# Design and Analysis of MEMS Linear Phased Array

^{*}

## Abstract

**:**

## 1. Introduction

_{x}Ti

_{1−x}O

_{3}, PZT) bulk materials, piezoelectric micro-machined ultrasonic transducer (pMUT) fabricated by piezoelectric film deposition and micro-electro-mechanical system (MEMS) technology has great advantages in integration, which can structure system-in-package (SIP) and even system-on-chip (SOC) technologies. Moreover, the technical challenge of three-dimensional acoustic imaging is the fabrication of two-dimensional array transducers with many elements, high element density and small element size. Lapping and dicing bulk materials will become more difficult with traditional technologies of transducer fabrication. Furthermore, the high frequency MEMS transducers with good resolution are easier to achieve than those prepared by traditional fabrication technologies, and the vibration of MEMS piezoelectric transducer is mostly a bending vibration with the advantages of high sensitivity, wide bandwidth, flexible design, etc. [1]. As an important pMUT array, a MEMS linear phased array has been developed [2,3,4,5].

## 2. MEMS Linear Phased Array Element Structure

_{2}/Si film as the supporting layer, and Al film as the upper and lower electrode. Thus, the vibration membrane is Al/ZnO/Al/SiO

_{2}/Si composite structure (see Figure 1). Composite membrane can be considered as a square diaphragm that is fixed on all edge sides.

_{11}= 3 MHz.

_{r}= 3.23 MHz.

_{0}= 1.75 MHz.

Thickness of Si | Thickness of SiO_{2} | Thickness of ZnO | Length of Membrane |
---|---|---|---|

8 μm | 0.2 μm | 6 μm | 228 μm |

Material | Young’s Modulus (GPa) | Density (10^{3} kg/m^{3}) | Poisson Ratio |
---|---|---|---|

Si | 167 | 2.33 | 0.28 |

SiO_{2} | 72 | 2.30 | 0.16 |

ZnO | 120 | 5.68 | 0.446 |

**Figure 3.**Structure of one element (“multi-cell” combined by parallel connection). a, b and h represent element (“cell”) width, “cell” length, and “inter-cell” spacing, respectively.

**Figure 4.**Schematic diagram of linear phased array. a, b, d and h represent element (“cell”) width, “cell” length, element width and “inter-cell” spacing, respectively.

## 3. MEMS Linear Phased Array Beam Directivity

- The directivity of a single element

- 2.
- The uniform linear array directivity

## 4. Optimization and Simulation

#### 4.1. Optimization in the Elevation Direction (y-z Plane, α = α_{0} = 90°)

#### 4.1.1. Main Lobe

_{0}= 90°, the beam directivity function of Equation (11) can be simplified to:

_{1}(θ) is given by:

**Figure 6.**Directivity pattern of function (

**a**) ${D}_{1}\left(\mathsf{\theta}\right)$, (

**b**) ${D}_{2}\left(\mathsf{\theta}\right)$; and (

**c**) $D\left(\mathsf{\theta}\right)$ in y-z plane.

#### 4.1.2. Grating Lobe and Side Lobe

#### 4.2. Optimization in the Lateral Direction (x-z Plane, α = α_{0} = 0°)

#### 4.3. Simulation Results

**Figure 12.**Directivity of linear phased array: (

**a**) three-dimensional directivity; (

**b**) directivity pattern in x-y plane; (

**c**) directivity pattern in x-z plane; (

**d**) directivity pattern in y-z plane; (

**e**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=0\xb0$; and (

**f**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=90\xb0$.

**Figure 13.**Directivity of linear phased array after optimizing parameters in the lateral direction of the array: (

**a**) three-dimensional directivity; (

**b**) directivity pattern in x-y plane; (

**c**) directivity pattern in x-z plane; (

**d**) directivity pattern in y-z plane; (

**e**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=0\xb0$; and (

**f**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=90\xb0$.

**Figure 14.**Directivity of linear phased array after optimizing parameters comprehensively: (

**a**) three-dimensional directivity; (

**b**) directivity pattern in x-y plane; (

**c**) directivity pattern in x-z plane; (

**d**) directivity pattern in y-z plane; (

**e**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=0\xb0$; and (

**f**) directivity pattern when $\mathsf{\alpha}={\mathsf{\alpha}}_{0}=90\xb0$.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Fan, G.; Li, J.; Wang, C. Design and Analysis of MEMS Linear Phased Array. *Micromachines* **2016**, *7*, 8.
https://doi.org/10.3390/mi7010008

**AMA Style**

Fan G, Li J, Wang C. Design and Analysis of MEMS Linear Phased Array. *Micromachines*. 2016; 7(1):8.
https://doi.org/10.3390/mi7010008

**Chicago/Turabian Style**

Fan, Guoxiang, Junhong Li, and Chenghao Wang. 2016. "Design and Analysis of MEMS Linear Phased Array" *Micromachines* 7, no. 1: 8.
https://doi.org/10.3390/mi7010008