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New delay-time modulation scheme for optical pump–probe scanningtunneling microscopy (OPP-STM) with minimized light-intensity
modulation
To cite this article: Osamu Takeuchi et al 2019 Jpn. J. Appl. Phys. 58 SIIA12

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REGULAR PAPER

Japanese Journal of Applied Physics 58, SIIA12 (2019)https://doi.org/10.7567/1347-4065/ab1255

New delay-time modulation scheme for optical pump–probe scanning tunnelingmicroscopy (OPP-STM) with minimized light-intensity modulation
Osamu Takeuchi*, Hiroyuki Mogi, Zi-Han Wang, Cheul Hyun Yoon, Atsushi Taninaka, Shoji Yoshida, andHidemi Shigekawa*
Department of Applied Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan*

E-mail: takeuchi@bk.tsukuba.ac.jp; hidemi@ims.tsukuba.ac.jp

Received December 22, 2018; accepted February 15, 2019; published online July 8, 2019
Optical pump–probe scanning tunneling microscopy (OPP-STM) with square-wave delay-time modulation is capable of resolving nanoscale
ultrafast dynamics because it does not require illumination intensity modulation that disturbs precise STM measurement. It has been overlooked,
however, that when the delay time between the pump and probe pulses is modulated by periodically changing the emission timing of either thepump pulse or the probe pulse, with the other remaining the same, the illumination intensity is slightly but finitely modulated with the same
periodicity as a side effect. We propose a new delay-time modulation scheme that periodically changes the emission timing of both pulses, which
can greatly reduce the side effect and remove the induced fake signal in OPP-STM measurements. © 2019 The Japan Society of Applied Physics

1. Introduction

Optical pump–probe scanning tunneling microscopy (OPPSTM) with a square-wave delay-time modulation1–3) is oneof few successful examples1–10) among a number of efforts tocombine STM11,12) with an optical pump–probe technique13)
for constructing a microscope that has ultimate spatial andtemporal resolution at the same time. Though STM has true
atomic resolution11) its temporal resolution is very limited.
To overcome the limitation, a number of efforts have been
made to improve the bandwidth of the tunnel current
ampliﬁer.14–16) Today, however, commonly available tunnel
current ampliﬁers for an ultra-high-vacuum (UHV) STM still
have a temporal resolution of 1 ms to 10 μs. Thus, even on a
microsecond timescale, an OPP-STM technique is valuable
while typical pump–probe measurements without a STM
focus mainly on picosecond to subfemtosecond timescales.13)
Although there are a number of successful examples of timeresolved STM that do not utilize laser pulses,17–23) thanks to
its ultimate time resolution, OPP-STM with femtosecond
laser pulses has the widest applicable range of timescales,from about 10 fs to 10 μs.
Historically, one of the biggest problems in developing an
OPP-STM has been that periodic modulation of the pumplaser intensity for lock-in detection is not appropriate for
OPP-STM, although it is commonly adopted in other OPP
measurements without a STM. When the illumination intensity is periodically modulated, the heat arriving at the
STM tip is modulated, causing thermal expansion andshrinkage of the STM tip with the same periodicity as thatof the intensity modulation. Since the STM tunnel current isextremely sensitive to the tip–sample distance, the thermal
expansion and shrinkage of the STM tip causes oscillation of
the tunnel current at a large amplitude and hides the small
time-resolved signals. Furthermore, when the thermal change
in the tip length exceeds the tip–sample distance, themeasurement becomes unstable due to the periodic collisionof the tip and the sample.
On the other hand, lock-in detection of the STM tunnel
current synchronously with square-wave delay-time modulation is effective for constructing an OPP-STM,1,3,14) partly
because it does not require intensity modulation. When the
delay time is periodically switched between two values Dt1

