**3.1 Ion beam orientation control of wurtzite thin film by ion beam irradiation**

Polycrystalline films tend to grow in their most densely packed plane parallel to the substrate plane. Bravais proposed the empirical rule that the growth rate of the crystal plane is proportional to the surface atomic density. Namely, the lattice plane with higher surface atomic density grows more rapidly. Curie argued that the growth rate perpendicular to a plane is proportional to the surface free energy (Curie, 1885).

Ion bombardment during film deposition can modify this preferred orientation of the films. This is usually explained by a change in anisotropy of the growing rate of the crystal plane in the grain, which is reflected by the difference in the degree of the ion channeling effect or ion-induced damage in the crystal plane (Bradley et al., 1986; Ensinger, 1995; Ressler et al., 1997; Dong & Srolovitz, 1999). For example, during ion beam irradiation, the commonly observed <111> preferred orientation in a face-centered cubic film changes to a <110> preferred orientation, which corresponds to the easiest channeling direction (Van Wyk & Smith, 1980; Dobrev, 1982). In-plane texture controls have also been achieved by optimizing the incident angle of the ion beam (Yu et al., 1985; Iijima et al., 1992; Harper et al., 1997; Kaufman et al., 1999; Dong et al., 2001; Park et al., 2005).

In wurtzite films, for example, the surface energy densities of the (0001), (11 2 0) and (10 1 0) planes of the ZnO crystal are estimated to be 9.9, 12.3, 20.9 eV/nm2, respectively (Fujimura et al., 1993). The (0001) plane has the lowest surface density. Thus, the ZnO film tends to grow along the [0001] direction. When wurtzite crystal is irradiated with ion beam, the most densely packed (0001) plane should incur more damage than the (10 1 0) and (11 2 0) planes, which correspond to channeling directions toward the ion beam irradiation. We can therefore expect that the thermodynamically preferred (0001) oriented grain growth will be disturbed by ion damage so that the damage-tolerant (10 1 0) or (11 2 0) orientated grains (caxis parallel oriented grain) will preferentially develop instead.

On this basis, in-plane and out-of-plane orientation control of AlN and ZnO films by means of ion beam-assisted deposition technique, such as evaporation (Yanagitani & Kiuchi, 2007c) and sputtering (Yanagitani & Kiuchi, 2007e, 2011b) was achieved. c-axis parallel oriented can be obtained even in a conventional magnetron sputtering technique using a low pressure discharge ( <0.1 Pa) (Yanagitani et al., 2005) or RF substrate bias (Takayanagi, 2011), which leads ion bombardment on the substrate. Figure 4 shows the XRD patterns of the ZnO films deposited with various ion energy and amount of flux in ion beam assisted evaporation (Yanagitani & Kiuchi, 2007c). Table 1 shows the ion current densities in the case of "Large ion flux" and "Small ion flux" in Fig 4. The tendency of the (10 1 0) orientation is enhanced with increasing ion energy and amount of ion irradiation, demonstrating that the ion bombardment induced the (0001) orientation to change into a (10 1 0) orientation, which corresponds to the ion channeling direction.

technique of c-axis normal film has been well established, but effective electrometrical coupling is weak (*keff*=0.04-0.06) (Corso et al., 2007; Milyutin et al., 2008). The former has large electrometrical coupling (*k*15=0.24) (Yanagitani et al., 2007a), and recently the c-axis parallel oriented film can be easily obtained by using ion beam orientation control technique

**3. Ion beam orientation control technique for shear mode piezoelectric films** 

Polycrystalline films tend to grow in their most densely packed plane parallel to the substrate plane. Bravais proposed the empirical rule that the growth rate of the crystal plane is proportional to the surface atomic density. Namely, the lattice plane with higher surface atomic density grows more rapidly. Curie argued that the growth rate perpendicular to a

Ion bombardment during film deposition can modify this preferred orientation of the films. This is usually explained by a change in anisotropy of the growing rate of the crystal plane in the grain, which is reflected by the difference in the degree of the ion channeling effect or ion-induced damage in the crystal plane (Bradley et al., 1986; Ensinger, 1995; Ressler et al., 1997; Dong & Srolovitz, 1999). For example, during ion beam irradiation, the commonly observed <111> preferred orientation in a face-centered cubic film changes to a <110> preferred orientation, which corresponds to the easiest channeling direction (Van Wyk & Smith, 1980; Dobrev, 1982). In-plane texture controls have also been achieved by optimizing the incident angle of the ion beam (Yu et al., 1985; Iijima et al., 1992; Harper et al., 1997;

In wurtzite films, for example, the surface energy densities of the (0001), (11 2 0) and (10 1 0) planes of the ZnO crystal are estimated to be 9.9, 12.3, 20.9 eV/nm2, respectively (Fujimura et al., 1993). The (0001) plane has the lowest surface density. Thus, the ZnO film tends to grow along the [0001] direction. When wurtzite crystal is irradiated with ion beam, the most densely packed (0001) plane should incur more damage than the (10 1 0) and (11 2 0) planes, which correspond to channeling directions toward the ion beam irradiation. We can therefore expect that the thermodynamically preferred (0001) oriented grain growth will be disturbed by ion damage so that the damage-tolerant (10 1 0) or (11 2 0) orientated grains (c-

On this basis, in-plane and out-of-plane orientation control of AlN and ZnO films by means of ion beam-assisted deposition technique, such as evaporation (Yanagitani & Kiuchi, 2007c) and sputtering (Yanagitani & Kiuchi, 2007e, 2011b) was achieved. c-axis parallel oriented can be obtained even in a conventional magnetron sputtering technique using a low pressure discharge ( <0.1 Pa) (Yanagitani et al., 2005) or RF substrate bias (Takayanagi, 2011), which leads ion bombardment on the substrate. Figure 4 shows the XRD patterns of the ZnO films deposited with various ion energy and amount of flux in ion beam assisted evaporation (Yanagitani & Kiuchi, 2007c). Table 1 shows the ion current densities in the case of "Large ion flux" and "Small ion flux" in Fig 4. The tendency of the (10 1 0) orientation is enhanced with increasing ion energy and amount of ion irradiation, demonstrating that the ion bombardment induced the (0001) orientation to change into a (10 1 0) orientation, which

**3.1 Ion beam orientation control of wurtzite thin film by ion beam irradiation** 

(presented in next section), even in a large area (Kawamoto et al., 2010).

plane is proportional to the surface free energy (Curie, 1885).

Kaufman et al., 1999; Dong et al., 2001; Park et al., 2005).

axis parallel oriented grain) will preferentially develop instead.

corresponds to the ion channeling direction.


