Japanese Journal of Applied Physics
Vol. 44, No. 7B, 2005, pp. 5354–5357#2005 The Japan Society of Applied Physics

Analysis of Time-Resolved Tunnel Current Signal in Sub-Picosecond Range
Observed by Shaken-Pulse-Pair-Excited Scanning Tunneling Miscroscopy
Osamu T AKEUCHI, Masahiro AOYAMA and Hidemi S HIGEKAWA
Institute of Applied Physics, 21st Century COE, CREST JST, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan(Received January 17, 2005; accepted February 25, 2005; published July 26, 2005)

The data analysis procedure for the time-resolved tunnel current signal obtained by the shaken-pulse-pair method was studied.
The ﬁtting function composed of a step function and two double exponential functions that decay from delay time zero
towards negative and positive inﬁnities, respectively, reproduced the experimental data. In the analysis, the eﬀects of theinterference of the two pulses in a pulse pair, the ﬁnite width of impinging pulses, the amplitude of the delay time modulationand the lock-in time constant were considered, for obtaining accurate decay parameters. [DOI: 10.1143/JJAP.44.5354]
KEYWORDS: scanning tunneling microscopy, temporal resolution, femtosecond laser

A new research ﬁeld of femtosecond-angstrom technology
is emerging from the combination of two noble measurement techniques, i.e., the pump-probe ultrafast measurement
using a femtosecond pulsed laser and the atom-resolving
measurement using a scanning tunneling microscope (STM).
In this ﬁeld, ultrafast phenomena that occur in angstrom
regions are investigated to assist the fundamental understanding in the basic research of science and the improvement of the future nanotechnology. There have been several
approaches proposed thus far to realize such measurement.1–10) Among them, we adopted the pulse-pair-excited
STM (PPX-STM) method as the best candidate to accomplish both femtosecond and angstrom resolutions, and haveproposed the shaken-pulse-pair-excited STM (SPPX-STM)
setup, which can detect a small time-resolved tunnel current
signal with a high precision, avoiding the tip-expansion/
shrinking problem caused by the heat brought by laser
illumination.8–10) In the present study, we investigate theanalysis procedure of the time-resolved tunnel current signal
obtained by SPPX-STM measurement. In this procedure, theaccurate decay parameters of the ultrafast transient states are
retrieved from experimental data, with eliminating thedistortion due to the ﬁnite temporal width of laser pulses,
the interference of the paired pulses, the shaking amplitude
and the time constant of lock-in detection.
In a PPX-STM measurement, the tunnel gap of an STM is
illuminated by a sequence of paired laser pulses, typically,
with the pulse width tpulse of 10 –100 fs, delay time between
paired two pulses td of .500 ps and inter-pulse-pair period
trep of 10 ns. Since trep is so short, the current–voltage
converter (IVC) of the STM, whose typical cutoﬀ frequency
is 100 kHz, does not resolve each possible current spike inthe instantaneous tunnel current It ðtÞ that is caused by the
excitation of a sample by each laser pulse pair. Instead, theIVC merely detects the temporally averaged tunnel current
signal It ðtd Þ ¼ It ðtÞ. Even in such cases, when the dependence of It ðtÞ on the illumination intensity has any nonlinearity, It ðtd Þ changes when the delay time td is swept. Thisis easily understood as follows. When td is suﬃciently large,
two independent current pulses are generated by a pulse pair,each of which corresponds to each laser pulse in the pair. On
the other hand, when td is close to zero, only one current
pulse is generated, which is as large as that generated by one
laser pulse with a twofold intensity. When nonlinearity

