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Pump-probe Kelvin-probe force microscopy: Principle of operation and resolution
limits
J. Murawski, T. Graupner, P. Milde, R. Raupach, U. Zerweck-Trogisch, and L. M. Eng
Citation: Journal of Applied Physics 118, 154302 (2015); doi: 10.1063/1.4933289
View online: http://dx.doi.org/10.1063/1.4933289
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/118/15?ver=pdfcov
Published by the AIP Publishing
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Pump-probe Kelvin-probe force microscopy: Principle of operation
and resolution limits
J. Murawski, T. Graupner, P. Milde,
a)
R. Raupach, U. Zerweck-Trogisch,
b)
and L. M. Eng
Institute of Applied Physics, Technische Universit€
at Dresden, D-01062 Dresden, Germany
(Received 6 July 2015; accepted 3 October 2015; published online 15 October 2015)
Knowledge on surface potential dynamics is crucial for understanding the performance of modern-
type nanoscale devices. We describe an electrical pump-probe approach in Kelvin-probe force
microscopy that enables a quantitative measurement of dynamic surface potentials at nanosecond-
time and nanometer-length scales. Also, we investigate the performance of pump-probe Kelvin-
probe force microscopy with respect to the relevant experimental parameters. We exemplify a
measurement on an organic field effect transistor that verifies the undisturbed functionality of our
pump-probe approach in terms of simultaneous and quantitative mapping of topographic and elec-
tronic information at a high lateral and temporal resolution. V
C2015 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4933289]
I. INTRODUCTION
Kelvin-probe force microscopy (KPFM) has proven a
reliable tool for measuring local contact potential differences
(CPDs) on the nanometer length scale.
1–3
Despite numerous
advances since its first appearance,
4,5
the quantitative investi-
gation of dynamic CPDs with KPFM at the nanosecond-time
scale remains a challenge. Yet, knowing the temporal devel-
opment of surface potentials is crucial for understanding the
underlying electrodynamics in nanoscale structures, such as
the switching behavior of nanodevices or integrated circuits.
Nunes et al. were the first to introduce a junction-mixing
scanning tunneling microscope (STM) enabling time-resolved
tunneling current measurements down to the picosecond-time
regime.
6,7
At the same time, Bridges et al. started to comple-
ment electrostatic force microscopy with a heterodyne nullify-
ing technique in order to resolve digital voltage signals in
bit-lines close to the Gbit/s data rate with sub-nanosecond pre-
cision.
8,9
This approach already enabled quantitative electro-
dynamic investigations at the sub-nanosecond-time scale with
an atomic force microscope (AFM). A decade later Coffey
and Ginger coined the term time-resolved electrostatic force
microscopy by evaluating the frequency shift of an oscillating
tip upon externally induced stimuli in the scanning condi-
tion.
10
With this method, they obtained both spatial and tem-
poral information and were able to record decay rates in the
millisecond-time regime. More recent works include quantita-
tive CPD measurements recorded from organic or ferroelectric
thin films using standard KPFM setups.
11–13
Here, the band-
width of the control loop allows for a temporal resolution in
the millisecond range.
In this work, we describe the modification of a
frequency-modulated KPFM (FM-KPFM) setup. As in the
early junction-mixing approaches, we take advantage of the
non-linear electric force interaction between tip and sample,
which is independent of the cantilever dynamics and the
control electronics’ bandwidth.
6–9
We establish a pump-
probe scheme by switching the low-frequency modulation
voltage Vmod synchronously to pump pulses that cause a tem-
poral change of the local CPD. Here, we demonstrate that
pump-probe Kelvin-probe force microscopy (pp-KPFM) pre-
serves the full functionality of standard FM-KPFM, i.e., a
high spatial resolution and undisturbed sample topography
measurements, while additionally providing the desired tem-
poral resolution needed for the quantitative investigation of
surface-bound periodic processes.
In Section II, we give an introduction into the physics of
pp-KPFM. The technical realisation is then introduced in
Section III. Finally, the experimental parameter space and re-
solution limits are discussed in great detail in Sections IV
and V, respectively.
