# Compensation method for temperature drift of monocrystalline silicon pressure sensor

**The introduction**

At present, the highest temperature drift index of monocrcrystalline silicon pressure sensors at home and abroad is 4-0.0l % FS / ~C, and most of the compensation temperature range is -20 ~ 85℃. In some cases, the actual operating temperature range is 45 ~ 125oC. The temperature drift should be reduced to ± 0.05% FS / ~C; The research of temperature compensation of pressure sensor has been carried out in the world, including hardware compensation and software compensation. In this paper, the mechanism of temperature drift of a monocrystalline silicon pressure sensor and the compensation technology are studied. The thermal zero drift and thermal sensitivity drift of the monocrystalline silicon pressure sensor can reach ± 0.014% FS / ~C in the temperature range of -45 ~ 85℃, so as to meet the practical needs.

**1. Temperature drift mechanism**

Monocrystalline silicon pressure sensor is made of the piezoresistive effect of monocrystalline silicon. The piezoresistive coefficient varies with the temperature, so the piezoresistive effect principle itself can cause the temperature drift of the sensor output. In addition, the manufacturing process of semiconductor sensitive elements will also bring the overall temperature drift of the sensor, such as the inequality of bridge resistance, leakage current of bridge arm resistance, assembly stress, etc. 2 j. Piezoresistive coefficient π is a parameter to measure the piezoresistive effect of monocrystalline silicon materials. The piezoresistive coefficient of each crystal in the direction of monocrystalline silicon is different. For example, to describe the relationship between piezoresistive effect and resistance value in the orthogonal coordinate system,

Longitudinal stress; Is transverse stress; Is the stress in the direction perpendicular to and; Is the longitudinal piezoresistive coefficient; Is the transverse piezoresistive coefficient; Is the piezoresistive coefficient in the direction perpendicular to and and.

P-type silicon and N-type silicon at room temperature are dominated by piezoresistivities π11, π12, π44. Taking P-type silicon as an example, the components of piezoresistivities depend on π44, π11, π12, and the piezoresistivities π44 change with temperature. The variation of piezoresistive coefficient π44 with temperature is also related to the surface impurity concentration, and its relation curve is shown in FIG. 1.

**2. Analysis of temperature drift characteristics**

The piezoresistive pressure sensor signal conversion is realized through the Whistden bridge, as shown in Figure 2.

FIG. 1 Relation curves of piezoresistive coefficient π44 with temperature at different impurity concentrations

Fig 2 Scheme ofV~neatstonebridge

If r1=r3=r2=r4, then △r1=△r3=△r2=△r4. When the input voltage Vi is applied to one set of diagonal points of the bridge, the output voltage V0 is generated at the other set of diagonal points, whose output is

At this point, since △r is proportional to the pressure on the diaphragm, the pressure sensor will output an electrical signal proportional to the pressure P, thus achieving the pressure measurement.

The optimal characteristic of the pressure sensor is that the output only changes linearly with the change of the measured pressure. However, it can be seen from the temperature drift generation mechanism that the change of the ambient temperature will definitely cause the change of the sensor output without taking any measures. The output variation shows that the zero output, sensitivity and other parameters change with the ambient temperature.

**3 Compensation Method**

3.1 Compensation Principle

The temperature characteristics of pressure sensor can be compensated from two aspects: zero temperature drift and sensitivity temperature drift. At present, there are many compensation methods, such as thermistor compensation method, series and parallel resistance compensation method, SCM real-time compensation method, active circuit segment compensation method and so on. The compensation circuit principle of the studied monocrystalline silicon pressure sensor is shown in Figure 3.

