High-Throughput Measurement of the Contact Resistance of Metal Electrode Materials and Uncertainty Estimation

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Article High-Throughput Measurement of the Contact Resistance of Metal Electrode mAterials and Uncertainty Estimation

Chao Zhang and Wanbin Ren *

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China; [email protected] * Correspondence: [email protected]

Received: 30 October 2020; Accepted: 4 December 2020; Published: 6 December 2020

Abstract: Low and stable contact resistance of metal electrode mAterials is mAinly demanded for reliable and long lifetime electrical engineering. A novel test rig is developed in order to realize the high-throughput measurement of the contact resistance with the adjustable mechanical load force and load current. The contact potential drop is extracted accurately based on the proposed periodical current chopping (PCC) method in addition to the sliding window average ﬁltering algorithm. The instrument is calibrated by standard resistors of 1 mΩ, 10 mΩ, and 100 mΩ with the accuracy of 0.01% and the associated measurement uncertainty is evaluated systematically. Furthermore, the contact resistance between standard indenter and rivet specimen is measured by the commercial DMM-based instruments and our designed test rig for comparison. The variations in relative expanded uncertainty of the measured contact resistance as a function of various mechanical load force and load current are presented.

Keywords: electrode mAterial; high-throughput characterization; contact resistance; measurement; uncertainty estimation

1. Introduction Metal electrode mAterials are widely used in the electrical and electronic engineering for conducting and/or switching current, such as connectors [1], electromechanical devices [2], thin-film devices [3], microelectromechanical system [4], and switchgear [5], etc. The roughness of the mAterial surfaces causes only small peaks or asperities within the apparent surface to be in contact. The induced constriction resistance and film resistance together mAke up the contact resistance. Today, ‘High performance and high reliability’ of electromechanical devices and electronic components that are used in the high-end equipment mAnufacturing industry is always required. Therefore, the optimal selection method for supporting electrode mAterial and contact resistance measuring method are needed to mAke them perfect. For example, the contact resistance measurement has been successfully used to evaluate the conditions of mAin contacts and arcing contacts without dismantling the high voltage SF6 circuit breaker [6]. Additionally, it could be used to estimate the contact a-spot temperature, and further judge the contact welding situation by classical Voltage–Temperature theory [5,7]. Particularly, the contact resistance results could be selected as the criteria of contact mAterial surface quality, including roughness, hardness, or contamination situation [8,9]. The value of contact resistance is normally very small, ranging from microohms to a few milliohms in cases of practical interest. However, for contacts with worn surface or corroded or contaminated surface, the contact resistance dramatically increases into the scale of ohms or higher [10–12]. The general described contact resistance test methods are characterized as four-terminal Kelvin configuration.

Electronics 2020, 9, 2079; doi:10.3390/electronics9122079 www.mdpi.com/journal/electronics Electronics 2020, 9, 2079 2 of 13

The challenge of measuring microohm scales of contact resistance is that the value is so low level that overwhelmed by the diverse noise easily. Particularly, the thermal potentials are the mAin source of influencing the measured voltage signals. Either AC or DC test currents mAy be used, but the most general method of eliminating the effects of thermal potentials is to mAke forward-and-reverse-current readings and calculating resistance. The measurement accuracy of contact resistance could reach up to 0.1 µΩ by using the innovative methods [13–17]. The scientific instruments for single pair contact mAterial are developed by mAny researchers in order to investigate and evaluate the electrical contact characteristics. Some instruments also include fretting mode and corrosion film current-voltage (I-V) characteristics and environmental atmosphere application [13]. Particularly, the nano-scale electrical contact resistance tool (nanoECR, BRUKER, Minneapolis, MN, USA), provide a powerful solution for simultaneous, in-situ electrical and mechanical measurements [17]. Unfortunately, the mentioned contact resistance measurement apparatus are always based on the commercial digital multimeter for the research work in the laboratory. Additionally, only one contact pair could be tested in one experiment so that the test efficiency is very low. Nevertheless, the loading range of the contact force is too large (up to 1 ton) and the loading accuracy ( 1 kg) is too low. These could not meet the contact resistance measurement requirements ± within 500 g contact force for batches of rivet contacts in engineering. Consequently, the mAin goal of the present work is to fill this gap by developing an apparatus which allow simultaneous automated measurements of contact force and contact resistance with the variable contact current and open voltage. This apparatus should also provide motion mechanism for precise positioning among samples and associated control programme which satisfy the high-throughput measurement. In this paper, we design a novel test rig (including the circuit and associated programme for measuring the low value contact resistance, the electrical actuators combinations and the auxiliary optical observation unit) that could meet the mentioned requirement. A suit of DC standard resistors are selected as the calibration source for minimizing the measurement error. Further, the contact resistance results of electrode mAterials are measured and compared with the use of our designed test rig and commercial Digital Multimeter instruments simultaneously. Finally, the uncertainty of measured contact resistance is estimated and analysed in detail.

2. Description of the New Designed Test Rig In general, the new designed test rig allows studying the high-throughput measurement of contact resistance between two electrode mAterials under the selectable load force and load current. It was designed to fulﬁll the goals mentioned in the introduction:

Variable load forces to achieve pure elastic or elastic–plastic contact mode. • Diﬀerent electrical current levels to discriminate the roles of electrical loads and mechanical loads • in contact resistance. Highly eﬃcient test for batches of rivet contacts: 10 s for single contact pair and 2 min for mAximum • 12 contact pairs automatically. Measurement principle conforming to the regulation of Standard Test Methods ASTM B539-2013 • and ASTM B667-2014.

