# Quality Factor Improvement of a Thin-Film Piezoelectric-on-Silicon Resonator Using a Radial Alternating Material Phononic Crystal

^{*}

*Micromachines*in 'Engineering and Technology' 2023)

## Abstract

**:**

_{anchor}) from 60,596 to 659,536,011 at the operating frequency of 175.14 MHz, which is about 10,000 times higher. The motion resistance of the RAM-PnC resonator is reduced from 156.25 Ω to 48.31 Ω compared with the traditional resonator. At the same time, the insertion loss of the RAM-PnC resonator is reduced by 1.1 dB compared with the traditional resonator.

## 1. Introduction

## 2. Phononic Crystal and the Theory of Wave Propagation

#### 2.1. Phononic Crystal Structure and Band Gap Calculation

_{1}of the W layer is 6 μm, the width a

_{2}of the Si layer is 10 μm, and the height of the W layer and the Si layer is H = 10 μm. A radial periodic unit is alternately formed by W and Si, and its length is a = 16 μm. Silicon is an anisotropic material, and its crystal orientation and elastic coefficient influence the simulation results. In this paper, the parameters of Si are the crystal orientation, and the elastic coefficients are shown in Table 1.

_{or}and z are defined. The dependent variable u

_{or}≡ u/r is introduced to avoid dividing r, leading to axis problems. In Equations (4)–(7), r = 0, w is the displacement in the z direction. Periodic boundary conditions are imposed on the element in the r direction as follows:

_{r}is defined as a one-dimensional block wave vector along the radial direction. The free boundary is applied to the plate surface along the z direction. By scanning the wave vector k

_{r}along the boundary of the first Brillouin zone, the dispersion curve ω = ω (k) and the eigen-displacement field can be obtained. The structure used in this section is one-dimensional in the radial direction, so the Brillouin zone boundary ranges from Γ (0,0) to R (1,0), which is different from the two-dimensional or three-dimensional phononic crystal structure.

#### 2.2. Band Gap Optimization of Phononic Crystals

#### 2.3. Transmission Characteristic

## 3. The Design of TPOS Resonator

_{31}piezoelectric coefficient of the AlN material, the electric field causes the plane expansion deformation of the piezoelectric film, thereby exciting the resonator to cause lateral expansion mode resonance.

_{p}is the phase velocity associated with the lateral spreading mode, E and ρ denote Young’s modulus and the density of the Si layer, respectively, n. This provides the order of the resonant mode.

## 4. Discussion

_{u}) can be obtained by calculating the 3dB bandwidth.

_{−3dB}is the −3 dB bandwidth, IL is insertion loss, max {Re(Y11)} is the maximum real part of admittance, f

_{p}is the frequency at which the impedance amplitude is at the maximum, and f

_{s}is the frequency when the impedance amplitude is the minimum.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Five-period RAM-PnC transmission line model. (

**a**) 3D schematic diagram and (

**b**) 2D cross sectional diagram. Point A represents input (excitation signal) and point B represents output signal.

**Figure 5.**The simulation results of the RAM-PnC transmission curve (122–225 MHz) under the conditions of 2D (

**a**) and 3D (

**b**), respectively.

**Figure 6.**Simulation diagrams of quarter piezoelectric MEMS resonators: (

**a**) the traditional-type TPOS MEMS resonator; (

**b**) RAM-PnC TPOS MEMS resonator.

**Figure 7.**The total displacement distribution of the 9th-order width-extended resonant mode of (

**a**) the ordinary resonator and (

**b**) array plate resonator with RAM-PnC is shown in the figure; the Z-direction displacement distribution of the 9th-order width-extended resonant mode of the (

**c**) ordinary resonator and (

**d**) array plate resonator with RAM-PnC is shown in the figure.

**Figure 8.**The (

**a**) total displacement field (μm) diagram and (

**b**) Z-direction displacement field (μm) diagram of the traditional resonator and the RAM-PnC resonator in the 9th-order width extension mode on the A-A′ cross-section, and the (

**c**) total displacement field (μm) diagram and (

**d**) Z-direction displacement field (μm) diagram of the traditional resonator and the RAM-PnC resonator in the 9th-order width extension mode on the B-B′ cross-section.