and Dt2 and the tunnel current is lock-in detected, the inphase lock-in output is proportional to the difference between
the time-averaged tunnel currents for the two delay times,
It (Dt1) - It (Dt2 ). Here, It (Dt ) represents the time-averaged
tunnel current for a delay time of Dt. Thus, the delay-timedependence of the time-averaged tunnel current can be
accurately obtained by sweeping Dt1 with ﬁxed Dt2.
So far, three methods are known for modulating the delay
time between pump and probe pulses in OPP-STM using asquare wave with a large amplitude (∼μs): the pulse-pickerbased method,1) the pulse-generator-based method2) and thetriggerable pulsed-laser-based method.3) In all cases, previous
delay-time modulations were made by adjusting the arrival
time of either the pump pulse or the probe pulse periodically,
while leaving the other unchanged. Such delay-time modulation is accompanied by a slight but ﬁnite modulation of thetime-averaged light intensity with the same periodicity as aside effect, especially when the delay time is modulated witha large amplitude, and this was neglected. Although a Ti:
sapphire femtosecond laser can have true femtosecond time
resolution, the optical setup for this costs so much that it has
not been widely used. On the other hand, the recently
reported pulse-generator-based method with a continuous
laser and electro-optic modulator (EOM) and the triggerablelaser-based method with two externally triggerable nanosecond pulsed lasers can be built with much smaller costs (by afactor of about 100) than the pulse-picker-based method with
two Ti:sapphire femtosecond lasers synchronized to eachother. Because of their low cost and easier handling, thenewly reported OPP-STMs are expected to be widely used byresearchers in the future. Such OPP-STM measurements arenegatively affected by the unwanted intensity modulation due
to delay-time modulation.
In this study, we investigate in detail the intensity
modulation caused by a square-wave delay-time modulationand propose a new delay-time modulation scheme that cancompletely suppress the out-of-phase component of theillumination intensity modulation and greatly suppress its
in-phase component. The efﬁciency of the new scheme is
conﬁrmed by measuring the intensity itself and by applying it
to measure the delay-time-dependent tunnel current from a
WSe2 sample. Though the measurement in this study wasdone using a triggerable-laser-based OPP-STM system, theSIIA12-1© 2019 The Japan Society of Applied Physics

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Fig. 1. (Color online) (a) Conventional square-wave delay-time modulation accompanies out-of-phase intensity modulation as a side effect. (b) In the
new delay-time modulation scheme, the intensity modulations of Lasers 1
and 2 compensate each other so that the out-of-phase intensity modulation
disappears.

proposed scheme is also applicable to pulse-picker-based
OPP-STM and pulse-generator-based OPP-STM.
2. Intensity modulation due to delay-time modulation

First, we brieﬂy explain how a square-wave delay-time
modulation causes an intensity modulation as a side effect. In
Fig. 1(a), we assume that Laser 1 emits pulses at a ﬁxed
repetition rate and the emission timing of Laser 2 is adjusted
to realize the delay-time modulation. As clearly seen in theﬁgure, the modulation of delay time causes a dense andsparse laser pulse distribution in the time domain and resultsin modulation of the time-averaged intensity of laser 2. Notethat the intensity modulation is out of phase with the delaytime modulation by π/2. In addition, although it is difﬁcult to
see this in the ﬁgure, a small amount of in-phase intensity
modulation is caused by this delay-time modulation as
described in the following sections.
In an OPP-STM measurement with phase-sensitive lock-in
detection, the in-phase and out-of-phase components of thetunnel current signal can be observed separately. So, even if
we have a small-amplitude fake out-of-phase signal due tothe unwanted intensity modulation, it does not affect themeasurement of the time-resolved tunnel current signal thatappears in the in-phase component. As we will see later,
however, the amplitude of the out-of-phase intensity modulation can be more than 1% when large-amplitude delay-time
modulation is performed. Such a large amplitude of intensity
modulation may disturb the measurement, making the STM
measurement unstable. Of course, OPP-STM measurement isvery sensitive to in-phase intensity modulation because thefake signal induced by the modulation cannot be separated
from the time-resolved tunnel current signal.
Figure 1(b) shows how the newly proposed scheme ofdelay-time modulation can suppress the out-of-phase intensity modulation. There, the emission timings of Lasers 1 and
2 are both shifted in opposite directions to modulate the delay
time. In this case, the individual time-averaged intensities ofLasers 1 and 2 are still modulated periodically but theirpolarities are opposite. Thus, the out-of-phase component of
the total intensity modulation is completely nulliﬁed as longas the two lasers have the same average intensity. We will seethat the small in-phase component is also reduced by halfwith this sequence.
To further reduce the residual in-phase component, we
propose a complex delay-time modulation scheme, in whichemission timings of individual pulse pairs in a period ofdelay-time modulation are precisely adjusted. Since complete
correction requires heavy calculation to determine the amountof adjustment for each pulse pair, we also propose a
simpliﬁed method for the calculation that can be done inreal time with an average ﬁeld-programmable gate array(FPGA) chip, which can reduce the in-phase component by afactor of about 40 compared with the conventional delay-time
modulation scheme.
3. Theoretical calculation
3.1. Intensity modulation with the conventional
delay-time modulation scheme