II. THE PHYSICS OF PUMP-PROBE KELVIN PROBE
FORCE MICROSCOPY
Kelvin-probe force microscopy is based on minimizing
the electric force caused by the local contact potential differ-
ence VCPD between tip and sample. Minimization is achieved
by applying a compensation voltage Vdc to the tip, equaling
VCPD. Usually, the temporal behavior of VCPD(t) is of less
importance, hence nullifying the mean value
VCPD within
10–100 ms is sufficient. In order to enhance the detection
sensitivity, the electric force is modulated by a sinusoidal
voltage VmodðtÞ¼vmod sinðxmod tÞat frequency xmod. These
three voltages cause a total electric force Fel between tip and
sample that equals
3,14
Fel ~
r;t
ðÞ
¼1
2
@C~
r
ðÞ
@zVdc þVCPD ~
r
ðÞ
þVmod t
ðÞ
2;(1)
where Cdenotes the tip-sample capacitance, and zis the tip-
sample distance. For KPFM, only the term at frequency
xmod is relevant
Fxmod
el ~
r;t
ðÞ
¼@C~
r
ðÞ
@zVdc þVCPD ~
r
ðÞ
Vmod t
ðÞ
:(2)
a)
Electronic mail: peter.milde@tu-dresden.de.
b)
Also at Institut f€
ur Luft- und K€
altetechnik, Bertolt-Brecht-Allee 20,
D-01309 Dresden, Germany.
0021-8979/2015/118(15)/154302/8/$30.00 V
C2015 AIP Publishing LLC118, 154302-1
JOURNAL OF APPLIED PHYSICS 118, 154302 (2015)
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The modulated force Fxmod
el becomes zero either when
the compensation voltage matches the contact potential
difference (Vdc ¼VCPD—constituting the standard way of
operating KPFM) or whenever the modulation voltage itself
becomes zero (Vmod ¼0). For pp-KPFM, we employ the lat-
ter case by multiplying the modulation voltage Vmod with the
function
Pðxreptþudel Þ
¼1udel xrept2pkudel þus;k2Z
0 else;
((3)
where xrep is the repetition rate of the resulting electric
pulses, us¼xrep sis the pulse phase-width of pulse width
s, and udel ¼xrep tdel is the phase-offset of the pulses at the
time delay tdel relative to the beginning of the repetition
period Trep. Hence, we generate probe pulses within a sinu-
soidal envelope, as shown in Fig. 1(a).
Due to this pulse-amplitude modulation, we excite our
investigated system electrically only in the on-time window
Trep kþtdel tTrep kþtdel þs;k2Z, and only sys-
tem responses that fall into this on-time window remain de-
tectable. Furthermore, when we synchronize the repetition
frequency xrep to a periodic pump signal [as schematically
shown in Fig. 1(c)], the time-sensitive pp-KPFM not only
detects the static CPD
VCPD but also is equally able to moni-
tor the time-dependent system response ~
VCPD convolved
with the probe pulse P.
In order to quantify the time-dependent CPD ~
VCPD,the
electric force between tip and sample Fel needs to be mini-
mized in the above-stated time window. Conveniently, this
force leads to a modulation of the AFM’s cantilever reso-
nance frequency which manifests as a sideband of the canti-
lever oscillation signal at frequencies x06xmod, as shown
in the inset of Fig. 1(b). Demodulating the sideband signal
by a lock-in amplifier (LIA) renders the following error
signal X:
X/vmodfg½Vdc þ
VCPDð~
rÞ þ ½ ~
VCPDð~
r;tÞPðudelÞg ;(4)
where vmod denotes the amplitude of the modulation voltage,
g¼s=Trep is the duty cycle of the function P, and
½~
VCPDð~
r;tÞPðudelÞstands for the convolution of the time-
dependent potential ~
VCPD with the probe pulse function Pat
a specific phase offset udel
~
VCPD ~
r;t
ðÞ
P
udel
ðÞ
¼1
Trep ðt0þTrep
t0
~
VCPD ~
r;xrept
Pxreptþudel
ðÞ
dt:(5)
Finally, a Kelvin control loop nullifies the detected error
signal Xby applying the compensation voltage
Vdc ~
r;udel
ðÞ
¼
VCPD ~
r
ðÞ
þ1
g
~
VCPD ~
r;t
ðÞ
P
udel
ðÞ
:(6)
This way, besides the time-independent contact potential dif-
ference
VCPDð~
rÞalso the time-dependent CPD ~
VCPDð~
r;tÞis
accessible. The temporal resolution is determined by the
convolution term in Eq. (5) and is, therefore, limited to the
pulse width s. A schematic of the here-described pp-KPFM
set-up is shown in Fig. 1(b).
