Single-chip 3D electric ﬁ eld microsensor

This paper presents a single-chip 3D electric ﬁ eld microsensor, in which a sensing element is set at the center to detect the Z -axis component of an electrostatic ﬁ eld. Two pairs of sensing elements with the same structure are arranged in a cross-like con ﬁ guration to measure the X - and Y -axis electrostatic ﬁ eld components. An in-plane rotary mechanism is used in the microsensor to detect the X -, Y -, and Z -axis electrostatic ﬁ eld components simultaneously. The proposed microsensor is compact and presents high integration. The microsensor is fabricated through a MetalMUMPS process. Experimental results show that in the range of 0 – 50 kV/m, the linearity errors of the microsensor are within 5.5 % , and the total measurement errors of the three electrostatic ﬁ eld components are less than 14.04 % .


Introduction
Electrostatic field measurement is crucial in many industrial and scientific areas, such as high voltage direct current (HVDC) power system monitoring [1], lightning hazard warning [2,3], and space plasma studies [4,5]. Consequently, sensors that can accurately detect and quantify electrostatic fields in natural and artificial environments are in demand. Various sensors that can measure electrostatic fields have been developed, and most of them can be classified into four categories, namely, double probes [6], field mills [1,7], optical sensors [8][9][10], and micromachined electric field sensors (MEFSs) [11][12][13][14][15][16][17][18][19][20]. Double probes and field mills are fabricated through traditional machining methods; as a result, they possess large volumes and complex structures and entail high power costs. Optical sensors are based on electrooptic effect or fiber and demonstrate excellent sensitivity; however, they suffer from complicated measurement systems [21], phase bias, and temperature stability problems [22]. Currently, Various MEFSs have been proposed due to the rapid development of micromachining technology. MEFSs possess intrinsic advantages of low power cost, compact size, and batch producibility. MEFSs are based on the principle of charge induction. An alternating charge is induced by periodically changing the electrostatic field on the surface of the sensing electrodes, and the alternating current (AC) with respect to the strength of the electrostatic field around the sensors can be measured.
Most reported MEFSs are single-axis ones, so they cannot measure all three Cartesian components of an electrostatic field. The atmospheric electric field near the surface of the Earth is perpendicular to the ground. However, unlike this electric field, the electrostatic field in several cases (e.g., under HVDC transmission lines [1] and in the ionosphere [4,5]) has an unknown direction before measurement. Therefore, measuring 3D electrostatic fields is indispensable. Wang et al. [20] introduced a biaxial MEFS that can sense an in-plane electrostatic field but has no axis to sense the vertical component; the author asserted that monolithic 2D or 3D MEFSs require high structural integrity and an accurate decoupling calibration method. By deriving a coupling sensitivity matrix, Wen et al. [23] and Fang et al. [24] distributed three 1D MEFSs in-plane and orthogonally to measure a 3D electrostatic field. In their studies, the elimination of coupling interference among the three components of the electrostatic field simply relied on an algorithm instead of the structural design. Although their proposed devices are larger than single-chip MEFSs, their methods can be easily implemented and are minimally restrictive.
To address the need for 3D electrostatic field measurement, this study proposes a single-chip 3D electric field microsensor, in which three orthogonal sensing axes are placed in one chip. An in-plane rotary mechanism is adopted in the microsensor to detect X-, Y-, and Z-axis electrostatic field components simultaneously. The 3D electric field microsensor is compact and presents high integration.
The structure of this paper is as follows. Section 1 provides a brief introduction to the need for 3D MEFS and presents related studies. Section 2 describes the proposed single-chip 3D electric field microsensor. Section 3 discusses the capability of the proposed microsensor to measure 3D electrostatic fields and the optimization of electrodes through finite element analysis (FEA). Section 4 presents the fabrication process. Experiments are conducted in Section 5 to characterize the 3D electric field microsensor.