2.1. Mechanical Structures The designed mechanical structure (shown in Figure1) is placed in a dust-tight transparent Plexiglas housing which is secured on a vibration isolation base to ensure the stability of the measurement. The rivet samples holder is fixed on the base. Furthermore, there are multiple workstations in the holder which could clamp mAximum 12 rivets simultaneously in one row. The clamping structure is designed suitable for different contact dimensions. The minimum shank diameter of rivet samples should be no less than 1 mm. The counterpart probe could be a silver palladium AgPd alloy indenter with 10 µm gold coating (hemispherical shape, 0.5 mm diameter) or Electronics 2020, 9, x FOR PEER REVIEW 3 of 14 Electronics 2020, 9, x FOR PEER REVIEW 3 of 14 palladiumElectronics 2020 AgPd, 9, 2079 alloy indenter with 10 μm gold coating (hemispherical shape, 0.5 mm diameter)3 of or 13 apalladium mated rivet. AgPd The alloy roughness indenter of thewith indenter 10 μm tipgold is coatingmeasured (hemispherical by a con-focal shape, optical 0.5 microscope mm diameter) (LEXT or 3000,a mated Olympus, rivet. The Tokyo, roughness Japan) of and the the indenter surface tip roughness is measured (SRa) by isa con-focal0.4 μm, calculated optical microscope from a scan (LEXT size a mAted rivet. The roughness of the indenter tip is measured by a con-focal optical microscope (LEXT of3000, 50 μOlympus,m × 50 μ m.Tokyo, Figure Japan) 2 schematically and the surface shows roughness the four (SRa)-wire is measurement 0.4 μm, calculated setup, from including a scan sizethe 3000, Olympus, Tokyo, Japan) and the surface roughness (SRa) is 0.4 µm, calculated from a scan size probeof 50 holderμm × 50 structure μm. Figure and the2 schematically rivet clamping shows struct theure four of one-wire measurement measurement workstation. setup, including It is noted the of 50 µm 50 µm. Figure2 schematically shows the four-wire measurement setup, including the thatprobe the holder surfaces× structure of components and the rivetwithin clamping the applied struct currenture of oneand measurementtest voltage circuits workstation. are electroplated It is noted probe holder structure and the rivet clamping structure of one measurement workstation. It is noted withthat thegold surfaces to reduce of componentsthe connection within resistance. the applied Furthermore, current and the coaxialtest voltage shielded circuits lines are are electroplated selected to that the surfaces of components within the applied current and test voltage circuits are electroplated reducewith gold the tointerference reduce the from connection external resistance. signals. The Furthermore, probe is attached the coaxial to a “bow” shielded type lines Beryllium are selected bronze to with gold to reduce the connection resistance. Furthermore, the coaxial shielded lines are selected beltreduce (stiffness the interference is about from0.4 N/mm) external to signals. achieve The the probe flexible is attached contact to witha “bow” low type load Beryllium force. A bronze force to reduce the interference from external signals. The probe is attached to a “bow” type Beryllium transducerbelt (stiffness is connected is about vertically0.4 N/mm) with to it achievefor the measurement the flexible contactof contact with force. low The load probe force. could A move force bronze belt (stiffness is about 0.4 N/mm) to achieve the flexible contact with low load force. A force accuratelytransducer among is connected each workstations vertically with in it“X” for axisthe measurementdirection and ofmakeup contact mechanical force. The probe contact could with move test transducer is connected vertically with it for the measurement of contact force. The probe could move sampleaccurately in “Z” among axis directioneach workstations using two in electric “X” axis actuators direction (the and step makeup position mechanical is 0.15 μm). contact The maximum with test accurately among each workstations in “X” axis direction and mAkeup mechanical contact with test contactsample forcein “Z” could axis directionbe set as 5using N with two a electric resolution actuators of 0.5 (themN. step Additionally, position is an 0.15 auxiliary μm). The observation maximum sample in “Z” axis direction using two electric actuators (the step position is 0.15 µm). The maximum unit,contact which force includescould be seta coloras 5 N CCD with acamera resolution (MV-SUB1600C-T, of 0.5 mN. Additionally, Mindvision, an auxiliary Shenzhen, observation China) contact force could be set as 5 N with a resolution of 0.5 mN. Additionally, an auxiliary observation connectedunit, which with includes the zoom a lenscolor with CCD the pixelcamera of 1.34(MV-SUB1600C-T, μm × 1.34 μm, isMindvision, placed parallel Shenzhen, to the indenter China) unit, which includes a color CCD camera (MV-SUB1600C-T, Mindvision, Shenzhen, China) connected inconnected “X” axis withdirection. the zoom The capturelens with pictures the pixel could of 1.34 be read μm from× 1.34 USB3.0 μm, is interfaceplaced parallel of camera to the connected indenter with the zoom lens with the pixel of 1.34 µm 1.34 µm, is placed parallel to the indenter in “X” axis within “X” PC. axis The direction. appearance The of capture designed pictures instrument could× beis shown read from in Figure USB3.0 3. interface of camera connected direction. The capture pictures could be read from USB3.0 interface of camera connected with PC. with PC. The appearance of designed instrument is shown in Figure 3. The appearance of designed instrument is shown in Figure3. Axis “Z” electric Force Axisactuator “Z” transducer electric Force Industrialactuator transducer camera Industrial Axiscamera “Y” electric Axisactuator “Y” electric actuator Bow type Probe holder spring Bow type Probe holder Axis “X” spring electric Axisactuator “X” electric Rivetactuator samples holder X Rivet samples Y Vibrationholder Z X isolation base Vibration Z Y isolation base Figure 1. 3D model of the mechanical structure (without housing). Figure 1. 3D model of the mechanical structure (without housing). (a) (a)

(b) U+ I (b) Loading U+ I V direction Loading V direction I U- I U-

Figure 2. a Figure 2. TheThe schematic schematic of of the the clamping clamping test test rivet rivet contact. contact. (a () )The The top top view view of of the the rivet rivet samples samples holder. holder. (b) The four-wire conﬁguration including the probe holder structure and the rivet clamping structure (Figureb) The four-wire2. The schematic configuration of the clamping including test the rivet probe contact. holder (a structure) The top andview the of rivetthe rivet clamping samples structure holder. of one measurement workstation. of(b one) The measurement four-wire configuration workstation. including the probe holder structure and the rivet clamping structure of one measurement workstation.

Electronics 2020, 9, 2079 4 of 13 Electronics 2020, 9, x FOR PEER REVIEW 4 of 14

FigureFigure 3. 3. AppearanceAppearance of the designed instrument. instrument.