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exists, the total intensity of current pulses is diﬀerent inthese two cases, and it can be observed in the temporally
averaged tunnel current It ðtd Þ. In an intermediate case, thesecond laser pulse impinges the sample in an excited state by
the ﬁrst pulse. The current spike due to the second laser
pulse has a diﬀerent amplitude from that due to the ﬁrst laser
pulse even when the two laser pulses have exactly the same
intensity. The amplitude of the second current pulse ismeasured in It ðtd Þ as a function of td .
Consequently, the time-resolved tunnel current signal
It ðtd Þ shows either a peak or a dip at td ¼ 0 and decays on
both negative (td < 0) and positive (td > 0) sides. Whether apeak or dip appears is dependent on speciﬁc physicalsystems. We obtain the lifetime of the photoexcited state of
the sample from the decay of the It ðtd Þ curve. When the twopulses have the same intensity, the curve is symmetricagainst td ¼ 0. In comparison with a conventional purely
optical pump-probe measurement, the ﬁrst pulse in a pulse
pair is used for pumping the sample, and the tunnel current
change due to the second pulse is detected as the probe
signal. Since the measurement probes the tunnel current, thismethod has an angstrom spatial resolution in addition to a
femtosecond time resolution based on the pump-probemechanism.
In practice, how to detect the very small delay-timedependent component of It ðtd Þ with a suﬃcient accuracy
becomes the main problem. One has to detect a 1 fA–1 pA
deviation of 1 nA tunnel current. In the SPPX-STM
measurement technique, td is modulated periodically as td ¼
td0 þ td sin !t, and It ðtd Þ is processed by a lock-in ampliﬁer.
As described previously,8) this method enables the elimination of the broadband noise in a tunnel current signal
without introducing thermal expansion and shrinking of the
STM tip. The obtained signal corresponds to the diﬀerentiated tunnel current by the delay time, dIt =dtd . We cannumerically integrate the signal to obtain the It ðtd Þ curve.
As described in detail elsewhere,10) we have recently
succeeded in observing a time-resolved tunnel current signal
from a low-temperature-grown GaN As1 ( ¼ 0:36%)
sample. In this study, we consider the data analysis
procedure to retrieve the accurate decay parameters of thephotoexcited ultrafast states from the obtained results.
The measurement was carried out under the following
conditions. The Ti:Sapphire oscillator emitted laser pulses
with an average intensity of 300 mW, a central wavelengthof 800 nm, a bandwidth of 30 nm, a pulse width of 25 fs, and5354

O. T AKEUCHI et al.

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5355

Differentiated Tunnel Current [A/s](a)up scandown scan

0.2
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-40

-20

0
Delay Time [ps]

20

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(b)
0

50

100

150
Time [s]200250Fig. 1. (a) Tunnel current, (b) in-phase lock-in signal, (c) out-of-phaselock-in signal, and (d) delay time sweep for typical SPPX-STM
measurement.

a pulse repetition rate of 80 MHz. The delay line was 150 ps
long and the delay line modulation frequency was 20 Hz.
The central value of the modulation was swept by atrianglular wave with a periodicity of 200 s. The lightintensity at the tip-sample gap was 10 mW and the polarity
was s-polarized. The eﬀective numerical aperture (NA) of
the objective lens was 20 and the incidence angle of thelaser pulses was 40 – 50 from the surface normal. A weak
feedback to the STM z-piezo was applied with a cutoﬀ
frequency below 0.2 Hz, and the STM set point was adjusted
to be 100 pA for a sample bias voltage of 2 V. The ﬁrst
stage of the STM preampliﬁer had a magniﬁcation of 109 .
The time constant of the lock-in ampliﬁer was 100 ms andthe decay slope was 24 dB/oct.
Figure 1 shows a typical experimental result. Raw tunnel
current, in-phase and out-of-phase lock-in signals, and delay
time are plotted against time for the ﬁrst 1.5 scans of delay
time as gray lines. Although high- and low-frequency noises
are included, the peak-to-peak amplitude of the tunnel
current ﬂuctuation is less than 10% of the reference value(100 pA). In an actual measurement, 10 –100 sweeps were
performed, and the result was averaged in order to reducethe broadband noise. The black lines represent the results
obtained as averages of 32 scans. As well known, the noiselevel is inversely proportional to the square root of thenumber of scans. Since the thermal drift of the tip-sample
position parallel to the sample aﬀects the spatial resolutionof the experiment, a highly stable tip position must be
achieved to analyze the local structure with a large numberof scans. In this experiment, the sample is homogeneous andno spatial variation of the time resolved signal is expected.
Figure 2(a) shows the obtained signal as a function ofdelay time. The spectrum for the upward scan (solid) and the
downward scan (dashed) were separately averaged, each ofwhich represents the data obtained with increasing anddecreasing delay time, respectively. Generally, there is aslight shift between the two signals due to the time constantof the lock-in ampliﬁer.
The measured signal is numerically integrated to obtain
the delay-time-dependent tunneling current, as shown in
Fig. 2(b). Since the integral constant cannot be obtained by
the experiment, the absolute value of the tunnel current isundetermined. Here, the value at the left end of the graph istaken to be zero. In this system, the tunnel current increased