Working principle and structure
Electrostatically actuated MEFSs can be classified into two categories according to the placement of the sensing and shielding electrodes. The first is vertical MEFS, in which sensing electrodes are patterned over an insulating layer on the substrate beneath the grounded shutter-like shielding electrodes. The second category is lateral MEFS, in which grounded shielding and sensing electrodes are fabricated on the same plane. Compared with lateral MEFS, vertical MEFS has a smaller conversion gain because of its fringe fields at the sidewalls. Therefore, a lateral MEFS-based design was used in this study.
A schematic of the proposed 3D electric field microsensor is shown in Fig. 1. The structures of the device can be classified as fixed or movable. The fixed structures include all strip-type sensing and fixed driving electrodes. The movable structures make up the in-plane rotating structure, which is composed of all strip-type shielding electrodes, movable driving electrodes, and four serpentine springs. The strip-type sensing and strip-type shielding electrodes constitute the sensing elements. The fixed and movable driving electrodes use angular driving comb fingers and work together as push-pull comb drives.
Three orthogonal sensing axes are placed in one chip. The Z sensing element is set at the center to detect the Zaxis component of the electrostatic field. Two pairs of sensing elements [(X +, X -) and (Y +, Y -)] with the same structure are arranged in a cross-like pattern around the Z sensing element. In the radial direction, the Z sensing element is connected to four symmetrical serpentine springs, whose other ends are fixed to the anchors. These four serpentine springs are used to support the in-plane rotating structure and to achieve large rotation, as demonstrated in previous studies [25]. The push-pull comb drives are located between two adjacent springs. When the in-plane rotation is excited by the push-pull comb drives, the strip-type shielding electrodes oscillate back and forth and cover the sidewalls of the strip-type sensing electrodes.
Electrodes are equipotential on the condition of electrostatic equilibrium, which leads to the distortion of the nearby electric field. Regardless of whether the external electric field is along the radial direction or perpendicular to the plane, an electric field can be generated on the surfaces of the sensing electrodes and is always normal to the surfaces, including the sidewalls, in an inward or outward direction. Therefore, the strength of the electric field on the sidewall changes, and alternating current is produced by periodically covering the sidewalls of the sensing electrodes. The output alternating current, i s , is defined as where ε 0 is the permittivity of free space, E n is the component of the electric field normal to the sensing electrodes, and A is the effective area of the sensing electrodes. The measurements of the Xand Y-axis electrostatic field components are based on the strength of the distorted electric field in the X +, X -, Y +, and Y - Fig. 1 Schematic of the 3D electric field microsensor sensing elements. The differential output of the X + and Xsensing elements is used to represent the X-axis component of the electrostatic field, and the differential output of the Y + and Ysensing elements is used to represent the Y-axis component.

