  5%. For similar electrode structure a sharp resonance on conductance occurs for lithium niobate at h/k  8% and for lithium tantalate at h/k  9% [10,11]. In the work [12] was an attempt to explain a strong localization of quasi-longitudinal wave vibrations in the internal area of the electrode on the surface of LiNbO3 crystals. The authors indicate that the reflections of quasi-longitudinal wave in the periodic electrode structure introduce a significant effect on appearing of resonance behavior of admittance. For aluminum electrodes coherence interference occurs at h/k  5% for KTA crystals. For lithium niobate and tantalate crystals the maximum coherence

(b)

Fig. 2. (a) Effective permittivity function e/e0 and (b) IDT conductance on X-cut of KTA crystals, where e0 is the permittivity of vacuum.

R.M. Taziev / Ultrasonics 54 (2014) 425–427

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x3

x1 Fig. 3. (a) FEM mesh geometry and contour maps of (b) normal U3 and (c) longitudinal U1 displacement components of vibration at resonance frequency f0 = 317 MHz for one period length of infinite periodic structure with h/k = 5% in X-cut of KTA crystals.

interference occurs for the ratio h/k  8% and h/k  9%, respectively [10]. It should be noted, that the numerical value of thickness of the aluminum electrode at which are observed the resonance peaks of conductance are in good agreement with the experimental values for lithium niobate and tantalate crystals [13]. Our numerical study of resonance behavior of infinite electrode structure by FEM [14] (FlexPDE6, PDE Solutions Inc.), which is presented in Fig. 3, shows that the resonance oscillation occurs only when the all electrodes begin to oscillate in phase, driven by electric potential differences between adjacent electrodes. The oscillation of each electrode has a predominantly longitudinal component of elastic displacement U1, localized in the electrode area (see Fig. 3c). This explains why the quasi-longitudinal wave propagation in periodic structure is localized near the surface of KTA crystals. The weak interaction between adjacent electrodes has a predominantly normal to the surface plane elastic displacement U3 of vibration (see Fig. 3b). From Fig. 3, one can see that each electrode can be considered also as a simple strip elastic resonator attached on the free surface of piezoelectric crystal. A weak interaction of elastic resonators leads to the coherent interference in the structure at a certain driven frequency. It should be noted that sharp response in conductance of IDT grating structure with electrode thickness h/k  5% at frequency f0 = 318 MHz obtained by our software FEM/BEM [8] is in excellent agreement with the resonance frequency f0 = 317 MHz obtained by FEM (FlexPDE) for geometry shown in Fig. 3a. For X-cut and Z-axis propagation direction of wave, the piezoelectric coefficient e33 plays an important role on excitation of elastic vibration of electrodes by electric field generated by potential difference between adjacent electrodes. 3. Conclusion Our numerical studies of surface and quasi-longitudinal acoustic wave properties in potassium titanyl arsenate crystal show that, besides alpha-quartz, lithium niobate, lithium tantalate and langasite, it is promising for SAW device applications. SAW

electromechanical coupling coefficients in KTA crystal occupies an intermediate position between those for alpha-quartz and lithium tantalate. For SAW propagation direction along h = 30° away from X-axis, the electromechanical coupling coefficient is about 9 times larger than those in well-known ST-cut of a-quartz. The resonator on quasi-longitudinal waves in X-cut of KTA crystals exhibits a sharp response in IDT conductance at resonance frequency, which is promising for high-frequency SAW devices. References [1] Z. Liu, Q. Wang, X. Zhang, Z. Liu, J. Chang, H. Wang, et al., A KTiOAsO4 Raman laser, Appl. Phys. B 94 (2009) 585–588. [2] V.V. Atuchin, L.I. Isaenko, O.Yu. Khyzhun, L.D. Pokrovsky, A.K. Sinelnichenko, S.A. Zhurkov, Structural and electronic properties of the KTiOAsO4 (0 0 1) surface, Opt. Mater. 30 (2008) 1149–1152. [3] N. Dong, F. Chen, D. Jaque, Q. Lu, Micro second harmonic and Raman spectra of He+ implanted KTiOPO4 waveguides, Opt. Express 19 (2011) 13934–13939. [4] D.K.T. Chu, J.D. Bierlein, R.G. Hunsperger, Piezoelectric and acoustic properties of potassium titanyl phosphate (KTP) and its isomorphs, IEEE Trans. Ultrason. Ferroelect. Freq. Control 39 (1992) 683–687. [5] Z.L. Gao, Y.X. Sun, X. Yin, S.P. Wang, M.H. Jiang, X.T. Tao, Growth and electricelastic properties of KTiOAsO4 single crystal, J. Appl. Phys. 108 (2010) 024103. [6] D.K.T. Chu, J.D. Bierlein, Surface acoustic wave and Bleustein–Gulyaev wave generation in KTiOPO4 crystals, Appl. Phys. Lett. 63 (1993) 2041–2043. [7] W. Soluch, Calculation of Bleustein–Gulyaev waves parameters in KTiOPO4 crystal, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 (1995) 977. [8] R.M. Taziev, FEM/BEM for simulation of LSAW devices, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 (2007) 2060–2069. [9] J.J. Campbell, W.R. Jones, A method for estimating optimal crystal cuts and propagation direction for excitation of piezoelectric surface waves, IEEE Trans. Sonics Ultrason. 15 (1968) 209–217. [10] A. Isobe, M. Hikita, K. Asai, Q values of longitudinal leaky SAWs propagating on rotated Y-cut LN substrates along the perpendicular to the X axis, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52 (2005) 1812–1816. [11] V.I. Grigorievski, Fast leaky surface acoustic waves on lithium niobate and lithium tantalate, Proc. IEEE Ultrason. Symp. 1 (2000) 259–262. [12] V.P. Plessky, T. Makkonen, M. Salomaa, Leaky SAW in an isotropic substrate with thick electrodes, Proc. IEEE Ultrason. Symp. 1 (2001) 239–242. [13] T. Makkonen, V.P. Plessky, V.I. Grigorievski, L. Kopp, M. Solal, W. Steichen, et al., FEM/BEM simulation and experimental study of LLSAW resonator characteristics on YZ-LiNbO3, Proc. IEEE Ultrason. Symp. 1 (2002) 317–320. [14] FlexPDE6. PDE Solutions Inc. URL .