For very small duty cycles g, Eq. (6) can be approxi-
mated by a Taylor series as
Vdcð~
r;udelÞ¼½
VCPDð~
rÞþ ~
VCPDð~
r;udelÞ
¼VCPDð~
r;udelÞ:(7)
FIG. 1. (a) Schematic of the pump-probe scheme. Probe pulses with a sinusoidal envelope (yellow dashed line) are synchronized to a square wave pump signal
(green solid line). The zoom-in shows a single repetition cycle Trep. (b) Sketch of the signal path in the pp-KPFM set-up. The modulation voltage is mixed
with the square wave signal P. The resulting probe signal enables time-resolved surface potential measurements. Both the probe signal as well as the control
voltage of the pp-KPFM loop are summed up and applied to the tip. The spectrum of the resulting cantilever motion is shown in the inset on the top left. (c)
Schematic of the tip-sample system used for all characterization measurements. The red cross on the sample indicates that the position of the tip was kept fixed
during these experiments.
154302-2 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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III. DUAL CONTROL LOOP pp-KPFM
According to Eq. (7), our pump-probe approach enables
the Kelvin control loop to match and detect the time-
dependent potential ~
VCPDð~
r;tÞwithin the mentioned on-time
window Trep kþtdel tTrep kþtdel þs;k2Z. The
compensation voltage Vdc, however, is applied continuously
throughout the whole repetition period Trep. This implies that
although the potential is compensated correctly within the
on-time window, the time-averaged potential ^
VCPDð~
rÞmay
significantly deviate from the time-resolved value at udel ,
thus inducing cross-talk from the pp-KPFM compensation
voltage Vdc onto the measured topography.
Fig. 2depicts this effect. A square-wave voltage is
applied to a gold sample at a frequency of xrep ¼32 kHz,
while the phase delay udel of the probe pulse is steadily
increased, as outlined in Fig. 1(a). In this pp-KPFM point-
measurement, the tip stays at one point above the sample and
is not scanned (see Fig. 1(c)). The measured height appears
to be smallest and least disturbed when the delay reaches the
slopes of the square-wave voltage where the time-averaged
CPD ^
VCPD coincides with the time-resolved CPD ~
VCPD and
is, therefore, exactly compensated: Vdc ¼~
VCPD ¼^
VCPD.
At all other phase delays, the measured height appears
falsely larger due to an additional electric force arising from
the mismatch of applied compensation voltage Vdc and time-
averaged CPD ^
VCPD.
In order to minimize the induced topographic artefacts,
we employ a second control loop in parallel to the time-
resolved control loop, as schematically depicted in Fig. 3.
This second standard KPFM control loop compensates
solely the time-averaged potential ^
VCPDð~
rÞand, hence, mini-
mizes any time-averaged electric force that might adversely
affect the topography measurement. The first control loop in
turn remains sensitive to any time-dependent signal and
applies its compensation voltage only within the desired on-
time windows defined by the function P. The dual control
loop approach thus minimizes the overall topography error
while preserving time-resolved CPD measurements.
Notably, the two KPFM control loops need to operate at
their own and independent modulation frequency, which we
set to xavg for the time-averaging Kelvin control loop.
Furthermore, we denote the two modulation amplitudes with
vmod and vavg. Also the compensation voltage splits into the
two terms ~
Vdc and ^
Vdc, stemming from the time-sensitive
and the time-averaging control loop, respectively.
Note that only the modulation voltage Vmod and the
time-dependent compensation voltage ~
Vdc are pulse-
FIG. 2. Topographic height zas a function of the phase delay udel
¼xdel tdel of the probe pulse at the slope of the square wave pump signal
(green dashed line). The probe pulse width is represented by the tanned rec-
tangle in the background. When using a single control loop for pp-KPFM
(blue solid line), the minimal height occurs at the slope of the pump signal,
since the average electrostatic force is minimized only at this phase delay.
With the dual control loop pp-KPFM (purple dashed-dotted line), the correct
height value is always measured regardless of the phase delay.