Modeling of the 3D electric field microsensor
A modeling analysis was conducted to investigate the capability of the proposed microsensor in 3D electrostatic field measurement. The microsensor structure is complex; thus, a simplified microsensor model, in which all the electrodes are omitted, was initially adopted in a simulation to study the microsensor response to a 3D electrostatic field. The parameters of the electrodes were subsequently optimized to increase the output of the microsensor. Finally, the resonant frequency of the in-plane rotation mode was obtained through a simulation.
3.1 Modeling of 3D electrostatic field measurement Figure 2 illustrates the simulation model for the response of the proposed microsensor to a 3D electrostatic field with different directions. Five sensing elements were simplified based on theirs outlines, and all the electrodes were disregarded. The Z sensing element was simplified into an annular plate located at the center, and the X +, X -, Y +, and Ysensing elements were all annular sector plates forming a cross-like configuration around the Z sensing element. All five simplified sensing elements were coaxially placed. In addition, the push-pull comb drives and serpentine springs were disregarded. An electrostatic field with a strength of E 0 was applied. The angle between the electrostatic field and the Z-axis was q. The angle between the projection of the electrostatic field on the X-Y plane and X-axis was φ. Therefore, where E x , E y , and E z are the X-, Y-, and Z-axis components of the electrostatic field, respectively. Q x + , Q x -, Q y + , Q y -, and Q z are the induced charges on the upper surfaces of the five sensing elements.
where Q x is the differential output of the X-axis sensing component and Q y is the differential output of the Y-axis sensing component. The characteristics of Q x , Q y , and Q z with respect to q and φ should be similar to those of E x , E y , and E z , respectively, to measure the 3D electrostatic field accurately.
A simulation analysis was conducted with the FEA method. The boundary conditions for the simulation strictly follow calibration. Firstly, a sufficiently large rectangular free space was created. In this free space, the simplified microsensor was placed at the center. Two opposite sides were selected, and opposite voltages were applied to generate a uniform electrostatic field. An electrostatic field from different directions was generated by rotating the rectangular free space. Second, the five simplified elements were all grounded in the simulation because the potentials of all the sensing and shielding electrodes were set to zero in the testing circuit. E 0 was set to 10 V/m. Q x , Q y , and Q z were calculated when the direction of the applied electrostatic field changed circumferentially. As shown in Fig. 3(a), when q was fixed, the curves of Q x and Q y showed good sinusoidal characteristics with a 90°phase difference, whereas Q z did not change. The curves were in accordance with E x , E y , and E z . As shown in Fig. 3(b), when φ was fixed, Q x , Q y , and Q z versus q were quarter-sine curves, which agreed well with E x , E y , and E z , respectively. The simulation results demonstrated that the characteristics of Q x , Q y , and Q z with respect to q and φ were similar to those of E x , E y , and E z , respectively. Therefore, the proposed 3D electric field microsensor can measure 3D electrostatic fields accurately.
However, the magnitude of Q z is much lower than that of Q x and Q y because of the differences in the sensing areas and numbers of sensing elements; thus, Q x , Q y , and Q z cannot represent the applied electrostatic field directly without introducing sensitivity factors. Furthermore, in 3D electrostatic field measurement, coupling interference among the three components of the electrostatic field is unavoidable. Therefore, a sensitivity matrix was employed to compensate for these differences and for decoupling. The sensitivity matrix is discussed in detail in Section 5.2.

Electrode analysis
Strip-type electrodes were used in the proposed 3D electric field microsensor. All the electrodes were designed into Fig. 2 Simulation model for the response of the proposed microsensor to a 3D electrostatic field with different directions annular sector strips with large lengths and small dihedral angles on their two sidewalls. All electrodes were coaxially placed, given that the microsensor is based on in-plane rotation. For each sensing element, a pair of a sensing electrode and a shielding electrode with the same length (L), height (h), and inner radius (R) was periodically arranged, as shown in Fig. 4. w sn and w sh are the inner arc lengths of the sensing and shielding electrodes, respectively. The inner arc length between sensing electrode 1 and shielding electrode 1 is w g1 , and the inner arc length between sensing electrode 1 and shielding electrode 2 is w g2 . The sum of w g1 and w g2 is w T , which remains unchanged whenever w g1 and w g2 vary due to the rotation of the shielding electrodes. Furthermore, the inner arc length between sensing electrode 1 and shielding electrode 1 is w e when both are in the equilibrium position. These parameters determine the amount of induced charge. Therefore, an analysis should be conducted to optimize these parameters and improve the output of the proposed microsensor.
A MetalMUMPS process was implemented to fabricate the 3D electric field microsensor. This process is discussed in detail in Section 4. In accordance with the Metal-MUMPS design rules, h was set to be 20 mm, and the minimum feature size of the metal layer was 8 mm. A 3D simulation was conducted to determine the remaining parameters by the FEA method. The electrode parameters were divided into two: One for the X +, X -, Y +, and Ysensing elements and another for the Z sensing element. These two groups of parameters should be optimized separately.
For the X +, X -, Y +, and Ysensing elements, L and R were preset to 1000 and 2500 mm, respectively. The presumed vibration amplitude in the inner arc was set to 10 mm. The values of w sn , w sh , w T , and w e should be determined through a simulation. Therefore, the induced charges on sensing electrode Q versus w g1 were simulated with different inner arc lengths of sensing electrode w sn . The results are shown in Fig. 5(a). A small w g1 resulted in a small amount of induced charge on the sensing electrode ig. 4 Schematic of strip-type electrodes but a high change rate of induced charge. Therefore, if the amplitude of the vibration is fixed, then a small w e indicates a large peak-to-peak value of induced charge DQ. However, due to the impact of the squeeze-film damping factor between the sensing and shielding electrodes, both electrodes cannot be placed too close to each other when they are in the equilibrium position. In our design, for X +, X -, Y +, and Ysensing elements, w e was set to 30 mm. A uniform external electric field with a strength of 1 kV/m was vertically applied to the electrodes. Moreover, the potentials of the sensing and shielding electrodes were set to zero.
To obtain an optimal w sn , a simulation was conducted on the peak-to-peak values of induced charge DQ in the sensing electrode in vibration versus w sn with different inner arc lengths of shielding electrode w sh . As shown in Fig. 5(b), DQ increased with respect to w sn with a low gradient. DQ increased by approximately 2% as w sn increased from 8 to 16 with different w sh values. This outcome suggests that w sn exerts minimal influence on DQ. Moreover, a long w sn may reduce the number of sensing units for each sensing element and consequently reduce the output of the proposed microsensor. Therefore, w sn was set to 10 mm for the X +, X -, Y +, and Ysensing elements.
To determine w sh , a simulation was conducted on the peak-to-peak values of induced charge DQ in the sensing electrode in vibration versus w sh . According to the results shown in Fig. 5(c), DQ increased with increasing w sh . However, DQ increased by less than 4% when w sh increased from 8 to 16 μm with different w sh values. We conclude that w sh exerts minimal influence on DQ. A long w sh results in a large mass of the resonance structure and consequently decreases the resonant frequency and output of the proposed microsensor; thus, w sh was set to 10 mm. The peak-to-peak value of induced charge per unit length, Dq, was calculated with Eq. (7) to optimize w T conveniently.
The calculated Dq versus w T curve is shown in Fig. 5(d). The maximum value of Dq was achieved when w T approached 110 mm. A long w T resulted in a small mass of the resonance structure and consequently increased resonant frequency and improved the output of the proposed microsensor. Thus, w T was to 110 mm.
A similar simulation was performed with the FEA method for the Z sensing element. L and R were preset to 700 and 300 mm, respectively. The presumed vibration amplitude in the inner arc was set to 1.2 mm. The values of w sn , w sh , w T , and w e were determined through a simulation. The electrode parameters are listed in Table 1.

