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Verification of non-contacting surface electric potential measurement model using contacting electrostatic voltmeter
Journal of Electrostatics 67 (2009) 453–456
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Verification of non-contacting surface electric potential measurement model using contacting electrostatic voltmeter Apra Pandey a,1, Jerzy Kieres a,1, Maciej A. Noras b, * a b
Trek, Inc., 11601 Maple Ridge Rd., Medina, NY 14103, USA Dept. of Engineering Technology, Univ. of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 28223, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2008 Received in revised form 29 November 2008 Accepted 31 January 2009 Available online 15 February 2009
Measurements of surface charge and potential became very common in industrial applications and academic research. In this paper authors present use of a contacting ultra-high input impedance voltmeter in the areas where traditionally the non-contacting measurement methods were used. With very low input capacitance of the order of 1015 F, and very high input resistance of the order of tens of teraohms, there is practically no charge transfer from the measured object to or from the instrument. Experiment presented in this paper explains a correlation between the non-contacting and contacting measurement techniques using a finite element analysis model. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Surface charge measurements Input impedance Electrostatic voltmeter
1. Introduction The first non-contacting method of electrostatic field and potential measurement was developed at the end of 19th century by Lord Kelvin [1]. The Kelvin probe, and then the later developments of the rotating vane fieldmeter and the induction probe are well-known examples of non-contacting electrostatic measurement instruments. Lack of physical contact between the examined object and the sensor of the instrument assures that no charge is transferred. However, every time such non-contacting instrument is used, one of the most fundamental questions asked by the user is: what is the surface area that the instrument is looking at? What is the charge distribution in that area? Spatial resolution of noncontacting meters depends on the size of the sensor and the distance between the sensor and the object under test. A simplified method for the measured surface area calculation is presented in Fig. 1. In the case of a circular sensor with the diameter A at the distance H from the surface, assuming that the ‘‘view’’ angle equals 45 , the diameter of the circular surface measured by the sensor is:
D ¼ A þ 2$H:
(1)
* Corresponding author. E-mail addresses: [email protected] (A. Pandey), [email protected] (M.A. Noras). 1 Tel.: þ1 585 798 3140. 0304-3886/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2009.01.053
This purely empirical formula allows for quick assessment of either electrostatic potential, or electrostatic field, or surface charge only in case when the electric charge is distributed uniformly over the whole surface area under investigation. It works fine for the conducting surfaces, but becomes imprecise when dealing with semiconducting or dielectric objects. In this paper authors discuss influence of the charge nonuniformity on readings of a noncontacting voltmeter and compare them with measurement collected with the ultra-high impedance contacting voltmeter. Performance of the contacting instrument is also evaluated,
Fig. 1. The cantilever beam designed for an electrostatic voltmeter (ESVM), dimensions are in mm.
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A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
Fig. 2. Driven shield technique [3].
including method used for the input resistance and input capacitance measurement. 2. Evaluation of the input impedance of the contacting electrostatic voltmeter (ESVM) Construction and details of operation of the contacting ESVM used in the experiments are described in one of the previous
publications [2]. Typical constructions of contacting instruments such as those developed by Keithley [3] use a guarding (shield) technique, where the electric potential of the shielding system is feedback-driven to that of the voltage sensor (Fig. 2). The measurement method is based on the concept of input bias current cancellation. The input bias current value is recorded and stored. Another circuit produces an output current equal in magnitude to the value of this bias current but opposite in polarity. This current is applied to the input of the amplifier to cancel the bias current [2]. Proper nullification of the input bias current of the pre-amplifier circuit along with independent bootstrapping of the amplifier power supply allows for increase of the input resistance to the range of 30 TU and lowering of the input capacitance to 5.3 fF with the electrostatic potential measurement range up to 2 kV. Fig. 3 presents a test setup used for the input resistance and capacitance evaluation. The capacitor used in the test was a 2.2 pF 0.5 pF COG (Electronics Industries Alliance specification for capacitor with the temperature coefficient of 0 ppm/ C, 30 ppm/ C) with two 5 mm diameter circle electrodes soldered to it. The value of the capacitance was confirmed with the Stanford Research Model SR 715 LCR meter (measurement accuracy 0.2%). To avoid the influence of the surrounding objects on the capacitance of the setup, a shielded box was used. The capacitor was charged to a pre-determined voltage level. Each time the voltmeter probe contacted the electrode of the capacitor, it was anticipated that a portion of electric charge will transfer between the probe and the electrode. The method used here was a slight modification of the technique described elsewhere [2]. The calculated input capacitance of the voltmeter was equal to 5.3 fF and the input resistance was 30 TU.