FIG. 3. Sketch of the signal path in the
dual control loop pp-KPFM set-up.
The output of the time-sensitive pp-
KPFM loop, i.e., the sum of modula-
tion and control voltage, is mixed with
the square-wave signal P. The result-
ing probe signal enables time-resolved
surface potential measurements. A sec-
ond Kelvin control loop with Kelvin
modulation frequency xavg is used in
order to minimize the average electro-
static force. Both the probe signal as
well as the output of the second Kelvin
loop are summed up and applied to the
tip. The spectrum of the resulting can-
tilever motion is shown in the inset on
the top left.
154302-3 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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amplitude-modulated, while the modulation voltage Vavg of
the second, time-averaging control-loop as well as its com-
pensation voltage ^
Vdc keep their integrity. In total, the volt-
age applied to the tip reads as Vtip ¼ð~
Vdc þVmodÞP
þ
Vdc þVavg, as illustrated in Fig. 3.
This dual-loop approach results in two distinct error sig-
nals Xmod and Xavg at their respective frequencies xmod and
xavg, as indicated by the inset in Fig. 3
Xmod /gf~
Vdc þ^
Vdc þ
VCPDð~
rÞg þ ½ ~
VCPDð~
r;tÞPðudelÞ;
(8)
Xavg /g
~
Vdc þ^
Vdc þ
VCPDð~
rÞþ ^
VCPD:(9)
In analogy to our previous considerations, these two
error signals are nullified when each control loop applies its
respective compensation voltage ~
Vdc or ^
Vdc
~
Vdc ~
r;udel
ðÞ
¼ ^
Vdc ~
r
ðÞ
þ
VCPD ~
r
ðÞ
þ1
g
~
VCPD ~
r;t
ðÞ
P
udel
ðÞ
;
(10)
^
Vdcð~
r;udelÞ¼½g
~
Vdcð~
r;udelÞþ
VCPDð~
rÞþ ^
VCPDð~
rÞ :
(11)
For small duty cycles, the convolution term in Eq. (10) again
can be approximated by a Taylor series. Rearranging Eqs.
(10) and (11), we find
~
Vdc ~
r;udel
ðÞ
¼ 1
1g
~
VCPD ~
r;udel
ðÞ
^
VCPD ~
r
ðÞ
;(12)
^
Vdc ~
r;udel
ðÞ
¼
VCPD ~
r
ðÞ
þ1
1g
^
VCPD ~
r
ðÞ
g
1g
~
VCPD ~
r;udel
ðÞ
:(13)
Since both ~
Vdc and ^
Vdc compensate more than the time-
dependent or the time-averaged CPD only, we further com-
pute from Equations (12) and (13) the time-averaged CPD
^
V
dcð~
rÞ¼ ^
Vdcð~
r;udelÞþg
~
Vdcð~
r;udelÞ
¼½
VCPDð~
rÞþ ^
VCPDð~
rÞ ;(14)
as well as the time-resolved CPD
~
V
dcð~
r;udelÞ¼ ^
Vdcð~
rÞþ ~
Vdcð~
r;udelÞ
¼½
VCPDð~
rÞþ ~
VCPDð~
r;udelÞ
¼VCPDð~
r;udelÞ:(15)
The purple dashed-dotted line in Fig. 2illustrates a
point-measurement similar to the previous one, this time
recorded with the dual control loop pp-KPFM setup. As
shown, no cross-talk between electric signal and measured
height is discernible over the whole period.
To exemplify the cross-talk between the two control
loops, we used the same sample and applied a square-wave
voltage as in the previous experiments with the exception
that the repetition frequency was chosen to xrep ¼20 MHz.
Fig. 4(a) depicts the data as recorded by the two control
loops. As shown, the time-dependent signal is centered
around 0 V in accordance to Eq. (12). Furthermore, there
is a distinct cross-talk from the time-dependent CPD
visible in the time-averaged signal. Finally, the undisturbed
time-resolved CPD has been retrieved by computation after
Eq. (15).
