An Ultra-low Thermal Sensitivity Drift Piezoresistive Pressure Sensor Compensated by Passive Resistor/Thermistor Network

This paper presents a piezoresistive pressure sensor that exhibits extremely low thermal sensitivity drift across a broad range of temperatures, which integrates a passive resistor/thermistor network for compensation. Standard microfabrication processes were conducted to fabricate the sensor chip. From the experimental results, the proposed sensor demonstrated an extremely low thermal sensitivity drift of 0.01% FS/°C within temperature range of -55 °C to 85 °C, which is a significant improvement compared with the sensor with no temperature compensation (0.17% FS/°C) and the sensor with conventional temperature compensation (0.09% FS/°C). The compensation method developed in this study has the potential to serve as a facilitating instrument in pressure measurements with large temperature variations.


Introduction
Since C.S. Smith discovered the piezoresistive effect in 1954 [1], piezoresistive pressure sensors have undergone significant developments for decades.Nowadays, piezoresistive pressure sensors have gained significant popularity in various industries, including medical, petrochemical, automotive, and so on [2][3].Nevertheless, temperature changes have a big impact to the sensor [4], which restricts its utilization in wide-temperature range scenarios.Therefore, it is necessary to implement temperature compensation.
The software compensation can be accomplished through some algorithms [5][6].Despite the relatively high precision of the software compensation, the incorporation of the additional signal processing circuit results in an increased cost for the piezoresistive pressure sensor, hence limiting its widespread usage.Hardware compensation utilizes the passive components to compensate the temperature drift, which is currently the most prevalent approach [7].However, it is worth noting that the traditional passive compensation method often exhibits limited accuracy and poor sensitivity.
This study introduces a novel compensation network that utilizes resistor and thermistor to passively compensate for the thermal sensitivity drift in piezoresistive pressure sensors.In contrast to conventional hardware compensation methods, this approach exhibits a significantly reduced thermal sensitivity drift while simultaneously minimizing sensitivity loss.Fig. 1(a), (b) shows the structure of the proposed MEMS piezoresistive pressure sensor, which mainly comprises a glass cap for hermetic package, and an SOI wafer with sensing elements.Fig. 1(c) shows the configuration of the sensor, including a glass block to eliminate package stress, a Kovar base to mount the sensor, a threaded interface to introduce external pressure, and a back housing to accommodate the compensation circuit and lead-out wire.All structures were interconnected through laser welding.

Compensation Methods
The sensor's output voltage may be expressed as [8]: where Uo and UB denote the output singal and input singal.σ and π44 denote the stress and stress-to-resistance conversion coefficient of piezoresistors.Given the same external pressure and sensor configuration, the stress σ can be considered to be temperature independent if thermal effect is disregarded.Therefore, the output of the sensor was affected by UB and π44 when the environment changes, as depicted in Equation 2. In this formula, TCS stands for temperature-dependent output changes, whereas TCUB and TCπ44 stand for temperature-dependent bridge voltage and piezoresistive coefficient changes, respectively.
When no adjustment is performed, the TCUB is zero because the sensor is usually linked directly to a constant DC source.TCS is equivalent to TCπ44 in this instance.The magnitude of TCπ44 in p-type silicon with a doping concentration between 10 18 cm -3 and 10 21 cm -3 is around -0.2%•°C -1 [9], as Figure 2(a) illustrates.Consequently, uncompensated piezoresistive pressure sensors exhibit significant thermal sensitivity drift, hence necessitating the temperature compensation.
As seen in Fig. 2(b), the traditional adjusting approach depends a constant resistor linked in series with the piezoresistor network.In this setting, the output voltage and the corresponding temperature coefficient are depicted in Equation 3 and 4, respectively, where UI and R0 denotes the input voltage and series resistor, RB and TCRB denote the resistance and temperature coefficient of resistance of Wheatstone bridge.0  5, the loss of sensitivity under the optimal series resistor can be obtained, as depicted in Equation 6.It can be seen that the optimal series resistor exists only when TCRB is greater than |TCπ44|.Nevertheless, if |TCπ44| is only slightly smaller than TCRB, the sensitivity of the sensor will be significantly reduced after compensation.Hence, in order to maintain high output while decreasing the temperature effect, it is vital to ensure that |TCπ44| is considerably lower than TCRB.However, as depicted in Figure 2(a), the magnitudes of |TCπ44| and TCRB are very similar within a wide range of doping concentrations [9], making it impossible for conventional method to attain ideal compensation.
Figure 2(c) shows the proposed passive resistor/thermistor compensation network.A thermal resistor RT with a large positive TCR was linked in parallel with the Wheatstone bridge, in contrast to the traditional compensating approach.As a result, the TCRB of the Wheatstone bridge has been enhanced without changing |TCπ44|, thereby enabling the sensor to effectively eliminate its TCS while preserving a high level of sensitivity.

Fabrication and Characterization
The precise manufacturing procedure is depicted in Figure 3(a), along with important phases including etching, anodic bonding, and deposition.Figure 4(a) indicate that the output was significantly influenced by temperature.The traditional compensation approach reduced the sensor's TCS from 0.17% FS/°C to 0.09% FS/°C by connecting a resistor R0 in series with the piezoresistors network, but at the price of the sensor's output, which was reduced from 58 mV to 32 mV @20°C.As a comparison, by adding a thermistor in parallel with the Wheatstone bridge, the sensor could achieve a significantly reduced TCS compared to the conventional compensation method (from 0.09% FS/℃ to 0.01% FS/℃), while maintaining equivalent sensitivity.

Conclusion
This article introduced a method for compensating thermal sensitivity drift in piezoresistive pressure sensors by passive resistor/thermistor networks.The approach described in this paper linked a thermal resistor with a large positive TCR in parallel with the piezoresistors network, in contrast to the traditional compensating method.This modification serves to decrease the ratio between TCπ44 and TCRB of Wheatstone bridge, which enabling the sensor to effectively eliminate its TCS while preserving a high level of sensitivity.The experimental findings show that the suggested compensatory strategy may considerably lower the TCS to 6% at the price of a 45% decrease in sensitivity, which is a considerable improvement over the traditional compensation method.

2. 1 Figure 1 .
Figure 1.(a) Schematic of the developed sensor chip, and the corresponding (b) cross-sectional view and (c) assembly of the sensor.

Figure 2 .
Figure 2. (a) The relationship between doping concentration and TCR and TCπ of p-type silicon; (b) Conventional compensation method; (c) Proposed resistor/thermistor compensation network.The ideal resistance of the series resistor R0 may be found by using Equation5and putting Equation 4 into Equation2with TCS set to 0. Next, by putting Equation 3 into Equation5, the loss of sensitivity under the optimal series resistor can be obtained, as depicted in Equation6.

Figure 3 (
b) shows the manufactured sensor chip and the accompanying assembled structure.

Figure 3 .
Figure 3. (a) Precise manufacturing procedure of the developed sensor chip; (b) The images of fabricated sensor chips and assembling.

Figure 4 .
Figure 4. (a) Original output of the sensor without compensation; (b) The temperature drift of the full scale output under different compensations.