Comparative study of piston mode designs for temperature-compensated surface acoustic wave resonators using SiO₂/LiNbO₃ structure

Temperature-compensated (TC) surface acoustic wave (SAW) devices are widely used in current mobile phones. One type of TC technology is the use of layered substrate structures in which a piezoelectric LiTaO₃ (LT) or LiNbO₃ (LN) layer is bonded to a substrate with a small coefficient of thermal expansion, such as silicon or sapphire. ^1–9) Another one is the deposition of a SiO₂ layer on interdigital transducers (IDTs) and reflectors on an LT/LN substrate. ^10–25) The incredible SAW structure using an ultra-thin LT/LN layer can be regarded as a combination of these technologies. ^26–30) Among them, SiO₂ covered 128°YX-LN is most commonly used as the TC-SAW structure. ^{12,13,21–25)}

In this configuration, one of the most important design goals is the suppression of transverse mode resonances. Now the "piston mode" technique is widely used for the suppression of transverse modes. The technique was first proposed for bulk acoustic wave devices ³¹⁾ and then applied to SAW devices. ^32–36) Solal et al., proposed the use of the "hammer head" structure placed at the end of IDT. ³²⁾ Its variations are deposition of metal dots above the IDT aperture ends ^35,36) and metal stripes on the SiO₂ layer surface. ³³⁾ These extra elements serve as phase shifters to make the aperture edges behave mechanically free for lateral SAW propagation.

The authors compared the applicability of these piston mode techniques for TC-SAW resonators on 131°YX-LN with SiO₂ overlay. ³⁷⁾ This paper is an extended version of Ref. 37, and is aimed at discussing the applicability of these three-piston mode techniques systematically and more in detail. The three structures are designed by the three-dimensional (3D) finite element method (FEM), and it is shown how design parameters affect spurious responses and how each structure should be designed.

Roughly speaking, the phase shift is mostly determined by the total mass of extra elements and SiO₂ which overlaid on the piston region. The applicability of the "hammer head" design is limited due to the weaker impact of the extra elements when the SiO₂ layer is thick. Namely, transverse modes can be suppressed only when the SiO₂ layer is thin. In contrast, the designs using metal dots or stripes can work well even when the SiO₂ layer is thick.

It should be noted that the deposition of metal dots or stripes makes the main resonance split in two due to the mass loading. Thus, their thickness should be limited so that the split of the main resonance is negligible. Since thicker is preferable in principle, the thickness should be set close to this limitation. Then required width of metal dots or stripes will be determined to give sufficient transverse mode suppression.

It is interesting to note that the required width of metal dots is about two times larger than that of stripes for the given metal thickness. This can be understood due to the difference in the metallization ratio (MR) in the extra elements.

Figure 1 shows the cross-sectional view of the SiO₂/131°YX-LN structure used for the 3D FEM analysis. Cu is chosen as the IDT material, and the top surface of the covering SiO₂ layer is assumed to be flattened. The perfect matching layer (PML) is given at the bottom surface of LN. No additional loss is included in the simulation. Table I shows its design parameters.

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Figure 2 shows the top view of four IDT patterns used in this discussion. PMLs are given to the left and right boundaries while the periodic boundary conditions are applied to the top and bottom boundaries. Figure 2(a) shows the basic structure without the extra elements (design A), and Fig. 2(b) shows a piston mode design (design B) with widened IDT electrode ("hammer head") edges. In the design shown in Fig. 2(c) (design C), Cu stripes are deposited on the top surface of the SiO₂ layer while Cu dots are added to the IDT aperture edges in the design shown in Fig. 2(d) (design D) on the top of IDT electrode.

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Figure 3 shows admittance (Y) and conductance (G) of these designs calculated by the 3D FEM. Results giving the best transverse mode suppression are shown for designs B, C and D. When the piston design is not applied (design A), transverse mode resonances are clearly seen above the main resonance [see Fig. 3(a)].

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Figure 3(b) shows the calculated Y and G of design B when the MR and length of hammer heads are set at 0.9 and 0.53 p_I, respectively. Transverse modes could not be suppressed well using this design. Its reason will be discussed in Sect. 3.1.

Figure 3(c) shows the calculated Y and G of design C, where the thickness h_stripe and width w_stripe of Cu stripes are set at 0.037 p_I and 0.13 p_I, respectively. It is seen that the transverse mode resonances are well suppressed.

Figure 3(d) shows the calculated Y and G of design D, where the thickness h_dot and width w_dot of Cu dots are set at 0.037 p_I and 0.32 p_I, respectively. Transverse mode resonances are well suppressed also for this case.

3.1. Piston B design

Figure 4 shows the variation of Y of design B with h_SiO2 when the metallization ratio and length of hammer heads are set at 0.9 and 0.53 p_I, respectively. It is seen that transverse resonances can be suppressed to some extent when h_SiO2 is reduced to 0.08p_I. Further calculation indicated that good transverse resonance suppression can be achieved when h_SiO2 is reduced to 0.06p_I after slight MR reduction.