Table 1. Ion current densities in "Large ion flux" and "Small ion flux"

Fig. 4. 2θ–ω scan XRD patterns of the ZnO films deposited without ion irradiation, and with ion irradiation of 0-1 keV with "Large ion flux" and "Small ion flux" (Yanagitani & Kiuchi, 2007c)

Figure 5 shows the XRD patterns of the samples deposited under the conditions that various RF and DC bias are applied to the substrate. Although any dramatic change in usual (0001)

Shear Mode Piezoelectric Thin Film Resonators 511

where *f*p and *f*s are the parallel resonant frequency and series resonant frequency,

However, it takes considerable time and effort to fabricate FBAR structure which have selfstanding piezoelectric layer. It is convenient if *k* value can be determined from as deposited structure, namely so-called an HBAR (high-overtone bulk acoustic resonator) or composite resonator structure consisting of top electrode layer/piezoelectric layer/bottom electrode layer/thick substrate. Methods for determining the *k* value of the films from HBAR structure are more complex than that for the self-supported single piezoelectric film structure (FBAR structure). Several groups have investigated methods for the determination of *kt* value from the HBAR structure (Hickernell, 1996; Naik, et al., 1998; Zhang et al., 2003). One of the easiest ways of *k* determination is to use a conversion loss characteristic of the HBAR structure. When the thickness of electrode layers is negligible small compared with that of piezoelectric layer, capacitive impedance of resonator is equal to the electrical source impedance, and *k* value of the piezoelectric layer is smaller than 0.3, conversion loss *CL* is approximately represented by *k* value at parallel resonant frequency (Foster et al., 1968):

<sup>10</sup> <sup>2</sup> 10log <sup>8</sup>

where, *Z*s and *Z*p is acoustic impedance of the substrate and piezoelectric layer, respectively. However, various inhomogeneities sometimes exist in the film resonator, such as nonnegligible thick and heavy electrode layers, thickness taper, or the piezoelectrically inactive layer composed of randomly oriented gains growing in the initial stages of the deposition. In this case, the *k* values of the film can be determined so as to match the experimentally measured conversion losses (*CL*) of the resonators with theoretical minimum *CL* by taking *k* value as adjustable parameter. The theoretical *CL* in this case can be calculated by Mason's equivalent circuit model including electrode layer, film thickness taper and piezoelectrically inactive layer. This method allows various inhomogeneous effect of film to be taken into

The experimental *CL* of HBAR can be determined from reflection coefficients (S11) of the resonators, which can be obtained using a network analyzer with a microwave probe. The inverse Fourier transform of S11 frequency response of the resonator gives the impulse response of the resonator in the time domain. In the HBAR structure, the impulse response is expected to include echo pulse trains reflected from the bottom surface of the substrate, and the insertion loss of resonator can be obtained from the Fourier transform of the first echo in this impulse response. This experimental insertion loss *ILexperiment* includes doubled *CL* in the piezoelectric film and round-trip diffraction loss *DL* and round-trip propagation

> ( ) exp <sup>1</sup> , <sup>2</sup>

*CL IL DL PL* = −− *eriment* (24)

**4.2 Experimental method to estimate conversion loss of HBAR structure** 

loss *PL* in the silica glass substrate. Therefore, *CL* can be expressed as

*<sup>Z</sup> CL*

*s p*

≈ ⋅ (23)

*k Z* π

*f f <sup>f</sup> <sup>k</sup> f f*

*p s s p p*

(22)

 π<sup>−</sup> <sup>=</sup>

<sup>2</sup> tan 2 2

π

respectively.

account (Yanagitani et al., 2007b, 2007c).

preferred orientation is not occurred in the case of positive or negative DC bias, (0001) orientation changed to (11 2 0) and (10 1 0) orientation with the increase of RF bias power which induces the bombardment of positive ion on substrate. Interestingly, the order of the appearance of the (0001) to (11 2 0) and (10 1 0) corresponds to the order of increasing surface atomic density, which may be the order of damage tolerance against ion bombardment.

In order to excite shear wave in the c-axis parallel film, c-axis is required to orient not only in out-of-plane direction but also in in-plane direction. The ion beam orientation control technique allows us to control even in in-plane c-axis direction and polarization by the direction of beam incident direction (Yanagitani et al., 2007d).

Fig. 5. 2θω scan XRD patterns of the samples deposited without bias, with 80 MHz RF bias of 50 to 250 W, or with -200 to 100 DC bias. All samples were measured at the center of the bias electrode (Takayanagi et al., 2011)

### **4. Method for determining** *k* **values in piezoelectric thin films**

### **4.1** *k* **value determination using as-deposited structure (HBAR structure)**

A method for determining piezoelectric property in thin films is described in this section. In general, electromechanical coupling coefficient (*k* value) in thin film can be easily determined by series and parallel resonant frequency of a FBAR consisting of top electrode layer/piezoelectric layer/bottom electrode layer or SMR (Solidly mounted resonator) consisting of top electrode layer/piezoelectric layer/bottom electrode layer/Bragg reflector. In case thickness of electrode film is negligible small compared with that of piezoelectric film. *k* of the piezoelectric film can be written as follows (Meeker, 1996):

preferred orientation is not occurred in the case of positive or negative DC bias, (0001) orientation changed to (11 2 0) and (10 1 0) orientation with the increase of RF bias power which induces the bombardment of positive ion on substrate. Interestingly, the order of the appearance of the (0001) to (11 2 0) and (10 1 0) corresponds to the order of increasing surface atomic density, which may be the order of damage tolerance against ion

In order to excite shear wave in the c-axis parallel film, c-axis is required to orient not only in out-of-plane direction but also in in-plane direction. The ion beam orientation control technique allows us to control even in in-plane c-axis direction and polarization by the

(1120)

80 MHz RF bias power:

20 25 30 35 40 45 50 55 60 65 70

of 50 to 250 W, or with -200 to 100 DC bias. All samples were measured at the center of the

A method for determining piezoelectric property in thin films is described in this section. In general, electromechanical coupling coefficient (*k* value) in thin film can be easily determined by series and parallel resonant frequency of a FBAR consisting of top electrode layer/piezoelectric layer/bottom electrode layer or SMR (Solidly mounted resonator) consisting of top electrode layer/piezoelectric layer/bottom electrode layer/Bragg reflector. In case thickness of electrode film is negligible small compared with that of piezoelectric

scan XRD patterns of the samples deposited without bias, with 80 MHz RF bias


Non-bias

100 V

DC bias voltage:

150 W

200 W

100 W 50 W

250 W

Film thickness:

10.0 μm

> 9.8 μm

> 9.8 μm

> 9.8 μm

> 6.9 μm

> 9.6 μm

> 7.5 μm

> 6.9 μm

> 8.8 μm

2θ(deg.)