IV. EXPERIMENTAL PARAMETER SPACE
A. Duty cycle and modulation voltage amplitude
Eq. (6) predicts the contact potential Vdcðudel Þto be
strongly dependent on the duty cycle g. This behavior was
calculated after Eq. (6) in Fig. 5(a) for the measurable con-
trast DV=Vrep of a square waveform of 50% duty cycle and
amplitude Vrep. In order to verify this prediction, we applied
FIG. 4. Measurement of a 20 MHz square-wave signal with an amplitude of
2 V using a 4 ns-wide pulse with 1 V amplitude as mixing function P. (a)
Overview over the compensation voltages of the time-sensitive control loop
~
Vdc (blue dashed-dotted line), the time-averaging control loop ^
Vdc (purple
dashed line), and the detected time-dependent surface potential ~
VCPD (or-
ange solid line) as a function of the delay time tdel .~
Vdc is partly visible in
^
Vdc, while ~
Vdc itself is shifted by ^
VCPD compared to ~
VCPD.~
VCPD itself is cal-
culated after Equation (15). (b) Oscilloscope measurement of the pump
square-wave signal (green dashed-dotted line) and of the probe pulse signal
P(yellow dashed line). The orange solid line displays the pp-KPFM
measurement.
154302-4 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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a square-wave voltage with repetition frequency xrep
¼100 kHz and amplitude Vrep ¼0:5 V to a highly p-doped
silicon sample for different duty cycles gand mapped the as-
deduced waveform by varying the phase delay udel in our
pp-KPFM set-up over a full repetition period Trep. For this
experiment, the tip stayed stationary at one point above the
sample. From the measured Vdcðudel Þ, we located the upper
and lower voltage plateau as well as their difference, which
reveals the contrast DV=Vrep.
Fig. 5(a) plots the resulting voltage contrast DV=Vrep as
a function of duty cycle g. Generally, measurement and
theory match excellently, especially with respect to the con-
trast loss at higher duty cycles. Surprisingly, for very small
duty cycles, a logarithmic decrease reduces the measured
contrast. This observation was reproduced on different sam-
ples with different measurement parameters, and also using
different setups. Although the origin of this deviation is not
entirely understood, it is reasonable to assume that the side-
band amplitude drops below the noise level for small duty
cycles, making stable pp-KPFM operation at a useful band-
width impossible.
The severe reduction in error signal magnitude is indi-
cated in Fig. 5(b), where the output voltage Xof the time-
sensitive LIA is shown as a function of the compensation
voltage Vdc for different duty cycles g. For decreasing duty
cycles, the sensitivity @X
@Vdc reduces linearly with gfollowing
the prediction of Eq. (4).
Since the error signal Xin Eq. (4) depends also on the
modulation voltage amplitude vmod, we repeated the previous
experiment varying vmod only. The inset of Fig. 5(a) depicts
the resulting signal contrast DV=Vrep as a function of duty
cycle gfor various modulation voltage amplitudes vmod.As
already mentioned, the signal contrast declines logarithmi-
cally for small duty cycles. Yet, larger modulation ampli-
tudes vmod seem to shift the onset of the decline towards
smaller duty cycles, supporting the above-stated assumption
that an insufficiently low error signal Xmight be causing the
decline.
Hence, our data suggest to employ larger modulation
voltage amplitudes vmod at small duty cycles g. Yet, the mod-
ulation voltage amplitude should be chosen carefully and
accordingly to the investigated system, for increasing the
amplitude can simultaneously enhance parasitic electric
interactions between tip and sample.
15
Finally, we face a trade-off between high temporal reso-
lution, i.e., small duty cycles g, and a sufficiently large error
signal Xin the experiment. We thus recommend to keep the
duty cycle above 0.1% in order to mitigate contrast loss to
less than 3 dB. Moreover, we also advise to adjust the repe-
tition frequency xrep in accordance to the desired temporal
resolution sin order to sustain a reasonable error signal am-
plitude X.
B. Repetition frequency
In theory, there are no limits with respect to the repeti-
tion frequency xrep. Experimentally, the repetition frequency
and any resonance frequency of the KPFM setup should be
incommensurate, especially with respect to the tip resonance
x
0
and the modulation frequencies xmod and xavg.
To exemplify the broad frequency range that is accessi-
ble via pp-KPFM, we repeated the former experiment for
different signal frequencies ranging from 10 Hz <xrep
<1 MHz. As expected, the full signal contrast is obtained
for all frequencies xrep, as evident from Fig. 6. However, as
indicated by the insets, measurements at low signal frequen-
cies may misrepresent the applied square-wave signal and,
hence, increase measurement errors. This stems from various
system resonances of the setup at these frequencies cross-
talking into the measured signal, as well as from the similar-
ity of signal and modulation frequency. At duty cycles above
g¼5%, correct and stable pp-KPFM measurements over the
entire repetition frequency range are possible with the upper
frequency limit given only by the signal generator in use.
