Japanese Journal of Applied Physics
Vol. 46, No. 8B, 2007, pp. 5626–5630#2007 The Japan Society of Applied Physics

Kelvin Probe Force Microscopy without Bias-Voltage Feedback
Osamu T AKEUCHI, Yoshihisa O HRAI, Shoji Y OSHIDA, and Hidemi SHIGEKAWA
Institute of Applied Physics, CREST-JST, 21st Century COE, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan(Received January 30, 2007; revised May 16, 2007; accepted May 19, 2007; published online August 23, 2007)

A variation of Kelvin probe force microscopy that does not require bias-voltage feedback for contact potential diﬀerence(CPD) detection was proposed. Two independent lock-in ampliﬁers were used to measure the ﬁrst- and second-orderderivatives of the electrostatic force exerted on the cantilever, and CPD was deductively determined from these signals. The
application of this technique to the unsaturated Au/Si(111)-5  2 system conﬁrmed that the instability of the measurement
system resulting from bias-voltage feedback can be completely eliminated and that CPD measurement at a ﬁnite bias voltage
is possible. [DOI: 10.1143/JJAP.46.5626]
KEYWORDS: Kelvin probe force microscopy, atomic force microscopy

1.

derivative of the electrostatic energy Ees stored in thecapacitance with respect to the probe–sample distance z:

Introduction

Kelvin probe force microscopy (KFM)1,2) is known as oneof the most powerful measurement techniques for visualizing the nanometer-scale variation of a sample surface’s
electrostatic potential that is possibly modulated by localized
charges and dipole moments at the surface. KFM has been
applied to a variety of metal, semiconductor and organic
surfaces to study, for example, the photochemical reactions
on surfaces, next-generation data storage devices andprimitive electronic devices.3–8) KFM is based on themeasurement of the contact potential diﬀerence (CPD)
between the apex of the conductive cantilever probe of anoncontact atomic force microscopy (nc-AFM) system andthe local sample surface area under the probe. Since CPD isdeﬁned as the surface potential diﬀerence between two
objects, the CPD variation observed in KFM directly reﬂects
the spatial variation in the surface potential of the sample
surface relative to that of the probe apex. In conventional
KFM, CPD is obtained using a bias-voltage-feedback circuitthat nulliﬁes the electric ﬁeld between the probe and thesample. Thus, it fundamentally involves instability ofmeasurement system due to the possible oscillation of the
feedback loop. The instability must be prevented by having
the feedback gain low; then, however, the measurementtakes quite a long time. In order to eliminate the instability
fundamentally, in this study, we investigated a new setup for
KFM that does not involve bias-voltage feedback andclariﬁed its advantages and disadvantages with respect to theconventional method.
2.

KFM without Bias-Voltage Feedback

At ﬁrst, we will review the fundamentals of KFM. Whenthe conductive cantilever probe approaches the sample
surface, it experiences the interaction force F induced by the
sample surface. Generally, F is composed of the atomic
force Fatom and the electrostatic force Fes . The former is thesum of the van der Waals force and chemical bonding force,and the latter reﬂects CPD:
F ¼ Fatom þ Fes :ð1Þ

The electrostatic component originates from the charge thatis stored in the capacitance C formed between the probe andthe sample surface. The component can be expressed as theE-mail address: takeuchi@bk.tsukuba.ac.jp

Fes ¼

dEes
1 dC
ðVCPD  Vs Þ2 :
¼
2 dz
dz

ð2Þ

Here, VCPD is the contact potential diﬀerence and Vs is the
sample bias voltage. The frequency shift  f measured in ncAFM is approximately proportional to the derivative of theinteraction force with respect to z:
f /dF dFatom 1 d 2 C¼
ðVCPD  Vs Þ2 :
þ
dz
2 dz2
dz

ð3Þ

Here, it is assumed that VCPD is not a function of z. Note that
this condition might not occur on an insulating surface or asemiconductor surface with a low density of surface state
due to the leakage of the electric ﬁeld into the sample.9,10)
Equation (3) indicates that the total frequency shift as afunction of Vs is a parabolic function, which has theminimum at Vs ¼ VCPD , as illustrated in Fig. 1(a).
In a conventional KFM, the ﬁrst derivative of  f ðVs Þ isdetected by a lock-in ampliﬁer with sample-bias-voltage
modulation, as illustrated in Fig. 2(a). The obtained  f 0 ðVs Þ
is proportional to the diﬀerence between Vs and VCPD , asillustrated in Fig. 1(b): f 0 ðVs Þ /d2 C
ðVs  VCPD Þ:
dz2