**4. Method for determining** *k* **values in piezoelectric thin films** 

film. *k* of the piezoelectric film can be written as follows (Meeker, 1996):

**4.1** *k* **value determination using as-deposited structure (HBAR structure)** 

direction of beam incident direction (Yanagitani et al., 2007d).

(0002)

(1010)

bombardment.

Intensity (a.u.)

10 kcps

Fig. 5. 2θω ×0.1

bias electrode (Takayanagi et al., 2011)

$$k^2 = \frac{\pi}{2} \frac{f\_s}{f\_p} \tan \left(\frac{\pi}{2} \frac{f\_p - f\_s}{f\_p}\right) \tag{22}$$

where *f*p and *f*s are the parallel resonant frequency and series resonant frequency, respectively.

However, it takes considerable time and effort to fabricate FBAR structure which have selfstanding piezoelectric layer. It is convenient if *k* value can be determined from as deposited structure, namely so-called an HBAR (high-overtone bulk acoustic resonator) or composite resonator structure consisting of top electrode layer/piezoelectric layer/bottom electrode layer/thick substrate. Methods for determining the *k* value of the films from HBAR structure are more complex than that for the self-supported single piezoelectric film structure (FBAR structure). Several groups have investigated methods for the determination of *kt* value from the HBAR structure (Hickernell, 1996; Naik, et al., 1998; Zhang et al., 2003). One of the easiest ways of *k* determination is to use a conversion loss characteristic of the HBAR structure. When the thickness of electrode layers is negligible small compared with that of piezoelectric layer, capacitive impedance of resonator is equal to the electrical source impedance, and *k* value of the piezoelectric layer is smaller than 0.3, conversion loss *CL* is approximately represented by *k* value at parallel resonant frequency (Foster et al., 1968):

$$\text{CL} = 10 \log\_{10} \frac{\pi}{8k^2} \cdot \frac{Z\_s}{Z\_p} \tag{23}$$

where, *Z*s and *Z*p is acoustic impedance of the substrate and piezoelectric layer, respectively. However, various inhomogeneities sometimes exist in the film resonator, such as nonnegligible thick and heavy electrode layers, thickness taper, or the piezoelectrically inactive layer composed of randomly oriented gains growing in the initial stages of the deposition. In this case, the *k* values of the film can be determined so as to match the experimentally measured conversion losses (*CL*) of the resonators with theoretical minimum *CL* by taking *k* value as adjustable parameter. The theoretical *CL* in this case can be calculated by Mason's equivalent circuit model including electrode layer, film thickness taper and piezoelectrically inactive layer. This method allows various inhomogeneous effect of film to be taken into account (Yanagitani et al., 2007b, 2007c).

### **4.2 Experimental method to estimate conversion loss of HBAR structure**

The experimental *CL* of HBAR can be determined from reflection coefficients (S11) of the resonators, which can be obtained using a network analyzer with a microwave probe. The inverse Fourier transform of S11 frequency response of the resonator gives the impulse response of the resonator in the time domain. In the HBAR structure, the impulse response is expected to include echo pulse trains reflected from the bottom surface of the substrate, and the insertion loss of resonator can be obtained from the Fourier transform of the first echo in this impulse response. This experimental insertion loss *ILexperiment* includes doubled *CL* in the piezoelectric film and round-trip diffraction loss *DL* and round-trip propagation loss *PL* in the silica glass substrate. Therefore, *CL* can be expressed as

$$\text{CL} = \frac{1}{2} \left( \text{ } \text{IL}\_{\text{exp} \, c \, \text{current}} - \text{DL} - \text{PL} \right) . \tag{24}$$

Shear Mode Piezoelectric Thin Film Resonators 513

*v*<sup>1</sup> *v*<sup>2</sup> *Zp*tanh (γ

*Zp* /sinh (

γ*pdp*)

*pdp Z* / 2) *<sup>p</sup>*tanh (

*F*<sup>1</sup> *F*<sup>2</sup>

γ*pdp* / 2)


*i*

*V*

Substrate

Electrode layer

*C0*

…

…

Electrode layer

*de*<sup>2</sup> / 2)

*Ze* / sinh (

γ*<sup>e</sup>*2*de*2)

, <sup>1</sup>

*<sup>F</sup>* <sup>=</sup>

*Substrate*

0 1 *s*

*Z*

(28)

1 : φ0

*v*<sup>1</sup> *v*<sup>2</sup> *Zp*tanh (γ

(a) (b)

Electrode layer

*Ze*<sup>1</sup> / sinh (

γ *e*1 *de*1 )

Fig. 7. Equivalent circuit model of the over-moded resonator structure

*C0*

tanh (γ*<sup>e</sup>*1*de*<sup>1</sup> / 2)

multiplying each circuit element.

*FTransformer*

0

1/ 0 0

φ

<sup>=</sup>

0

φ

Electrode

*Zp* /sinh (

γ *pdp* )

Fig. 6. Equivalent circuit model of (a) non-piezoelectric (b) piezoelectric elastic solid

Piezoelectric layer

*Zp*tanh (

1 : φ0

*-C0*

γ*pdp*/2)

Piezoelectric layer

layer Air Substrate

*Zs Ze*<sup>1</sup>

It is convenient to derive whole impedance of the circuit by using *ABCD*-parameters (Paco et al., 2008) As shown in Eqs. (28)-(32), *ABCD*-parameters of whole circuit is derived

> , <sup>0</sup> 0

10 1 *Electric port j C <sup>F</sup> j C*

ω

1 0 1 1/

<sup>−</sup> = ⋅

ω

*Zp* / sinh (

γ *p dp*)

*Ze* tanh (γ*e*2

*pdp Z* / 2) *<sup>p</sup>*tanh (

*F*<sup>1</sup> *F*<sup>2</sup>

γ*pdp* / 2)

where diffraction loss *DL* can be calculated according to the method reported by Ogi *et al*. (Ogi et al., 1995). This method is based on integration of the velocity potential field in the divided small transducer elements, which allows calculation of the *DL* with electrode areas of various shapes. The round-trip propagation loss *PL* is given as

<sup>2</sup> 2 , *<sup>s</sup> PL ds <sup>f</sup>* α= (25)

where *ds* is the thickness of the substrate, α<sup>s</sup> represents the shear wave attenuation in the substrate, for example, α<sup>s</sup> / *f* 2 = 19.9×10-16 (dB·s2/m) in silica glass substrate (Fraser, 1967).

