Use of periodic 2D pillar array for performance enhancement of AlN-based SMR BAW resonators

Now, RF bulk acoustic wave (BAW) resonators employing AlN thin films ^1–6) are widely used and indispensable in the RF frontend of mobile communication terminals. ^7–9)

RF BAW resonators employ acoustic resonance of piezoelectric thin membranes, and they should be isolated acoustically from surroundings necessary for their physical support. This isolation is realized by two methods. One employs physical support of free-standing membranes at their side edges, and this type is called the film bulk acoustic resonator (FBAR). ^10,11) Another one employs the Bragg reflector directly attached to the membrane. This type is called a solidly mounted resonator (SMR). ¹²⁾

SMR-type BAW resonators possess several advantages such as good power durability and structural robustness compared with FBAR. ⁸⁾ However, they also have some demerits. One is the reduction of the effective electromechanical coupling factor k_eff ² due to penetration of acoustic waves into the Bragg reflector. ^10,11) Second is the necessity of a certain number of layers for the acoustic mirror to achieve enough acoustic reflectivity.

In Ref. 13, the authors indicated that k_eff ² of SMR can be enhanced close to that of FBAR when the two-dimensional (2D) pillar array made of SiO₂ is used as the top SiO₂ layer of the Bragg reflector. It should be noted that when the pillars are aligned periodically with a periodicity much smaller than the lateral acoustic wavelength, the structure looks uniform, and its properties are simply given by the ensemble average of those of employed pillar material and air. ¹⁴⁾ Furthermore, owing to the periodicity, random scattering does not occur, and thus this configuration is ideally lossless. It was also shown that the use of a 2D periodic pillar array also enhances the reflectivity of the Bragg reflector.

By the way, the periodic arrangement of the 2D pillar array will also create anisotropy of wave propagation along the membrane, and the anisotropy may offer a significant impact on transverse mode resonances, whose complete suppression is mandatory in current high-performance BAW devices. ^15–18) Anisotropy control is one of the hottest research topics in surface acoustic wave (SAW) devices for suppression of transverse mode resonances. ^19–21) Its basic idea is to make lower-order transverse resonances to the main resonance, and the remaining weak higher-order ones are suppressed well by the piston design, ^22–24) which was originally proposed for BAW devices. ¹⁵⁾ Anisotropy control is also believed to be crucial to suppress lateral leakage and achieve high Q. ^25,26)

This is an extended version of Ref. 13, and discusses the applicability of periodic 2D pillar arrays to the AlN-based SMR-type BAW resonators from various aspects. In addition to enhancement of both k_eff ² and reflectivity of the Bragg reflector, anisotropy control is also discussed for suppression of transverse mode resonances and lateral leakage.

2.1. Characteristic of multi-layered structure

The properties of periodic structures called photonic or phononic crystals are studied extensively. However, most of the previous works employ the Bragg reflection in the structures for synthesis of desired properties. In this work, the main concern is the use of an ensemble average of employed material properties instead.

First, consider a one-dimensional (1D) muti-layered structure shown in Fig. 1. When the thickness of each layer is assumed to be much smaller than the acoustic wavelength, the structure can be regarded as homogenous material, and the compliance toward the thickness direction is given by the ensemble average of compliance of the layer while the stiffness of the in-plane directions is given by ensemble average of stiffness of layers. This means when very soft and very hard materials are combined for example, this structure looks very soft toward the thickness direction and very hard toward the lateral directions. Thus, large anisotropy can be synthesized. It should be noted that when the layer composition is periodic and its periodicity is much smaller than the acoustic wavelength, scattering does not occur except for reflection at the top and bottom surfaces due to intrinsic impedance mismatch.

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2.2. Resonator design

According to this principle described in Sect. 2.1, the periodic 2D pillar array is arranged as Fig. 2(a) and embedded in the Bragg reflector composed of SiO₂ and W in the AlN-based SMR as shown in Figs. 2(b) and 2(c). Pillar material is SiO₂ and gaps among pillars are vacant, i.e., vacuum. The portion framed by dotted red lines is the unit cell of a period P and the width w of pillars are equal in the x- and y-directions, thus the structure possesses four-fold symmetry in the x–y plane.

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The 3D periodic finite element method (FEM) is applied for the structure shown in Figs. 2(b) and 2(c). The periodic boundary conditions are given to all side boundaries, and a perfect matching layer (PML) is given to the Si bottom surface. Designed structural parameters defined in Fig. 2(c) are listed in Table I. It should be noted that each layer thickness of the Bragg reflector is set to obtain relatively high reflectivity for both longitudinal and shear waves. ²⁷⁾

Table I. Designed structural parameters.

Parameters	Value
Piezoelectric layer thickness (tAlN)	1 μm
Electrode thickness (tRu)	0.3 μm
Low impedance layer thickness (tL)	0.53 μm
High impedance layer thickness (tH)	0.94 μm
Periodicity of pillars (P)	P
Pillar thickness (h)	h
Width of pillar (w)	w
Duty ratio of SiO2 (w/P)	w/P

First, P is set very tiny (10 nm) making the pillar array behave uniformly.