**Figure 9.**(

**a**) Schematic diagram of admittance (Y11) and susceptance (G) curves of traditional TPOS MEMS resonators; (

**b**) RAM-PnC MEMS resonator admittance (Y11) and susceptance (G) curve diagram.

**Figure 10.**(

**a**) Insertion loss (S21) curve of the traditional TPOS MEMS resonator; (

**b**) Insertion loss (S21) curve of the RAM-PnC TPOS MEMS resonator.

Parameter Name (Abbreviated) | Value |
---|---|

Young’s modulus (E) | E_{x} = E_{y} = 169 GPa, E_{z} = 130 GPa |

Poisson’s ratio (σ) Shear modulus (G) Density (ρ) | σ_{xy} = 0.064, σ_{yz} = 0.36, σ_{zx} = 0.28G _{z} = 50.9 GPa, G_{x} = G_{y} = 79.6 GPa2330 kg/m ^{3} |

Materials | W | Al | Ag | Pt | Cu | Au |
---|---|---|---|---|---|---|

Density (g/cm^{2}) | 18.7 | 2.7 | 10.5 | 21.4 | 8.94 | 19.32 |

Longitudinal velocity (cm/s) × 10^{2} | 5.23 | 6.32 | 3.6 | 3.96 | 4.65 | 3.24 |

Acoustic impedance (g/cm^{2} s) | 97.86 | 17.1 | 37.8 | 84.74 | 41.55 | 62.6 |

Parameters | Values (Unit) |
---|---|

Simulated resonant frequency (f_{0}) | 175 (MHz) |

Wavelength (λ) | 47.9 (µm) |

Inter digitated transducer (IDT) finger (n) | 9 |

Tethers width (W_{t}) | 15 (µm) |

Tethers length (L_{t}) | 47.9 (µm) |

Electrode gap (G_{e}) | 4 (µm) |

Resonator width (W_{r}) | 215.55 (µm) |

Resonator length (L_{r}) | 646.65 (µm) |

Thickness of Al (T_{Al}) | 0.5 (µm) |

Thickness of AlN (T_{AlN}) | 0.1 (µm) |

Height of Si substrate (HS) | 10 (µm) |

Parameters | Traditional | RAM-PnC |

Resonant frequency (f_{r}), MHz | 175.14 | 175.14 |

Insertion loss (IL), dB | 6.2 | 5.1 |

Motional resistance (Rm), Ω | 6.45 | 0.08 |

Coupling coefficient (K^{2}_{eff}), % | 0.0228 | 0.0228 |

Q_{anchor} | 60,596 | 659,536,011 |

Loaded quality factor (Q_{l}) | 8146 | 9467 |

Unloaded quality factor (Q_{u}) | 15,966 | 21,317 |

FOM | 8.3 | 11.1 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, C.; Su, M.; Workie, T.B.; Tang, P.; Ye, C.; Bao, J.-F.
Quality Factor Improvement of a Thin-Film Piezoelectric-on-Silicon Resonator Using a Radial Alternating Material Phononic Crystal. *Micromachines* **2023**, *14*, 2241.
https://doi.org/10.3390/mi14122241

**AMA Style**

Zhu C, Su M, Workie TB, Tang P, Ye C, Bao J-F.
Quality Factor Improvement of a Thin-Film Piezoelectric-on-Silicon Resonator Using a Radial Alternating Material Phononic Crystal. *Micromachines*. 2023; 14(12):2241.
https://doi.org/10.3390/mi14122241

**Chicago/Turabian Style**

Zhu, Chuang, Muxiang Su, Temesgen Bailie Workie, Panliang Tang, Changyu Ye, and Jing-Fu Bao.
2023. "Quality Factor Improvement of a Thin-Film Piezoelectric-on-Silicon Resonator Using a Radial Alternating Material Phononic Crystal" *Micromachines* 14, no. 12: 2241.
https://doi.org/10.3390/mi14122241