# Design Optimization and Fabrication of High-Sensitivity SOI Pressure Sensors with High Signal-to-Noise Ratios Based on Silicon Nanowire Piezoresistors

^{1}

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## Abstract

**:**

^{1}

^{8}cm

^{−3}and geometry of 10 µm long SiNW piezoresistor of 1400 nm × 100 nm cross area and 6 µm thick diaphragm of 200 µm × 200 µm are required. Then, the proposed SiNW pressure sensor is fabricated by using the standard complementary metal-oxide-semiconductor (CMOS) lithography process as well as wet-etch release process. This SiNW pressure sensor produces a change in the voltage output when the external pressure is applied. The involved experimental results show that the pressure sensor has a high sensitivity of 495 mV/V·MPa in the range of 0–100 kPa. Nevertheless, the performance of the pressure sensor is influenced by the temperature drift. Finally, for the sake of obtaining accurate and complete information over wide temperature and pressure ranges, the data fusion technique is proposed based on the back-propagation (BP) neural network, which is improved by the particle swarm optimization (PSO) algorithm. The particle swarm optimization–back-propagation (PSO–BP) model is implemented in hardware using a 32-bit STMicroelectronics (STM32) microcontroller. The results of calibration and test experiments clearly prove that the PSO–BP neural network can be effectively applied to minimize sensor errors derived from temperature drift.

## 1. Introduction

^{−1}. Nevertheless, it is noteworthy that tradeoffs should be made in the optimization design of NEMS piezoresistive pressure sensors. Obviously, noise determines the minimum detection signal, which is a very important factor in the performance of the pressure sensors, so the presence of noise is the limiting factor in the sensor design and also needs to be carefully considered [5,6,25]. In other words, the sensor design parameters must be properly chosen to balance the pressure sensitivity and voltage noise sources of the NEMS piezoresistive pressure sensor given a set of design and operating constraints, especially where a high signal-to-noise ratio (SNR) is required for the faithful measurement of the small pressure differentials [26]. However, an exhaustive analysis considering the influences of doping concentration and the geometry of SiNW piezoresistors on optimizing the performance of the NEMS piezoresistive pressure sensors in terms of sensitivity and signal-to-noise ratio has been rarely reported till now.

## 2. Configuration of the SiNW Pressure Sensor and Basic Theory

#### 2.1. Structure of the SiNW Pressure Sensor

#### 2.2. The Sensitivity of the SiNW Pressure Sensor

_{R}, the piezoresistive pressure sensitivity S is given by

_{L}and π

_{T}refer to the longitudinal piezoresistive coefficient (for stress applied parallel to the current flow in the piezoresistor) and transverse piezoresistive coefficient (for stress applied perpendicular to the current flow), respectively, while σ

_{L}and σ

_{T}are the longitudinal and transverse stress in the SiNW piezoresistors formed by the external pressure ΔP. For the NEMS piezoresistive pressure sensor with complex structure, the stress σ of its sensitive element is obtained by ANSYS finite element simulation.

_{0},T

_{0}) stands for the piezocoefficient value for the SiNW of low doping concentration (n

_{0}) at room temperature (T

_{0}). The Fermi integral is the function of temperature (T) and the Fermi energy (E

_{F}), and K

_{B}denotes the Boltzmann constant. The Fermi energy is determined from n. It is found that the piezoresistive effect significantly decreases at high temperature and doping concentration due to carrier-phonon scattering as well as carrier-carrier scattering. In fact, the piezoresistive coefficients of the SiNWs are sensitive to many other quantities such as size, orientation and band structure [31,32,33,34]. According to the published papers [17,18,19,20,21], the SiNWs have giant piezoresistive effect. The reason for higher piezoresistance is thanks to reduced dimensions, increased surface depletion region and enhanced surface trapping effect under pressure [17,20,23,24,35].