Figure 3 shows the variation of the effective coupling coefficient k_eff ² with h/t_AlN and w/P, where k_eff ² is defined as:

$$\begin{eqnarray}&&{k}_{{\rm{eff}}}^{2}=\frac{{\pi }^{2}}{8}\frac{\left({f}_{{\rm{a}}}^{2}-{f}_{{\rm{r}}}^{2}\right)}{{f}_{{\rm{a}}}^{2}}\end{eqnarray} \tag{ 1 }$$

where f_r and f_a are the resonance and anti-resonance frequencies, respectively. It is seen that k_eff ² changes parabolically with h/t_AlN and takes a maximum when h/t_AlN ∼0.65. On the one hand, k_eff ² increases monotonically with a decrease of w/P and becomes insensitive to h/t_AlN. Note that k_eff ² in this configuration is 8.01% for the free-standing FBAR and that of SMR-BAW with uniform SiO₂ is 7.01%.

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Figure 4 shows the admittance Y characteristics of SMR-BAW resonators without and with slotted SiO₂ with w/P = 0.4 and h/t_AlN = 0.65. The addition of the slotted pillars enhances k_eff ² from 7.08% to 7.88% without generating spurious resonances.

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Next, variation of Y with P is investigated for the case where w/P and h are fixed at 0.4 and 0.65 μm, respectively and Figure 5 shows the result. With an increase in P, a spurious resonance appears close to the main resonance and overlaps with it. This spurious response is caused by coupling between the thickness resonance and that of the pillars. This spurious resonance seems insignificant when P is smaller than 1 μm.

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Figure 6 shows the variation of the Bode Q ²⁸⁾ with the number N of Bragg reflector layers. Two types of calculations are shown: (a) with slotted SiO₂, and (b) without slotted SiO₂. In these calculations, P, h, and w/P are equal to 0.7 μm, 0.65 μm, and 0.4, respectively. The Q enhancement is obvious. Namely, a relatively high Q close to 5000 can be achievable even at N = 2 when the slotted SiO₂ is applied while N = 4 is necessary to get reasonable Q when the slotted SiO₂ is not applied.

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The wavenumber β_x of laterally propagating SAW is calculated as a function of frequency f for the structure shown in Fig. 2. In this case, a phase shift of -β_x P is given between left and right boundaries in the FEM model of Fig. 2(c), and the eigenfrequency f of the unit cell is calculated by changing β_x .

Figure 7 shows the variation of this β_x –f relation with w/P. Two kinds of branches are given in this figure. Solid lines are those given by the conventional SAW mode existing even when the slots are not given while broken lines are those given by the "pillar" mode which is generated by coupling of the SAW mode with the pillar resonance (See the resonance pattern given in the lower right corner of the figure).

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It is seen that when two branches are far, the SAW mode branch exhibits the so-called type-Ⅱ dispersion where f decreases with β_x . When two branches are in proximity, the SAW mode branch is bent and changed to the type-I dispersion, where f increases with β_x when 0.48 < w/P < 0.49, and the dispersion curve becomes maximally flat when w/P = 0.47. This result reveals that the change in the dispersion relation is caused by the coupling of the SAW mode with the pillar mode.

Next, the influence of the dispersion control is investigated using a 3D FEM model shown in Fig. 8 where the periodic boundary condition is given to the y-direction. Periodic pillars are extended to the outside of the active region with a width of 60 μm to avoid discontinuity at side boundaries of the active region. In addition, Al rims are given there for Q enhancement, ^29,30) and their thickness t_r and width w_r are set at 0.5 μm and 0.4 μm, respectively. PMLs are applied to two sides and bottom of the whole structure.

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Figure 9(a) shows the calculated Y and G of the structure. For comparison, those cases without the slots are also shown in the figure. When the slots are not given, owing to the type-Ⅱ dispersion, a series of transverse resonances appear below the main resonance. ¹⁶⁾ In contrast, owing to the flattened dispersion, these spurious resonances are well suppressed when the slots are given. In addition, k_eff ² is increased significantly. Figure 9(b) shows calculated Bode Q. ²⁸⁾ It is seen that the Q value is also enhanced significantly by applying the periodic slots.

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This paper discussed the applicability of the 2D periodic pillar array as the first layer of the acoustic mirror for AlN-based SMR-BAW resonators.

It was shown that k_eff ² can be enhanced close to that of free-standing FBAR when w/P is set small. It was also shown that the use of a 2D pillar array can enhance the reflectivity of the Bragg reflector.

It was demonstrated that SAW propagation along the surface can be controlled owing to anisotropy created by the periodic 2D pillar arrays, and transverse mode resonances can be suppressed well under the proper setting of the periodic 2D pillar arrays.

This work was supported 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.