Modal simulation
In the FEA-based modal simulation, the resonant frequencies of the first six orders in the vibration mode were 838.68, 1076.0, 1076.0, 1150. 7, 1454.4, and 1934.7 Hz. The in-plane rotation mode, which is the working mode of the microsensor, was the fifth order in the vibration mode with a resonant frequency of 1454.4 Hz. The remaining five vibration modes were out-of-plane vibrations. The different resonant directions ensured that the other vibration modes did not interfere with the in-plane rotation.

Fabrication
The sensor was fabricated through a MetalMUMPS process [26]. Figure 6 illustrates the fabrication process.
(a) A 2-mm-thick oxide, which served as an isolation  Fig. 6 Main steps of the MetalMUMPS process layer, was grown on the surface of the starting n-type (100) silicon wafer, followed by the deposition of a 0.5-mm-thick sacrificial phosphosilicate glass (PSG) layer. (b) The sacrificial PSG layer was patterned. Afterward, a 0.35 mm silicon layer of nitride and a 0.7 mm layer of polysilicon were deposited, and the polysilicon layer was subsequently patterned.
(c) The second silicon nitride layer was deposited and patterned as a protection material.
(d) After the deposition and patterning of the second sacrificial PSG layer, a metal layer consisting of a 10-nmthick chrome layer and a 25-nm-thick platinum layer was deposited through a lift-off process.
(e) The wafers were coated with a thick layer of photoresist and patterned subsequently. This process formed a patterned stencil on the electroplated metal layer.
(f) A 20-mm-thick nickel layer was electroplated as the metal structure.
(g) The photoresist stencil was chemically removed.
(h) The metal structure was released by hydrogen fluoride (HF), and the remaining sacrificial layers and oxide layer over the trench areas were removed. Subsequently, the substrate layer was subjected to potassium hydroxide (KOH) etching, which formed a 25 mm groove.
Scanning electron microscope (SEM) photos of the fabricated sensor are shown in Fig. 7. The sensor size is approximately 11 mm Â 11 mm.