Now the above discussion is precisely studied using theoretical calculations. First, let us assume the total laser intensity
can be expressed as
I (t ) =⎡I0 ¥ Nmod / 2 ⎢ ⎛⎜m - 1/2n ⎞⎟d ⎜t - Dt11 ååfrep
fmod ⎟⎠
2frep n =-¥ m = 1 ⎢⎣ ⎝⎛m - 1/2n ⎞⎟+ d ⎜⎜t - Dt21 frep
fmod ⎟⎠⎝⎛
m - 1/2
n + 1 / 2 ⎞⎟+ d ⎜⎜t - Dt12 frep
fmod ⎟⎠⎝⎤⎛
m - 1/2
n + 1 / 2 ⎞⎟ ⎥+ d ⎜⎜t - Dt22 ,⎟frep
fmod ⎠ ⎥⎦⎝(1 )where d is the delta function, frep is the averaged laser pulse
repetition rate, fmod is the delay-time modulation frequency(with Nmod = frep /fmod ), Δt11 and Δt12 are the delay times ofLasers 1 and 2, respectively, in the ﬁrst half of themodulation period, Δt12 and Δt22 are those in the second
half and I0 is the averaged total intensity. Here, it is assumed
that Lasers 1 and 2 have the same intensity and that Nmod isan even number. The ﬁrst two delta functions in Eq. (1)represent the pulses of Lasers 1 and 2 in the ﬁrst half of themodulation period and the last two those in the second half.
Thus, the effective delay time between Lasers 1 and 2 is
Dt21 - Dt11 = Dt1 in the ﬁrst half of the modulation period
and Dt22 - Dt12 = Dt2 in the second half. Here, we assume
for simplicity that the laser pulse width is short enough to be
represented by the delta functions. The effect of a ﬁnite pulse
width will be discussed later.
Since we are interested in the amplitude of intensity
modulation due to delay-time modulation at fmod , weestimate the lock-in output when the total laser intensity in
Eq. (1) is lock-in detected with the reference frequency of
fmod . The lock-in output in the complex representation can becalculated as

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Jpn. J. Appl. Phys. 58, SIIA12 (2019)

IL = fmod

ò0

O. Takeuchi et al.

-1

f mod

I (t ) 2 exp (-i 2pfmod t ) dt

2 I0
p /Nmod
2p i sin (p /Nmod )´ (e-i 2pfmod Dt11 + e-i 2pfmod Dt21 - e-i 2pfmod Dt12 - e-i 2pfmod Dt22 )=~2 I0 fmod {-(Dt11 + Dt 21 - Dt12 - Dt 22)2222+ ipfmod (Dt11+ Dt 21- Dt12- Dt 22)}.

(2 )From this point, it is assumed for approximation that the-1delay times are much smaller than f modand 1  Nmod. With
this notation, the in-phase component with delay-time
modulation corresponds to the imaginary part of IL.
The lock-in output for the conventional scheme of thedelay-time modulation between Dt1 and Dt2 can be calculated
by substituting Dt11 = Dt12 = 0, Dt21 = Dt1 and Dt22 = Dt2
into Eq. (2) asIL =~p / Nmod2 I0(e-i2pfmod Dt1 - e-i2pfmod Dt2)
2p i sin (p / Nmod )2 I0 fmod (Dt2 - Dt1) - i 2 pI0 fmod2 (Dt22 - Dt12).
(3 )The normalized amplitude IL /I0 without the approximation-1
is plotted as a function of Dt1 in Fig. 2(a) with Dt2 = f rep/2,
frep ~ 100 kHz, fmod ~1 kHz and Nmod = 100. The real part,i.e. the out-of-phase component (red curve), is proportional tothe delay-time modulation amplitude Dt2 - Dt1 and its
magnitude is about 1.4% at most. Compared with the realpart, the imaginary part (blue curve) looks almost zero in theﬁgure. As seen from the zoomed plot (light blue curve),
however, it has a ﬁnite amplitude which is almost parabolic,
whose vertex is at Dt1 = 0 and whose magnitude is about 100
times smaller than that of the real part. Precisely, the imaginary-1part at Dt1 = 0 is (p /4) Nmod
times the real part at-1
Dt1 = -f rep/2.
3.2. Reduction of the out-of-phase component
The lock-in output for the new scheme that moves pump andprobe pulses in the opposite direction as illustrated inFig. 1(b) can be calculated by substituting Dt11 = -Dt1 /2,
Dt12 = -Dt2 /2, Dt21 = Dt1 /2 and Dt22 = Dt2 /2 into
Eq. (2):IL =p / Nmod2 I0
p i sin (p / Nmod )´ [cos (2pfmod Dt1/ 2) - cos (2pfmod Dt2 / 2)]~ -i