C. Temporal resolution limit
The ultimate temporal resolution of pp-KPFM is deter-
mined by the convolution term in Eq. (6) and, therefore, only
limited to the probe pulse width s. In order to study this limit
of pp-KPFM, we applied a square waveform with a signal
frequency of 20 MHz and a signal amplitude of Vrep ¼2Vto
a copper sample and probed the pp-KPFM response with a
4 ns-wide pulse, which is the smallest possible pulse width in
our current electronic setup. Fig. 4(b) depicts the signal
FIG. 5. (a) Contrast DV=Vrep of a square-wave signal, as measured by pp-
KPFM as a function of probe duty cycle g. The green solid line represents
the calculated contrast, whereas dots represent measured results. Overall, the
measured contrast falls in line with our predictions, except for duty cycles
below 1 %. For these g, a logarithmic decrease sets in, which is exemplified
in the inset for different modulation voltage amplitudes vmod : The lower the
modulation amplitude the earlier the decline sets in. The yellow dashed lines
depict a schematic of the corresponding probe signal at small and large duty
cycles, respectively. (b) Error signal Xas a function of compensation voltage
Vdc at different probe duty cycles g. As shown in the inset, for falling gwe
observe a linear decrease of the sensitivity @X
@Vdc, i.e., the slope of the error
signal.
154302-5 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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shapes as measured with an oscilloscope, revealing a full-
width-at-half-maximum of 4:5 ns for the probe pulse and a
rise time of 4 ns for the square waveform used here.
As shown in Fig. 4(b), the measured pp-KPFM signal is
blurred with a total rise time of 10 ns which arises from three
contributions: (i) the 4 ns rise time of the pump signal, (ii)
the convolution of the pump signal with the 4 ns-wide probe
pulse, and (iii) another 2 ns due to the wiring setup of the
sample. Although they contribute to the blurring of the meas-
ured signal, the rise time of the pump signal as well as the
wiring per se pose no limit to pp-KPFM but are merely
sampled and reproduced here. Therefore, we can conclude
that the intrinsic temporal resolution of our setup is indeed
limited by the probe pulse width s. The temporal resolution
might be enhanced by utilizing a faster pulse generator.
Nevertheless, even when operated at the actual temporal
resolution limit, pp-KPFM renders the true signal amplitude
and reproduces the overall signal shape, which enables quan-
titative inspection of a multitude of electrodynamic proc-
esses on the nanosecond-time and nanometer-length scale.
V. THE LATERAL RESOLUTION OF pp-KPFM
In order to verify the ability to acquire topographic and
time-resolved CPD data simultaneously, we performed pp-
KPFM scans on a pentacene-based bottom gate organic
field-effect transistor (OFET) in coplanar geometry possess-
ing interdigitating gold contacts as source and drain electro-
des
16
with a channel length of L¼5lm. The scan area was
chosen from the edge of the source electrode to the corner of
the drain electrode, as indicated in Fig. 7(a).
Fig. 7(b) provides the topography of the scan area dis-
playing the two elevated electrodes at the left hand-side and
at the bottom right corner, as well as the channel region in-
between. The gold electrodes are covered with small penta-
cene grains, while the channel region is coated with larger
pentacene grains featuring scattered taller bulk phase grains.
The displayed topography was acquired simultaneously to
and unimpaired by the time-resolved CPD data in a single
pass scan, demonstrating the functionality and stability of
the dual control loop pp-KPFM.
A fixed voltage VGS was applied to the bottom gate elec-
trode in order to generate a fixed background charge-carrier
density; the source electrode was grounded while a square-
wave voltage was applied to the drain electrode with an
amplitude of VDS ¼2 V at a frequency of xrep ¼50 kHz.
The CPD development was captured by taking 40 frames
with a temporal resolution of s¼2ls over the full repetition
period of 20 ls. A selection of four frames is shown in
Figs. 7(c)–7(f) (Multimedia view).
