Double-Pass Te ahe z Time-Domain Spec oscopy o 2D
Ma e ials
Da id A cos,* Daniel Nu˜no, Ma ía C. San os, and Nú ia Fe e -Anglada*
1. In oduc ion
Cu en ly, he cha ac e iza ion o 2D ma e ials, such as g aphene
and ew-laye ansi ion me al dichalcogenides (TMDCs), is a
majo ocus in ma e ials science and enginee ing, d i en by
hei po en ial o di e se applica ions. These applica ions
include high-pe o mance ene gy s o age,
[1,2]
gas sensing,
[3–5]
biomedical de ices,
[6,7]
wa e pu ifica ion,
[8,9]
and elec onic de ices,
[10–13]
among o he s.
In he e ahe z (THz) ange, 2D ma e ials
a e also highly p omising, as hey can be
employed in bo h emission and de ec ion
s ages,
[14,15]
enabling he de elopmen o
op ical modula o s,
[16]
esona o s,
[17]
and
op ical logic ga es a THz equencies.
[18]
Tungs en disulfide (WS
2
) is a TMDC
ha consis s o a laye o ungs en a oms
sandwiched be ween wo laye s o sul u
a oms, held oge he by s ong in-plane
co alen bonds. Simila o g aphi e and
i s single-laye (SL) o m, g aphene,
TMDC bulk c ys als a e composed o
s acked SLs connec ed by weak ou -o -plane
an de Waals o ces, which enable easy
ex olia ion o he 2D laye s.
[13]
These ma e-
ials, analogous o g aphene, exhibi excep-
ional op ical and elec ical p ope ies,
anging om insula o s o me als o , as
in he case o WS
2
, semiconduc o s wi h ei he di ec o indi ec
bandgaps.
[19]
I is well known ha he bandgap o WS
2
depends
on i s numbe o laye s. In SL WS
2
, he gap is di ec wi h a alue
o 2.03 eV, whe eas in bulk WS
2
, he gap is indi ec , wi h a alue
o 1.32 eV.
[20]
This di ec gap in SL WS
2
has been shown o esul
in pho oluminescence, making WS
2
a s ong candida e o ans-
pa en , flexible, and e ficien op oelec onic de ices.
[21]
Rega ding he analysis echnique, THz ime-domain spec os-
copy (THz-TDS) is a nondes uc i e spec oscopic echnique
commonly used o explo e he p ope ies o ma e ials wi hin
he THz equency ange, ypically spanning om 0.1 o
10 THz. This echnique u ilizes sho pulses o THz adia ion
o ga he ime- esol ed in o ma ion abou he sample, which
can hen be ans o med in o equency-domain da a, p o iding
spec al insigh s wi hou damaging he samples. THz–TDS
has p e iously been applied o WS
2[22,23]
and o he 2D ma e ials
such as MoS
2[24]
and g aphene on a ious subs a es,
[25–28]
as well o he e os uc u es con aining WS
2
,
[29]
o assess op ical
ansmi ance and su ace conduc i i y in he THz equency
ange.
The p ima y objec i e o his wo k is o p esen an al e na i e
configu a ion o he THz–TDS echnique, based on a Michelson
in e e ome e , wi h mul iple po en ial configu a ions. We aim o
demons a e ha his new se up can e ec i ely ob ain da a
om bo h subs a es and 2D laye s when ope a ed on a single
b anch, accoun ing o he THz beam passing h ough he
sample wice. Specifically, we use his se up o ob ain he ans-
mi ance and su ace conduc i i y o a WS
2
sample on used
qua z.
D. A cos
Depa men o Enginee ing
Uni e si a de Vic–Uni e si a Cen al de Ca alunya (UVic–UCC)
Ca e de la Lau a 13, 08500 Vic, Spain
E-mail: da id.a cos@u ic.ca
D. A cos, N. Fe e -Anglada
Depa men o Physics
Uni e si a Poli ècnica de Ca alunya (UPC) Campus No d
J. Gi ona 3, 08034 Ba celona, Spain
E-mail: [email p o ec ed]
D. Nu˜no, M. C. San os
Depa men o Signal Theo y and Communica ions
Uni e si a Poli ècnica de Ca alunya (UPC) Campus No d
J. Gi ona 1, 08034 Ba celona, Spain
The ORCID iden ifica ion numbe (s) o he au ho (s) o his a icle
can be ound unde h ps://doi.o g/10.1002/pssb.202400323.
© 2024 The Au ho (s). physica s a us solidi (b) basic solid s a e physics
published by Wiley-VCH GmbH. This is an open access a icle unde he
e ms o he C ea i e Commons A ibu ion License, which pe mi s use,
dis ibu ion and ep oduc ion in any medium, p o ided he o iginal wo k is
p ope ly ci ed.
DOI: 10.1002/pssb.202400323
Te ahe z ime-domain spec oscopy (THz–TDS) is a nondes uc i e imaging and
cha ac e iza ion echnique. I is cu en ly used in he field o ma e ial science o
ob ain he su ace conduc i i y and ansmi ance o bulk and 2D ma e ials in he
ange om hund eds o GHz up o ew THz. In his esea ch, an al e na i e se up
o he THz–TDS echnique is p oposed, based on a Michelson in e e ome e ,
wi h a double pass h ough he sample using a mi o and a semi anspa en
wa e . A single-b anch configu a ion is used o cha ac e ize a ew-laye WS
2
sample on a used qua z subs a e. The objec i es o he expe imen a e o
demons a e ha he configu a ion is iable o ob aining he pa ame e s o he
sample and he subs a e, o p esen he models and equa ions used, and o
explain he ad an ages and limi a ions o he me hod compa ed o he ans-
mission configu a ion. The op ical ansmi ance and su ace conduc i i y o WS
2
a e ob ained wi h he new configu a ion in he equency ange om 0.2 o
1.2 THz. Raman spec oscopy is used o analyze he sample quali y be o e
pe o ming he measu emen s.