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This may be explained by the fact that larger h_SiO2 gives deeper SAW energy penetration to the SiO₂ layer and makes impact of the extra elements weaker. This means applicability of the design B is limited intrinsically to cases when the SiO₂ layer is thin under comparison with designs C and D.

3.2. Piston C design

Figure 5(a) shows the variation of Y of design C with h_stripe when w_stripe is fixed at 0.13 p_I. It is seen that although transverse modes are well suppressed when h_stripe = 0.037 p_I, ∣Y∣ of the main resonance is small. This height reduction is due to split of the main resonance to two instead of the Q reduction. In fact, this additional resonance can be seen clearly below the main resonance when h_stripe > 0.037 p_I.

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Figure 6 shows the total displacement at the two spurious peaks m₁ and m₂ in Fig. 5(a). Clear energy concentration, i.e. resonance, is seen near the Cu stripe region. Existence of two resonances and asymmetry of the resonance pattern are due to intrinsic anisotropy in LN. Their frequencies do not change with w_stripe so much. On the other hand, a larger h_stripe is preferable for transverse mode suppression for a wide frequency range as shown in Fig. 5(a) when h_stripe is set from 0.016p_I to 0.037p_I. This is because the transmission phase in the phase shifters changes rapidly with the frequency near their resonance. Thus h_stripe should be set to close to this limit, namely 0.037 p_I when h_SiO2 is set at 0.3p_I.

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Figure 5(b) shows the variation of Y of the design C with w_stripe when h_stripe is fixed at 0.037 p_I. The split of main resonance becomes obvious when w_stripe is larger than 0.14 p_I, and spurious resonances can be well suppressed when h_stripe is circa 0.13 p_I.

Figure 7 shows the variation of optimal w_stripe giving the best transverse mode suppression with h_stripe. Similar responses can be achieved even when w_stripe is set a little longer (or shorter) when h_stripe is set a little smaller (or larger).

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Figure 8 shows the admittance curves of corner conditions in Fig. 7. Figure 8(a) shows variation of Y of the design C with w_stripe when h_stripe is fixed at 0.026 p_I, it can be seen that optimal w_stripe should be 0.19 p_I which has been shown in Fig. 7. Figure 8(b) also shows the optimal w_stripe of design C should be 0.11 p_I when h_stripe is fixed at 0.047 p_I.

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3.3. Piston D design

The procedure for the Piston D design is quite similar to the Piston C design described above.

Figure 9(a) shows the variation of Y of design D with h_dot when w_dot is fixed at 0.32 p_I. The split of main resonance can be also seen clearly for this case when h_dot > 0.037 p_I. This additional resonance is due to a SAW resonance of the Cu dot region. Thus, we can conclude that h_dot should be set close to 0.037 p_I when h_SiO2 is set at 0.3p_I.

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Figure 9(b) shows the variation of Y of design D with w_dot when h_dot is set at 0.037 p_I. It is seen that most of all spurious resonances disappear and a clean response is achieved by setting w_dot to 0.32 p_I.

In Fig. 7, variation of optimal w_dot with h_dot is shown also for this case. The variation is similar to Design C.

Figure 8(c) shows the optimal w_dot of the design D should be 0.42 p_I when h_dot is fixed at 0.026 p_I while Fig. 8(d) shows the optimal w_dot of the design D should be 0.23 p_I when h_dot is fixed at 0.047 p_I, the variation of optimal w_dot with h_dot is shown in Fig. 7.

Note that the optimal w_dot (design D) is about two times larger than the optimal w_stripe (design C) for given Cu thickness. This can be understood due to the fact the metal dots cover only IDT fingers in this case while the metal stripes cover also gaps between fingers.

These results confirm that the phase shift given by the extra elements is mostly determined by the total mass of extra elements and SiO₂ which is overlaid on the piston region in rough approximation.

This paper compared three different piston mode designs for the TC-SAW resonator, and their design procedures were explained in detail.

It was shown that in rough approximation, phase shift given by the extra elements is determined by the total mass of extra elements and SiO₂ which overlaid on piston region. The hammer head design without additional metal layers does not work properly due to the weaker impact of the extra elements when the SiO₂ layer is thick. On the other hand, piston designs using metal dots or stripes are effective for the transverse mode suppression even when the SiO₂ layer is thick.

Although larger metal thickness is preferable for wideband operation, it also causes another resonance just below the main resonance. Thus, the optimal metal thickness can be estimated from this trade-off, and then the optimal metal width can be found to achieve good transverse mode suppression for the determined metal thickness.

In practice, other factors such as other spurious responses and fabrication tolerance must be also taken into account. The authors believe that the design procedures given in this paper will be helpful even for such cases.

This work was supported in part by the Research Project under Grant A1098531023601318 and in part by the National Natural Science Foundation of China and the China Academy of Engineering Physics under Grant U1430102.