An anti-charge-interference three-dimensional electric field sensor

A major concern in the development of three-dimensional (3D) microelectromechanical system electric field sensors (EFSs) is space charge interference. With space charges in the surrounding environment, charges may accumulate at the surface of the EFS, which affects the accuracy of the electric field measurement. There is a lack of relevant mechanism research and solutions for this problem. Here, an anti-charge-interference 3D EFS is presented, which consists of three electric field sensing elements and a reference element. By establishing the model of the sensing element, the relationship of the electric field at the sensing chip with the distance between the sealing cap and the sensing chip is explored. The theoretical basis of the measurement method of the 3D electric field based on a coplanar structure is introduced. Then, the influence of charge accumulation is overcome by a differential calculation between the output signals of the reference element and sensing elements. The anti-charge-interference 3D EFS prototype is developed. Experimental results show that the measurement error of the anti-charge-interference 3D EFS is 4.01% and the linearity is better than 1% under an electric field of 0–50 kV m−1.


Introduction
The measurement of three-dimensional (3D) electric fields is essential in many sectors, including meteorology, electric power, industrial production, and scientific research.In meteorology, the detection of electric fields in thunderstorm clouds allows for the study of their charge distribution and lightning warnings [1][2][3].The electric fields in thunderstorm clouds have a 3D dynamic nonuniform distribution [4].Therefore, the use of 3D electric field sensors (EFSs) is * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.necessary.In the electric power sector, the amplitude and direction of electric field near power equipment and transmission lines can be monitored by 3D EFSs to determine the operational status of them and realize the emergencies, such as operational faults, insulation defects, and line icing, warning and location more accurately [5][6][7][8].In industrial production, the monitoring of the production environment using 3D EFSs can warn against and locate static electricity [9,10], thus preventing production accidents.In scientific research, 3D EFSs can measure the electric field of the ionosphere and provide vital information on global electric field distribution, benefiting geophysical analysis [11].
Because MEMS sensing chips are susceptible to environmental influences, they must be packaged accordingly.In the process of 3D electric field measurement in many fields, charged particles may be present in the measurement area.For instance, the ionosphere and thunderstorm clouds contain a significant number of charged particles [23,24], highvoltage DC (HVDC) transmission lines generate ion flow fields [25], and electrostatic charges exist in industrial production environments [26].In such scenarios, charges may accumulate on the surface of the MEMS EFSs' package, leading to interference with the electric field measurement.To solve this problem, a combined difference method was proposed [27], but no experimental verification was conducted.A novel MEMS sensor for measuring spatial DC electric fields in an ion flow field was developed [28,29].However, it is limited to one-dimensional electric field measurement under HVDC transmission lines.
In this paper, a theoretical model for packaging MEMS EFSs is introduced, and the impact of surface charge accumulation on electric field measurements is investigated.Through principle analysis and simulation, an anti-charge-interference 3D EFS is designed.Additionally, the influence of different structural parameters on the anti-interference performance and sensitivity is studied using finite-element simulation.A prototype of the sensor is developed, incorporating four MEMS electric field sensing chips.The sensor is tested and verified under condition of charge interference to assess its effectiveness.

Effect of charges at the sealing cap on the electric field at the sensing chip
The MEMS electric field sensing chips used in this paper are horizontal resonant electric field sensing chips with coplanar electrodes and electrostatic excitation [30].The feature size of electrodes in the MEMS electric field sensing chip is typically at micron scale.These electrodes are susceptible to various environmental factors, including ambient temperature, humidity, air pressure, and dust particles.As a result, it is necessary to package the sensing chip for survival during practical applications.Such a packaged chip is referred to as the sensing element.Figure 1 illustrates the structure diagram of the sensing element, which comprises a metal substrate, an insulating sidewall, and a metal sealing cap.The sensing chip is positioned on the substrate while maintaining a certain distance from the sealing cap.The sealing cap diameter is larger than the outer diameter of the sidewall, which prevents the ion flow from reaching the sidewall during subsequent experimental verification.In the presence of space charges in the surrounding environment, charges may accumulate at the surface of the sealing cap, leading to an additional interfering electric field.As the accumulation charges increase, so does the interfering electric field, resulting in a higher measurement error.Figure 2(a) shows the charge distribution at the sealing cap under the external electric field (E).Equal amounts of positive and negative charges are distributed at the upper and lower surfaces of the sealing cap. Figure 2(b) depicts the charge accumulation at the sealing cap.When positively charged particles accumulate at the upper surface of the sealing cap, the electrons within the sealing cap are attracted to move upward, leaving behind positively charged atoms at the lower surface.Consequently, the electric field intensity inside the sealing cap is zero.Figure 2(c) represents the superposition of the charges from (a) and (b) at the sealing cap.When charges accumulate at the sealing cap surface, the electric field at the sensing chip (E sum ) is composed of the electric field caused by E and the interfering electric field generated by the accumulated charges.Assuming that the electric field caused by E is E 0 and the interfering electric field is E 1 , formula (1) can be obtained according to the principle of electric field superposition:

The electric field at the sensing chip caused by E
In figure 2(a), under the influence of E, negative charges and positive charges are generated at the upper and lower surfaces of the sealing cap respectively.The electric field generated by the charges at the contact point of the sealing cap and the sidewall is not considered.As shown in figure 3, the sealing cap is a metal disk with radius a and thickness h, the distance between the sealing cap and the sensing chip is d, the width of the sidewall is w, and the positive and negative charge density induced at the surface of the sealing cap is σ 0 .As shown in figure 4, E 0 consists of three components: where E + and E − are the electric fields generated by the positive and negative charges, respectively, at the surface of the sealing cap.Because the induction area of the sensing chip is small, the electric field intensity at the center of the sensing chip is equivalent to the electric field intensity at the sensing chip.Taking an annulus with radius r and width dr at the sealing cap, the quantity of positive and negative charges at the annulus is dq 0 = σ 0 2π rdr.Because the annulus is symmetric about the center of the sealing cap, the component, which is parallel to the sealing cap, of the electric field intensity generated at  the sensing chip by charges at various points throughout the annulus is zero.Thus, the directions of the differential electric field intensities dE + and dE − generated by the positive and negative charges at the entire annulus are perpendicular to the sealing cap, and the magnitude can be expressed by formulas (3) and (4): where ε 0 (≈ 8.854 × 10 −12 F m −1 ) is the vacuum dielectric constant.By integrating dE + and dE − , the magnitudes of E + and E − can be expressed by formulas ( 5) and ( 6): Because the sealing cap and sidewall are very thin, h and w can be neglected when d ≫ h, a ≫ w.Under this condition, E + ≈ −E − , thus E 0 ≈ E. Therefore, the electric field at the sensing chip is approximately equal to E. Accordingly, E 0 does not change with d.

The interfering electric field at the sensing chip
In figure 2(b), the sealing cap is considered a thin metal disk.As shown in figure 3, the radius of the sealing cap is a, the distance between the sealing cap and the sensing chip is d, the charge at the upper and lower surfaces of the sealing cap is q 1 , and the charge density of the sealing cap is σ 1 .σ 1 can be expressed by formula (7) [31]: Shown in figure 5 is an annulus with radius r and width dr at the sealing cap.Because the annulus contains two sides, the amounts of charge on this annulus are dq 1 = 2σ 1 2π rdr.The direction of the differential electric field intensity dE 1 generated by charges at the entire annulus is perpendicular to the sealing cap, and the magnitude can be expressed by formula (8): where ε 0 (≈ 8.854 × 10 −12 F m −1 ) is the vacuum dielectric constant.By integrating, it can be obtained that E 1 is: = According to formula ( 9), E 1 is related to the cap radius a and the distance between the sealing cap and the sensing chip d.Assuming that q 1 is 10 −10 C and a is 15 mm, the values of E 1 can be obtained by formula (9).As shown in figure 6, an increase in d results in a decrease in E 1 .