Fig. 3. Test setup for input resistance and capacitance measurement.
A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
455
Fig. 4. Surface potential measurement setup. (a) Non-contacting. (b) Contacting.
3. Surface charge evaluation using contacting and noncontacting ESVM The list of equipment used in the experiments consists of Trek Model 334 ESVM with the side-view probe (sensor 5 mm in diameter) and the prototype PR0623 contacting ESVM. For surface potential evaluation a simple setup shown in Fig. 4 was used. The 50 cm by 50 cm test plate was made of Lexan with average thickness of 5 mm, backed with an electrically grounded stainless steel plane. The Lexan plate was tribocharged by rubbing it with a cotton cloth and then the surface potential measurements were taken with the non-contacting voltmeter. Two probe to surface distances were selected: 10 and 6 mm. The potential was recorded at every point of the 48 mm by 48 mm grid with 8 mm increments in the X and Y direction. The test was repeated for exactly the same probe locations with the contacting ESVM probe. Fig. 5 presents the surface potential distribution as recorded by the contacting probe. Since the measurement points on the Lexan plate surface were
Electric potential at the surface 45
600
40
400
35
200
Y, mm
30
0
25
−200
20
−400
15
−600
10
−800
5 0
−1000 0
10
20
30
40
X, mm Fig. 5. Surface potential distribution measured with the contacting ESVM, data interpolated between the measurement points (8 mm 8 mm grid). The colorbar represents values of the electric potential in Volts.
separated, the values of the potential between the points were linearly interpolated. Fig. 6 presents comparison between measurements taken over the grid points with the non-contacting ESVM and computer simulation (carried out using COMSOL Multiphysics) of the potential distribution based on the values of the electric potential on the surface, as measured with the contacting ESVM.
4. Discussion While considering data presented in Fig. 6, it can be immediately noticed that, predictably, the distance between the noncontacting sensor and the Lexan plate affected the value recorded by the instrument. Let’s consider, for example, point with the highest positive potential on the plane. The value as measured by the contacting meter was þ864 V. The non-contacting meter recorded, at exactly the same location, þ636 V (6 mm) and þ128 V (10 mm). The FEA model predicts correspondingly þ26 V and 5 V. In order to explain this discrepancy we need to consider the superposition of all the fields and associated with them electric potential values, coming from the surface charges on the plane at a given location where the probe is. The noncontacting ESVM will, by its operation principle, produce that averaged potential on the probe body. However, it will take into consideration only the surface area that is ‘‘seen’’ by the sensor, neglecting the influence of the electrostatic potentials beyond its viewing scope. The model in COMSOL considers influence of all the surface potential values that were present in the grid. Let’s then modify the model, so at the point where the electrostatic potential is evaluated, only the surface potential values within the sensor scope are considered. For the 6 mm distance from the surface, according to Equation (1), the radius of the area seen by the probe should be 8.5 mm. The simulated potential value at 6 mm is then þ352 V. At the 10 mm distance the corresponding view radius is 12.5 mm, and the calculated potential is þ343 V. If, instead of using the fixed values of the potential at the given point seen by the sensor, the linearly interpolated potential distribution is used (again, within the sensing area), the modeled values of the potential become much closer to the potentials recorded by the non-contacting ESVM: 626 V for the 6 mm distance and 120 V for the 10 mm distance.
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A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
Fig. 6. Surface potential measurement results and corresponding COMSOL models. (a) Measurement at 6 mm. (b) Model at 6 mm. (c) Measurement at 10 mm. (d) Model at 10 mm.
5. Conclusion Comparison of the results the non-contacting and contacting measurements of the electrostatic potentials on the surface of the dielectric plane indicates that knowledge of the spatial resolution of the instruments used in experiment is very important. Very frequently the surface charge distribution is nonuniform, and investigation of such nonuniformity can become quite challenging. A contacting ESVM proves to be very useful in this case, providing potential readings from the very well defined area of contact. By using the Comsol modeling, authors tried to prove that direct
comparison of the mathematical models (finite element analysis, in this case) with measurement results obtained via non-contacting methods requires good knowledge of measurement principles (spatial resolution). References [1] L. Kelvin, Contact electricity of metals, Philos. Mag. 46 (1898) 82–120. [2] M.A. Noras, Ultra high impedance voltmeter for electrostatic applications, in: Proc. of 2005 IEEE-IAS Annual Meeting, 2005, pp. 2194–2197. [3] Low Level Measurements. Precision DC Current, Voltage and Resistance Measurements, Keithley, 1998.
