Design of Silicon-on-Sapphire Pressure Sensor For High Temperature And High Pressure Applications

Abstract: In this paper, a design scheme of high pressure and high temperature piezoresistive pressure sensor is presented. In order to meet the design requirements, SOS(silicon on sapphire) technology and circular flat diaphragm structure are adopted. Through theoretical analysis, the geometric dimensions of the diaphragm and the position of the piezoresistors on the SOS wafer are optimized for high sensitivity and linearity. A circle flat diaphragm with a radius of 2.5mm and a thickness of 0.8mm is designed, which enables the sensor to operate in high pressure condition (such as 28 MPa). The design is verified by the FEM (finite element method), and the simulation results are consistent with the theoretical results. It is also proved that the design of circular diaphragm has higher sensitivity compared to the square and rectangular diaphragm. With the advantages of high temperature resistance, wide operation range, high sensitivity and good linearity, the design ought to be an ideal candidate for high temperature and high pressure sensing in real application.


Introduction
Pressure sensor is one of the most commonly used sensors in industrial field, which plays an important role in process controls, petrochemical and other industries [1].With the development of measurement technique, high pressure and high temperature pressure sensor for measurements in harsh environments has become a hot research topic [2].Due to the influence of temperature, it is very strict in material selection and structure design to ensure good sensitivity and linearity.Nowadays the commonly used pressure sensors include strain gauge, capacitance transducer, optical fiber grating sensor, piezoelectric transducer, and piezoresistive sensor, etc., among which the piezoresistive sensor is the maturest in application [3].Piezoresistive pressure sensor generally utilizes the periphery fixed circular flat diaphragm or square flat diaphragm [4].In order to overcome the influence of high temperature, the diaphragm material includes polysilicon, sapphire, SiC, diamond, etc. [5].
Through the selection of different materials and diaphragm structures, some research institutions have put forward designs of piezoresistive pressure sensors.Zhe Niu et al. [3] adopted rectangular membrane and thick film structure and designed a SOI(silicon-on-insulator) pressure sensor with an operation range of 0~150MPa.The fabricated sensor achieved a favorable linearity of 0.13% and a high sensitivity of 1.1126mV/MPa.S. Santosh Kumar et al. [6] evaluated the sensitivity and non-linearity of polysilicon piezoresistive pressure sensors with different diaphragm sizes.Experimental results indicated that the sensor with a diaphragm edge length of 1,280μm was found to have optimum characteristics, and sensitivity of 3.35-3.73mV/Bar and non-linearity of <0.3 % were obtained in the pressure range of 0-30 Bar.
After analyzing the advantages and disadvantages of various materials and diaphragm structures, this paper designs a high pressure and high temperature SOS pressure sensor based on circular flat diaphragm structure.In order to achieve high linearity and sensitivity, while obeying the rules of allowable stress, the optimal design of diaphragm size and position of the resistors is made through theoretical analysis and verified by finite element simulation software.Compared with the conventional piezoresistive pressure sensor, this design has the advantages of high temperature resistance, wide operation range, high sensitivity and good linearity.