### **4.3 Conversion loss simulation in HBAR by Mason's equivalent circuit model**

Electromechanical coupling coefficient *k* can be estimated by comparing an experimental *CL* with a theoretical *CL* of the HBAR. One-dimensional Mason's equivalent circuit model is convenient tool for simulating theoretical *CL* of the resonator. Generally, in case nonpiezoelectric elastic solid vibrates in thickness mode, its can be described as T-type equivalent circuit (Fig. 6 (a)) where *F*1 and *F*2 are force and *v*1 and *v*2 are particle velocity acting on each surface of elastic solid. Piezoelectric elastic solid can be represented as the Mason's three ports equivalent circuit which includes additional electric terminal concerning electric voltage *V* and current *I* (Fig. 6 (b)) (Mason, 1964). Here, γ is propagation constant, *Z* is acoustic impedance and *dp* is thickness of elastic solid. To take account of attenuation of vibration, mechanical quality factor *Q*m is defined as *Q*m= *cr*/*ci* where *cr* and *ci* are real part and imaginary part of elastic constant, respectively. Using mechanical quality factor *Q*m, propagation constant γ and acoustic impedance *Z* are given as:

$$\gamma = j\rho \sqrt{\frac{\rho}{c\_r \left\{ 1 + j \text{ (1/Q}\_m\text{)} \right\}}} \text{, } Z = S \sqrt{\rho c\_r \left\{ 1 + j \text{ (1/Q}\_m\text{)} \right\}} \tag{26}$$

where ρ is density of the elastic solid and *S* is electrode area of the resonator. Static capacitance *C*0 and ratio of transformer φ0 in the circuit are given as:

$$\mathbf{C}\_{0} = \mathbf{c}\_{11}^{S} \frac{\mathbf{S}}{d\_{p}} \,, \ \phi\_{0} = \left[ \frac{\mathbf{C}\_{0} \mathbf{v}\_{p} Z\_{p}}{d\_{p}} \left( \frac{k\_{15}^{2}}{1 - k\_{15}^{2}} \right) \right]^{\frac{1}{2}} \,, \tag{27}$$

where *d* is the thickness of the layers, 11 *S* ε is permittivity, and *v* is the velocity of the shear wave. Subscript *p*, *e*1*, e*2 and *s* respectively represent piezoelectric layer, top electrode layer, bottom electrode layer and substrate. *k* value affects the equivalent circuit through the ratio of transformer φ0.

Equivalent circuit for the over-moded resonator structure is given in Fig. 7 by cascade arranging non-piezoelectric and piezoelectric part as described in Figs. 6 (a) and (b). Substrate thickness is assumed infinite to ignore reflection waves from bottom surface of the substrate in this case. When the surface of the top electrode is stress-free, the acoustic input port is shorted. As top electrode part circuit can be simplified, three-port circuit in Fig. 7 is transformed to the two-ports circuit shown in Fig. 8 (Rosenbaum, 1988).

where diffraction loss *DL* can be calculated according to the method reported by Ogi *et al*. (Ogi et al., 1995). This method is based on integration of the velocity potential field in the divided small transducer elements, which allows calculation of the *DL* with electrode areas

> <sup>2</sup> 2 , *<sup>s</sup> PL ds <sup>f</sup>* α

Electromechanical coupling coefficient *k* can be estimated by comparing an experimental *CL* with a theoretical *CL* of the HBAR. One-dimensional Mason's equivalent circuit model is convenient tool for simulating theoretical *CL* of the resonator. Generally, in case nonpiezoelectric elastic solid vibrates in thickness mode, its can be described as T-type equivalent circuit (Fig. 6 (a)) where *F*1 and *F*2 are force and *v*1 and *v*2 are particle velocity acting on each surface of elastic solid. Piezoelectric elastic solid can be represented as the Mason's three ports equivalent circuit which includes additional electric terminal concerning electric voltage *V* and current *I* (Fig. 6 (b)) (Mason, 1964). Here,

propagation constant, *Z* is acoustic impedance and *dp* is thickness of elastic solid. To take account of attenuation of vibration, mechanical quality factor *Q*m is defined as *Q*m= *cr*/*ci* where *cr* and *ci* are real part and imaginary part of elastic constant, respectively. Using

γ

, *ZS c j Q* = + ρ

<sup>2</sup> <sup>2</sup> <sup>0</sup> <sup>15</sup>

0 2

*p p p CvZ k d k*

<sup>=</sup> <sup>−</sup>

0 in the circuit are given as:

15 , <sup>1</sup>

1

is permittivity, and *v* is the velocity of the shear

α

**4.3 Conversion loss simulation in HBAR by Mason's equivalent circuit model** 

= (25)

<sup>s</sup> represents the shear wave attenuation in the

and acoustic impedance *Z* are given

*r m* { } 1 1( ) (26)

(27),

γis

<sup>s</sup> / *f* 2 = 19.9×10-16 (dB·s2/m) in silica glass substrate (Fraser, 1967).

of various shapes. The round-trip propagation loss *PL* is given as

where *ds* is the thickness of the substrate,

α

mechanical quality factor *Q*m, propagation constant

*j*

Static capacitance *C*0 and ratio of transformer

where *d* is the thickness of the layers, 11

φ0.

γ ω=

*r m* { } 1 1( )

is density of the elastic solid and *S* is electrode area of the resonator.

φ

*S* ε

φ

wave. Subscript *p*, *e*1*, e*2 and *s* respectively represent piezoelectric layer, top electrode layer, bottom electrode layer and substrate. *k* value affects the equivalent circuit through the ratio

Equivalent circuit for the over-moded resonator structure is given in Fig. 7 by cascade arranging non-piezoelectric and piezoelectric part as described in Figs. 6 (a) and (b). Substrate thickness is assumed infinite to ignore reflection waves from bottom surface of the substrate in this case. When the surface of the top electrode is stress-free, the acoustic input port is shorted. As top electrode part circuit can be simplified, three-port circuit in Fig. 7 is

*c jQ* ρ

> 0 11 *S p*

*<sup>S</sup> <sup>C</sup> <sup>d</sup>* <sup>=</sup> ε,

transformed to the two-ports circuit shown in Fig. 8 (Rosenbaum, 1988).