2
2 pI0 f mod2(Dt22 - Dt12).

Fig. 2. (Color online) Intensity modulation amplitude due to delay-time
modulation (a) for the conventional scheme and (b) for the new schemewithout and (c) with correction for the residual imaginary part.

3.3. Correction for the residual in-phase component(4 )The normalized amplitude IL /I0 without the approximation is plotted as a function of Dt1 in Fig. 2(b) with the same
parameters as Fig. 2(a). The result becomes a pure
imaginary number, i.e. the real part is completely nulliﬁedby this scheme as shown by the red curve. On the other
hand, the imaginary part is exactly the half of that of Eq. (3)as shown by the blue and light blue curves. In the above
condition, the new scheme reduces the intensity modulation
amplitude ∣IL∣ from ∼1.4% to ∼0.55 × 10−4, i.e. by a factor
of about 200.

If one wants to completely nullify both the real part andimaginary parts of IL, Eq. (2) requires Dt11 + Dt21 2
2
Dt12 - Dt22 = 0 and Dt112 + Dt21
- Dt122 - Dt22
= 0. Thiscondition, however, ends up with Dt11 - Dt12 = Dt21 Dt22 = 0 , i.e. zero modulation amplitude. This means that
we need a more complex scheme of delay-time modulation tocorrect for the residual in-phase component where Dt11, Dt21,
Dt12, and Dt22 are no longer constant in the period of delaytime modulation.
In order to correct for the component, let us assume Nmod ismultiple of 4 and we selectively displace the emission timingof the (Nmod /4 - k )th pulse pair by -Dt and that of the(Nmod /4 + k )th pulse pair by +Dt from those in the newscheme. Then the lock-in output is altered from Eq. (4) by

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O. Takeuchi et al.

2 I0{cos [2p {(k - 1 / 2) / Nmod + fmod Dt1/ 2 + fmod Dt}]iNmod
- cos [2p {(k - 1 / 2) / Nmod + fmod Dt1/ 2}]+ cos [2p {(k - 1 / 2) / Nmod - fmod Dt1/ 2 + fmod Dt}]- cos [2p {(k - 1 / 2) / Nmod - fmod Dt1/ 2}]}

DIL =

~

i2 2 2pI0
2 p (k - 1 / 2 )frep Dt sin
.
2
Nmod
Nmod

Note that such a symmetric shift of two pulse pairs makes
DIL a pure imaginary number. Thus, we can correct for theimaginary residue in Eq. (4) by selecting k and Dt properly.
Hereafter, we assume the delay times are controllable with
-1
pulse
f rep
/Nrep as a unit, with Nrep being an integer. If alln(k )pairs corresponding to k are displaced by Dt (k ) = f N , therep rep
total difference in IL can be written asDIL ~i2 2 2pI0
2
Nmod
Nrep

Nmod / 4

å n(k ) sin

k= 1

2 p (k - 1 / 2 )
.
Nmod

(6 )

2 2 2pI0
p
sin
~
2
Nmod
Nmod Nrep

2 (2p )2 I0
.
3
Nmod
Nrep

Nrep
n22 - n12
=.
8Nrep
32

(8 )

(9 )