#### 2.3. The SNR of the SiNW Pressure Sensor

_{B}denotes the Boltzmann constant, T is the temperature, R is the resistance of the double SiNW piezoresistor, n is the carrier’s concentration, q is the electron charge, μ is the hole mobility and l, w, and t are the length, width, and thickness of the nanowire piezoresistor, respectively.

^{−6}and 5.7 × 10

^{−6}in single crystal silicon [38].

## 3. Sensor Design

#### 3.1. Design Optimization Based on Finite Element Simulation

#### 3.2. Sensor Sensitivity and SNR Analysis

^{−4}K

^{−1}by linear fitting.

^{1}

^{8}to 5 × 10

^{1}

^{8}cm

^{−3}. Taking into account the good Ohmic contact and the low power consumption of SiNW pressure sensor, p-type implantation of 5 × 10

^{1}

^{8}cm

^{−3}is then chosen in this paper. In Figure 7b, we can also find that the SNR has been improved after considering the giant piezoresistive effect. In short, our work shows that we can optimize the design to reduce the noise and improve the signal-to-noise ratio of piezoresistive pressure sensor using SiNW. We hope that the results of these theories can be helpful for future design of experiment methods to achieve the most optimized sensor.

## 4. Fabrication Process of SOI Piezoresistive Sensor

^{1}

^{3}Dose/cm

^{2}were implanted on the top silicon layer for the piezoresistance of the SiNW, followed by annealing for dopant activation. Then, the extra SiO

_{2}layer of 50 nm and silicon nitride layer (SiN

_{x}) of 100 nm were deposited on both sides of SOI wafer by using low pressure chemical vapor deposition (LPCVD). The compressive stress formed in the SiO

_{2}adhesive layer compensates the tensile stress in the SiN

_{x}layer. For SiNW pattern and electrical isolation, they were patterned and the top silicon layer was etched by deep reactive ion etching (DRIE), and the SiO

_{2}in the SOI wafer provides an etch stop barrier. In order to fabricate metal pad, after etching extra SiO

_{2}and SiN

_{x}layers on front side, a 1.5 µm thick Aluminum was deposited onto the silicon contact surfaces while the Al pad is patterned by using a liftoff process. Besides, SiNW structures like bridge shape were released through buffered oxide etcher (BOE) solution and critical point drying. In order to protect against corrosion of Aluminum structures, they are covered by thick photoresist mask. After that, the tetramethyl ammonium hydroxide (TMAH) wet etch is conducted to release the diaphragm structure. The substrate of the SOI wafer is ground to 675 µm, and backside of the substrate was gradually etched by 363 K TMAH in many etch steps to obtain diaphragm less than 6 µm thickness. Finally, the extra SiO

_{2}and SiN

_{x}mask layers on backside were removed using BOE solution and CF

_{4}gas, and then a Pyrex glass 7740 wafer of 500 µm thickness was placed on the etched backside of the SOI wafer and anodically bonded by applying an electric field (900 V DC) across the bonding interface at 360 °C. The bonding process is carried out in a vacuum environment.

## 5. Experimental Section and Discussion

#### 5.1. Experimental Setup

#### 5.2. Sensor Output Result

^{−4}K

^{−1}by linear fitting and is in the same order of magnitude as the theoretical predicted value. As discussed in the previous theoretical study, this is mainly due to the fact that the piezoresistive coefficient decreases with increasing temperature. For the constant-current case (0.05 mA, around 5 V equivalent voltage), sensor of the released double SiNW measured by a quarter Wheatstone bridge has sensitivity of 495 mV/V·MPa at room temperature and it has 1.4 times more sensitivity than the released single SiNW pressure sensor [7], which matches well with the previous theoretical predictions.