Analysis and Design
Since the p-n junction which isolates the piezoresistor and substrate is easy to get damaged at high temperature, traditional diffused silicon piezoresistive pressure sensors fail to work at a high temperature above 100 °C.The SOS structure is a monocrystalline silicon film (0.1-0.5μm) grown on single-crystal sapphire (Al 2 O 3 ) by heteroepitaxy technology.The evident advantage of SOS usage is a significant extension of the operating temperature range due to the absence of a p-n junction.This design enables the sensor to operate in a wide temperature range (from -272 to +350°C), as well as bringing a lot of advantages such as high precision, wide measuring range, small hysteresis, corrosion resistance, etc.
Figure 1 is a schematic of SOS pressure sensor.The design includes a bilayered elastic element made from a titanium-alloy diaphragm and a SOS sensing element.The pressure applied to the sensor causes a deformation of the bilayered elastic element, which leads to the changes of silicon piezoresistors in the Wheatstone bridge.The bridge circuit outputs a voltage signal proportional to the pressure, thus realizing the measurement of pressure.The sensing element of the sensor is the bilayered elastic element, in which the titanium-alloy diaphragm plays the main role.Figure 2 shows the schematic of an edge-clamped circular flat diaphragm with a radius of R 0 and a thickness of H.When the diaphragm is deformed under the pressure of p, the upper surface of the diaphragm will be subjected to stress.The maximum stress lies at the edge of the diaphragm: ( ) Where σ max is the maximum stress on the diaphragm, and σ r (R 0 ) represents the stress at the edge of the diaphragm.To improve the sensitivity of the sensor, it is appropriate to increase the value of σ max .But there will be a nonlinear relationship between the measured pressure and the strain of diagram when the value of σ max increase to a certain extent.According to the mechanical properties, following rule should be obeyed to ensure the stability of the sensor: Where K S is the safety factor, and σb represents the allowable stress for the material.Take the safety factor of 1.7, the allowable stress of 441MPa and the maximum pressure of 28MPa into calculation, boundary relationship between R 0 and H must fit: The R is designed as 2.5mm to meet the design requirements of the sensor.According to the formula, the minimum value of H is 0.711mm.So, 0.8mm is selected as the thickness of the diaphragm.The design ensures the stability of the diaphragm, as well as good sensitivity and linearity.
In order to convert the pressure signal into a voltage signal, four piezoresistors are fabricated on the SOS wafer by bulk-micromachining technology.During the design of the resistors, some rules must be obeyed as follows: (a) The initial resistances should be equal; (b) When pressure is applied, two resistors should have an increase in resistance, while the other two are the opposite.It is a necessary condition for the composition of Wheatstone bridge; (c) The change value of the four resistors must be equal and as large as possible, which will ensure a good sensitivity and linearity.
Implanting resistors at the edge of the diaphragm (r=R 0 ) is proved to get the largest stress, which will also result in the largest value of resistors.Taking into account the size of the resistor, the design of r=2.3mm is made.For the (100) P-type silicon, it has the largest piezoresistive coefficient along the crystal direction <011>.Besides, longitudinal piezoresistive coefficient is opposite to the transverse piezoresistive coefficient in this direction (π a =-π n =1/2π 44 ).Thus, the position of the resistors can be set in accordance with the method in Figure 3.When pressure is applied, R 1 and R 3 increase, while R 2 and R 4 decrease.According to the piezoresistive effect, all of them have the same rate of change: Where π 44 is the shear piezoresistive coefficient.σ r and σ θ represent the radial stress and tangential stress.The Wheatstone bridge circuit is shown in Figure 4.The output of the bridge is The input pressure signal is finally converted into output voltage signal.The design can get a high sensitivity as well as ensure a good linear relationship between the measured pressure and output voltage.However, due to the thickness of the diaphragm and other reasons, the stress condition of the diaphragm is different from the theoretical value.In order to guarantee the feasibility of the design, a series of analyses based on the finite element method (FEM) are made in Section 3.

FEM Analysis
Based on the ANSYS, a circular flat diaphragm with 5mm diameter and 0.8mm thickness is created.The elastic modulus of titanium-alloy is 108GPa, and the poisson ratio is 0.33.A fixed boundary condition is applied surrounding the diaphragm, and the pressure applied to the lower surface is set as 28 MPa.A path is made across upper surface to find out the relationship between the stress and the distance.Figure 5 is the simulation result of the von-Mises stress distribution for the diaphragm.From Figure 5, conclusion can be drawn that the stress on the upper surface of the diaphragm only varies with the distance from the position to the center.Figure 7 shows the simulation results of deflections of the diaphragm under various pressures.In the figure, square flat diaphragm (4.43×4.43×0.8mm), rectangular flat diaphragm (6.26×3.13×0.8mm)and circular flat diaphragm (R 0 =2.5mm,H=0.8mm)are compared.The size is decided based on keeping equal area and thickness for the three diaphragm.It can be seen from Figure 7 that the circular flat diaphragm has the largest deflection, which means it achieves the highest sensitivity.The results also demonstrate that the linearity is very good for this design.

Conclusion
This article proposes a design method for SOS pressure sensor working in high pressure and high temperature environment.The work focuses on the optimal design of geometric dimensions of the diaphragm and positions of the piezoresistors.In order to achieve high sensitivity and linearity, silicon on sapphire technology and circular flat diaphragm structure are adopted, and optimal design is made by analysing the stress distribution.The design is verified by the finite element method, and the results prove it to be fully feasible.With the advantages of high temperature resistance, wide operation range, high sensitivity and good linearity, the design ought to have a wide range of applications.

Figure 6
Figure6shows the von-Mises stress along the path.It indicates that the maximum stress lies at the edge of the diaphragm, which is consistent with the theoretical result.The design to arrange resistors at the edge of the diaphragm will result in a highest sensitivity.

Figure 7 .
Figure 7. Deflections of the diaphragm under various pressures.