Nmod / 4

(10)

p
,
Nmod

1/4

Nrep

ò∣n ∣/(2N ) sin 2pxdx = 32 cos (pn1/Nrep).
rep

For example, the normalized lock-in output (IL + DIL ) /I0
without approximation is plotted as a function of Dt1 withn = 4, Nrep = 2036, Nmod = 100 and a delay-time resolutionof 5 ns in Fig. 2(c). The real part is unchanged from zero, asshown by the red curve. The imaginary part becomes zero at-1
Dt1 = 0 and Dt1 = f rep/2, as shown by the blue curve. In
between, it has small negative values which approximately
correspond to the difference between a parabolic function anda cosine function. As a result, with this correction, theresidual imaginary part is reduced from 1.1 ´ 10-4 to
2.7 ´ 10-6 , i.e. by a factor of about 40.
With smaller Nmod , approximation of the summation by acosine function that is used in Eq. (13) becomes poor. Evenso, the above scheme makes IL + DIL zero at Dt1 = 0 and-1
Dt1 = f rep/2. In between, the residue is also reduced by afactor of about 40, although the delay-time dependence
differs from that in Fig. 2(c).
Some additional optimization may be possible, dependingon the conditions. When Eq. (12) is slightly modiﬁed to⎧k < ⌊∣n1∣Nmod / (2Nrep)⌋0⎪n(k) = ⎨ n - ⌊n frac (∣n1∣Nmod / (2Nrep ))⌋ k = ⌊∣n1∣Nmod / (2Nrep)⌋⎪⌊∣n1∣Nmod / (2Nrep)⌋ < k ,
n
⎩

(14)

So, if we select n, Nrep, and Nmod to meetsin

2 p (k - 1 / 2 )
Nmod

(13)

(7 )

On the other hand, when we let n(k ) = n for all k,
2 p (k - 1 / 2 )n=
å n(k ) sin
p .
N
mod
2 sin
k= 1
Nmod

n sin

1

When frep = 100 kHz and fmod =1 kHz with a delay-time
resolution of 5 ns, it follows that Nrep = 2000 andNmod = 100. Thus, Eq. (8) gives ~2.8 ´ 10-8I0, which canbe regarded as zero in almost all applications.
In a practical experiment, however, it is often too complex,
and also not required, to fully optimize the values of n(k ) .
Therefore, we propose a simpliﬁed scheme to easily selectvalues of n(k ) , which can reduce the imaginary component in
Eq. (4) by a factor of about 40. First, we choose n 2 = Nrep /2.
Then, the maximum of ∣IL∣ is at n1 = 0. There,

16

where frac(·) denotes the fractional part function and ⌊·⌋ denotes
the ﬂoor function. Note that, when 1  Nmod , the summation in
Eq. (6) can be represented by a cosine function ask =∣ n1∣ Nmod / 2Nrep

Thus, by fully optimizing all the values of n(k ) , ∣IL + DIL∣
can be reduced to be smaller than the coefﬁcient of n(1) ,

Nrep

(12)

~ nNmod

Nmod / 4⎡ n2 - n2
2 p (k - 1 / 2 ) ⎤1´⎢- 2+ å n(k ) sin
⎥.
8Nrep
Nmod
⎦
⎣
k= 1

n=

⎧
k < ⌊∣n1∣Nmod / (2Nrep )⌋ + 1
0⎪n (k) = ⎨ n - ⌊n frac (∣n1∣Nmod / (2Nrep ))⌋ k = ⌊∣n1∣Nmod / (2Nrep )⌋ + 1⎪
n⌊∣n1∣Nmod / (2Nrep )⌋ + 1 < k ,⎩å

i2 2 2pI0
2
Nmod
Nrep

-

in-phase component with reasonable accuracy by setting

Nmod / 4n1n
and Dt2 = f N2 , we obtainrep Nrep
rep rep

Given Dt1 = f
IL + DIL ~

(5)

(11)

IL + DIL is nulliﬁed at n1 = 0. For example, when
Nmod = 100 and Nrep = 2036, Eq. (11) gives n ~ 3.997.
Thus, with n = 4, ∣IL + DIL∣ becomes more than three ordersof magnitude smaller than ∣IL∣ at n1 = 0.
When n1 ¹ 0, ∣IL∣ increases parabolically according to
Eq. (7). Taking the similarity of a parabolic function and acosine function into account, we can correct for the parabolicby omitting “+1” in the speciﬁcation of the range of k, theresidual in-phase component becomes much smaller in therange of delay time ∣Dt1∣ < 4 ms, as shown by the light blue
curve in Fig. 2(c). This “optimization,” however, only works
for a ﬁnite range of Nmod. Note that, especially for a small
Nmod , Eq. (14) can give a very poor result.
3.4. Different intensities for pump and probe pulses
So far we have assumed that the intensities of Lasers 1 and 2
are exactly the same. On the other hand, if they have different
intensities I1 and I2, the lock-in output for the conventional

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O. Takeuchi et al.

scheme, Eq. (3) becomesp / Nmod2 I2(e-i2pfmod Dt1 - e-i2pfmod Dt2)
p i sin (p / Nmod )IL =~ 2 2 I2 fmod (Dt2 - Dt1)
- i2 2 pI2 fmod2 (Dt22 - Dt12).