+

substrate, for example,

as:

where ρ

of transformer

Fig. 6. Equivalent circuit model of (a) non-piezoelectric (b) piezoelectric elastic solid

Fig. 7. Equivalent circuit model of the over-moded resonator structure

It is convenient to derive whole impedance of the circuit by using *ABCD*-parameters (Paco et al., 2008) As shown in Eqs. (28)-(32), *ABCD*-parameters of whole circuit is derived multiplying each circuit element.

$${}\_{F\_{\text{Transformer}}} = \begin{bmatrix} 1 \ / \phi\_0 & 0 \\ 0 & \phi\_0 \end{bmatrix} {}\_{\text{'}} F\_{\text{Electric part}} = \begin{bmatrix} 1 & 0 \\ jo \text{C}\_0 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & -1 \ / \ jo \text{C}\_0 \\ 0 & 1 \end{bmatrix} {}\_{\text{'}} F\_{\text{Substate}} = \begin{bmatrix} 1 & Z\_s \\ 0 & 1 \end{bmatrix} \tag{28}$$

Shear Mode Piezoelectric Thin Film Resonators 515

*IL G G*

*GG B* = = + +

Figure 9 (a) shows the pure shear mode theoretical and experimental *CL* curves of the c-axis parallel film HBAR as an example. By comparing experimental curve with theoretical curves

Mason's model (a)

0 100 200 300 400 500 600 700 800 900 Frequency (MHz)

Model including inactive layer

Experiment

0 100 200 300 400 500 600 700 800 900 Frequency (MHz)

Fig. 9. Frequency response of the experimental shear mode *CL* (open circles). (a) The simulated shear mode *CL* curves (solid line) in various *k*15 values and (b) the curve simulated by the model including various thickness of piezoelectrically inactive layer (Yanagitani & Kiuchi, 2007c)

Propagation loss

Propagation loss

*CL*

**4.4** *k* **value determination from conversion loss curves** 

60

50

40

*k*15= 0.12 *k*15= 0.16 *k*15= 0.20 *k*15= 0.26

30

Conversion loss (dB)

20

10

0

60

(b)

50

40

30

*d*n= 1μm

*d*n= 0μm

*d*n= 2μm

Conversion loss (dB)

20

10

0

( ) <sup>10</sup> 2 2 4 10log . <sup>2</sup>

*S f S f f*

Experiment

(34)

Hence the *CL* is

$$F\_{\text{Pizo}+\text{Ecktode layer}} = \begin{bmatrix} 1 & Z\_p \end{bmatrix} \begin{pmatrix} \sinh\left(\mathcal{Y}\_p d\_p\right) \\ 1 \end{pmatrix} \begin{bmatrix} 1 & 0 \\ 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ \mathcal{Z}\_{e1} \tanh\left(\mathcal{Y}\_{e1} d\_{e1} / \mathcal{Z}\right) + Z\_p \tanh\left(\mathcal{Y}\_p d\_p / \mathcal{Z}\right) \end{bmatrix} \begin{bmatrix} 1 \\ 1 \end{bmatrix}$$

$$\cdot \begin{bmatrix} 1 & Z\_p \tanh\left(\mathcal{Y}\_p d\_p / \mathcal{Z}\right) \\ 0 & 1 \end{bmatrix} \tag{29}$$

$$F\_{\text{Cautter}-\text{electrode}} = \begin{bmatrix} 1 & Z\_{\iota2}\tanh(\chi\_{\iota2}d\_{\iota2}/2) \\ 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 \\ \sinh(\chi\_{\iota2}d\_{\iota2})/Z\_{\iota2} & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & Z\_{\iota2}\tanh(\chi\_{\iota2}d\_{\iota2}/2) \\ 0 & 1 \end{bmatrix} \tag{30}$$

$$F\_{\text{Substrate}} = \begin{bmatrix} \mathbf{1} & Z\_s \\ \mathbf{0} & \mathbf{1} \end{bmatrix} \tag{31}$$

$$F\_{\text{Ours}-\text{unadal resonator}} = F\_{\text{Electric part}} \cdot F\_{\text{Transformer}} \cdot F\_{\text{Pins}\text{-Elowder layer}} \cdot F\_{\text{Concentrelator}} \cdot F\_{\text{Substrate}} \tag{32}$$

Fig. 8. Simplification of equivalent circuit model for over-moded resonator structure

Insertion loss *IL* is expressed as the ratio of the signal power delivered from a source into load resistance to the power delivered from a source into the inserted network. *IL* of the resonators can be calculated with the following equation using conductance of the electrical source *GS* (0.02 S), input conductance *Gf*, and susceptance *Bf* of the circuit model, which can be derived from *ABCD*-parameter to Y-parameter conversion of eq. (32):

$$\text{Re}\left\{ \left( \text{G}\_f + jB\_f \right) \frac{\text{G}\_s^2}{\left( \text{G}\_S + \text{G}\_f \right)^2 + B\_f^2} \right\} \tag{33}$$
 
$$\text{ML} = 20 \log\_{10} \frac{\text{G}\_S + \text{G}\_f \times \text{G}\_f}{\text{G}\_S / 4} \,\text{-}\,\text{G} \tag{34}$$

Hence the *CL* is

514 Acoustic Waves – From Microdevices to Helioseismology

1 tanh( / 2)

0 1 sinh( ) / 1 0 1

γ

*<sup>F</sup>* <sup>=</sup>

γ*e*1

*Ze*<sup>1</sup> tanh (γ*<sup>e</sup>*1 *de*1)

Insertion loss *IL* is expressed as the ratio of the signal power delivered from a source into load resistance to the power delivered from a source into the inserted network. *IL* of the resonators can be calculated with the following equation using conductance of the electrical source *GS* (0.02 S), input conductance *Gf*, and susceptance *Bf* of the circuit model, which can

( )

*f f*

<sup>10</sup> 20log . <sup>4</sup>

*<sup>G</sup> e G jB*

*S*

*G*

( )

2

*Sf f*

ℜ + + + <sup>=</sup> (33)

*S*

*GG B*

<sup>2</sup> <sup>2</sup>

Fig. 8. Simplification of equivalent circuit model for over-moded resonator structure

be derived from *ABCD*-parameter to Y-parameter conversion of eq. (32):

*Zp*tanh (γ*p dp* / 2)

γ<sup>⋅</sup>

2 22 2 22 22 2 1 tanh( / 2) 1 0 1 tanh( / 2)

*ee e*

*d Z*

*Z*

*F F FF F F Over moded resonator Electric port Transformer* <sup>−</sup> = ⋅⋅ ⋅ ⋅ *Piezo Elecrode layer* <sup>+</sup> *Counterelectrode Substrate* (32)

*de*1) *Ze*1tanh (

 *Ze*2tanh (γ

*e ee e ee*

*Z d Z d*

= ⋅⋅

<sup>+</sup>

0 1 *Z d p pp*

*Substrate*

*Ze*<sup>1</sup> / sinh (

*Zp* / sinh (

Top electrode part

γ*<sup>p</sup>dp*)

*p p p*

γ

*Z d*

γ

<sup>−</sup>

*Ze*1 tanh (γ *e*1 *de*<sup>1</sup> / 2)


*C0*

*V*

*I*

1:φ0

*IL*

*Piezo Electrode layer*

*F*

*Counter electrode*

*F*

1 /sinh ( ) 1 0 0 1 1 tanh( / 2 ) tanh( / 2) 1

 = ⋅ <sup>+</sup>

γ

{ } 1 11

 γ

(29)

