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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
nondestructive 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.
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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
nondestructive 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.
 (check this in PDF content)

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Due to
nondestructive 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.
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Therefore an effect of stray capacitance between
probe and otherthansample 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.
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Therefore an effect of stray capacitance between
probe and otherthansample 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
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[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.
 (check this in PDF content)

 Start

2409
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Therefore an effect of stray capacitance between
probe and otherthansample 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
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[5]
 Suffix

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.
 (check this in PDF content)

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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 parallelplate 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.
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At the same time real Kelvin probe configuration in most cases is closer to parallelplate capacitor [2] therefore obtained results are
of limited applicability in most practical cases. Due
to complexity of mathematical model developed in
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[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.
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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
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[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.
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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.
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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 probetosample 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.
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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 probetosample gap d0 should be
less then lateral dimensions of the probe
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[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.
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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 lownoise preamplifier of
input signal.
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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.
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11941
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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
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[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.
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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
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