(15)

This is same as Eq. (3) except that I0 /2 in Eq. (3) becomes
I2 in Eq. (15). On the other hand, the lock-in output for the
new scheme without the correction, Eq. (4), becomes
IL =

~

2
p / Nmod{(I1 - I2)[sin (pfmod Dt1)
p sin (p / Nmod )- sin (pfmod Dt2)] - i (I1 + I2)[cos (pfmod Dt1)
- cos (pfmod Dt2)]}
2 (I1 - I2 ) fmod (Dt2 - Dt1)-i

2 p (I1 + I2 ) fmod2(Dt22 - Dt12).
2(16)

The imaginary part is as same as Eq. (4) taking I0 = I1 + I2
into account. In addition to this, however, a ﬁnite real partappears, which is proportional to the intensity difference
between the two lasers. Since the normalized form of the real
I -Ipart is 2 I1 + I2 fmod (Dt2 - Dt1), taking the requirement
1
2
I -I
-1
-1
into account, I1 + I2 should not-f rep Dt2 - Dt1  f rep
1
2
exceed Nmod / 2 times as the required relative accuracy tosuppress the magnitude of the real part below the value. For
example, if a relative accuracy of 10-5 is required with
I2
Nmod = 100, the ﬂuctuation amplitude at fmod of II1 should
1 + I2
not exceed 0.7 ´ 10-3.
When the intensities of the pump and probe pulses areintentionally chosen to have different values, one can stillnullify the real part of IL by having Dt11 /Dt21 =Dt12 /Dt22 = -I2 /I1 so that the weighted-average of theemission timing of each pulse pair is not changed by thedelay-time modulation. Letting Dt11 = -Dt1 I2 / (I1 + I2),
Dt21 = Dt1 I1/ (I1 + I2), Dt12 = -Dt2 I2 / (I1 + I2), Dt22 =Dt2 I1/ (I1 + I2), Eq. (7) becomes
IL + DIL ~i 2 2p (I1 + I2 )
2
Nmod

⎡
I1I2
´ ⎢f 2 (Dt22 - Dt12)⎣ (I1 + I2)2 rep+

Nmod / 4å 2frep Dt (k ) sin

k= 1

2 p (k - 1 / 2 ) ⎤
⎥.
Nmod
⎦

(17)

Thus, correction for the residual imaginary part is also
possible by properly selecting the timing shift for the kthpulse pairs, Dt (k ).
3.5. Finite pulse width
So far, the input of the lock-in ampliﬁer has been regarded asa sequence of delta functions. In a real experiment, however,the pulses in the signal have a ﬁnite width because of thelaser pulse shape and the impulse response of the photodetector. Such a signal can be represented by convoluting
I (t ) in Eq. (1) with the pulse shape and the impulse response.
On the other hand, as illustrated in Eq. (2), IL is the Fouriertransform of I (t ) at fmod . It is known that the Fouriertransform of a convolution integral is the product of its

Fig. 3. (Color online) Illustration of the OPP-STM setup. Emission timingsof two triggerable nanosecond pulsed lasers are controlled by a lab-built
FPGA circuit to modulate the delay time between pump and probe pulses.
The laser beams are coaxially aligned at a half mirror (H.M.) and illuminate
the sample under STM measurement. The tunnel current signal is lock-in
detected with the delay-time modulation frequency as the reference.

individual transforms. Thus, if the output of a photodetector
is lock-in detected, the result will be as same as that which we
obtained above except for a complex coefﬁcient of absolutevalue 1 that corresponds to the product of Fourier transformsof the pulse shape and the impulse response of the photodetector, which only rotates the phase of the obtained result.
Consequently, the lock-in output is independent of the pulse
shape or the impulse response of the detector if the reference
phase of the lock-in detection is carefully chosen to compensate for the phase rotation.
4. Experimental confirmation of the new delay-time
modulation scheme
4.1. Experimental setup