2.2.2.2. Electrical Electrical Control Control and and Measurement Measurement SystemSystem FigureFigure4 shows 4 shows the the schematic schematic diagram diagram of theof the electrical electrical control control and and measurement measurement system. system. The The core unitcore is theunit high-performance is the high-performance microcontroller microcontr (STM32F103,oller (STM32F103, STMicroelectronics, STMicroelectronics, Geneve, Switzerland), Geneve, whichSwitzerland), is used to which achieve is the used movement to achieve control the of movement electrical actuators control andof electrical the measurement actuators ofand electrical the signals.measurement The open of circuit electrical voltage signals. and theThe load open current circuit used voltage in the and measurement the load current of contact used resistance in the is providedmeasurement by the of 16-bit contact D/ resistanceA Converter is provided AD5541.The by the open 16-bit circuit D/A Converter voltage could AD5541.The be set from open 10 circuit mV to 6 Vvoltage with stepscould of be 1 set mV from and 10 the mV constant to 6 V with current steps source of 1 mV is capableand the constant to provide current 1 mA source to 1 A is with capable 1 mA to provide 1 mA to 1 A with 1 mA step and the accuracy of ±2.5%. The original sampled contact force step and the accuracy of 2.5%. The original sampled contact force signal UF and applied current signal UF and applied current± signal Uv (converted by a 2 Ω precise resistor) both are processed by signal Uv (converted by a 2 Ω precise resistor) both are processed by the low pass ﬁlter and unity gainthe ampliﬁerlow pass tofilter eliminate and unity the gain high amplifier frequency to noise.eliminate Furthermore, the high frequency the special noise. designed Furthermore, weak signal the processingspecial designed circuit isweak used signal for accurate processing restoring circuit theis used passing for accurate contact voltagerestoring drop the signal.passing Next,contact the voltage drop signal. Next, the processed signals of contact force UF, contact voltage drop Uc, open processed signals of contact force UF, contact voltage drop Uc, open circuit voltage Uo and contact circuit voltage Uo and contact current Uv are transmitted into the 24-bit Σ—Δ A/D Converter AD7193, current Uv are transmitted into the 24-bit Σ—∆ A/D Converter AD7193, which has the advantage which has the advantage of ultra-low noise and adjustable gain. Finally, above conditioned and of ultra-low noise and adjustable gain. Finally, above conditioned and converted digital signals are Electronicsconverted 2020 , digital9, x FOR signals PEER REVIEW are uniformly collected by the microcontroller for the next data processing5 of 14 uniformly collected by the microcontroller for the next data processing stage. stage.

Upper PC with Controlling and Processing Software USB Cable

UF 4-CH 24-bit CH1 Uc Overvoltage Micro Control Unit SPI ADC AD7193 with CH2 U protector STM32F103 Communication Programmable Gain CH3 o U (Within 2.5V) Amplifier CH4 v Series Communication Mechanical Module ADA U Low-pass 48 98 F Fi lter U Low noise unity F gain amplifier

Differential to Axix Z Motor Low Noise and Low Drift Amplifier M sin gle-ended Driver AD8221 1kHz Square Wave

180° phase Modulator Demulator Axix Y Motor Closed Filter M Contacts Driver Uc Variable Uc U+ Gain Open Ag-Pd Alloy Rivet Contacts (12) Uo Amplifier Axix X Motor Probe ... Contacts M Driver Resistance Uo V-groove Division Cond ucti ve Plate

Voltage Controlled I Referential ADA Uv Resistor Uv Low-pass 48 98 Current Source U- Fi lter Low noise unity AD5541 gain am plifier

Figure 4. Schematic diagram of the electrical control and measurement system. Figure 4. Schematic diagram of the electrical control and measurement system.

In order to guarantee the accurate and stable measurement for the contact potential drop signal in the microvolt range, two important highlights that is the periodical current chopping (PCC) method and the sliding window average filtering algorithm are proposed.

2.2.1. Periodical Current Chopping (PCC)

When the excitation current I is loaded, the contact voltage drop Uc could be expressed by

𝑈 =𝐼𝑅 +𝑈 +𝑈 (1) where Rc is the true value of contact resistance, Ur is the existed thermal potential, and Uh is the chemical potential on the contact interface. When the excitation current is broken, the contact voltage Uc* could be written as

∗ 𝑈 =0+𝑈 +𝑈 (2)

Thus, according to the Equations (1) and (2), the expression of the difference of Uc and Uc* could be expressed as

∗ 𝑈 −𝑈 =𝐼𝑅 (3) Therefore, if the used current chopping frequency is far higher than the variation rate of the thermal potential Ur and the chemical potential Uh, thus these two additional potentials are almost constant, and then their influence on the measurement results could be neglected. ∗ Considering the voltage value of 𝑈 and 𝑈 output by the amplified analog circuits always ∗ contains the offset voltage Us and the noise Uz, thus 𝑈 and 𝑈 are written by

𝑈 = 𝐴(𝑈 +𝑈 +𝑈) (4) ∗ ∗ 𝑈 = 𝐴(𝑈 +𝑈 +𝑈) (5) where A is the magnification factor, Uc and Uc* represent the expected true voltage value. The optimal period of current chopping is 1 s with the help of trial and error, and then the contact resistance Rc could be calculated by ∗ 𝑈 −𝑈 𝑅 = (6) 𝐴𝐼

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2.2.1. Periodical Current Chopping (PCC)

When the excitation current I is loaded, the contact voltage drop Uc could be expressed by

Uc = IRc + Ur + Uh (1) where Rc is the true value of contact resistance, Ur is the existed thermal potential, and Uh is the chemical potential on the contact interface.

When the excitation current is broken, the contact voltage Uc∗ could be written as

Uc∗ = 0 + Ur + Uh (2)

Thus, according to the Equations (1) and (2), the expression of the difference of Uc and Uc∗ could be expressed as Uc U∗ = IRc (3) − c Therefore, if the used current chopping frequency is far higher than the variation rate of the thermal potential Ur and the chemical potential Uh, thus these two additional potentials are almost constant, and then their influence on the measurement results could be neglected. ˆ ˆ Considering the voltage value of Uc and Uc∗ output by the amplified analog circuits always ˆ ˆ contains the offset voltage Us and the noise Uz, thus Uc and Uc∗ are written by

Uˆ c = A(Uc + Us + Uz) (4)

ˆ Uc∗ = A(Uc∗ + Us + Uz) (5) where A is the mAgniﬁcation factor, Uc and Uc∗ represent the expected true voltage value. The optimal period of current chopping is 1 s with the help of trial and error, and then the contact resistance Rc could be calculated by Uˆ c Uˆ ∗ R = − c (6) c AI

In order to filter the offset voltage Us efficiently, based on AC coupling amplifier principle a low noise low drift amplifying circuit is presented. The amplifying circuit mAinly includes DC-AC modulator, variable gain operational amplifier 8221, and synchronous demodulation filter. Meanwhile, the introduced 1 kHz square wave excitation source results into the amplifier frequency deviating from 0.1 Hz~10 Hz frequency band. The direct consequence of such modulation operation is the obvious suppression of flickering noise. The selected modulation frequency of 1 kHz is an exact multiple of power frequency of 50 Hz, and then the considerable disturbance from the power frequency is eliminated. Moreover, the introduced RC low-pass filter with the cutoff frequency of 10 Hz at the ˆ ˆ end of amplifier, could further filter the weak white noise in Uc and Uc∗.