^{−11}Pa

^{−1}, which is much higher by one order of magnitude than that of bulk silicon. They believe that the residual stress in the silicon wires with different widths has a very critical impact on their piezoresistive coefficient. However, due to various constraints, we do not carry out a more detailed analysis of the impact of residual stress on sensitivity of the pressure sensor. In order to ensure the measuring precision of the piezoresistive pressure sensor, we have proposed a compensation method based on the PSO–BP neural network to solve the temperature drift of the sensor and achieve a linear output in the entire measuring range.

#### 5.3. Data Fusion Using PSO–BP Algorithm

#### 5.3.1. PSO–BP Neural Network Algorithm Overview

#### 5.3.2. Temperature Compensation by PSO–BP Data Fusion Algorithm

_{p}represents the average output voltage of our sensor. According to Table 1, it is found that the U

_{p}changes with temperature T and hence there is a drift in the sensor output characteristics. The temperature drift can especially cause a few mV errors at full scale. Obviously, the pressure sensor is seriously influenced by the temperature. Then, MATLAB (version R2013b, MathWorks, Natick, MA, USA) is applied to establish a data fusion model based on the PSO–BP algorithm and process these training sample data. The training data must be pre-processed to prevent nodes quickly reaching a saturated state and becoming unable to continue learning. According to the “mapminmax” function of MATLAB, the normalized formula is as follows:

_{max}is 1 and y

_{min}is −1. x is the output value of SOI pressure sensor at a reference temperature, while x

_{max}and x

_{min}are the maximum and the minimum output values, respectively. On the basis of this formula, the training data in Table 1 can be normalized. Theoretical studies have proven that the three-layer neural network can realize any complex nonlinear mapping problem, so the prediction model adopts a three-layer BP neural network with a single hidden layer for temperature compensation. This paper sets the input layer with two nodes (corresponding to the temperature signal and pressure signal without compensation), the hidden layer with five nodes, and the output layer with one node (corresponding to pressure signal after compensation). The maximum training times is 1500, the target error is 5 × 10

^{−6}, the training function is “trainlm”, the learning function is “learngdm” and the learning rate is set to 0.01. The population size is set to 40, the inertia weight is set to 1, and learning factor is chosen to be 2.5. After the optimization algorithm terminates, connection weights between the input layer and hidden layer ω

_{1}, connection weights between the output layer and hidden layer ω

_{2}, scale factor b

_{1}and shift factor b

_{2}is:

^{−6}after 41 iterations of the training cycle. However, the calculation shows that the BP algorithm needs to be iterated 122 times to achieve similar target error, which manifests that PSO–BP algorithm significantly improves the operating efficiency. Figure 13d gives the temperature compensation errors of PSO–BP neural network and traditional BP neural network. It is clear that the compensation accuracy of PSO–BP neural network is significantly higher than that of the BP network.

## 6. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic diagram of the nanoelectromechanical system (NEMS) piezoresistive pressure sensor using double silicon nanowire (SiNW) piezoresistors; and (

**b**) the measurement principle of the SiNW pressure sensor.

**Figure 2.**(

**a**) Three-dimensional finite element mesh of single SiNW piezoresistive pressure sensor; (

**b**) three-dimensional finite element mesh of double SiNW piezoresistive pressure sensor; (

**c**) average stress distribution of single SiNW pressure sensor; (

**d**) average stress distribution of double SiNW pressure sensor; and (

**e**) average stress distribution of the SiNW.

**Figure 3.**ANSYS simulation results: (

**a**) the von Mises equivalent stress (SEQV) of double SiNW of 2 µm length vs. diaphragm size and membrane thickness; and (