Theoretical basis
In figure 7, the design of the anti-charge-inference 3D EFS is depicted.It comprises a metal grounded substrate and shell, three sensing elements (A, B, C), and a reference element (F).In the current simulations and experiments, the shell is without the bottom plate.The bottom plate can prevent the interference of the external electric field on the internal circuit, which will be considered in future research.The EFS is based on the coplanar structure, which means that these elements are distributed noncollinearly on the same substrate.The reference element has a different height from the sensing elements.Each element is a packaged one-dimensional MEMS electric field sensing chip.The coordinate system is established with the center of the substrate's bottom surface as the origin.The Zaxis is perpendicular to the substrate, the X-axis is parallel to the central line of sensing elements B and C, and the Y-axis is parallel to the central line of sensing elements A and B.
Figure 8(a) shows that when the external electric field is parallel to the Z direction, all four elements exhibit the same sensitivity to the electric field intensity.Moreover, figure 8(b) illustrates the distortion of the electric field near the substrate when the direction of the external electric field is in the positive X direction (assuming the rightward direction as positive).Due to the perpendicular nature of the electric field on the surface of the conductor, the electric field on the left side of the substrate points vertically downward, whereas on the right side, it points vertically upward.Consequently, sensing elements A and B exhibit a positive sensitivity to the electric field in the X direction (taking the downward direction as positive), while sensing element C and reference element F exhibit a negative sensitivity to the electric field in the X direction.Regarding the electric field in the Y direction, sensing element A and reference element F exhibit a positive sensitivity, whereas sensing elements B and C exhibit a negative sensitivity.Since elements have different sensitivity to X, Y, and Z direction, which can be used to demodulate the electric field in the X, Y, and Z direction.

Measurement method
Due to the minimal volume of the sensor relative to the entire testing area, it is assumed that the charge particle density or ion flow density is the same near the elements.An equal quantity of charges is assumed to accumulate at the sealing cap of the four elements.Assuming the charge to be positive, the electric field intensity at the sensing chip caused by the external field E and the interfering electric field generated by accumulated charges are E 0 and E 1 , respectively.Then the sensitivity formula of the four elements is: where V A , V B , V C , and V F are the outputs of these four elements, V 0A , V 0B , V 0C , and V 0F are the zero outputs of these four elements which are constants and can be obtained by calibration, k A , k B , k C , and k F are the sensitivities of these four elements.E 0A , E 0B , E 0C , and E 0F are the magnitudes of the electric field intensity caused by E, which are related to the positions of the elements on the substrate.E 1A , E 1B , E 1C , and E 1F are the magnitudes of the interfering electric field intensity generated by accumulated charges, which are related to the distance between sealing chip and sensing cap.Let the ratios of E 1F and E 1A , E 1B , and E 1C be respectively: By difference calculation and simplification, formula (12) can be obtained.
Formula (12) shows that the interfering electric fields E 1A , E 1B , E 1C , and E 1F are eliminated.E 0A , E 0B , E 0C , and E 0F can be expressed in the Cartesian coordinate system as: (13) where k xi , k yi , and k zi are the coupling sensitivity coefficients of element i (i = A, B, C, F) to the electric field in the orthogonal directions of X, Y and Z respectively.According to formulas ( 12) and ( 13), formula ( 14) can be obtained: where, S 0 and A 0 are the coupling sensitivity matrix and the total coupling sensitivity matrix of the sensor to the electric field, respectively.Therefore, the measurement algorithm of an arbitrary space electric field is:

Simulation verification
According to figure 7, the simulation model of the anti-chargeinterference 3D EFS is constructed.As shown in the figure 7, A, B, C, and F are four elements distributed at the surface of the grounded substrate.The side length of the substrate is 10 cm; the radius of the sealing cap of the elements is 15 mm.The distance between the sealing cap of reference element F and the sensing chip is fixed at 6 mm, and the distance between the sealing cap of sensing elements and the sensing chip is fixed at 15 mm.Through simulation and calculation, λ A , λ B , λ C , and the coupling sensitivity matrix S 0 can be obtained: ( To study the feasibility of the measurement method under electric fields in different directions, the following simulation is carried out.The charge quantity at the sealing caps is assumed to be 7 × 10 −11 C, and an electric field of 10 kV m −1 is applied in the air domain.The air domain rotates along the X direction.The electric field intensity values ( E A , E B , E C , E F ) at the sensing chips are recorded, which are utilized in formula (17) to obtain the simulation values of the field intensity.The simulation values of the electric fields in different directions are shown in figure 9.As shown in figure 9, this measurement method can accurately simulate and calculate To study the feasibility of the method under different magnitudes of electric fields, the following simulation is conducted.The sensor is positioned in a particular position by rotating the air domain 45 • along (1,1,1).Assuming that the quantity of charges at the sealing caps is 7 × 10 −11 C, different magnitudes of electric fields are applied in the air domain.The electric field intensity values (E A , E B , E C , E F ) at the sensing chips are recorded and utilized in formula (17) to obtain the simulation values of the field intensity.Simulation values of different magnitudes of electric fields are shown in figure 10.As shown in figure 10, this method can simulate and calculate the values of different magnitudes of electric fields.The maximum deviation is 55 V m −1 at 1000 V m −1 , accounting for 5.5% of the applied field.
To study the influence of different quantities of accumulated charges on the method, the following simulation is carried out.The air domain is rotated 45 • around (1,1,1) to locate the sensor in a particular position, and an electric field of 10 kV m −1 is applied in the air domain.Assuming quantities of charges at sealing caps are 7 × 10 −12 -7 × 10 −11 C, the electric field intensity values (E A , E B , E C , E F ) at sensing chips, which are recorded every 7 × 10 −12 C, are utilized in formula (17) to obtain the simulation values of the field intensity.As shown in figure 11, this method can simulate and calculate the values of electric field intensity under different charge accumulations.The maximum deviation is 97 V m −1 accounting for 0.97% of the applied electric field.

Parameter optimization of elements
Element parameter optimization is conducted to minimize the deviation in electric field intensity at the sensing chip caused by the external electric field between sensing elements and the reference element and maximize the difference in electric field intensity generated by accumulated charges.The optimized parameters include sealing cap radius (a), sealing cap thickness (h), sidewall thickness (w), and distance between the sealing cap and the sensing chip (d).The simulation model is shown in figure 1. Applying an electric field of 10 kV m −1 in the air domain.

Sealing cap radius.
The relationship between the electric field intensity at the sensing chip and the variable d is determined under different values of a through simulation.Figure 12 shows that the electric field intensity remains relatively stable when the value of a is within the range of 15-20 mm.
Assuming a charge quantity of 10 −10 C at the sealing cap, the relationship between the electric field intensity and the variable d is determined under different values of a through simulation.Figure 13 shows that a smaller value of a corresponds to a more pronounced change in electric field intensity as d varies.To account for the dimension of the sensing chip, a is set to 15 mm.

Sealing cap thickness.
The relationship between the electric field intensity and the variable d is determined under different values of h through simulation.Figure 14 shows that the electric field intensity experiences minimal variation when h ranges from 0.5 mm to 0.9 mm.In this paper, h is set to 0.7 mm.

Sidewall thickness.
The relationship between the electric field intensity and the variable d is determined under different values of w through simulation.Figure 15 shows that the electric field intensity experiences minimal variation when w ranges from 0.9 mm to 1.1 mm.In this paper, w is set to 1 mm.

The distance between the sealing cap and the sensing chip.
The relationship between the electric field intensity caused by the external electric field and the variable d is determined through simulation.As shown in figure 16, the electric field intensity at the sensing cap caused by the external electric field remains relatively stable as d increases when the value of d is within the range of 6-20 mm.
Assuming a charge amount of 10 −10 C at the sealing cap, the relationship between the electric field intensity generated by accumulated charges and the variable d is determined through simulation.As shown in figure 16, the electric field generated by the charges exhibits rapid changes when the value of d is within the range of 3-15 mm.Therefore, d of the sensing elements is set to 15 mm, while d of the reference element is set to 6 mm.

Sensor parameter optimization 4.2.1. The distance between elements.
The simulation model is shown in figure 7. By applying an electric field of 5 kV m −1 in the Y direction, the ratio of the electric field intensity at the sensing chip to the applied electric field intensity is obtained, that is, the coupling sensitivity.The relationship between coupling sensitivity and distance between elements is obtained through simulation.Figure 17 shows that an increase in the distance of elements results in an amplified coupling sensitivity.To account for the overall size of the sensor, the distance between elements is set to 60 mm.

