- 1
- Noras M.A. Charge Detection Methods for Dielectrics – Overview. Available at: http:// www.trek.com. (accessed 18.03.2012).

Total in-text references: 3- In-text reference with the coordinate start=1181
- Prefix
- Keywords: contact potential difference, Kelvin probe, compensating technique, dynamic response, measurement uncertainty. Introduction The most common method of contact potential difference (CPD) measurements
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- [1]
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- is Kelvin– Zisman technique which implements vibrating capacitor probe (also called Kelvin probe) [2]. Due to non-destructive character and extreme sensitivity to any changes in surface properties CPD measurements can be used to characterize precision surfaces of semiconductor wafers, sensor structures, micromechanics etc.

- In-text reference with the coordinate start=3714
- Prefix
- Main methods used are mathematical and computer modeling with respect to the vibrating Kelvin probe’s output signal model developed in a previous study [6]. The study is focused on compensation scheme of CPD measurements as the most common case in measurement practice
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- [1]
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- . Experimental Classic Kelvin probe can be described as a dynamic (vibrating) capacitor where one plate (sample surface) is immovable whereas other (probe’s sensor) vibrates in the direction orthogonal to the sample surface.

- In-text reference with the coordinate start=5092
- Prefix
- The mount is not vibrating, so the mount to sample distance d is constant and: d0 + d1 = d. (2) Actual CPD between sample and probe’s tip is U0. U1 is parasitic CPD between probe’s tip and mount. This parasitic CPD exists because of differrence in work function between probe and mount materials
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- [1]
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- and could not be eliminated. To improve spatial resolution of the scanning Kelvin probe the probe-to-sample gap d0 should be less then lateral dimensions of the probe [7] so combination of probe and sample can be treated as parallel plate capacitor with one vibrating plate.

- In-text reference with the coordinate start=1181
- 2
- Taylor D.M. Measuring techniques for electrostatics. Journal of Electrostatics, 2001, no. 52, pp. 502–508.

Total in-text references: 2- In-text reference with the coordinate start=1295
- Prefix
- Introduction The most common method of contact potential difference (CPD) measurements [1] is Kelvin– Zisman technique which implements vibrating capacitor probe (also called Kelvin probe)
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- [2]
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- . Due to non-destructive character and extreme sensitivity to any changes in surface properties CPD measurements can be used to characterize precision surfaces of semiconductor wafers, sensor structures, micromechanics etc.

- In-text reference with the coordinate start=2777
- Prefix
- The geometry of Kelvin probe’s sensing plate was thought to be hemispherical allowing author to treat the electric charge of a plate as point charge. At the same time real Kelvin probe configuration in most cases is closer to parallel-plate capacitor
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- [2]
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- therefore obtained results are of limited applicability in most practical cases. Due to complexity of mathematical model developed in [5], A. Hadjadj then used mostly empirical approach for calculation of measurement errors based on introduction of experimentally determined coefficients.

- In-text reference with the coordinate start=1295
- 3
- Zharin A. L. Contact Potential Difference Techniques as Probing Tools in Tribology and Surface Mapping, in book: Scanning Probe Microscopy in Nanoscience and Nanotechnology (edited by B. Bhushan), Springer Heidelberg Dordrecht London New York, 2010, pp. 687–720.

Total in-text references: 1- In-text reference with the coordinate start=1658
- Prefix
- Due to non-destructive character and extreme sensitivity to any changes in surface properties CPD measurements can be used to characterize precision surfaces of semiconductor wafers, sensor structures, micromechanics etc. A method can be used to reveal stressed areas, chemical impurities, dislocation sites and other surface defects
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- [3]
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- including that of submicron scale. At the same time, high sensitivity to the factors mentioned means that Kelvin probe is sensitive to any surface adjacent to the probe, e.g. constructive parts of the measurement installation made of metal.

- In-text reference with the coordinate start=1658
- 4
- Baikie I.D., Mackenzie S., Estrup P.J.Z., Meyer J.A. Noise and the Kelvin method Rev. Sci. Instrum, 1991, vol. 62, no. 5, pp. 1326–1332.

Total in-text references: 2- In-text reference with the coordinate start=2358
- Prefix
- Therefore an effect of stray capacitance between probe and other-than-sample metal surfaces must be taken into consideration and analyzed thoroughly. An influence of stray capacitance on Kelvin probe’s input was studied by D. Baikie
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- [4]
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- and A. Hadjadj [5] but obtained results were mostly of empirical character. A. Hadjadj [5] used both theoretical and experimental methods. The geometry of Kelvin probe’s sensing plate was thought to be hemispherical allowing author to treat the electric charge of a plate as point charge.

- In-text reference with the coordinate start=13303
- Prefix
- Under such conditions a mean value of stray signal is calculated to be about 1,5 mV or 0,8 % of stray CPD voltage with amplitude of oscillation about 0,6 mV. This result is in a good agreement with D. Baikie
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- [4]
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- and A. Hadjadj [5] empirical conclusions stating that stray CPD reduction factor approximately equals to the relation of str ay and measurement vibrating capacitors gaps d1/d0. Modeling also demonstrated that grows of the reduction factor with rising the ratio d1/d0 is not linear: whereas d1/d0 is growing twice, the reduction factor grows for almost 20 dB. 01×

- In-text reference with the coordinate start=2358
- 5
- Hadjadj A., Rota i Cabarrocas P., Equer B. Analytical compensation of stray capacitance effect in Kelvin probe measurements. Rev. Sci. Instrum., 1995, vol. 66, no. 11, pp. 5272–5276.