Tunnel Current Deviation [pA]

Delay Time [ps]Lock-in X,Y [A/s]Current [pA]

Jpn. J. Appl. Phys., Vol. 44, No. 7B (2005)

up scandown scan

1.0
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-20

0
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40

Fig. 2. (a) Raw and (b) integrated signals of SPPX-STM from GaNAs
sample.

when the delay time decreased. There are two decay
components with a fast (<2 ps) and a slow (50 ps) decay
time. The plot is asymmetric against td ¼ 0. This is due tothe diﬀerent light intensities of the two pulses (1:2 in thiscase). The stronger pulse impinged on the sample ﬁrst in the
td < 0 region.
First, we consider the eﬀect of the interference between
the pump and probe pulses. The SPPX-STM method isknown to be superior to other methods, because it does notmodulate the illumination intensity; thus, the thermal
expansion/shrinking problem of the STM tip does not exist.
As discussed previously,8) however, the constant excitation
intensity is not preserved when the delay time becomes close
to zero. When the delay time is as small as the pulse width,
the interference between the two pulses causes the oscillation of the average illumination power. This can have aconsiderable eﬀect on the tunnel current. How should aninterference eﬀect be observed in an experiment?
In an ideal case, the averaged laser power oscillates fromzero to twofold the original power by the interference, as
shown in Fig. 3(a). This oscillation results in the oscillationin the tunnel current signal shown as the thin line in
Fig. 3(b). Such oscillation is induced, for example, by themodulation of tip-sample separation due to the thermal
expansion/shrinking of the STM tip and by the modulationof the surface potential of a semiconductor sample due tovarying surface photovoltage eﬀect amplitude. In general,
the tunnel current dependence on the illumination intensity
is highly nonlinear. Thus, the oscillation causes a spike inthe low-passed tunnel current signal shown as the thick line.
As the simplest approximation, this tunnel current spike
can be considered as a delta function, in comparison with theamplitude of the delay time modulation, td , in most cases.
Then, the tunnel current under the delay time modulation as
a function of time can be represented as
dIt
sin !tdtd
þ It0 ðtd0 þ td sin !tÞ

It ðtd0 þ td sin !tÞ ¼ It ðtd0 Þ þ td

ð1Þ

Jpn. J. Appl. Phys., Vol. 44, No. 7B (2005)

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Tunnel Current Deviation [a.u.](b)Normalized Light Intensity(a)O. T AKEUCHI et al.

Raw data
Low passed

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Tunnel Current Deviation [pA]5356

fitting function
backgroundexponential 2
exponential 1

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(c)

(d)

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6

4

Tunnel Current [a.u.]

Lockin Signal [a.u.]

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Fig. 4. Fitting function for time-resolved tunnel current spectrum (black)and its components (gray).

5
4
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1
0

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Fig. 3. (a) Illumination intensity oscillating due to intereference eﬀect. (b)Tunnel current response for oscillation. (c) Interference eﬀect inderivative curve for ideally short laser pulse (dotted) and for that of
25 fs width (solid). (d) Integrated signals.

with the angular frequency !, the center position of thedelay time td0R and the current
It0 . Using the
P spike intensity
0
relationship ð f ðxÞÞdx ¼ f ðxn Þ¼0 j1= f ðxn Þj, the output of
the lock-in signal when td < td0 < td is represented asZ!
0
It ðtd0 þ td sin !tÞ  sin !t dtSðtd Þ ¼
2
ð2Þ
1 dIt
4 0
1
¼ td
þ
It qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ :2 dt0 td
ðt =t0 Þ2  1dd