**b**) SEQV of double SiNW vs. the length and width of double SiNW.

**Figure 4.**ANSYS simulation results: (

**a**) SEQV of SiNW vs. silicon dioxide thickness; and (

**b**) SEQV of SiNW vs. the remaining underlying silicon thickness.

**Figure 5.**(

**a**) Relative resistance change as a function of the applied pressure for single and double SiNW and bulk silicon; (

**b**) variation of the sensitivity of double SiNW pressure sensor with the doping concentration; and (

**c**) variation of the sensitivity of double SiNW pressure sensor with the temperature.

**Figure 6.**(

**a**) Variation of the voltage noise with the length of SiNW; (

**b**) variation of the voltage noise with the thickness of SiNW; (

**c**) variation of SNR with the length of SiNW; and (

**d**) variation of SNR with the thickness of SiNW.

**Figure 7.**(

**a**) Variation of the voltage noise with doping concentration of the SiNW piezoresistor; and (

**b**) variation of SNR with doping concentration of the SiNW piezoresistor.

**Figure 8.**Process flow of the proposed SiNW piezoresistive pressure sensor (the drawing is not to scale). (

**a**) P-type ion implantation and annealing were performed on the front side of (100) silicon on insulator (SOI) wafer; (

**b**) Silicon dioxide and silicon nitride were deposited on both sides by using low pressure chemical vapor deposition (LPCVD); (

**c**) SiNWs were formed by using deep reactive ion etching (DRIE) on front side; (

**d**) Metal deposition and patterning on front side were carried out to form electric pads; (

**e**) Wet etch was performed to release SiNWs on front side through buffered oxide etcher solution; (

**f**) Inductively coupled plasma (ICP) etch was applied to remove silicon nitride on backside and the corrosion window is formed; (

**g**) The tetramethyl ammonium hydroxide (TMAH) backside etch to release the diaphragm; (

**h**) Field-assisted silicon-glass bonding is carried out in a vacuum environment.

**Figure 9.**(

**a**) A photograph of the fabricated SOI pressure sensor die using double SiNW before the release; and (

**b**) a photograph of packaged pressure sensor.

**Figure 10.**Photographs of the proposed SiNW pressure measurement system and calibration and test experimental setup. The CTS-150 constant temperature and pressure chamber is manufactured by Cliphyco Instruments Co., Limited (Hong Kong, China).

**Figure 11.**(

**a**) Dependence of the output voltages of SOI pressure sensor without compensation on the pressure with temperature from −20 to 50 °C; and (

**b**) the relationship curve between the sensitivity and temperature.

**Figure 12.**Flowchart depicting the particle swarm optimization–back-propagation (PSO–BP) neural network algorithm.

**Figure 13.**(

**a**) The prediction output of the PSO–BP neural network algorithm; (

**b**) fitness curve; (

**c**) mean-squared error curve of the PSO–BP neural network algorithm; and (

**d**) error curves of BP algorithm and the PSO–BP algorithm

**Figure 14.**(

**a**) The relationships between the actual measurement pressures of the digital SiNW pressure sensor designed in the paper and the calibration pressure at different temperature; and (

**b**) the absolute error between the corrected pressures and the calibration pressures at different temperature.

**Table 1.**The calibration sample data of the SiNW pressure sensor for the training of the PSO–BP compensation algorithm, which are obtained with pressures from 0 to 100 kPa and with temperatures from −20 to 50 °C.

Pressure | P = 0 kPa | P = 10 kPa | P = 20 kPa | P = 30 kPa | P = 40 kPa | P = 50 kPa | P = 60 kPa | P = 70 kPa | P = 80 kPa | P = 90 kPa | P = 100 kPa | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Temperature | ||||||||||||

T = −20 °C | U_{p} = 2.20 mV | U_{p} = 7.68 mV | U_{p} = 15.12 mV | U_{p} = 20.00 mV | U_{p} = 28.88 mV | U_{p} = 35.44 mV | U_{p} = 42.11 mV | U_{p} = 48.88 mV | U_{p} = 56.00 mV | U_{p} = 63.13 mV | U_{p} = 68.96 mV | |

T = −10 °C | U_{p} = 4.40 mV | U_{p} = 8.44 mV | U_{p} = 14.96 mV | U_{p} = 21.81 mV | U_{p} = 28.12 mV | U_{p} = 34.72 mV | U_{p} = 41.00 mV | U_{p} = 48.08 mV | U_{p} = 54.89 mV | U_{p} = 61.88 mV | U_{p} = 66.71 mV | |