 γ

(31)

γ *e*1 *de*1 )

 *Ze*<sup>2</sup> / sinh (

*<sup>e</sup>*2 *de*2/ 2) *Zs*

γ *<sup>e</sup>*2 *de*<sup>2</sup> )

*F2*

*v2*

(30)

*e ee p p p*

*Z dZ d*

$$\text{CL} = \frac{\text{IL}}{2} = 10 \log\_{10} \frac{4 \,\text{G}\_{\text{S}} \text{G}\_{f}}{\left( \text{G}\_{\text{s}} + \text{G}\_{f} \right)^{2} + \text{B}\_{f}^{2}}. \tag{34}$$

### **4.4** *k* **value determination from conversion loss curves**

Figure 9 (a) shows the pure shear mode theoretical and experimental *CL* curves of the c-axis parallel film HBAR as an example. By comparing experimental curve with theoretical curves

Fig. 9. Frequency response of the experimental shear mode *CL* (open circles). (a) The simulated shear mode *CL* curves (solid line) in various *k*15 values and (b) the curve simulated by the model including various thickness of piezoelectrically inactive layer (Yanagitani & Kiuchi, 2007c)

Shear Mode Piezoelectric Thin Film Resonators 517

Auld, B. A. Acoustic Fields and Waves in Solid. (1973). Vol. 1, pp. 73–76, A Wiley-

Bond, W. (1943). The Mathmatics of the Physical Properties of Crystals. *Bell System Technical* 

Bradley R. M.; Harper J. M. E. & Smith, D. A. (1986). Theory of Thin–film Orientation by Ion bombardment during deposition. *J. Appl. Phys*., Vol. 60, No. 12, pp. 4160–4164. Corso, C. D.; Dickherber, A. & Hunt, W. D. (2007). Lateral Field Excitation of Thickness

Dobrev, D. (1982). Ion-beam-induced Texture Formation in Vacuum-condensed Thin Metal

Dong, L. & Srolovitz, D. J. (1999). Mechanism of Texture Development in Ion-beam-assisted

Dong, L.; Srolovitz, D. J.; Was, G. S.; Zhao, Q. & Rollett, A. D. (2001). Combined Out-of-

Ensinger, W. (1995). On the Mechanism of Crystal Growth Orientation of Ion Beam Assisted Deposited Thin Films. *Nucl. Instrum. Meth. Phys. Res. B*, Vol. 106, pp. 142–146. Foster, N. F.; Coquin, G. A.; Rozgonyi, G. A. & Vannatta, F. A. (1968). Cadmium Sulphide

Fraser, D. B.; Krause, J. T. & Meitzler, A. H.; (1967). Physical Limitations on the Performance

Fujimura, N.; Nishihara, T.; Goto, S.; Xu, J. & Ito, T. (1993). Control of Preferred Orientation for ZnOx Films: Control of Self-texture. *J. Crystal Growth*, Vol. 130, pp. 269–279. Harper, J. M. E.; Rodbell, K. P.; Colgan, E. G. & Hammond, R. H. (1997). Control of In-plane

Hickernell, F. S. (1996). Measurement Techniques for Evaluating Piezoelectric Thin Films.

Iijima, Y.; Tanabe, N.; Kohno, O. & Ikeno, Y. (1992). In-plane Aligned YBa2Cu3O7-x Thin

Kaufman, D. Y.; DeLuca, P. M.; Tsai, T. & Barnett, S. A. (1999). High-rate Deposition of

Kawamoto, T.; Yanagitani T.; Matsukawa, M.; Watanabe, Y.; Mori1, Y.; Sasaki, S. & Oba M.

Kushibiki, J-I.; Akashi, N.; Sannomiya, T.; Chubachi, N.; & Dunn, F. (1995). VHF/UHF

Sputtering. *J. Vac. Sci. Technol. A*, Vol. 17, pp. 2826–2829.

*Ferroelect., Freq. Contr*., Vol. 42 No. 6, pp. 1028–1039

Shear Mode Waves in a Thin Film ZnO Solidly Mounted Resonator. *J. Appl. Phys.*

plane and In-plane Texture Control in Thin Films using Ion Beam Assisted

and Zinc Oxide Thin-Film Transducers. *IEEE Trans. Sonic. Ultrason*., Vol. 15, pp. 28–

of Vitreous Silica in High‐frequency Ultrasonic and Acousto‐optical Devices. *Appl.* 

Texture of Body Centered Cubic Metal Thin Films. *J. Appl. Phys.* Vol. 82, pp. 4319–

Films Deposited on Polycrystalline Metallic Substrates. *Appl. Phys. Lett.*, Vol. 60,

Biaxially Textured Yttria-stabilized zirconia by Dual Magnetron Oblique

(2010). Large-Area Growth of In-Plane Oriented (11-20) ZnO Films by Linear Cathode Magnetron Sputtering. *Jpn. J. Appl. Phys*. Vol. 49 pp. 07HD16-1–07HD16-4.

Range Bioultrasonic Spectroscopy System and Method. *IEEE Trans. Ultrason.,* 

**5. References** 

41.

4326.

No. 6, pp. 769–771.

Interscience Publication.

*Journal*, Vol. 22, pp. 1–72.

Vol. 101, pp. 054514-1–054514-7.

Curie, P. (1885). *Bull. Soc. Franc. Miner. Crist*. Vol. 8 p. 145.

*Phys. Lett*. Vol. 11, No. 10, pp. 308–310.

*Proc. IEEE Ultrason. Symp*., pp. 235–242.

Films. *Thin Solid Films*, Vol. 92, No. 1-2, pp. 41–53.

Deposition. *J. Appl. Phys. Lett.*, Vol. 75, No. 4, pp. 584–586.

Deposition. *J. Mater. Res.*, Vol. 16, No. 1, pp. 210–216.

at minimum *CL* point (near the parallel resonant frequency), we can determine the *k*15 value of the film. As shown in Fig. 9 (b), effective thickness of the piezoelectrically inactive layer *d*<sup>n</sup> in the initial stages of the deposition also can be estimated from comparison of the curves. Figure 10 shows the correlation between *k*15 value and crystalline orientation of the film. FWHM values of ψ-scan and φ-scan curve of the XRD (X-ray diffraction) pole figure show the degree of crystalline orientation in out-of plane and in-plane, respectively. Thicker films tend to have large *k*15 values even though they have same degree of crystalline orientation as thinner one. This kind of correlations and inhomogeneities characterization in wafer can be easily obtained from as-deposited film structure, by using present *k* value determination method.