The shape of the substrate.
By adjusting substrate shape in figure 7 to a cylinder and applying an electric field of 5 kV m −1 in the Y direction, the relationship between the coupling sensitivity and the distance of elements is determined through simulation.Figure 17 shows that the coupling sensitivity is greater when the substrate is cuboid, as opposed to a cylindrical one.Consequently, this paper opts for a cuboid substrate.
Based on the aforementioned analysis, the key parameters of the anti-charge-interference 3D EFS are shown in table 1.

Prototype and test system
A photo of the anti-charge-interference 3D EFS prototype is shown in figure 18, which comprises three sensing elements, a reference element, a substrate, a metal shell and signal amplification circuits.Sensing elements and reference element are positioned on the upper surface of the substrate.The rotation of the sidewall allows for the adjustment of the distance between the sealing cap and the sensing chip.Polytetrafluoroethylene, which has poor hygroscopicity, is selected as the sidewall.Each element corresponds to a signal amplification circuit, whose function is to carry out I/V conversion and differential amplification of the output signals to eliminate the commonmode noise interference.
Figure 19 shows the anti-charge-interference 3D EFS calibration and test system.The system primarily consists of two main parts: the ion flow generation and control section, and the test area.The ion flow generation and control section is composed of a metal bottom plate, parallelly arranged corona wires, an ion flow control sheet, and a lower plate of parallel metal plates.By applying voltage to the corona wires, space charges are generated, leading to the formation of an ion flow driven by high voltage.By employing different voltage settings on the ion flow control sheet and the lower plate, the ion  flow entering the test area can be regulated and made uniform.The test area consists of a bracket, upper and lower plates of parallel plates, and a ground plate.The sensor is fixed at the center of the ground plate by the bracket.Adjusting the voltage between the two plates enables the generation of a uniform electric field, while electric fields in different directions can be simulated by rotating the bracket.

Calibration
First, the sensitivities of the four sensing chips are obtained through calibration, and the resulting calibration curves are shown in figure 20.Then, the coupling sensitivities of the 3D EFS to the X, Y, and Z directions are calibrated.By rotating the sensor, the uniform electric field is aligned parallel to the Z, X, and Y directions.Electric fields of 0-50 kV m −1 are applied by changing the voltages of the upper and lower plates in each direction.The sensitivity coefficients of each element in three directions are determined through linear fitting, and the calibration curves are shown in figure 21.Finally, by applying voltages on each part of the test system: 17.2 kV for corona wires, 4 kV for the ion flow control sheet, 3 kV for the lower plate, and −3 kV for the upper plate, the ion flow field and electric field exist simultaneously in the test area.The ion flow field accumulates charges at sealing caps to simulate charge interference.As ions accumulate at the sealing cap, a reverse electric field is generated to hinder further accumulation of ions [29].The output values of the four elements are recorded when charges reach saturation, that is, when the outputs stabilize.The λ can be determined by employing formula (11).According to the aforementioned calibration results, the total coupling sensitivity matrix is:

Experimental verification
A anti-charge-interference 3D EFS arbitrary angle rotation experiment is carried out in the test system.The electric field measured by the EFS is compared with the actual applied electric field to verify the feasibility of the method and ascertain the accuracy of the calibrated total coupling sensitivity matrix.
An ion flow field is applied in the test area to accumulate the charges at the sealing caps until outputs of elements stabilize.By rotating the sensor, the uniform electric field is aligned parallel to the Z, X, and Y directions.Electric fields of 0-50 kV m −1 are applied by changing the voltages of the upper and lower plates in each direction.The output values of the four elements are recorded.Subsequently, the sensor is rotated to several different angles and electric fields of 0-50 kV m −1 are applied.The output values are recorded.By employing formula (15), the electric field intensity values are calculated and then compared with the corresponding values of the applied electric field intensity.
As shown in table 2, the measured electric field intensity values and the applied electric field intensity values maintain   represents the angle between the external electric field E and the positive direction of the Z-axis, while φ represents the angle between the projection of E on the X-Y plane and the positive direction of the X-axis.Any direction of an electric field can be represented using β and φ.The relationship between the components (E x , E y , E z ) of E in three directions and β and φ is given by formula ( 19):   As shown in table 3, by substituting the output values of the four elements into equation (15), the components of E can be calculated.The direction of E can be determined using equation (19).Furthermore, figure 23 displays the fitted curves representing the measured electric field intensity values obtained at various angles.It is worth noting that the linearity of the EFS is better than 1%.
To study the influence of different quantities of accumulated charges on the method, the following experiment is carried out.By applying varying voltages on each part of the test system, different electric fields and ion flow fields are applied in the test area to accumulate the different quantities of charges at the sealing caps until outputs of elements stabilize.Subsequently, the sensor is rotated to several angles.The output values are recorded.As shown in table 4, the measured electric field intensity values and the applied electric field intensity values maintain good consistency when different quantities of charges accumulate at the sealing cap.The maximum error is 3.76%.