The calculated value obtained for dIt =dtd ¼ 0 and td ¼
1 ps is shown as a dotted line in Fig. 3(c). In this equation,
the signal diverges when td0 ! td , which does not happen,
however, for a ﬁnite pulse width. The result for the pulse
width of 25 fs is shown as a solid line. The integration ofthese curves results in half ellipses with the lateral width of2td , as shown in Fig. 3(d).
As determined from the second term of eq. (2), theinterference eﬀect on the lock-in signal is proportional to It0
and td1 . In addition, when the change in It0 is due to thethermal expansion of the STM tip, the amplitude of thesignal decreases when !td increases. Consequently, theinterference signal can be eﬀectively decreased by increasing td and !. Actually, interferrence eﬀect was not notablein the present experimental result.
Now we consider the ﬁtting procedure for the experimental data with simple mathematical models. As shown
later, for this particular experimental data, two double
exponential functions that decay from td ¼ 0 to negative andpositive inﬁnities with a step function at td ¼ 0 successfully
ﬁt the tunnel current response on the delay time, It ðtd Þ.
Figure 4 shows the ﬁtting function (black line) and its
components (gray lines). Two double exponential functions
on both positive and negative sides have the same lifetimes,
although their amplitudes diﬀer. The magnitude of the step
function corresponds to the diﬀerence in amplitude between
two double exponential functions; thus, the ﬁtting function iscontinuously connected at td ¼ 0. This diﬀerence in baseline indicates the existence of physical process(es) withlarger time scale(s). Consequently, there are ﬁve parameters
to be ﬁt: two lifetimes and two amplitudes for the double

exponential function on the positive side, and the relative
magnitude between the positive and negative sides. Here,one must note that the absolute base-line position is anarbitrary parameter that cannot be determined by theexperiment.
For accurate ﬁtting, one should not directly compare theﬁtting function mentioned above and an integrated experimental data, because the latter is strongly aﬀected bymeasurement parameters, such as the laser pulse width,
amplitude of the delay time modulation, and lock-in time
constant. We must consider these parameters as follows.
The eﬀect of a ﬁnite pulse width can be easily consideredby convoluting the pulse shape onto the original ﬁtting
function. The shape of an ultrashort laser pulse is known tobe well approximated by a hyperbolic secant function. Thus,
the ﬁtting function is deformed asZ0ð3ÞIt ðtd Þ ¼ A It ðtÞ sech2 ðt  td Þdt;with A as the normalizing factor. Typically, the pulse width
is chosen to be suﬃciently small compared to the decay
constants of the physical system. In such cases, this eﬀect isnegligible. Otherwise, the analysis suﬀers from impossibilityof distinguishing the interference eﬀect from the ultrafast
decay processes. Under the present experimental condition,
this eﬀect was negligible.
On the other hand, the delay time modulation and thelock-in detection generally aﬀect the result. The larger themodulation amplitude is, the larger the detected signal we
can obtain. In addition, the larger the lock-in time constantis, the less noise the data contains. Thus, a large modulation
amplitude with a large lock-in time constant is favorable for
maximizing the signal-to-noise ratio. However, such a
condition deforms the obtained data considerably. Thus,
one must optimize the parameters.
In our experiment, the delay time was controlled by thecomposition of a triangular wave of 40 ps amplitude at
5 mHz and a sinusoid modulation of 0:7 ps amplitude at
20 Hz. The tunnel current expected for this input can beobtained by simply assigning this modulated triangular wave
into eq. (3). In the actual measurement, the low-frequency
component of the tunnel current signal is compensated by
the weak z-feedback of the STM. When the cutoﬀ frequencyof the feedback system is chosen properly, however, theinﬂuence on the detection of the modulated component is
negligible.
In the lock-in ampliﬁer, the tunnel current signal ismultiplied by the sinusoid wave at the modulation frequency

Tunnel Current Deviation [pA]

O. T AKEUCHI et al.

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Delay Time [ps]Differentiated Current [A/s]

Jpn. J. Appl. Phys., Vol. 44, No. 7B (2005)

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experimentfitting

1.0
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Fig. 5. Experimental (gray) and ﬁtting (black) curves for time-resolved
diﬀerentiated tunnel current. The delay time sweep is plotted on the rightaxis.

and then processed by low-pass ﬁlter. The low-pass ﬁlter ischaracterized by its time constant T and the decay slope in
the high-frequency region. For example, the ﬁrst-order ﬁlter
has a slope of 6 dB/oct, and the second-, third- and fourthorder ﬁlters have 12, 18, and 24 dB/oct slopes,
respectively. The transmission function of the nth ﬁlter isrepresented as Tn ðsÞ ¼ 1=ð1 þ sTÞn and its impulse responseis
ILP ðtÞ ¼ Ctn1 expðt=TÞ;ð4Þ