### **4.5 Conclusion**

In this chapter, shear mode piezoelectric thin film resonators, which is promising for the acoustic microsensors operating in liquid, were introduced. Theoretical predictions of electromechanical coupling and tilt of wave displacement as functions of c-axis tilt angle showed that pure shear mode excitation by using c-axis parallel oriented wurtzite piezoelectric films expected to achieve high-Q and high-coupling sensor. Fabrication of c-axis parallel oriented films by ion beam orientation control technique and characterization of the film by a conversion loss of the as-deposited resonator structure were discussed.

Fig. 10. *k*15 values of the ZnO piezoelectric layers as a function of multiplication of ψ-scan and φ-scan profile curve FWHM values extracted from XRD pole figure (indicating the degree of crystalline orientation in out-of-plane and in-plane) (Yanagitani et al., 2007b)

### **5. References**

516 Acoustic Waves – From Microdevices to Helioseismology

at minimum *CL* point (near the parallel resonant frequency), we can determine the *k*15 value of the film. As shown in Fig. 9 (b), effective thickness of the piezoelectrically inactive layer *d*<sup>n</sup> in the initial stages of the deposition also can be estimated from comparison of the curves. Figure 10 shows the correlation between *k*15 value and crystalline orientation of the film.

the degree of crystalline orientation in out-of plane and in-plane, respectively. Thicker films tend to have large *k*15 values even though they have same degree of crystalline orientation as thinner one. This kind of correlations and inhomogeneities characterization in wafer can be easily obtained from as-deposited film structure, by using present *k* value determination

In this chapter, shear mode piezoelectric thin film resonators, which is promising for the acoustic microsensors operating in liquid, were introduced. Theoretical predictions of electromechanical coupling and tilt of wave displacement as functions of c-axis tilt angle showed that pure shear mode excitation by using c-axis parallel oriented wurtzite piezoelectric films expected to achieve high-Q and high-coupling sensor. Fabrication of c-axis parallel oriented films by ion beam orientation control technique and characterization of the film by a conversion loss of the as-deposited resonator structure

0 100 200 300 400 500 600 700


)

ψ-scan

φ

2 4 6 8 10 12 Film thickness (μm)



FWHM values of

**4.5 Conclusion** 

were discussed.

*k*15

and φ 0.30

0.20

0.10

0.00

ψ


Fig. 10. *k*15 values of the ZnO piezoelectric layers as a function of multiplication of

Single crystal (*k*15=0.26)

method.

ψ


φ


Shear Mode Piezoelectric Thin Film Resonators 519

Van Wyk, G. N. & Smith, H. J. (1980). Crystalline Reorientation Due to Ion Bombardment.

Weber, J.; Albers, W. M.; Tuppurainen, J.; Link, M.; Gabl, R.; Wersing, W. & Schreiter, M.

Wingqvist G.; Anderson H.; Lennartsson C.; Weissbach T.; Yantchev V. & Lloyd Spetz A.

Wingqvist, G. (2010). AlN-based Sputter-deposited Shear Mode Thin Film Bulk Acoustic

Wingqvist, G.; Bjurstrom, J.; Liljeholm, L.; Yantchev, V. & Katardjiev, I. (2007). Shear mode

Wittstruck, R. H.; Tong, X.; Emanetoglu, N. W.; Wu, P.; Chen, Y.; Zhu, J.; Muthukumar, S.;

Yanagitani, T. & Kiuchi, M. (2007c). Control of In-plane and Out-of-plane Texture in Shear

Yanagitani, T. & Kiuchi, M. (2007e). Highly Oriented ZnO Thin Films Deposited by Grazing

Yanagitani, T. & Kiuchi, M. (2011b). Texture Modification of Wurtzite Piezoelectric Films by

Yanagitani, T., Matsukawa, M., Watanabe, Y., Otani, T. (2005). Formation of Uniaxially (11-2

Yanagitani, T.; Arakawa, K.; Kano, K.; Teshigahara, A.; Akiyama, M. (2010). Giant Shear

Yanagitani, T.; Kiuchi, M.; Matsukawa, M. & Watanabe, Y. (2007b). Shear Mode

Yanagitani, T.; Morisato, N.; Takayanagi, S.; Matsukawa, M. & Watanabe, Y. (2011a) c-axis

Textured ZnO Films. *J. Appl. Phys*., Vol. 102, pp. 024110-1–024110-7. Yanagitani, T.; Kiuchi, M.; Matsukawa, M. & Watanabe, Y. (2007d). Characteristics of Pure-

*Trans. Ultrason., Ferroelect., Freq. Contr*., Vol. 54, No. 8, pp. 1680–1686. Yanagitani, T.; Mishima, N.; Matsukawa, M. & Watanabe, Y. (2007a). Electromechanical

(2006). Shear Mode FBARs as Highly Sensitive Liquid Biosensors. *Sens. Actuators A*,

(2009). On the Applicability of High Frequency Acoustic Shear Mode Biosensing in View of Thickness Limitations Set by The Film Resonance. *Biosens. Bioelectron*., Vol.

Resonator (FBAR) for Biosensor Applications. *Surf. Coat. Tech*., Vol. 205, No. 5, pp.

AlN Thin Film Electro-acoustic Resonant Sensor Operation in Viscous Media. *Sens.* 

Lu, Y.; & Ballato, A. (2003) Characteristic of MgxZn1-xO Thin Film Bulk Acoustic Wave Devices. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr.*, Vol. 50, pp. 1272–

Mode Piezoelectric ZnO Films by Ion-beam Irradiation. *J. Appl. Phys.*, Vol. 102, pp.

Ion-beam Sputtering: Application to Acoustic Shear Wave Excitation in the GHz

0) Textured ZnO Films on Glass Substrates. *J. Cryst. Growth*, Vol. 276, No. 3-4, pp.

Mode Electromechanical Coupling Coefficient *k*15 in c-axis Tilted ScAlN Films. *Proc.* 

Electromechanical Coupling Coefficient *k*15 and Crystallites Alignment of (11-20)

shear Mode BAW Resonators Consisting of (11-20) Textured ZnO Films. *IEEE* 

Coupling Coefficient *k*15 of Polycrystalline ZnO Films with the c-axes Lie in the Substrate Plane. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr*., Vol. 54, No. 4, pp.

Zig-Zag ZnO Film Ultrasonic Transducers for Designing Longitudinal and Shear

*Nucl. Instrum. Meth.*, Vol. 170, pp. 433–439.

*Actuators B*, Vol. 123, No. 1, pp. 466–473.

Range. *Jpn. J. Appl. Phys*. Vol. 46, pp. L1167–L1169.

Ion Beam Irradiation. *Surf. Coat. Technol*., in press.

*2010 IEEE Ultrason. Symp.,* pp. 2095–2098*.*

Vol. 128, No. 2, pp. 84–88.

24 No. 11, pp. 3387–3390.

1279–1286

1277.