2.2.2. Sliding Window Average Filtering Algorithm In order to further improve the measurement accuracy and stability of contact resistance, the sliding window average filtering algorithm is used to filter the contact voltage and contact current signals digitally. The amplitude-frequency response function of the sliding window average filter with width N could be written as  ωN  sin( ) jω(N 1) jω  2  − − H e =  e 2  ω  (7) N sin( 2 ) Electronics 2020, 9, x FOR PEER REVIEW 6 of 14

In order to filter the offset voltage Us efficiently, based on AC coupling amplifier principle a low noise low drift amplifying circuit is presented. The amplifying circuit mainly includes DC-AC modulator, variable gain operational amplifier 8221, and synchronous demodulation filter. Meanwhile, the introduced 1 kHz square wave excitation source results into the amplifier frequency deviating from 0.1 Hz~10 Hz frequency band. The direct consequence of such modulation operation is the obvious suppression of flickering noise. The selected modulation frequency of 1 kHz is an exact multiple of power frequency of 50 Hz, and then the considerable disturbance from the power frequency is eliminated. Moreover, the introduced RC low-pass filter with the cutoff frequency ∗ of 10 Hz at the end of amplifier, could further filter the weak white noise in 𝑈 and 𝑈 .

2.2.2. Sliding Window Average Filtering Algorithm In order to further improve the measurement accuracy and stability of contact resistance, the sliding window average filtering algorithm is used to filter the contact voltage and contact current signals digitally. The amplitude-frequency response function of the sliding window average filter with width N could be written as 𝜔𝑁 𝑠𝑖𝑛( ) () 2 𝐻(𝑒 )= 𝜔 𝑒 (7) 𝑁𝑠𝑖𝑛( ) Electronics 2020, 9, 2079 2 6 of 13

When the window width N is 20 and the sampling frequency fs is 10 Hz, the variations in

amplitudeWhen the response window of widththe filterN isas 20a function and the of sampling frequency frequency is shownf sinis Figure 10 Hz, 5. theThe variations essence of in the amplitudeproposed response filtering algorithm of the filter is asa low–pass a function digital of frequency filter. Thus, is shown the amplitude in Figure response5. The essence that is ofthe the ratio proposedof the output filtering signal algorithm to the input is a signal low–pass decreases digital with filter. the Thus, increasing the amplitude frequency responseof input signal. that is When the ratiothe ofcutoff theoutput frequency signal fco toof thedigital input filter signal is 0.22 decreases Hz, the with sign theal amplitude increasing decreases frequency to of 0.707 input times signal. the Whenmaximum the cuto valueff frequency and thef gainco of reaches digital filter −3 dB. is 0.22Thus, Hz, the the signal signal sampling amplitude pe decreasesriod is set toas 0.7074 s to times obtain thethe mAximum stable measurement value and the results. gain reaches 3 dB. Thus, the signal sampling period is set as 4 s to obtain − the stable measurement results.

0.22Hz Amplitude response (dB) response Amplitude

Frequency ω/(2π) (Hz) FigureFigure 5. 5.The The amplitude-frequency amplitude-frequency response response of of the the designed designed digital digital ﬁlter. filter. 3. Standard Resistance Calibration and Uncertainty Estimation 3. Standard Resistance Calibration and Uncertainty Estimation According to the above mentioned test principle, the measurement results of contact resistance is According to the above mentioned test principle, the measurement results of contact resistance written by is written by Uc U0 Rc = − (8) 𝑈I −𝑈 𝑅 = (8) where U0, Uc and I are the arithmetic means of drift voltage𝐼 when no current is applied, the measured contactwhere voltage U0, Uc and drop I are and the the arithmetic applied test means current of drift for onevoltage sampling when periodno current (4 s). is applied, the measured contactTo further voltage validate drop and the accuracythe applied and test stability current of for designed one sampling circuits, period the DC (4 standard s). resistors (BZ3, Shanghai Precision Instrument, China) with the rated value of 1 mΩ, 10 mΩ, and 100 mΩ and the accuracy of 0.01% are selected as the test sample. The applied current is set from 1 mA to 100 mA and the test current interval is 1 mA and 10 mA corresponding to the current ranges from 1 mA to 10 mA and 10 mA to 100 mA. Furthermore, 20 series of tests are conducted under each current value. The measured values of U0, Uc, and I could be considered as the independent quantities. Thus, the combined standard uncertainty for the measured resistance could be calculated as [18] s 2 2 2 ∂Rc 2 ∂Rc 2 ∂Rc 2 U(Rc) = ( ) u(Uc) + ( ) u(U0) + ( ) u(I) (9) ∂Uc ∂U0 ∂I

2 where the sensitivity coeﬃcients ∂R/∂Uc = 1/I, ∂R/∂U = 1/I and ∂R/∂I = (Uc U )/I could be 0 − − − 0 obtained from Equation (8) and u(Uc), u(U0) and u(I) are the type A evaluation of standard uncertainty for the variables Uc, U0, and I to reﬂect the deviation of repeated measurement. Thus, the combined standard uncertainty could be further written as r 2 2 2 1 2 1 2 Uc U0 2 U(Rc) = ( ) u(Uc) + ( ) u(U ) + ( − ) u(I) (10) I − I 0 − I Electronics 2020, 9, 2079 7 of 13

The expanded uncertainty of measurement stated as the combined standard uncertainty of measurement multiplied by a coverage factor k = 2, corresponding to a coverage probability of approximately 95%. Taking the standard resistance with rated value of 1 mΩ measured by 10 mA as an example, the measurement results and corresponding measurement uncertainty are shown in Table1. The available estimate of the measured resistance is 1.004 m Ω and the expanded uncertainty is 0.00096 mΩ corresponding to a coverage probability of approximately 95%. It is noted that the drift voltage U0 is about 26.6% of the total contact voltage drop (10.073 µV), which is the sum of the absolute value of the measured Uc and U0, and is almost constant for various load current. The proposed periodical current chopping method could solve this problem readily to realize the precise measurement of the low value resistance. Similarly, the test results and uncertainty estimation for standard resistors of 1 mΩ, 10 mΩ, and 100 mΩ under load currents of 1 mA, 10 mA, 50 mA, and 100 mA are listed in Table2. Furthermore, the variations in contact resistance as a function of the applied current from 1 mA to 100 mA logarithmically are plotted in Figure6.