ð4Þ

Negatively feeding back this value to the bias voltage with
an appropriate gain results in the automatic adjustment of Vs
to VCPD . Thus, recording the bias voltage, with the probe
scanned over the sample surface, enables the mapping ofCPD. Typical experimental conditions are a bias modulation
frequency of 1 kHz, a bias modulation amplitude of 1 V anda scan rate of 20 min/image. KFM often takes quite a longtime because one cannot have too large gain for the biasvoltage-feedback circuit to prevent the instability of themeasurement system owing to the oscillation of the feedback
circuit.
Here, we propose a new technique to determine CPD
without a bias-voltage-feedback circuit. Instead, anotherlock-in ampliﬁer is added to the system to measure thesecond harmonic component of the frequency shift, as
illustrated in Fig. 3. This signal gives the second-orderderivative of the frequency shift  f 00 ðVs Þ. Since the ﬁrst
derivative is a linear function, this value is constant against
the bias voltage, as illustrated in Fig. 1(c).

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O. T AKEUCHI et al.

(a)

(c)

(b)

Δf

Δf ''

Δf '

Δfatom
0

VCPD

Vs

Vs

VCPD

VCPD

Vs

Fig. 1. Bias voltage dependences of (a) primitive, (b) ﬁrst-, and (c) second-order derivatives of frequency shift in nc-AFM.

(a)

(b)

Fig. 2. Schematics of KFM systems: (a) conventional system with bias-voltage feedback, (b) proposed system without bias-voltage
feedback.

(c)

(b)

(a)

Fig. 3. Experimental bias voltage dependences of (a) frequency shift, (b) !-component from lock-in ampliﬁer, and (c) 2!-component
from lock-in ampliﬁer.

 f 00 ðVs Þ /d2 C¼ const:dz2

ð5Þ

Thus, if  f 0 and  f 00 are measured simultaneously at a
certain bias voltage, Vs0 , VCPD can be derived as
VCPD ¼ Vs0   f 0 ðVs0 Þ= f 00 ðVs0 Þ:

ð6Þ

Since this method does not involve the bias-voltage feedback, it is free from the instability due to such feedback. In
the next section, we demonstrate the characteristics of thistechnique using a well-known heteroepitaxy system of an
unsaturated Au/Si(111)-5  2 surface.

3.

Experimental Procedure

The experiment was performed with a commercial ultrahigh vacuum nc-AFM system (Omicron VT-STM/AFM)
whose base pressure was less than 1  108 Pa. The Si
substrate, mounted on a sample holder, was degassed for10 h before being ﬂash heated to 1200  C to remove theoxide layer. Then, the substrate was slowly cooled in orderto form a well-ordered Si(111)-7  7 structure. Golddeposition was performed using a tungsten ﬁlament at a
rate of 1 ML/min at a substrate temperature of 650  C. The
measurement was carried out at room temperature using a5627

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O. T AKEUCHI et al.

measurements at a frequency of 1 kHz, a small phase shift
and the attenuation of the signal owing to the ﬁnite
bandwidth is unavoidable. Thus, the calibration of the signal
is necessary to compensate for this eﬀect. We deﬁne thelock-in outputs for ! and 2! components as X! and X2! .
These signals are related to  f 0 and  f 00 as
X! ¼ A f 0 ðVs ÞVs ;X2! ¼ B f 00 ðVs ÞVs2 =2;

Fig. 4. Calculated CPD from experimental results in Fig. 3. The precisionof the measurement was determined to be 2 – 3 mV.

Ti–Pt-coated cantilever with a spring constant of 5.0 N/m
and a resonant frequency of 160 kHz (MikroMasch). The
amplitude and frequency of the bias-voltage modulation
were 1 Vrms and 1020 Hz, respectively. Unless otherwise
stated, the time constant for the two lock-in ampliﬁers(Stanford Research Systems SR830) was 10 ms with a slopeof 6 dB/oct. Outputs from the lock-in ampliﬁers wereconnected to the auxiliary inputs of the AFM electronics to
be stored. Then, the CPD image was numerically calculated
oﬀ-line using data analysis software (WaveMetrics Igor
Pro).
4.