with the normalizing factor C. The output of the lock-in
ampliﬁer can be numerically simulated by the sameprocedure, i.e., convoluting the impulse response to thesignal after multiplying the sine wave.11) The calculated
result for the best ﬁt is shown by the black line in Fig. 5,
with the experimentally obtained averaged signal (gray line)
and the delay time. It can be seen that the experimental result
is reproduced well, including the asymmetry between the
upward scan and the downward scan, which is due to thelock-in time constant.
The ﬁtting is carried out by adjusting the ﬁtting
parameters to have the best ﬁt between the experimental
data and the ﬁnally obtained numerical model. For thepresent example, the parameters listed in Table I give thebest ﬁt. Here, the parameters for the slow decay component
have a relatively poor accuracy. This is because theamplitude of the delay time sweep was small. The otherparameters, including that of the fast decay component
whose decay time is comparable to the amplitude of thedelay time modulation, can be accurately obtained. Figure 6
shows the It ðtd Þ curve of the best ﬁt and the integrated
experimental data, which was obtained by averaging the data
for the upward and downward scans. The disagreement
between the two curves indicates the necessity of a carefulﬁtting procedure as discussed above.
Before summarizing the result, we must mention thevalidity of the model function used in this study for ﬁtting.

Table I. Fitting parameters obtained from SPPX-STM data for GaNAs.
Amplitude of the fast decay component

0:55  0:014 pA

Lifetime of the fast decay component
Amplitude of the slow decay component

0:653  0:025 ps
2:36  0:15 pA

Lifetime of the slow decay component

55:1  5:0 ps

Shift of the base line at td ¼ 0

2:66  0:15 pA-20

0
Delay Time [ps]20

40

Fig. 6. Integrated spectra from experimental data (gray) and best ﬁt(black).

Although we observed that the double exponential function
reproduced our experimental data considerably well, thedetailed analysis that considers the nonlinear dynamics inthe sample predicts that the signal does not generally haveexponential shapes.12) Experiments with a higher precision
and a wider sweep of delay time must be carried out to
discuss the deviation of data from the exponential decay andphysical origin of the ultrafast response.
As a summary, the data analysis procedure for the timeresolved tunnel current signal from a shaken-pulse-pairexcited STM measurement was examined. The eﬀects of theinterference of the two pulses in a pulse pair, the ﬁnite pulse
width, the amplitude of the delay time modulation and thetime constant of the lock-in detection were considered for
obtaining the accurate parameters of the ultrafast transientstate of a nanoscale measurement target.
Acknowledgment
This work was supported in part by a Grant-in Aid for
Scientiﬁc Research from the Ministry of Education, Culture,
Sports, Science and Technology, Japan.
1) S. Weiss, D. Botkin, D. F. Ogletree, M. Salmeron and D. S. Chemla:
Phys. Status Solidi B 188 (1995) 343.
2) M. R. Freeman, A. Y. Elezzabi, G. M. Steeves and G. Nunes, Jr.: Surf.
Sci. 386 (1997) 290.
3) N. N. Khusnatdinov, T. J. Nagle and G. Nunes, Jr.: Appl. Phys. Lett.
77 (2000) 4434.
4) R. J. Hamers and D. G. Cahill: J. Vac. Sci. & Technol. B 9 (1991) 514.
5) M. J. Feldstein, P. Vohringer, W. Wang and N. F. Scherer: J. Phys.
Chem. 100 (1996) 4739.
6) V. Gerstner, A. Knoll, W. Pteiﬀer, A. Thon and G. Gerber: J. Appl.
Phys. 88 (2000) 4851.
7) R. H. M. Groeneveld and H. van Kempen: Appl. Phys. Lett. 69 (1996)
2294.
8) O. Takeuchi, R. Morita, M. Yamashita and H. Shigekawa: Jpn. J.
Appl. Phys. 41 (2002) 4994.
9) Mono-Cycle Photonics and Optical Scanning Tunneling Microscopy
Route to Femtosecond Angstrom Technology, eds. M. Yamashita, H.
Shigekawa and R. Morita (Springer, Heidelberg, 2005) Springer Series
in Optical Sciences, Vol. 99.
10) O. Takeuchi, M. Aoyama, R. Oshima, Y. Okada, H. Oigawa, N. Sano,
H. Shigekawa, R. Morita and M. Yamashita: Appl. Phys. Lett. 85(2004) 3268.
11) By simply following the described procedure, spikes might appear in
the calculated signal at the turning points of delay time sweeps. The
polarity and height of the peaks depend on the relative phase between
the delay time modulation and the sweep. By averaging the number ofsweeps with random relative phases, these peaks are smoothed out.
12) O. Takeuchi, M. Aoyama and H. Shigekawa: unpublished.