Table 1. Measured results and corresponding uncertainty. (standard resistance of 1 mΩ and load current of 10 mA).

Parameter Value Type Uncertainty

Uc/µV 7.3877 A 0.0035 U /µV 2.6853 A 0.0033 0 − I/mA 10.0246 A 0.0002

Table 2. Measurement results and corresponding expanded uncertainty. (standard resistance of 1 mΩ, 10 mΩ and 100 mΩ).

Combined Expanded Load Current R R Error s c Standard Uncertainty (mA) (mΩ) (mΩ) (mΩ) Uncertainty (k = 2) 1 1 1.002 0.002 0.00619 0.01239 1 10 9.962 0.038 0.00537 0.00974 − 1 100 99.75 0.25 0.002916 0.05832 − 10 1 1.004 0.004 0.00048 0.00096 10 10 10.002 0.002 0.00057 0.00115 10 100 99.93 0.07 0.0032 0.0064 − 50 1 1.005 0.005 0.00008 0.00016 50 10 10.021 0.021 0.00016 0.00032 50 100 99.95 0.05 0.00186 0.00372 − 100 1 1.005 0.005 0.00005 0.0001 100 10 10.021 0.021 0.00015 0.0003 100 100 99.97 0.03 0.00176 0.00352 −

The measured contact resistance decreases and the fluctuation range enlarges with the test current decreasing for the standard resistance of 1 mΩ, 10 mΩ and 100 mΩ. This could be attributed to the fact that the voltage drop would be interfered by the noise signal easily under the lower test current from 1 mA to 10 mA. Thus, the contact resistance would fluctuate locally. After that, the measurement resistance is close to the nominal value and would be stable. The results show that the error between the measured resistance and rated values of standard resistors under different current load is smaller than 1%, even including the low level measurement under dry circuit conditions where the contact current is limited to 1 mA and the contact potential drop on resistor of 1 mΩ is below 1 µV. As expected, the deviation of measured resistance apparently increases with the smaller load current. Particularly, the highest deviation of each standard resistance appears when the load current is 1 mA. The test uncertainty ratio between the required error limit and expanded measurement uncertainty is higher than 10 for three scales of standard resistors, except for the case of 1 mΩ with current of 1 mA. This results indicate that the presented method is directly applicable for measurements of the low Electronics 2020, 9, x FOR PEER REVIEW 8 of 14

Table 2. Measurement results and corresponding expanded uncertainty. (standard resistance of 1 mΩ, 10 mΩ and 100 mΩ).

Load Current Rs Rc Error Combined Standard Expanded Uncertainty (mA) (mΩ) (mΩ) (mΩ) Uncertainty (k = 2) 1 1 1.002 0.002 0.00619 0.01239 1 10 9.962 −0.038 0.00537 0.00974 1 100 99.75 −0.25 0.002916 0.05832 10 1 1.004 0.004 0.00048 0.00096 10 10 10.002 0.002 0.00057 0.00115 10 100 99.93 −0.07 0.0032 0.0064 50 1 1.005 0.005 0.00008 0.00016 50 10 10.021 0.021 0.00016 0.00032 50 100 99.95 −0.05 0.00186 0.00372 Electronics1002020 , 9, 2079 1 1.005 0.005 0.00005 0.0001 8 of 13 100 10 10.021 0.021 0.00015 0.0003 resistance100 value. Furthermore,100 99.97 the mAximum −0.03 combined0.00176 standard uncertainty u = 0.00619 0.00352 m Ω is taken as the type B evaluation of standard uncertainty to further estimate the deviation of the test results.

1.020 10.04

1.015 10.02 1.010

1.005 10.00

1.000 (mΩ) (mΩ) s s

R R 9.98 Avearge resistance 0.995 Avearge resistance

0.990 9.96 0.985

0.980 9.94 1101002 5 20 50 1101002 5 20 50 Test current I (mA) Test current I (mA) (a) (b)

100.00

99.96

99.92

99.88 Avearge resistance 99.84 (mΩ) s R 99.80

99.76

99.72

99.68 12 5 10 20 50 100 Test current I (mA) (c)

FigureFigure 6. 6.MeasurementMeasurement results results for for standard standard resistance resistance ofof 11 mmΩΩ,, 10 10 m mΩΩ,, and and 100 100 m mΩΩunder under the the current current fromfrom 1 mA 1 mA to to 100 100 mA. mA. (a ()a )1 1m mΩΩ. .((bb) )10 10 m mΩΩ..( (cc)) 100 100 m mΩΩ.. 4. Electrical Contact Resistance and Uncertainty Estimation The measured contact resistance decreases and the fluctuation range enlarges with the test current4.1. Experimental decreasing Detailsfor the standard resistance of 1 mΩ, 10 mΩ and 100 mΩ. This could be attributed to the fact that the voltage drop would be interfered by the noise signal easily under the lower test Two representative metal electrical electrode mAterials, which are the copper alloy electroplated current from 1 mA to 10 mA. Thus, the contact resistance would fluctuate locally. After that, the with gold (thickness of 1 µm) and the silver cadmium oxide (AgCdO), are selected as experimental measurement resistance is close to the nominal value and would be stable. The results show that the specimens. Samples are all ﬂat type and the dimension parameters are explained in Figure7. error between the measured resistance and rated values of standard resistors under different current The specimens were degreased using alcohol and distilled water in an ultrasonic cleaner, dried, and carefully mounted in the instrument. The movable indenter with curvature radius of r = 0.5 mm is mAde of silver palladium alloy (AgPd) electroplated with gold (thickness of 10 µm). The experiments are carried out in ambient lab air. Electronics 2020, 9, x FOR PEER REVIEW 9 of 14

load is smaller than 1%, even including the low level measurement under dry circuit conditions where the contact current is limited to 1 mA and the contact potential drop on resistor of 1 mΩ is below 1 μV. As expected, the deviation of measured resistance apparently increases with the smaller load current. Particularly, the highest deviation of each standard resistance appears when the load current is 1 mA. The test uncertainty ratio between the required error limit and expanded measurement uncertainty is higher than 10 for three scales of standard resistors, except for the case of 1 mΩ with current of 1 mA. This results indicate that the presented method is directly applicable for measurements of the low resistance value. Furthermore, the maximum combined standard uncertainty u = 0.00619 mΩ is taken as the type B evaluation of standard uncertainty to further estimate the deviation of the test results.