For thermal zero drift, the method of series and parallel resistance is used to compensate. For thermal sensitivity drift compensation, the compensation circuit composed of constant current power supply, temperature control switch and active circuit is completed together, as shown in w4, w3, and w2 in Figure 3. The optimum sensitivity temperature coefficient of constant current power supply is 0.05% FS / ~C, which can not meet the actual needs. After the first compensation of constant current power supply, the sensor uses the active circuit segment compensation method to compensate again, so that it can reach a higher compensation level. Firstly, the sensitivity output characteristics of the compensation sensor are detected, and the segmented temperature point is determined according to the detection data, and the segmented point of w3 switch is set at the temperature point. Then, the switch is switched on in the negative temperature zone, and the high warped end of the sensitivity temperature coefficient curve of -45℃ is leveled down. In the positive temperature zone, R6 is switched on, and the high warped end of the sensitivity temperature coefficient curve of 85℃ is leveled down. FIG. 4 shows the typical variation of the sensitivity output of the sensor with a measurement range of 0 ~ 1MPa with temperature: FIG. 4(a) is the sensitivity of the sensor with a single constant current power supply compensation - temperature characteristic curve; FIG. 4(b) shows the sensitivity - temperature characteristic curve of the sensor when the constant current power supply is in parallel with a single resistor R5. FIG. 4(c) Sensitivity - temperature characteristic curve of the sensor when the constant current power supply is paralleled with the segmented resistors R5 and R6.

Fig 3 Sch(~me ofcom persation principle

(b)curveofsensitivity stemperatureattheconditionofconstant currentsourccwithshuntresislaneeR5

(c)curveofsensitivityf$temperatureattheconditionofconstant currentsourceandsubsectioncompensation

Fig 4 Curveofsensitivit' teperature before and after eom pcnsalion

**3.2 Compensation calculation method**

3.2.1 Constant current power supply compensation calculation

Under certain doping concentration, the resistance temperature coefficient of the sensitive element is positive, and the constant current power supply can be used to compensate the sensitivity temperature coefficient of the sensitive element.

The constant current supply current I is determined according to the design sensitivity of the practical sensitive element. As can be seen from Figure 5, its current is where V8 is the input voltage R8, R9 and R10 are the input and ground resistance respectively.

**3.2.2 Calculation of series and parallel resistance network**

Firstly, the pressure and temperature characteristics of the product are tested. Based on the measured data, the resistance values of each series and parallel resistance are calculated.

(1) Test low temperature Tc, high temperature Th, lower limit pressure Po and upper limit pressure P, as well as the output voltage and bridge voltage under the constant current supply mode.

(2) Calculation of zero compensation resistance: Variables A, B, C, D are introduced to calculate the zero compensation resistance

Where, Voc and Voh are zero output voltage V at low temperature and high temperature respectively, V2c and V2h are full scale output voltage at low temperature and high temperature respectively,V; Ec and Eh are respectively the bridge voltage at low and high temperature, V; Po, P2 are the upper limit and lower limit pressure respectively, MPa; Tc and Th are the lowest mild and highest temperature respectively, ℃.

In order to calculate the series compensation resistance R5 and correct the error caused by the introduction of resistors R3 and R4 into the bridge arm, the simplified formula is

The calculated resistance value of R3 can be positive or negative, and the positive or negative value of the resistance indicates the position of the resistance, as shown in Figure 3. Series compensation can be completed by R3 or R4, and the relationship between them is as follows:

When R8≥0, R4=R5, R3=0(short circuit); When R8<0, R3=R8, R4=0(short circuit). The zero temperature parallel compensation resistance Rp can be calculated from Equation (10)

As above, the position of resistance Rp also has two cases: when Rp ≥ 0, R2=Rp, Rl=∞(open circuit); When Rp<0, Rl=Rp, R2=∞(open).

**(3) Calculation of sensitivity subsection compensation resistance**

In order to improve the precision of parallel compensation of fixed resistance, a combined temperature control switch (part w2 of FIG. 3) is used to realize piecewise compensation to improve the compensation accuracy. It can be seen that l6 ~ 20℃ can be used as the compensation segment point, or 0 ~ l0℃ can be used as the compensation segment point. The temperature control switch w2 is used to compensate the high temperature area and low temperature area respectively. Through the change of the bridge voltage signal of the sensor under the constant current source power supply, the action of the temperature control switch can be realized, so as to control the access of the resistance in parallel at both ends of the bridge, so as to reduce the temperature coefficient of the load resistance of the constant current source, so as to realize the segmented compensation. The formulas for calculating output voltage (Vc, Vh), resistance (Rc, Rh) and temperature compensation resistance R5, R6 of sensitivity at low and high temperature are given below

**4 Compensation results and analysis**

4.1 Comparison of parameters before and after sensor compensation

Table 1 lists the comparison results of parameters before and after compensation by using the series and parallel resistance network compensation, constant current supply compensation, active circuit segment compensation and other comprehensive methods.