Next, we conﬁrm the efﬁciency of the newly proposed delaytime modulation scheme by experiments. Our OPP-STM
setup is illustrated in Fig. 3. Two externally triggerable
pulsed lasers, NPL52B from Thorlabs Inc., with ∼8 ns pulse
width and wavelength 520 nm are used as Lasers 1 and 2.
The emission timings are controlled by a lab-built FPGA
circuit implemented in a Xilinx Kintex-7 chip on the FPGA
board XCM-112-160T from HuMANDATA Ltd. The internal circuit of Kintex-7 was run at a clock frequency of
200 MHz so that the emission timing could be adjusted with aresolution of 5 ns. For an OPP-STM measurement, two laser
beams are coaxially aligned at a half mirror (H.M. in theﬁgure) and focused onto the sample surface from a normal
incident angle. The measurement setup was equipped with anultra-high-vacuum multi-probe STM system from UNISOKU
Co., Ltd. with lab-built electronics and software. In thissystem, the STM tip is tilted from the sample surface normal.
Thus, the tip does not block the normal-incidence laser
illumination. The tunnel current is lock-in detected with thedelay-time modulation frequency as the reference.
4.2. Measurement of laser intensity
First, the total laser intensity measured by a photodiode (notshown in Fig. 3) was lock-in detected with the delay-time
modulation frequency as the reference. The lock-in output is

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O. Takeuchi et al.

Fig. 4. (Color online) Normalized lock-in output for laser intensity
measurements (a) with the old scheme, (b) with the new scheme without
correction for an imaginary residue and (c) with the new scheme withcorrection.

averaged for multiple sweeps of the delay time and plotted asa function of Dt1 with Nrep = 2036 and Nmod = 100, i.e.
-1frep ~ 100 kHz and fmod ~1 kHz with ﬁxed Dt2 = f rep/2 =5 ms, the same as those in Fig. 2. As expected in Fig. 2(a), theconventional delay-time modulation scheme causes a largeamplitude out-of-phase component that is proportional to
Dt2 - Dt1 (red curve) and the parabolic in-phase component(light blue curve) as shown in Fig. 4(a). The magnitude ofthese components also agrees with expectations.
With the new scheme without the precise correction, theout-of-phase component was greatly reduced as expected, as
shown by the red curve in Fig. 4(b). However, some small
unexpected out-of-phase component remained (red curve)
while the in-phase component agrees with the expectation(blue curve). Figure 4(c) shows the result for the new schemewith correction by Eq. (12) with n = 4. Since we spent moretime acquiring this result the noise level is greatly reduced.
As a result, the detailed shape of the unexpected component
can be seen (red curve). The unexpected out-of-phasecomponent resembles two exponential decays from Dt1 = 0
symmetrically towards the positive and negative directions
with a very long decay time (>3 μs). Since the amplitude anddecay time of this component change when we replace thephotodetector with another whose characteristics are different
from the original one, we interpret this unexpected component as originating from the nonlinear response of thephotodetector. The in-phase component (blue curve) was
greatly reduced from Fig. 4(b). Consequently, it was conﬁrmed that the newly proposed delay-time modulation
scheme efﬁciently reduces both the in-phase and out-ofphase components of the illumination intensity modulation.
4.3. OPP-STM measurement with the new delay-time
modulation scheme
Finally, OPP-STM measurement was performed with the newdelay-time modulation scheme. We chose WSe2 as the
sample, which is a layered indirect-bandgap semiconductor
with a relatively long carrier recombination lifetime.24,25) As
previously reported,3) this system exhibits two exponential
decay components in OPP-STM which have decay constantsof ∼0.15 μs and ∼1.5 μs, respectively. It was insisted thatthey correspond to the lifetimes of photocarriers in and out of
the tip-induced depletion region.26,27)
The OPP-STM result with the conventional delay-time
modulation scheme is shown in Fig. 5(a) with Nrep = 2036,
Nmod = 100 and a delay-time resolution of 5 ns, i.e.
frep ~ 100 kHz and fmod ~1 kHz with ﬁxed Dt2 =-1
f rep/2 = 5ms, as in Figs. 2 and 4. The sample bias voltage
VS is −1.2 V and the reference tunnel current Iref is −100 pA.
In addition to the time-resolved tunnel current signal thatappears in the in-phase component (blue curve), a small but
distinguishable fake signal appears in the out-of-phasecomponent (red and purple curves), which is proportional
to the delay-time modulation amplitude Dt2 - Dt1. As
discussed above, this fake signal is caused by unwanted
intensity modulation as a side effect of the delay-time
modulation. With the new modulation scheme with theprecise correction by Eq. (12) with n = 4, this fake signal
was completely removed (red and purple curves) while thetime-resolved tunnel current signal was unchanged (bluecurve), as shown in Fig. 5(b). In this experiment, the timeresolved tunnel current signal is so large that the effect of thein-phase intensity modulation was not observable. Note thatthe expected magnitude for the in-phase intensity modulationis smaller than that for the out-of-phase intensity modulation
by a factor of (4 /p ) Nmod ~ 127. Thus, the in-phase fakesignal in Fig. 5(a) is expected to be ∼3 fA in this experiment.
-2, whenSince the in-phase signal is proportional to Nmod
Nmod is smaller the fake signal indeed affects the experiment.
An OPP-STM result with Nmod = 8 is shown in Fig. 5(c).
Other parameters are VS = -1.2 V, Iref = -200 pA and
Nrep = 8332, i.e. frep ~ 24 kHz and fmod ~3 kHz with
-1
Dt2 = f rep/2 = 20 ms. With the conventional scheme, alarge fake signal appears in the real part that is proportional
to the delay-time modulation amplitude (red curve). In
Fig. 5(c), the delay-time-dependent tunnel current is distinguishable in the imaginary part. This is as same as inFig. 5(b). But how it looks in Fig. 5(c) is different from