Results and Discussion

At ﬁrst,  f ðVs Þ,  f 0 ðVs Þ, and  f 00 ðVs Þ curves were
measured for a Si(111)-7  7 surface to verify the validity of
the above discussion. For the curve measurements, theprobe–sample separation was determined with a sample bias
voltage of Vs ¼ 1:2 V, a sample bias modulation of 1 Vrms ,and a reference frequency shift of 61 Hz. Once these
conditions were achieved, the probe position was ﬁxed withthe z-piezo feedback disabled. Then, bias voltage was swept
from 1:2 to 0.5 V in 4.1 s. The result is shown in Fig. 3. As
seen, the curves are well described by the theoreticalprediction shown in Fig. 1. Sometimes, however, slightdeviations were observed owing to the small variation inprobe–sample distance during the curve measurement (datanot shown). Since such variations are due to the thermal driftof the system or the creep of the z-piezo device, once a stablecondition is achieved, no reproducible deviation wasnoticeable.
To examine the detection accuracy of the new procedure,
the CPD was calculated using eq. (6) and all the measured
points in the curves in Figs. 3(b) and 3(c). The result isplotted in Fig. 4 as the deviation from the zero-cross voltageof the  f 0 ðVs Þ curve. Even though  f exhibits relatively
large noise in this experiment, CPD was determined with a
precision of 2 – 3 mV, conﬁrming the eﬀectiveness of the
proposed technique. This precision can, of course, be
improved by using a larger time constant for lock-in
detection or, more desirably, by increasing the reference
frequency shift. Since increasing the reference frequency
shift increases  f 00 , the eﬀect of detection error in  f 0 and f 00 is reduced in eq. (6).
One point must be considered for the analysis. Althoughthe  f measurement bandwidth of the current state-of-theart nc-AFM systems is suﬃciently high for modulation

ð7Þ

where Vs is the modulation amplitude and A and B aremeasurement-system-dependent coeﬃcients that are slightly
smaller than unity. Note that A and B also diﬀer from eachother because the signal frequencies are diﬀerent. To
determine CPD using eq. (6), eq. (7) can be rewritten as 
 f 0 ðVs Þ
B Vs ðX! =X2! Þð8Þ
¼
00
 f ðVs ÞA
2
Thus, we need to determine the ratio B=A, which isdependent on the detector bandwidth of  f and themodulation frequency. This ratio can be obtained bymeasuring a set of X! ðVs Þ and X2! ðVs Þ curves at one placeon the sample as follows. The average slope of X! ðVs Þ gives
hdX! =dVs i ¼ Ah f 00 iVs ;ð9Þ

and the average of X2! ðVs Þ gives
hX2! i ¼ Bh f 00 iVs2 =2:ð10ÞHere, the brackets denote the average over the measured
voltage range. Thus, the ratio can be calculated asB
dX! 1 hX2! i
¼2
:
ð11Þ
A
Vs
dVs
In our experimental setup, this ratio was about 10% smaller
than unity, reﬂecting a slightly larger attenuation for the 2!
component. As long as metallic sample surfaces aremeasured, this ratio is independent of the physical systembeing measured; it is only dependent on the bandwidth of themeasurement system and the fundamental modulation
frequency. Thus, calibration is required only one time fora series of measurements. Finally, CPD can be obtained
from X! ðVs0 Þ and X2! ðVs0 Þ as

dX! 1
X! ðVs0 Þ
0
VCPD ¼ Vs 
hX2! i:
ð12Þ
X2! ðVs0 Þ
dVs
Next, the spatial variation of CPD was conﬁrmed with apartially covered Au/Si(111)-5  2 system. Figure 5 shows
the results. The measurement conditions were Vs ¼ 0:2 Vand  fref ¼ 60 Hz. As can be seen, the Au-covered areas
on the sample were imaged as clear depressions in the
topography and  f 0 images, and as convexes in the  f 00 and
CPD images. The measured diﬀerence in CPD between the
Au-covered and uncovered parts was always consistent withthose of previous reports.8) On the other hand, the contrasts
in the topography,  f 0 and  f 00 images were highly
dependent on bias voltage. The images in Fig. 6 were
measured using the same sample with the same probe butwith a diﬀerent bias voltage Vs ¼ 1:2 V. In this case, neither
the topography nor  f 00 images showed noticeable contrast( f 00 image not shown). This is because the observed heightdiﬀerence in the topography was almost completely due tothe Fes component of eq. (1). The structural corrugation of

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O. T AKEUCHI et al.

(a) Topo(b) Δf(c) Δf(d) CPD

Au
Si

Fig. 5. Images of unsaturated Au/Si(111)-5  2 surface taken using new
method: (a) topography, (b) !-component from lock-in ampliﬁer, (c) 2!component from lock-in ampliﬁer, and (d) CPD, at Vs ¼ 0:2 V, scan rateof 17 min/image, scan size of 300  300 nm2 , and 256 scan lines.