4. Electrical Contact Resistance and Uncertainty Estimation

4.1. Experimental Details Two representative metal electrical electrode materials, which are the copper alloy electroplated with gold (thickness of 1 μm) and the silver cadmium oxide (AgCdO), are selected as experimental specimens. Samples are all flat type and the dimension parameters are explained in Figure 7. The specimens were degreased using alcohol and distilled water in an ultrasonic cleaner, dried, and carefully mounted in the instrument. The movable indenter with curvature radius of r = 0.5 mm is made of silver palladium alloy (AgPd) electroplated with gold (thickness of 10 μm). The experiments Electronicsare carried2020 out, 9, 2079in ambient lab air. 9 of 13

Unit: mm

2.5 (a) (b)

Figure 7. The appearance and dimension parametersparameters of the rivet contact. (a) Appearance of the rivet contacts. ( b)The dimension parameters of specimen.

For direct comparison with the presented measurementmeasurement method, the commercial calibrated DC current source (6221, Keithley, Cleveland,Cleveland, OH, USA) and programmable nano-volt meter (2182 A, Keithley, USA)USA) are are introduced introduced to measureto measure the contactthe contact resistance resistance between between the indenter the indenter and rivet and samples. rivet Thesamples. setup The of experimental setup of experimental circuits is alsocircuits consistent is also withconsistent four-wire with configuration. four-wire configuration. As shown in As Figure shown8, thein Figure commercial 8, the commercial current source current is interfaced source is to interfaced a PC using to Ethernet a PC using to transmitEthernet the to transmit control instructions the control andinstructions measurement and measurement results. Four results. groups Four of SPDT groups switches of SPDT controlled switches bycontrolled PC are usedby PC to are switch used the to signalswitch measurementthe signal measurement channels and channels associated and measurement associated instruments.measurement The instruments. data acquisition The data and measurementacquisition and process measurement are controlled process with are controlled the help of with LabVIEW the help software of LabVIEW specifically software programmed specifically forprogrammed this purpose. for Figurethis purpose.9 illustrates Figure the 9 testingillustrates procedure. the testing Initially, procedure. the open Initially, circuit the voltage open 20circuit mV isvoltage applied 20 betweenmV is applied two contact between members. two contact That is members. sufficient That for the is drysufficient circuit for experiment. the dry circuit Next, theexperiment. indenter Next, is driven the indenter to approaching is driven the to rivet appr specimenoaching the until rivet the specimen contact force until reaches the contact the givenforce value.reaches After the given that, thevalue. load After current that, isthe applied load current and then is applied the contact and potentialthen the contact drop is potential recorded drop by the is proposedrecorded PCCby the method. proposed Keeping PCC themethod. mechanical Keeping contact the status,mechanical andthe contact four teststatus, probes and are the shift four to test the digitalElectronicsprobes multimeterare 2020 shift, 9, x to FOR the side PEER digital automatically. REVIEW multimeter The side contact automatically. resistance The is contact measured resistance again by is measured the commercial10 again of 14 instrumentsby the commercial with the instruments same load with current. the Insame order load to current. compare In the order measurement to compare accuracy the measurement for varied N, 0.2 N, 0.3 N, 0.4 N, and 0.5 N to change the contact area, and the applied current is set from 1 mA contactaccuracy resistance for varied values, contact the resistance mechanical values, load forcethe mechanical is set to 0.01 load N, 0.08force N, is 0.15set to N, 0.01 0.2 N,N, 0.30.08 N, N, 0.4 0.15 N, to 100 mA. and 0.5 N to change the contact area, and the applied current is set from 1 mA to 100 mA.

Personal Computer

Ethernet USB Cable

SPDT switches U+ I Keithley2182A The controlled I Indenter current source Series AD5541 comm. Trigger RS232 Link

AD7193 SPI comm. Rivet Keithley6221 The voltage collector

DMM-based Method U- PCC Method

Figure 8. Experimental circuits for the DMM-basedDMM-based method and PCC method.

Start

Output the open-circuit voltage

Load the contact force

Apply the test current by PCC method

Measure the potential signals and calculate contact resistance by PCC method Change the test current or given contact force Shift four switches

Apply the test current by DMM-based method

Measure the potential signals and calculate contact resistance by DMM-based method

Continue ？ YES

Stop

Figure 9. Testing procedure for the contact resistance under given contact force and test current.

4.2. Experimental Results and Discussion

Figure 10 shows the variations of measured contact resistance Rc versus the current load I with varied load force from 0.01 N to 0.5 N by the PCC method and DMM-based method for gold-plated copper alloy samples and AgCdO samples. As shown, the measured resistance of the PCC method

Electronics 2020, 9, x FOR PEER REVIEW 10 of 14

N, 0.2 N, 0.3 N, 0.4 N, and 0.5 N to change the contact area, and the applied current is set from 1 mA to 100 mA.

Personal Computer

Ethernet USB Cable

SPDT switches U+ I Keithley2182A The controlled I Indenter current source Series AD5541 comm. Trigger RS232 Link

AD7193 SPI comm. Rivet Keithley6221 The voltage collector

DMM-based Method U- PCC Method

Electronics 2020, 9, 2079 10 of 13 Figure 8. Experimental circuits for the DMM-based method and PCC method.

Start

Output the open-circuit voltage

Load the contact force

Apply the test current by PCC method

Measure the potential signals and calculate contact resistance by PCC method Change the test current or given contact force Shift four switches

Apply the test current by DMM-based method

Measure the potential signals and calculate contact resistance by DMM-based method

Continue ？ YES

Stop

FigureFigure 9. TestingTesting procedure for the contact resistance under given contact force and test current.