424-430.

701–704.

044115-1–044115-7.


Link, M.; Weber, J.; Schreiter, M.; Wersing, W.; Elmazria, O. & Alonot, P. (2007). Sensing

Matsumoto, Y.; Ujiie, T. & Kushibiki, J-I. (2000). Measurement of Shear Acoustic Properties

Meeker, T. R. (1996). IEEE Stabdard on Piezoelectricity (ANSI/IEEE Std. 176-1987). *IEEE* 

Milyutin, E. & Mural, P. (2010). Electro-Mechanical Coupling in Shear-Mode FBAR with

Milyutin, E.; Gentil, S. & Mural, P. (2008). Shear Mode Bulk Acoustic Wave Resonator

Mitsuyu, T.; Ono S. & Wasa, K. (1980). Structures and SAW Properties of Rf-sputtered

Naik, B. S.; Lutsky, J. J.; Rief R.; & Sodini, C. D. (1998). Electromechanical Coupling

Nakamura, K.; Shoji, T. & Kang, H. (2000). ZnO Film Growth on (0112) LiTaO3 by Electron

Ogi, H.; Hirao, M.; Honda T. & Fukuoka, H. (1995). Ultrasonic Diffraction from a Transducer

Paco, P.; Menéndez, Ó. & Corrales E. (2008) Equivalent Circuit Modeling of Coupled

Park, S. J.; Norton, D. P. & Selvamanickam, V. (2005). Ion-beam Texturing of Uniaxially

Ressler, K. G.; Sonnenberg, N. & Cima, M. J. (1997). Mechanism of Biaxial Alignment of

Rosenbaum, J. F. (1988). Bulk Acoustic Waves: Theory and Devices. Artech House Boston

Sauerbrey, G. (1959) Verwendung von Schwingquarzen zur Wägung Dünner Schichten und

Smith, R. T. & Stubblefield, V. E. (1969). Temperature Dependence of the Electroacoustical Constants of Li-doped ZnO Single Crystals. *J. Acoust. Soc. Am.*, Vol. 46, pp. 105. Takayanagi, S.; Yanagitani, T.; Matsukawa, M. & Watanabe Y. (2010). A Simple Technique

Textured Ni Films. *Appl. Phys. Lett.*, Vol. 87, pp. 031907–031909.

zur Mikrowägung. *Z. Physik*, Vol. 155, pp. 206–222.

*2010 IEEE Ultrason. Symp*. pp. 1060–1063.

Polarity. *Jpn. J. Appl. Phys*., Vol. 39, No. 6A, pp. L534–L536.

*Trans. Ultrason., Ferroelect., Freq. Contr*., Vol. 43, No. 5, pp. 719–772..

*Actuators B*, Vol. 121, No.2, pp. 372–378.

Vol. 58, No. 4, pp. 685–688.

084508-6.

2470.

257–263.

2, pp. 1191–1198.

No. 10, pp. 2637–2648.

2030–2037.

London.

*Meeting of Acoustical Society of Japan* (in Japanese)

Characteristic of High-freqency Shear Mode Resonators in Glycerol Solutions*. Sens.* 

of Water using the Ultrasonic Reflectance Method in Pulse-mode Operation. *Spring* 

Piezoelectric Modulated Thin Film. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr*.,

Based on c-axis Oriented AlN Thin Film. *J. Appl. Phys.* Vol. 104, pp. 084508-1–

Single-crystal Films of ZnO on Sapphire. *J. Appl. Phys*., Vol. 51, No. 5, pp. 2464–

Constant Extraction of Thin-lm Piezoelectric Materials Using a Bulk Acoustic Wave Resonator. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,* Vol.45, No.1, pp.

Cyclotron Resonance-assisted Molecular Beam Epitaxy and Determination of Its

with Arbitrary Geometry and Strength Distribution. *J. Acoust. Soc. Am*. Vol. 98, No.

Resonator Filters. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,* Vol. 55, No. 9, pp.

Oxide Thin Films during Ion-Beam-Assisted Deposition. *J. Am. Ceram. Soc.*, Vol. 80,

for Obtaining (11-20) or (10-10) Textured ZnO Films by RF Bias Sputtering," *Proc.* 


**23** 

Ivan D. Avramov

 *Bulgaria* 

**Polymer Coated Rayleigh SAW and STW Resonators for Gas Sensor Applications** 

Polymer coated gas-phase sensors using the classical Rayleigh-type surface acoustic wave (RSAW) mode have enjoyed considerable interest worldwide over the last two decades [1- 3]. This interest is motivated by their orders of magnitude higher sensitivity and larger dynamic range compared to bulk acoustic wave (BAW) sensors, fast response times, excellent overall stability, coming close to that of quartz crystal sensors, and low phase noise of the sensor system making high-resolution measurements possible [4]. Because of these features that are difficult to achieve with other technologies, RSAW based gas sensors have found successful application in a variety of industrial implementations such as electronic noses, systems for analysis of chemical and biological gases, medical diagnostics, environmental monitoring and protection, etc. [5-11]. On the other hand, surface transverse wave (STW) based gas sensors, even though sharing the same operation principle, have not been studied so extensively yet. The purpose of this article is to present and discuss systematic experimental data with both acoustic wave modes which will prove that STW based gas-phase sensors not only successfully compete with their RSAW counterparts but also complement them in applications where RSAW gas sensors reach their limits. Successful corrosion proof RSAW sensors using gold metallization for operation in highly

**2. Operation principle of RSAW/STW based resonant gas phase sensors** 

Both RSAW and STW based gas sensitive resonant sensors share the same operation principle illustrated in Fig. 1. The sensor device typically is a two-port RSAW or STW resonator on a temperature compensated rotated Y cut of quartz whose geometry has been optimized in such manner that the resonator retains a well behaved single-mode resonance and suffers minimum loss increase and Q-degradation after the gas sensitive layer, (typically a solid, semisolid or soft polymer film with good sorption properties), is deposited on its surface. On the other hand, the sensor has to have maximum active area in the centre of its geometry where the magnitude of the standing wave and deformation are maximized. Thus, strong interaction with the gas adsorbed in the polymer film occurs and maximum gas sensitivity is obtained. The sensor operation principle according to Fig. 1 is fairly simple. If a gas-phase analyte of a certain concentration is applied to its surface, gas molecules are absorbed by the sensing layer until thermodynamic equilibrium is achieved; i. e. the number

reactive chemical environments will also be presented.

**1. Introduction** 

*Georgi Nadjakov Institute of Solid State Physics, Sofia* 

Wave Resonant Frequencies and Modes. *IEEE Trans. Ultrason., Ferroelect., Freq. Contr.*, Vol. 58, No. 5, pp. 1062–1068.