T = 0 °C | U_{p} = 3.64 mV | U_{p} = 7.73 mV | U_{p} = 14.16 mV | U_{p} = 20.71 mV | U_{p} = 26.89 mV | U_{p} = 33.35 mV | U_{p} = 39.80 mV | U_{p} = 46.20 mV | U_{p} = 53.20 mV | U_{p} = 60.22 mV | U_{p} = 66.96 mV | |

T = 10 °C | U_{p} = 2.29 mV | U_{p} = 6.84 mV | U_{p} = 13.85 mV | U_{p} = 20.19 mV | U_{p} = 26.16 mV | U_{p} = 32.80 mV | U_{p} = 38.96 mV | U_{p} = 45.39 mV | U_{p} = 52.21 mV | U_{p} = 58.95 mV | U_{p} = 65.81 mV | |

T = 20 °C | U_{p} = 2.04 mV | U_{p} = 6.56 mV | U_{p} = 13.36 mV | U_{p} = 19.84 mV | U_{p} = 24.56 mV | U_{p} = 32.33 mV | U_{p} = 38.84 mV | U_{p} = 45.12 mV | U_{p} = 51.82 mV | U_{p} = 58.60 mV | U_{p} = 65.36 mV | |

T = 30 °C | U_{p} = 1.28 mV | U_{p} = 5.11 mV | U_{p} = 11.11 mV | U_{p} = 17.60 mV | U_{p} = 23.80 mV | U_{p} = 29.84 mV | U_{p} = 36.40 mV | U_{p} = 43.11 mV | U_{p} = 49.84 mV | U_{p} = 56.68 mV | U_{p} = 63.80 mV | |

T = 40 °C | U_{p} = 0.97 mV | U_{p} = 3.20 mV | U_{p} = 8.40 mV | U_{p} = 14.84 mV | U_{p} = 22.47 mV | U_{p} = 28.36 mV | U_{p} = 35.20 mV | U_{p} = 40.38 mV | U_{p} = 47.29 mV | U_{p} = 53.48 mV | U_{p} = 59.29 mV | |

T = 50 °C | U_{p} = 0.44 mV | U_{p} = 3.08 mV | U_{p} = 8.00 mV | U_{p} = 14.49 mV | U_{p} = 21.00 mV | U_{p} = 28.12 mV | U_{p} = 33.75 mV | U_{p} = 40.04 mV | U_{p} = 47.09 mV | U_{p} = 53.15 mV | U_{p} = 59.00 mV |

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**MDPI and ACS Style**

Zhang, J.; Zhao, Y.; Ge, Y.; Li, M.; Yang, L.; Mao, X. Design Optimization and Fabrication of High-Sensitivity SOI Pressure Sensors with High Signal-to-Noise Ratios Based on Silicon Nanowire Piezoresistors. *Micromachines* **2016**, *7*, 187.
https://doi.org/10.3390/mi7100187

**AMA Style**

Zhang J, Zhao Y, Ge Y, Li M, Yang L, Mao X. Design Optimization and Fabrication of High-Sensitivity SOI Pressure Sensors with High Signal-to-Noise Ratios Based on Silicon Nanowire Piezoresistors. *Micromachines*. 2016; 7(10):187.
https://doi.org/10.3390/mi7100187

**Chicago/Turabian Style**

Zhang, Jiahong, Yang Zhao, Yixian Ge, Min Li, Lijuan Yang, and Xiaoli Mao. 2016. "Design Optimization and Fabrication of High-Sensitivity SOI Pressure Sensors with High Signal-to-Noise Ratios Based on Silicon Nanowire Piezoresistors" *Micromachines* 7, no. 10: 187.
https://doi.org/10.3390/mi7100187