The onset of the repetition period Trep at tdel ¼0lsis
shown in Fig. 7(c). Most prominently, the drain electrode
FIG. 6. Contrast DV=Vrep as a function of probe duty cycle gat different rep-
etition frequencies xrep. For very low repetition frequencies, the contrast
error increases at low duty cycles due to cross-talk with various setup
resonances. For duty cycles above g¼5%, measurements are possible over
the entire frequency range.
FIG. 7. (a) Schematic of the investi-
gated OFET structure with interdigitat-
ing gold electrodes. The red frame
indicates the position of the studied
area. (b) Topography of the investi-
gated OFET with the source electrode
on the left hand-side, a corner of the
drain electrode at the bottom right, and
the channel region in between, all cov-
ered with 30 nm pentacene. The
dashed lines indicate the borders of the
electrodes in all images. (c)–(f) 2D pp-
KPFM measurements at designated
time delays tdel of the probe pulse rela-
tive to the beginning of the 20 ls pump
cycle as indicated by the respective
insets. The coloured isopotential lines
highlight the evolution of the CPD
within the OFET channel. (Multimedia
view) [URL: http://dx.doi.org/10.1063/
1.4933289.1]
154302-6 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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exhibits a 2 V lower CPD than the source electrode. Between
the electrodes, the surface potential drops according to the
charge-carrier distribution inside the channel region with a
notable drop close to the drain electrode, as indicated by the
accumulated isopotential lines. This drop hints at an insuffi-
cient charge-carrier density and space charge limited trans-
port.
16
8ls after switching, the picture changes in Fig. 7(e),
where now a more equidistant distribution of the isopotential
lines is observed, pointing to additional charge-carriers
injected from the source electrode.
Fig. 7(d) displays the time-resolved CPD shortly after
grounding the drain electrode. Although the gold electrode
has returned to zero potential now, the channel region still
exhibits significant excess charge-carriers, resulting in a non-
equilibrium potential distribution within the channel region.
It takes another 8 ls for the channel to completely deplete all
excess charge-carriers before the cycle restarts, as shown in
Fig. 7(f).
16
As observed in all pp-KPFM data recorded from this
OFET structure, the CPD step at the edge of the left elec-
trode demonstrates a lateral CPD resolution that is limited
solely by the 20 nm radius of the AFM tip.
VI. SUMMARY
We introduced a novel method to measure periodical
time-dependent contact potential differences quantitatively
on the nanometer-length scale by implementing a pump-
probe scheme into Kelvin-probe force microscopy. We have
shown that the resulting pump-probe-driven Kelvin control
loop can cause topographic artefacts, and presented a way
how to circumvent these by employing a second control loop
that minimizes the average CPD of the investigated time-
dependent CPD. Furthermore, we explored the parameter
space of pp-KPFM and demonstrated the technique’s stabil-
ity over a wide range of parameters while simultaneously
pointing to the boundaries of stable operation. We concluded
that the temporal resolution is only limited by the probe
pulse width s, which in turn is only bound to the bandwidth
of the employed pulse generator. Temporal resolutions even
in the sub-nanosecond-time regime are in reach with an
appropriate pulse generator. Moreover, we demonstrated the
unimpaired acquisition of topographic data and verified the
lateral resolution of pp-KPFM to the tip size. Future work
will extend this pump-probe method to other types of pump
mechanisms, as, for example, the optical excitation of
(photo-)voltage.
VII. COMPLEMENTARY INFORMATION
A. Experimental setup
Our pp-KPFM experiments were carried out with a
custom-made AFM. All scans were performed in non-
contact AFM (nc-AFM) mode using a digital phase-locked
loop with a bandwidth of 500 Hz to control the frequency
shift Dxat a constant cantilever oscillation amplitude
17
and
at room temperature. OFET measurements were carried out
with the same nc-AFM under a nitrogen atmosphere in order
to avoid degradation of the organic materials.
As depicted in Fig. 3, the signal path was altered slightly
in order to implement pp-KPFM into our existing FM-KPFM
setup. The first LIA demodulates the tip oscillation at x
0
and
supplies the following LIAs with the necessary side-band
information to demodulate the signals at xmod and xavg ,
respectively. Between the modulating sine generator of the
time-sensitive LIA and the AFM tip, a pulse generator and a
signal switch were added. The pulse generator provides tran-
sistor-transistor-logic pulses Pthat trigger the signal switch,
which in turn switches the modulation voltage Vmod as well
as the compensation voltage ~
Vdc added beforehand. This
results in a pulsed modulation voltage on top of a likewise
pulsed compensation voltage.