4.2 Main performance test results of the sensor

Table 2 shows the compensation results of major parameters such as temperature drift of six sensors.

For comparison, the measured ultrasonic signals were denoised by wavelet denoising method (dbl wavelet and four-layer decomposition were selected) in this paper. The processing results are shown in Figure 2(d). According to formula (7), the SNR of Figure 2(b), 2(c) and 2(d) is calculated as 1.2dB, 6.45dB and 6.47dB, respectively. The results show that both the proposed denoising method and wavelet denoising greatly improve the signal-to-noise ratio of ultrasonic defect signals. Moreover, the denoising effect of the proposed method is very close to that of wavelet denoising. In addition, this result also shows the correctness and effectiveness of the denoising method in this paper. Compared with the wavelet denoising method, the denoising method in this paper has the advantage of realizing the denoising through blind signal-noise separation. The denoising process is intuitive and the denoising effect is good.

**3 Conclusion**

This paper presents a method of ultrasonic signal denoising based on blind source separation. The proposed method is used to denoise the simulated ultrasonic signal, and is compared with the wavelet denoising method. The experimental results show that the proposed denoising method can effectively denoise the ultrasonic signal, greatly improve the signal-to-noise ratio and enhance the defect signal, and its denoising effect can be comparable to that of wavelet denoising. The feature of this denoising method is to realize the denoising of ultrasonic signal through blind source separation of ultrasonic signal and noise signal.

**References:**

[1] GustafssonM G。StepinskiT．Studiesofsplitspectrum processing，optimaldetection，and maximum likelihoodamplitudeestimationusingasimplecluttermodel[J]．Ultrasonics，1997，35(1)： 3l一52．

[2] DraiR，KhelilM，BenchaalaA．Timefrequencyandwavelettransform appliedtoselectedproblemsinultrasonicsnde[J]．NDT andEIntemational，2002，35(8)：567．

[3] Kim J，UdpaL，UdpaS．Multi-stageadaptivenoise cancellation forultrasonicNDE[J]．NDTandEInternational，2001，34(5)： 3l9．

[4] lzquierdoM AG，HemandezM G，Gmullem 0，eta1．Time—frequencywienerfilteringforstructuralnoise reduction[J]．Uhmsonics，2oo2，4o(1—8)：259．

[5] TakensF．Dynamicalsystemandturbulence，lecturenotes inmathematics[M]．Springer，1981．

[6] SanerT，YorkeJA，GrotepassM．Embedolagy[J]．J．Statistical Physics，1991，65：579—561．

[7] HyvarinenA．Fixed-pointalgorithmandmaximumlikelihoodestimationforindependentcomponentanalysis[J]．NeuralPl"OC~ - ingLetters，1999，10(1)：1．

[8] sAV，AVS．Therecurrentnormalizedrange method forrelevation offracturalstructureanditsapplicationtoaIlal sofEEG[J]． RadioelectronInform ，1998，(3)：162—165．

[9] ZhuY，WeiishtJP．Ultrasonicnondestructiveevaluationofhighly scatteringmaterialsusingadaptivefilteringanddetection[J]． IEEE Transactionson Ultrasonics，Ferroe lectrics，an d Frequency Control，1994，41(1)：26．

[10]Demi~ R，SaniieJ．Mode1．basedestima tionofultrasonicechoes parti：Analysisan d algorithms．IEEE Transactionson Ultrasonics[J]．Ferroelectrics，andFrequencyControl。2001，48：787．