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Verification of non-contacting surface electric potential measurement model using contacting electrostatic voltmeter Apra Pandey a,1, Jerzy Kieres a,1, Maciej A. Noras b, * a b
Trek, Inc., 11601 Maple Ridge Rd., Medina, NY 14103, USA Dept. of Engineering Technology, Univ. of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 28223, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 September 2008 Received in revised form 29 November 2008 Accepted 31 January 2009 Available online 15 February 2009
Measurements of surface charge and potential became very common in industrial applications and academic research. In this paper authors present use of a contacting ultra-high input impedance voltmeter in the areas where traditionally the non-contacting measurement methods were used. With very low input capacitance of the order of 1015 F, and very high input resistance of the order of tens of teraohms, there is practically no charge transfer from the measured object to or from the instrument. Experiment presented in this paper explains a correlation between the non-contacting and contacting measurement techniques using a finite element analysis model. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Surface charge measurements Input impedance Electrostatic voltmeter
1. Introduction The first non-contacting method of electrostatic field and potential measurement was developed at the end of 19th century by Lord Kelvin [1]. The Kelvin probe, and then the later developments of the rotating vane fieldmeter and the induction probe are well-known examples of non-contacting electrostatic measurement instruments. Lack of physical contact between the examined object and the sensor of the instrument assures that no charge is transferred. However, every time such non-contacting instrument is used, one of the most fundamental questions asked by the user is: what is the surface area that the instrument is looking at? What is the charge distribution in that area? Spatial resolution of noncontacting meters depends on the size of the sensor and the distance between the sensor and the object under test. A simplified method for the measured surface area calculation is presented in Fig. 1. In the case of a circular sensor with the diameter A at the distance H from the surface, assuming that the ‘‘view’’ angle equals 45 , the diameter of the circular surface measured by the sensor is:
D ¼ A þ 2$H:
(1)
* Corresponding author. E-mail addresses: [email protected] (A. Pandey), [email protected] (M.A. Noras). 1 Tel.: þ1 585 798 3140. 0304-3886/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2009.01.053
This purely empirical formula allows for quick assessment of either electrostatic potential, or electrostatic field, or surface charge only in case when the electric charge is distributed uniformly over the whole surface area under investigation. It works fine for the conducting surfaces, but becomes imprecise when dealing with semiconducting or dielectric objects. In this paper authors discuss influence of the charge nonuniformity on readings of a noncontacting voltmeter and compare them with measurement collected with the ultra-high impedance contacting voltmeter. Performance of the contacting instrument is also evaluated,
Fig. 1. The cantilever beam designed for an electrostatic voltmeter (ESVM), dimensions are in mm.
454
A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
Fig. 2. Driven shield technique [3].
including method used for the input resistance and input capacitance measurement. 2. Evaluation of the input impedance of the contacting electrostatic voltmeter (ESVM) Construction and details of operation of the contacting ESVM used in the experiments are described in one of the previous
publications [2]. Typical constructions of contacting instruments such as those developed by Keithley [3] use a guarding (shield) technique, where the electric potential of the shielding system is feedback-driven to that of the voltage sensor (Fig. 2). The measurement method is based on the concept of input bias current cancellation. The input bias current value is recorded and stored. Another circuit produces an output current equal in magnitude to the value of this bias current but opposite in polarity. This current is applied to the input of the amplifier to cancel the bias current [2]. Proper nullification of the input bias current of the pre-amplifier circuit along with independent bootstrapping of the amplifier power supply allows for increase of the input resistance to the range of 30 TU and lowering of the input capacitance to 5.3 fF with the electrostatic potential measurement range up to 2 kV. Fig. 3 presents a test setup used for the input resistance and capacitance evaluation. The capacitor used in the test was a 2.2 pF 0.5 pF COG (Electronics Industries Alliance specification for capacitor with the temperature coefficient of 0 ppm/ C, 30 ppm/ C) with two 5 mm diameter circle electrodes soldered to it. The value of the capacitance was confirmed with the Stanford Research Model SR 715 LCR meter (measurement accuracy 0.2%). To avoid the influence of the surrounding objects on the capacitance of the setup, a shielded box was used. The capacitor was charged to a pre-determined voltage level. Each time the voltmeter probe contacted the electrode of the capacitor, it was anticipated that a portion of electric charge will transfer between the probe and the electrode. The method used here was a slight modification of the technique described elsewhere [2]. The calculated input capacitance of the voltmeter was equal to 5.3 fF and the input resistance was 30 TU.
Fig. 3. Test setup for input resistance and capacitance measurement.