In order to compensate the average electrostatic error orig-
inating from the time-sensitive control loop, a third LIA was
employed operating at a separate modulation frequency xavg
followed by a conventional KPFM loop. The resulting com-
pensation voltage ^
Vdc as well as the second modulation voltage
Vavg are then added unaltered to the pulse-modulated signal
from the pp-KPFM branch and finally applied to the tip.
In all measurements, we employed tips from the
Olympus OMCL-AC240TM series. All LIAs are supplied by
Stanford Research with the first LIA being an SR844 and the
second two LIAs an SR830 each. For parameter space meas-
urements, a Stanford Research DG535 pulse generator to-
gether with a Mini Circuits ZASWA-2–50DR signal switch
were utilized, whereas the waveform generator was a
Tektronix AFG3252. For the temporal resolution limit mea-
surement, the same waveform generator was employed for
generating both the pump signal and the probe pulses. The
signal switch for the dual control loop pp-KPFM was built
around an Analog Devices ADL5391 and positioned in close
proximity (<50 mm) to the AFM tip in order to reduce wir-
ing influences. Signals different from the pp-KPFM measure-
ments were acquired directly at the output of the waveform
generator using a LeCroy wavepro 900 oscilloscope with an
attached Yokogawa PB500 probe. The gate voltage in the
OFET measurement was supplied by a Keithley 2602 source
meter, while the square wave pump voltage as well as the
probe pulses were again provided by a Tektronix AFG3252.
B. Large duty cycles
It is noteworthy that very large duty cycles grestore the
temporal resolution capability of the pump-probe approach
in analogy to what is known as Babinet’s principle in
optics.
18
The effect is best described by introducing the
function
Pðxreptþudel Þ¼1Pðxreptþudel Þ;(16)
with the complementary pulse width s¼Trep s. The error
signal Xin Eq. (4) then can be rewritten as
X/vmodfgðVdc þ
VCPDð~
rÞÞ þ ^
VCPDð~
rÞ
½~
VCPDð~
r;tÞPðudelÞg ;(17)
where ^
VCPDð~
rÞdenotes the time average of ~
VCPD integrated
over one repetition period Trep, and ½~
VCPDð~
r;tÞPðudelÞis
154302-7 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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the convolution of ~
VCPD with the function Pat a phase off-
set udel. Again nullifying X, the Kelvin control loop applies
the compensation voltage
Vdc ~
r;udel
ðÞ
¼
VCPD ~
r
ðÞ
þ1
g
^
VCPD ~
r
ðÞ
1
g
~
VCPD ~
r;t
ðÞ
P
udel
ðÞ
:(18)
In contrast to Eq. (6) where the value of the convolution
term was proportional to g, in this case the convolution term
scales proportionally to the complementary duty cycle
g¼ð1gÞ. This behavior reduces the absolute measured
signal contrast with increasing duty cycle g.
Furthermore, for g¼1, the convolution term vanishes
Vdcð~
r;udelÞ¼½
VCPDð~
rÞþ ^
VCPDð~
rÞ ;(19)
such that only the time-independent contact potential differ-
ence
VCPDð~
rÞand the time-averaged potential ^
VCPDð~
rÞremain
detectable, i.e., the result for standard KPFM is restored.
To illustrate these consequences, the solid line in
Fig. 5(a) represents the expected signal contrast DV=Vrep
for a 50% duty cycle square-wave signal plotted as a func-
tion of the probe duty cycle g. It becomes evident that the
penalty for an increased error signal strength Xat large g
manifests in the loss of signal contrast.
ACKNOWLEDGMENTS
We gratefully acknowledge financial support by the
German Science Foundation through the Cluster of
Excellence “Center for Advancing Electronics Dresden,” the
Grant No. ZE 891/1-1, and through the RTG 1401/2. The
authors thank Dr. Moritz Philipp Hein and Dr. Sylvia Nicht
for providing OFET samples.
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154302-8 Murawski et al. J. Appl. Phys. 118, 154302 (2015)
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