4.2. Experimental Results and Discussion Figure 10 shows the variations of measured contact resistance R versus the current load I with Figure 10 shows the variations of measured contact resistance Rcc versus the current load I with varied load force from 0.01 N to 0.5 N by the PCC method and DMM-based method for gold-plated copper alloy samples and AgCdO samples. As shown, the measured resistance of the PCC method agree well with that of DMM-based method under different combinations of current and force. It is noted that the proposed PCC method is simpler compared to the conventional DMM-based method due to two sampling points in one period. Furthermore, the mAximum sampling frequency of the proposed PCC method is 45 Hz, which is almost twice of the 24 Hz of the DMM method. This indicates that PCC method is more effective and sufficiently convincing in the measurement. For the case of 0.01 N load force, the contact resistance of gold-plated sample decreases from 18.11 mΩ to 14.65 mΩ with the test current from 1 mA to 100 mA and the mAjor drop of contact resistance concentrates on the current load from 6 mA to 20 mA, which demonstrate similar trends known as Branly effect [19,20]. For the load force higher than 0.01 N, the contact resistance decreases slightly in the whole test process. Such behavior is indicative of change of conduction area or conduction path, and the possible reason is surface film breakdown mechanisms induced by microscope thermal effects [21]. The contact resistance nonlinearly decreases with the ever-increasing mechanical load, which correlates well with those of the other researchers [22,23]. However, when the applied force increases from 0.01 N to 0.08 N, the contact resistance of AgCdO sample is almost constant. This suggests the occurrence of oxidation film in the samples, which are exposed in the air for a long time. Therefore, the film resistance is the mAjority of electrical contact resistance relative to the constriction resistance. The resistance decreases greatly from 38.09 mΩ to 10.7 mΩ when the contact load changes from 0.15 N to 0.5 N. Electronics 2020, 9, x FOR PEER REVIEW 11 of 14 agree well with that of DMM-based method under different combinations of current and force. It is noted that the proposed PCC method is simpler compared to the conventional DMM-based method due to two sampling points in one period. Furthermore, the maximum sampling frequency of the proposed PCC method is 45 Hz, which is almost twice of the 24 Hz of the DMM method. This indicates that PCC method is more effective and sufficiently convincing in the measurement. For the case of 0.01 N load force, the contact resistance of gold-plated sample decreases from 18.11 mΩ to 14.65 mΩ with the test current from 1 mA to 100 mA and the major drop of contact resistance concentrates on the current load from 6 mA to 20 mA, which demonstrate similar trends known as Branly effect [19,20]. For the load force higher than 0.01 N, the contact resistance decreases slightly in the whole test process. Such behavior is indicative of change of conduction area or conduction path, and the possible reason is surface film breakdown mechanisms induced by microscope thermal effects [21]. The contact resistance nonlinearly decreases with the ever-increasing mechanical load, which correlates well with those of the other researchers [22,23]. However, when the applied force increases from 0.01 N to 0.08 N, the contact resistance of AgCdO sample is almost constant. This suggests the occurrence of oxidation film in the samples, which are exposed in the air for a long time. Therefore, the film resistance is the majority of electrical contact resistance relative to the constriction Electronicsresistance.2020 The, 9, 2079resistance decreases greatly from 38.09 mΩ to 10.7 mΩ when the contact load changes11 of 13 from 0.15 N to 0.5 N.

60 20

PCC method 19 DMM-based method 18 PCC method 50 F = 0.01 N 17 DMM-based method F = 0.08 N 16 40 15 F = 0.01 N F = 0.15 N 14 (mΩ) c (mΩ) 13 c 30 F = 0.2 N R R 12 F = 0.08 N 11 F = 0.15 N 20 10 F = 0.3 N F = 0.2 N 9 F = 0.3 N F = 0.4 N 8 F = 0.4 N 10 F = 0.5 N F = 0.5 N 7 1 10 100 1 10 100 I (mA) I (mA) (a) (b)

Figure 10. The measured results with varied test current II and contact force force FF..( (aa)) Gold-plated Gold-plated rivet. rivet. (b) AgCdO AgCdO rivet. rivet.

Figures 11 and 12 show the variations of the relativerelative expanded uncertainty of the measured contact resistance versus the load current and load force for the gold-platedgold-plated contacts and AgCdO contacts, respectively.respectively. Furthermore, Furthermore, the expandedthe expand uncertaintyed uncertainty corresponding corresponding to a coverage to a probabilitycoverage probabilityof approximately of approximately 95% consists 95% of the consists type Aof evaluation the type A of evaluation standard uncertaintyof standard of uncertainty the uncorrelated of the uncorrelatedrepeatability andrepeatability the type Band evaluation the type ofB evaluati standardon uncertainty of standard for uncertainty the PCC method for the mentionedPCC method in mentionedSection3 for in each Section measurement 3 for each condition.measurement As shown, condition. the mAximumAs shown, relativethe maxi expandedmum relative uncertainty expanded of uncertaintythe gold-plated of the contact gold-plated and AgCdO contact contact and areAgCdO 3.29% contact and 1.01% are with3.29% current and 1.01% load ofwith 2 mA, current respectively. load of 2Furthermore, mA, respectively. the relative Furthermore, expanded the uncertainty relative expa of thended gold-plated uncertainty contacts of the is alwaysgold-plated higher contacts than that is alwaysof the AgCdO higher contactsthan that for of thethe sameAgCdO load contacts force and for currentthe same due load to theforce lower and contactcurrent resistancedue to thefor lower the contactgold-plated resistance contacts. for The the measurementgold-plated contacts. uncertainty The of measurement contact resistance uncertainty decreases of from contact 3.29% resistance to 0.76% decreasessharply in from the range 3.29% of to 1~10 0.76% mA sharply with thein the contact range force of 1~10 of 0.2 mA N. with This the could contact be attributed force of 0.2 to theN. This fact couldthat the be increasing attributed currentto the fact load that mAkes the increasing the contact current voltage load drop makes larger the and contact stable, voltage and thus drop the larger type ElectronicsAand evaluation stable, 2020 , and9 of, x FOR standard thus PEER the REVIEW uncertainty type A evaluation decreases. of After standard that, theuncertainty measurement decreases. uncertainty After ofthat, contact12 ofthe 14 measurementresistance is almost uncertainty a constant, of whichcontact means resistance that the is measurement almost a constant, results tends which to bemeans stable. that the measurement results tends to be stable. 3.5 1.1 1.0 3.0 F = 0.01 N F = 0.01N F = 0.08 N F = 0.08 N F = 0.15 N 2.5 0.8 F = 0.15 N F = 0.2 N F = 0.3 N

% F = 0.2 N c 2.0 % c R F = 0.3 N F = 0.4 N R

)/ 0.6 c F = 0.5 N )/

F = 0.4 N c R (

1.5 R

( U F = 0.5 N U 0.4 1.0

0.5 0.2

0.0 0.0 1101002 5 20 50 11010025 2050 I (mA) I (mA) (a) (b)

FigureFigure 11. TheThe variation variation of of the the expanded expanded uncertainty uncertainty of of the the contact resistance with varied contact current.current. ( (aa)) Gold-plated Gold-plated rivet. rivet. ( (bb)) AgCdO AgCdO rivet. rivet.