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Jpn. J. Appl. Phys. 58, SIIA12 (2019)

O. Takeuchi et al.

measurement was investigated in detail. When delay-time
modulation is done by shifting the emission timing of either
the pump or the probe pulse while that of the other isunchanged, intensity modulation that is out-of-phase with thedelay-time modulation is induced, the amplitude of which is
proportional to the delay-time modulation amplitude. In
addition to this, intensity modulation that is in phase withthe delay-time modulation is also induced, the amplitude ofwhich is a parabolic function of the delay time. A new delaytime modulation scheme was proposed, in which the emission timing of the pump and probe pulses are both shifted in
the opposite direction to realize delay-time modulation. With
this new scheme, the out-of-phase intensity modulation iscompletely nulliﬁed, while the in-phase intensity modulationis reduced by half. To reduce the residual in-phase intensity
modulation, a correction method for the new scheme is also
proposed, in which the emission timings of individual pulse
pairs in a half period of the delay-time modulation are
adjusted. The correction reduces the in-phase intensity
modulation in the conventional scheme by a factor of about
40. It was conﬁrmed that the corrected new scheme indeed
nulliﬁes the fake signals due to the unwanted intensity
modulation in OPP-STM measurement on WSe2. In thisstudy, the experiment was done with triggerable-laser-based
OPP-STM. However, the proposed scheme is also applicable
to pulse-picker-based OPP-STM or pulse-generator-based
OPP-STM.
Acknowledgments

Support from Japan Society for the Promotion of Science(Grants-in-Aid for Scientiﬁc. Research: 15H02023 and
17H06088) is acknowledged.

Fig. 5. (Color online) Lock-in output for OPP-STM measurements on
WSe2 (a) with the conventional scheme, (b) with the new scheme withcorrection by Eq. (12) and (c) with a smaller Nmod.

Fig. 5(b). In addition, however, the imaginary part with theconventional scheme shows a small downward bend aroundthe delay-time origin (light blue curve). The amount of
downward bending is reduced by half with the new schemewithout the correction (blue curve) and becomes almost zerowith the new scheme with the correction by Eq. (12) (purple
curve). This downward bending is due to in-phase intensity
modulation. Indeed, the relative magnitude of the fake signals
in the out-of-phase and in-phase components was as expected, (4 /p ) Nmod ~ 10. Consequently, for OPP-STM measurements, the proposed delay-time modulation scheme is
efﬁcient at removing the fake signals due to unwanted
intensity modulation caused as a side effect of square-wave
delay-time modulation.
5. Conclusions

The unwanted intensity modulation caused as a side effect ofsquare-wave delay-time modulation in an OPP-STM

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