Total in-text references: 5- In-text reference with the coordinate start=2379
- Prefix
- Therefore an effect of stray capacitance between probe and other-than-sample metal surfaces must be taken into consideration and analyzed thoroughly. An influence of stray capacitance on Kelvin probe’s input was studied by D. Baikie [4] and A. Hadjadj
- Exact
- [5]
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- but obtained results were mostly of empirical character. A. Hadjadj [5] used both theoretical and experimental methods. The geometry of Kelvin probe’s sensing plate was thought to be hemispherical allowing author to treat the electric charge of a plate as point charge.

- In-text reference with the coordinate start=2457
- Prefix
- Therefore an effect of stray capacitance between probe and other-than-sample metal surfaces must be taken into consideration and analyzed thoroughly. An influence of stray capacitance on Kelvin probe’s input was studied by D. Baikie [4] and A. Hadjadj [5] but obtained results were mostly of empirical character. A. Hadjadj
- Exact
- [5]
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- used both theoretical and experimental methods. The geometry of Kelvin probe’s sensing plate was thought to be hemispherical allowing author to treat the electric charge of a plate as point charge.

- In-text reference with the coordinate start=2928
- Prefix
- At the same time real Kelvin probe configuration in most cases is closer to parallel-plate capacitor [2] therefore obtained results are of limited applicability in most practical cases. Due to complexity of mathematical model developed in
- Exact
- [5]
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- , A. Hadjadj then used mostly empirical approach for calculation of measurement errors based on introduction of experimentally determined coefficients. These coefficients could be determined only on real probe, so the proposed model cannot be used in theoretical development of Kelvin probe design.

- In-text reference with the coordinate start=13326
- Prefix
- Under such conditions a mean value of stray signal is calculated to be about 1,5 mV or 0,8 % of stray CPD voltage with amplitude of oscillation about 0,6 mV. This result is in a good agreement with D. Baikie [4] and A. Hadjadj
- Exact
- [5]
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- empirical conclusions stating that stray CPD reduction factor approximately equals to the relation of str ay and measurement vibrating capacitors gaps d1/d0. Modeling also demonstrated that grows of the reduction factor with rising the ratio d1/d0 is not linear: whereas d1/d0 is growing twice, the reduction factor grows for almost 20 dB. 01×10-32×10-33×10-3 t, sec

- In-text reference with the coordinate start=14895
- Prefix
- The dependence is not linear: for d0/d1 = 1:20 stray CPD reduction factor is about 40 dB whereas for d0/d1 = 1:50 it reaches 60 dB. Similar results were obtained in experiments made by A. Hadjadj
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- [5]
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- . 2. Amplitude of AC component of a stray signal is one order of its mean value. Amplitude parameters of stray signal does not depend on vibration frequency of Kelvin probe. A numerical solution of stray signal mathematical model produces complex harmonic function with components in degrees 0, 1, 2 and –1 indicating the existence of lower and higher harmonics in

- In-text reference with the coordinate start=2379
- 6
- Tyavlovsky A.K., Gusev O.K., Zharin A.L. [Metrological performance modeling of probe electrometers capacitive sensors]. Devices and methods of measurement, 2011, no. 1, pp. 122–127 (in Russian).

Total in-text references: 1- In-text reference with the coordinate start=3589
- Prefix
- Present paper is devoted to the analytical study of stray capacitance and parasitic CPD effects and their influence on Kelvin probe’s performance and output signal. Main methods used are mathematical and computer modeling with respect to the vibrating Kelvin probe’s output signal model developed in a previous study
- Exact
- [6]
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- . The study is focused on compensation scheme of CPD measurements as the most common case in measurement practice [1]. Experimental Classic Kelvin probe can be described as a dynamic (vibrating) capacitor where one plate (sample surface) is immovable whereas other (probe’s sensor) vibrates in the direction orthogonal to the sample surface.

- In-text reference with the coordinate start=3589
- 7
- Tyavlovsky A.K. [Mathematical modeling of a distance dependence of a scanning Kelvin probe lateral resolution]. Devices and methods of measurement, 2012, no. 1, pp. 30–36 (in Russian). _____________________________________________________________

Total in-text references: 2- In-text reference with the coordinate start=5275
- Prefix
- This parasitic CPD exists because of differrence in work function between probe and mount materials [1] and could not be eliminated. To improve spatial resolution of the scanning Kelvin probe the probe-to-sample gap d0 should be less then lateral dimensions of the probe
- Exact
- [7]
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- so combination of probe and sample can be treated as parallel plate capacitor with one vibrating plate. The system including sample, probe and mount can be described as differential capacitor with static peripheral plates and vibrating central plate.

- In-text reference with the coordinate start=8780
- Prefix
- It must be noted, however, that the relation of the second harmonics of measurement and stray signal is much higher than the relation of their first harmonics due to differrence in modulation factors
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- [7]
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- . It means that rejecting of the first harmonic with measurements on the second harmonic of a signal could provide higher SNR value while using the low-noise preamplifier of input signal.

- In-text reference with the coordinate start=5275