3.5 1.1 1 mA 1.0 3.0 2 mA 1 mA 5 mA 2 mA 2.5 10 mA 0.8 5 mA 20 mA 10 mA 50 mA

% 2.0 % 20 mA c c 0.6

R 100 mA R 50 mA )/ )/ c c 100 mA

R 1.5 R ( ( U U 0.4 1.0

0.5 0.2

0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.00.10.20.30.40.5 F (N) F (N) (a) (b)

Figure 12. The variation of the expanded uncertainty of the contact resistance with varied contact pressure. (a) Gold-plated rivet. (b) AgCdO rivet.

As shown in Figure 12, the relative expanded uncertainty of the measured contact resistance fluctuates greatly from 0.02% to 3.29% for gold-plated samples and the maximum uncertainty always corresponds to the contact load of 0.2 N. For AgCdO samples, the relative expanded uncertainty increases with the applied force loading when the test current is smaller than 20 mA. After that, the maximum uncertainty always corresponds to load force of 0.3 N. This means that the reasonable determination of the contact force and applied current is important to evaluate the surface condition of materials with the help of contact resistance. Furthermore, the measurement uncertainty could also be taken as an auxiliary reference to determine if the surface condition is stable under the load current and load force. Meanwhile, for the metal material and its oxidation film with higher softening voltage, the larger test current would produce a larger and stable contact voltage drop across contacts, which is beneficial to being measured and evaluating the surface condition of material. For the metal material with larger hardness and denser film, the larger contact force between contacts would not destroy the surface of test material and the measurement results is also more stable.

5. Conclusions A novel high-throughput test rig, which could realize the accurate and in situ automated contact resistance measurement based on the precise motion control and circuit design, is described. A

Electronics 2020, 9, x FOR PEER REVIEW 12 of 14

3.5 1.1 1.0 3.0 F = 0.01 N F = 0.01N F = 0.08 N F = 0.08 N F = 0.15 N 2.5 0.8 F = 0.15 N F = 0.2 N F = 0.3 N

% F = 0.2 N c 2.0 % c R F = 0.3 N F = 0.4 N R

)/ 0.6 c F = 0.5 N )/

F = 0.4 N c R (

1.5 R

( U F = 0.5 N U 0.4 1.0

0.5 0.2

0.0 0.0 1101002 5 20 50 11010025 2050 I (mA) I (mA) (a) (b)

Figure 11. The variation of the expanded uncertainty of the contact resistance with varied contact Electronicscurrent.2020 ,(9a,) 2079Gold-plated rivet. (b) AgCdO rivet. 12 of 13

3.5 1.1 1 mA 1.0 3.0 2 mA 1 mA 5 mA 2 mA 2.5 10 mA 0.8 5 mA 20 mA 10 mA 50 mA

% 2.0 % 20 mA c c 0.6

R 100 mA R 50 mA )/ )/ c c 100 mA

R 1.5 R ( ( U U 0.4 1.0

0.5 0.2

0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.00.10.20.30.40.5 F (N) F (N) (a) (b)

Figure 12. TheThe variation of of the expanded uncertainty of the contact resistance with varied contact pressure. ( a) Gold-plated rivet. ( (bb)) AgCdO AgCdO rivet. rivet.

As shown in Figure 1212,, the relative expanded uncertainty of the measured contact resistance fluctuatesfluctuates greatly from 0.02% to 3.29% for gold-plated samples andand the mAximummaximum uncertainty uncertainty always corresponds to the contact load of 0.2 N. For AgCdO samples, the relative expanded uncertainty increases with with the the applied applied force force loading loading when when the the test test current current is smaller is smaller than than 20 mA. 20 mA. After After that, that, the maximumthe mAximum uncertainty uncertainty always always corresponds corresponds to load to load force force of of0.3 0.3 N. N. This This means means that that the the reasonable determination of the contact force and applied current is important to evaluate the surface condition of materials mAterials with with the the help help of of contact contact resistance. resistance. Furthermore, Furthermore, the the measuremen measurementt uncertainty uncertainty could also be taken as an auxiliary auxiliary reference reference to determine if the surface condition is stable under the load load current current and loadload force.force. Meanwhile, Meanwhile, for for the the metal metal mAterial material and and its oxidation its oxidation film with film higher with softeninghigher softening voltage, voltage,the larger the test larger current test wouldcurrent produce would produce a larger anda larger stable and contact stable voltage contact dropvoltage across drop contacts, across contacts, which is whichbeneficial is beneficial to being measuredto being measured and evaluating and evaluati the surfaceng the condition surface condition of mAterial. of material. For the metal For the mAterial metal materialwith larger with hardness larger hardness and denser and film, denser the larger film, contactthe larger force contact between force contacts between would contacts not destroywould not the destroysurface ofthe test surface mAterial of test and material the measurement and the measurement results is also results more is stable. also more stable.

5. Conclusions 5. Conclusions A novel high-throughput test rig, which could real realizeize the accurate and in situ automated automated contact resistance measurementmeasurement based based on on the the precise precise motion moti controlon control and circuitand circuit design, design, is described. is described. A special A mechanical structure allows multiple workstations clamping various rivets and four wires circuit configuration. The µV scales of contact voltage drop is measured accurately with the proposed periodical current chopping method and the sliding window average filtering algorithm, differently from other existing techniques. It is found that the measurement uncertainty of standard resistor is 0.00619 mΩ. The preliminary results showed good resolution of contact resistance measurement with the test rig with the various mechanical load force and current. The variations in contact resistance as a function of load force and current, as measured by the test rig, correlates well with existing theoretical results. The instrument is found capable of evaluating the surface features of metal mAterials directly and in real time.

Author Contributions: Conceptualization, W.R. and C.Z.; methodology, W.R. and C.Z.; software, C.Z.; validation, W.R. and C.Z.; formal analysis, W.R.; investigation, C.Z.; resources, W.R.; data curation, C.Z.; writing—original draft preparation, C.Z.; writing—review and editing, W.R.; visualization, C.Z.; supervision, W.R.; project administration, W.R.; funding acquisition, W.R. Both authors have read and agreed to the published version of the manuscript. Funding: This research was funded by The National Natural Science Foundation of China, grant number 51777039. The APC was funded by National Natural Science Foundation of China. Conﬂicts of Interest: The authors declare no conﬂict of interest. Electronics 2020, 9, 2079 13 of 13

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