(a) Topo(b) CPD(c) Topo(d) CPD

Fig. 6. Images taken using new method at diﬀerent scan rates: (a), (b)topography and CPD images taken with scan rate of 13 min/image andlock-in time constant of 10 ms; and (c), (d) images taken with scan rate of
3 min/image and lock-in time constant of 1 ms. For both cases, the otherconditions were Vs ¼ 1:2 V, a scan size of 450  450 nm2 and 256 scanlines.

the surface was negligible. In such cases, when the sample
bias voltage is applied at the mid point between the CPD’s of
the Au-covered and uncovered domains, the probe feels
exactly same Fes in diﬀerent domains, although the polarityof the electric ﬁeld in diﬀerent domains is reversed. In
addition, since  f 00 is directly dependent on probe–sample
separation,  f 00 also appears ﬂat.

Strong electrostatic force can be observed when a ﬁnite
electric ﬁeld exists between the probe and the sample. Thisis also important in terms of the spatial resolution and thesensitivity of measurement. When the sample bias voltage ismarkedly diﬀerent from CPD, the probe feels a large
electrostatic force. Thus, the z-piezo feedback circuit
separates the probe from the surface to maintain thefrequency shift at the reference value. This causes thespatial resolution of the topography and CPD images tobecome poor. Furthermore, when the probe–sample separation becomes large,  f 0 becomes large and  f 00 becomes
small. As a result, a small error in  f 0 and  f 00 detection
largely aﬀect the determination of CPD using eq. (6).
Consequently, for a precise measurement, the sample bias
voltage should be as close to the average CPD in the imaging
area as possible. Note that this condition is also preferred ina normal nc-AFM measurement.
The images in Fig. 6 were taken at the bias voltage
optimized as described above. Note that the spatial resolutions are improved compared with those in Fig. 5. Now,
we will discuss the scanning speed and noise level in KFM.
Figures 6(a) and 6(b) show topography and CPD images
simultaneously taken at a rate of 13 min/image with a lockin time constant of 10 ms, and Figs. 6(c) and 6(d) show
topography and CPD images taken at a rate of 3 min/image
with a time constant of 1 ms. When scan rate is increased, abroader signal detection bandwidth is required to measure
the more quickly changing signals. From this point of view,at ﬁrst glance, the new KFM system seems superior to theconventional system, because when the same time constantis used for the lock-in ampliﬁers, the signal from the new
system responds four to ten times more quickly than thatfrom the conventional system. This is because, in theconventional system, the signal is further delayed owing to
the feedback circuit.
However, taking the signal-to-noise ratio into account, theconclusion becomes diﬀerent. When the signal bandwidth isfurther limited by the bias-voltage-feedback circuit in theconventional system, the noise power is also reduced by thislimited bandwidth. Thus, if a signal-to-noise ratio on thesame order is required in the new system, the lock-in time
constant must be selected to be longer. In other words,
unless the noise power in  f is extremely small, theeﬀective measurement bandwidth is not limited by theexperimental setup but rather by the required signal-to-noise
ratio. Consequently, the advantage of the new system is notthat it directly provides an improved scan rate. Instead, it isthat it provides an instability-free way of optimizing the scanrate in order to achieve the required signal-to-noise ratio. As
shown in Figs. 6(c) and 6(d), the new system is completely
stable even when the signal-to-noise ratio in the CPD image
is quite low. In such a case, the conventional system easily
becomes unstable and rams the probe into the sample
surface.
Another advantage of the new system is its ability toimage surface potential under a ﬁnite bias voltage. On
semiconductor and insulator surfaces, it is known that thesurface potential is often bias voltage dependent.9–11) The
details of the dependence contains useful information onmaterial properties, such as the dielectric constant, thedopant density and the carrier density. For such an

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O. T AKEUCHI et al.

application, however, the primary limitation is that, when
the surface potential changes with respect to bias voltage
modulation for KFM, the correct values for  f 0 and  f 00
cannot be obtained. The experimental conditions must be
carefully chosen to overcome this problem.
5.

Conclusions

In summary, a new measurement technique for KFM wasproposed and its validity was conﬁrmed by its application to
the unsaturated Au/Si(111)-5  2 system. The new technique replaces the bias-voltage-feedback circuit of theconventional KFM system with a second lock-in ampliﬁer.
As a result, the instability of the bias-voltage-feedback loop
was completely eliminated. Since the new method canmeasure the contact potential diﬀerence under a ﬁnite bias
voltage between the probe and the sample, its futureapplication to semiconductor or insulating samples issuggested.
Acknowledgement
This work was supported in part by a Grant-in-Aid for

Scientiﬁc Research from the Ministry of Education, Culture,
Sports, Science, and Technology of Japan.

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