## 2 Design and Fabrication  
### Design and Fabrication of the Micro Sensor  
In general, a piezoresistive pressure sensor has a sensing diaphragm [24; 25; 26; 27]. For piezoresistive sensors, the sensitive diaphragms above the vacuum cavities are pressured and then generate stress. The variation of piezoresistors caused by the applied pressure is transferred into voltage due to the piezoresistive effect [28; 29]. Therefore, the performance of a piezoresistive sensor depends largely on the pressure sensitive diaphragm. Firstly, the dimensions of the pressure sensor's diaphragm were designed based on previous published work [12]. Then, the thickness of the diaphragm was determined by theoretical calculation from Expression (1), where \(P_{burst}\) is five times the maximum applied pressure, \(\sigma_{fracture}\) is the maximum stress of the diaphragm, \(A\) is the area of the diaphragm, \(h\) is its thickness, and \(v\) is the Poisson's ratio. The calculated minimum thickness is 26.87 \(\upmu\)m. Therefore, the simulation was done in COMSOL Multiphysics FEA (finite element analysis) software for a thickness of more than 30 \(\upmu\)m. Based on this, the pressure sensor models have an n-type silicon diaphragm with the dimensions 900 \(\times\) 450 \(\upmu\)m and thicknesses of 40 and 50 \(\upmu\)m. The von Mises stress induced in the diaphragm with various thicknesses were determined and evaluated with the analytic explanation for a face-loaded pressure of 5 MPa. The simulation results obtained from the FEA tool are shown in Figure 1a-d. Along the centerline of the diaphragm, the tensile stress at the diaphragm edge reaches its maximum and the compressive stress in the center of the diaphragm reaches its maximum. This resulted from the silicon diaphragm contracting at the center and stretching at the edges when the pressure was applied uniformly from the top. Therefore, the piezoresistors should be located in these places to increase the sensitivity. By comparing the simulation results of the pressure sensor models with different diaphragm thicknesses, it can be found that the surface stress of the pressure sensor with 40-\(\upmu\)m-thick membrane is larger, indicating that the thinner membrane thickness exhibits the higher sensitivity. \[P_{burst}=\frac{3.4}{1-v^{2}}\times\frac{\sigma_{fracture}\times h^{2}}{A} \tag{1}\]  
The schematic diagram of the proposed silicon piezoresistive pressure sensor is shown in Figure 2. The pressure sensor has a rectangular silicon diaphragm, which is fabricated on the device layer of a SOI wafer [30; 31]. By using buried-oxygen-layer etching stop technology [32], the diaphragm thickness of the pressure sensor can be precisely controlled. After one-mask deep reactive ion etching (DRIE), the pressure sensor's rectangular diaphragm is shaped. The thickness of the diaphragm is the same as that of the device layer. The piezoresistors are formed on the silicon diaphragm by boron ion implantation. Four  
Figure 1: Von Mises stress distribution under finite element analysis: (**a,c**) stress distribution under 5 MPa of face-loaded pressure; (**b,d**) transverse stress distribution along the centerline. piezoresistors are connected to a Wheatstone bridge structure by forming ohmic contact with aluminum wires. The contact area between the aluminum conductor and the heavily doped region of the piezoresistors has a great influence on the resistance value of the four piezoresistors in the Wheatstone bridge. Therefore, the consistency of ohmic contact area should be ensured by improving the accuracy of lithography and etching, and increasing the width of aluminum wire relative to that of piezoresistors. Furthermore, a layer of SiO\({}_{2}\) is deposited and patterned on the substrate in the plasma enhanced chemical vapor deposition (PECVD) system, as a passivation layer to improve the reliability of pressure sensors in harsh environments. Dimensions of the diaphragm and the piezoresistors are shown in Figure 2c.