Conclusion
A novel anti-charge-interference 3D EFS is designed and successfully fabricated.The sensor effectively reduces the interference of space charges on electric field detection and increases the accuracy of electric field intensity measurement.A model is established for the sealing cap surface charge and the internal electric field distribution of the sensing element under the influence of the external electric field and charge accumulation.The theoretical basis of the measurement method of the 3D electric field based on coplanar structure is introduced.The influence of charge accumulation is innovatively eliminated by the differential calculation between the output signals of the reference element and sensing elements.The experimental results show a maximum error of 4.01% and linearity better than 1% across the applied electric field range of 0-50 kV m −1 .

Figure 1 .
Figure 1.Structure diagram of the sensing element.

Figure 2 .
Figure 2. (a) Charge distribution at the sealing cap surface under the external electric field; (b) charge distribution at the sealing cap surface under the influence of accumulated charges; (c) charge distribution at the sealing cap surface under the influence of the external electric field and accumulated charges.

Figure 3 .
Figure 3. Parameter assumptions of the sensing element.

Figure 4 .
Figure 4.The components of electric field intensity generated by the external electric field.

Figure 5 .
Figure 5.The differential electric field generated by accumulated charges.

Figure 6 .
Figure 6.The relationship between the interfering electric field (E 1 ) and the distance between the sealing cap and the sensing chip (d).

Figure 7 .
Figure 7.The design of the anti-charge-interference 3D EFS.

Figure 8 .
Figure 8.(a) Distribution of the electric field generated by the external electric field in the Z direction; (b) distribution of the electric field generated by the external electric field in the X direction.

Figure 9 .
Figure 9.The simulation values of electric fields in different directions.

Figure 10 .
Figure 10.The simulation values for different magnitudes of electric fields.

Figure 11 .
Figure 11.The simulation values of electric field intensity under different quantities of charges at the sealing cap.

Figure 12 .
Figure 12.The electric field intensity caused by the external electric field versus the distance between the sealing cap and the sensing chip (d) under different sealing cap radius (a).

Figure 13 .
Figure 13.The electric field intensity generated by charges at the sealing cap versus the distance between the sealing cap and the sensing chip (d) under different sealing cap radius (a).

Figure 14 .
Figure 14.The electric field intensity caused by the external electric field versus the distance between the sealing cap and the sensing chip (d) under different sealing cap thickness (h).

Figure 15 .
Figure 15.The electric field intensity caused by the external electric field versus the distance between the sealing cap and the sensing chip (d) under different sidewall thickness (w).

Figure 16 .
Figure 16.The electric field intensity generated by the external electric field and charges at the sealing cap versus the distance between the sealing cap and the sensing chip (d).

Figure 17 .
Figure 17.The coupling sensitivity versus the distance of elements under different substrate shapes.

Table 1 .
Key Parameters of the Anti-Charge-Interference 3D EFS. the sealing cap and the sensing chip of sensing element (d A ,d B ,d C ) 15 The distance between the sealing cap and the sensing chip of reference element (d F ) 6

Figure 19 .
Figure 19.The anti-charge-interference 3D EFS calibration and test system.

Figure 20 .
Figure 20.Calibration curves of four sensing chips.

Figure 21 .
Figure 21.Calibration curves of four elements in three directions: (a) Z direction; (b) X direction; (c) Y direction.

Figure 22 .
Figure 22.The method of representing electric field direction.

Figure 23 .
Figure 23.Fitted curves of electric field intensity values measured at different angles.

Table 2 .
Outputs of sensors and measured electric field intensity values.

Table 3 .
The components and direction of measured electric field intensity.

Table 4 .
The experiment results under different quantities of charges at the sealing cap.