A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
455
Fig. 4. Surface potential measurement setup. (a) Non-contacting. (b) Contacting.
3. Surface charge evaluation using contacting and noncontacting ESVM The list of equipment used in the experiments consists of Trek Model 334 ESVM with the side-view probe (sensor 5 mm in diameter) and the prototype PR0623 contacting ESVM. For surface potential evaluation a simple setup shown in Fig. 4 was used. The 50 cm by 50 cm test plate was made of Lexan with average thickness of 5 mm, backed with an electrically grounded stainless steel plane. The Lexan plate was tribocharged by rubbing it with a cotton cloth and then the surface potential measurements were taken with the non-contacting voltmeter. Two probe to surface distances were selected: 10 and 6 mm. The potential was recorded at every point of the 48 mm by 48 mm grid with 8 mm increments in the X and Y direction. The test was repeated for exactly the same probe locations with the contacting ESVM probe. Fig. 5 presents the surface potential distribution as recorded by the contacting probe. Since the measurement points on the Lexan plate surface were
Electric potential at the surface 45
600
40
400
35
200
Y, mm
30
0
25
−200
20
−400
15
−600
10
−800
5 0
−1000 0
10
20
30
40
X, mm Fig. 5. Surface potential distribution measured with the contacting ESVM, data interpolated between the measurement points (8 mm 8 mm grid). The colorbar represents values of the electric potential in Volts.
separated, the values of the potential between the points were linearly interpolated. Fig. 6 presents comparison between measurements taken over the grid points with the non-contacting ESVM and computer simulation (carried out using COMSOL Multiphysics) of the potential distribution based on the values of the electric potential on the surface, as measured with the contacting ESVM.
4. Discussion While considering data presented in Fig. 6, it can be immediately noticed that, predictably, the distance between the noncontacting sensor and the Lexan plate affected the value recorded by the instrument. Let’s consider, for example, point with the highest positive potential on the plane. The value as measured by the contacting meter was þ864 V. The non-contacting meter recorded, at exactly the same location, þ636 V (6 mm) and þ128 V (10 mm). The FEA model predicts correspondingly þ26 V and 5 V. In order to explain this discrepancy we need to consider the superposition of all the fields and associated with them electric potential values, coming from the surface charges on the plane at a given location where the probe is. The noncontacting ESVM will, by its operation principle, produce that averaged potential on the probe body. However, it will take into consideration only the surface area that is ‘‘seen’’ by the sensor, neglecting the influence of the electrostatic potentials beyond its viewing scope. The model in COMSOL considers influence of all the surface potential values that were present in the grid. Let’s then modify the model, so at the point where the electrostatic potential is evaluated, only the surface potential values within the sensor scope are considered. For the 6 mm distance from the surface, according to Equation (1), the radius of the area seen by the probe should be 8.5 mm. The simulated potential value at 6 mm is then þ352 V. At the 10 mm distance the corresponding view radius is 12.5 mm, and the calculated potential is þ343 V. If, instead of using the fixed values of the potential at the given point seen by the sensor, the linearly interpolated potential distribution is used (again, within the sensing area), the modeled values of the potential become much closer to the potentials recorded by the non-contacting ESVM: 626 V for the 6 mm distance and 120 V for the 10 mm distance.
456
A. Pandey et al. / Journal of Electrostatics 67 (2009) 453–456
Fig. 6. Surface potential measurement results and corresponding COMSOL models. (a) Measurement at 6 mm. (b) Model at 6 mm. (c) Measurement at 10 mm. (d) Model at 10 mm.
5. Conclusion Comparison of the results the non-contacting and contacting measurements of the electrostatic potentials on the surface of the dielectric plane indicates that knowledge of the spatial resolution of the instruments used in experiment is very important. Very frequently the surface charge distribution is nonuniform, and investigation of such nonuniformity can become quite challenging. A contacting ESVM proves to be very useful in this case, providing potential readings from the very well defined area of contact. By using the Comsol modeling, authors tried to prove that direct
comparison of the mathematical models (finite element analysis, in this case) with measurement results obtained via non-contacting methods requires good knowledge of measurement principles (spatial resolution). References [1] L. Kelvin, Contact electricity of metals, Philos. Mag. 46 (1898) 82–120. [2] M.A. Noras, Ultra high impedance voltmeter for electrostatic applications, in: Proc. of 2005 IEEE-IAS Annual Meeting, 2005, pp. 2194–2197. [3] Low Level Measurements. Precision DC Current, Voltage and Resistance Measurements, Keithley, 1998.