Testing system
The testing circuit of the electric field microsensor consisted of driving signal generators, I-V converters, differential amplifiers, and lock-in amplifiers, as illustrated in Fig. 8. The I-V converter converted the measured alternating current produced by the microsensor to voltage. A high-precision 1 GW resistor was used in the I-V converter. The differential amplifier magnified the differential output of the two opposite sensing elements by 50 times. The differential amplifier can reduce common-mode noise and increase the signal-to-noise ratio. Notably, differential amplification is inapplicable to the Z-axis output because only one element senses the Z-axis component of the electrostatic field. After differential amplification, the output voltage was connected to a METEK Model 7270 lock-in amplifier. The lock-in amplifier adopted a reference signal at the same frequency as the driving signal to eliminate superfluous information, such as the frequency and phase of the sensing signal, and obtain the amplitude of the sensing signal with respect to the electrostatic field strength. A driving signal composed of 3.5 V of AC voltage and 80 V of common direct current (DC) bias voltage was applied to excite the sensor. The resonant frequency of in-plane rotation was 1291 Hz after sweeping frequency. The simplified structure for modal simulation and squeeze-film damping accounted for the difference between the simulated resonant frequency and detected resonant frequency.
Three metal plates were parallel and equally spaced in a uniform electrostatic field. A positive voltage was applied to the upper plate, whereas a negative voltage of the same value was applied to the lower plate. The sensor with its testing circuit was fixed to the center plate by a fixture with two rotating axes. The fixture was made of Teflon, which is a widely used insulation material. By rotating the fixture on these two axes, an electrostatic field in all directions was generated. A schematic of the testing system is provided in Fig. 9.

Calibration and decoupling sensitivity matrix
Electrostatic fields parallel to the X-, Yand Z-axis of the senor were applied. In each case, the outputs of the X-, Yand Z-axis sensing components with respect to the electrostatic field strength ranging from 0 to 50 kV/m were all recorded for calibration, as shown in Fig. 10.
The sensitivities and linearities of the X-, Yand Z-axis sensing components in the three cases are listed in Table 2. All the measured linearity errors were within 5.5%, which means that each sensing element showed a linear response to every component of the applied electrostatic field. The measured linearities indicated that the alternating current of each sensing axis could be at fA level with a 1 kV/m electric field. The coupling characteristics can be described by the following matrix.
where V q is the output of the q-axis sensing component, V q0 is the zero output of the q-axis sensing component, and coupling sensitivity k qi is the sensitivity of the q-axis sensing component to the electrostatic field in the direction i; i = x,y,z, and q = x,y,z. Therefore, the electrostatic field can be expressed as In this study, the coupling matrix is S ¼ k xx k xy k xz k yx k yy k yz k zx k zy k zz The sensor was rotated to several random angles. For each angle, electrostatic fields of 25 and 50 kV/m were applied. The outputs of the X-, Y-, and Z-axis sensing components were recorded to derive E x , E y , and E z with a coupling Fig. 8 Schematic of the testing circuit of the 3D electric field microsensor. V x , V y , and V z are the outputs of the X-, Y-, and Z-axis sensing components after testing Fig. 9 Schematic of the testing system matrix. Moreover, the strength of the applied electrostatic field was computed with The comparison between the calculated and applied electrostatic fields is presented in Table 3. The measurement errors were between 9.96% and 14.04%; thus, the calculated electrostatic field of the 3D electric field microsensor was consistent with the applied electrostatic field, but measurement errors still existed. These errors may be attributed to systematic errors, electric field distortion, and fabrication-induced sensor structure asymmetry.

Conclusions
This study presented a single-chip 3D electric field microsensor. An in-plane rotary mechanism was adopted in the microsensor to detect X-, Y-, and Z-axis electrostatic field components simultaneously. The proposed microsen-sor is compact and presents high integration. The microsensor's response to a 3D electrostatic field with different directions was investigated. The parameters of the strip-type electrodes were optimized with the FEA method. The characterization results showed that the measured linearity errors were within 5.5% in the range of 0 to 50 kV/m.