RESEARCH ARTICLE
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2. Sample Desc ip ion and Raman
In his s udy, we analyze a single ew-laye WS
2
sample p epa ed
a Sejong Uni e si y in Seoul, Ko ea, by he esea ch g oup o
P o . J. Eom. The sample was p oduced h ough chemical apo
deposi ion on a used qua z subs a e wi h a squa e su ace a ea
(20 mm pe side) and a hickness o 1.00 5% mm. Selec ing
his specific subs a e is c ucial o ensu ing THz ans-
pa ency. Fused qua z (silica) was chosen due o i s o ien a ion-
independen e ac i e index, unlike c ys alline qua z, whose
THz anspa ency a ies wi h c ys allini y.
[30]
The sample’s2D
na u e and quali y we e e ified h ough Raman spec oscopy,
using a 514 nm exci a ion lase line a 0.5 mW. The Raman spec-
um ob ained o WS
2
on used qua z is shown in Figu e 1.
The mos p ominen peaks in he spec um, loca ed a 353 and
419 cm
1
, co espond o WS
2
bands. Bulk WS
2
is cha ac e ized
by an E1
2g band a 351 cm
1
and an A
1g
band a 420 cm
1
. As he
numbe o laye s dec eases, he sepa a ion be ween hese peaks
also dec eases: he E1
2g band unde goes a blue shi , while he A
1g
band expe iences a edshi ,
[31–33]
as obse ed in ou spec a.
Addi ionally, a e co ec ing he subs a e e ec s and fi ing
he baseline, he E1
2g band a 353 cm
1
was decon olu ed in o
wo Lo en zian componen s, co esponding o he 2LA(M) band
a 349.4 cm
1
and he E1
2g ΓðÞband a 354.8 cm
1
. The in ensi y
a io I2LA=IA1G se es as an indica o o he numbe o WS
2
laye s, anging om 0.47 o bulk WS
2
o 2.2 o SL
WS
2
.
[31,33]
In ou spec a, he I2LA=IA1G a io is 0.61. Based on
he posi ion o hese h ee bands and he I2LA=IA1G a io, and
e e encing he wo ks o Loh e al.
[31]
and Be kdemi e al.
[33]
we conclude ha ou WS
2
sample con ains a leas 3–4 laye s.
3. Expe imen al Sec ion
The expe imen al se up
[34]
was based on he TERA K8 comme -
cial THz spec opho ome e om Menlo Sys ems, wi h a silicon
wa e placed in he middle o he THz beam pa h, ac ing as a
semi-mi o (see Figu e 2). The spec opho ome e ’s configu a-
ion was mainly based on a Michelson in e e ome e (see
Figu e 3), a echnique ha has been p e iously employed in
THz–TDS o imaging
[35]
and cha ac e iza ion,
[36]
al hough,
Figu e 1. Raman spec a o WS
2
sample.
Figu e 2. THz–TDS schema ic o he expe imen al se up.
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in ou expe imen , in e e ome y was no used o ex ac he
esul s.
Figu e 4 illus a es 16 possible configu a ions o he in e e -
ome e , a anged in a ma ix acco ding o he de ices included in
each a m (o b anch) o he in e e ome e . We designa ed
b anch A (see configu a ion X0) as he non-in e ing pa h and
b anch B (see configu a ion 0X) as he in e ing pa h, wi h in e -
sion occu ing due o he p esence o he L2 lens. In each b anch,
he ollowing ou scena ios could occu . The signal could be dis-
ca ded by edi ec ing he THz beam be o e i eached he
b anch’s mi o (X), so he con ibu ion om ha b anch was
no de ec ed by he ecei e . I he only elemen in he pa h
was he mi o , an ai e e ence (0) o he b anch was ob ained.
Finally, a ba e subs a e (1) o a 2D sample on he subs a e (2)
could be in oduced, in addi ion o he mi o , such ha he main
beam passed h ough he ma e ials wice be o e eaching he
ecei e . The combina ion o hese op ions o each b anch p o-
duces he 16 configu a ions shown in Figu e 4. I migh appea
ha he configu a ions below he diagonal we e edundan ,
excep o he sign in e sion, bu he use o he lens imp o ed
he spa ial esolu ion, making b anch B mo e sui able o
Figu e 3. Pho og aph o he Michelson in e e ome e assembly.
Figu e 4. All he p oposed configu a ions o he Michelson in e e ome e o measu ing 2D ma e ial samples and subs a es. Pa hs o b anches A and B
a e indica ed in configu a ions X0 and 0X, espec i ely.
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measu emen s o samples wi h small su ace a eas. In con as ,
he diagonal configu a ions (00, 11 and 22) did no esul in a
ully canceled signal due o abe a ion caused by he lens. In addi-
ion, in he 1X and 2X configu a ions, i he samples we e posi-
ioned nea he ocal plane o he lens, he con ibu ion o he
Gouy phase shi mus be conside ed when ex ac ing op ical
p ope ies, pa icula ly a low equencies.
[37,38]
The XX configu-
a ion could be used o e i y ha canceling he signals om bo h
b anches esul s in he ecei e de ec ing no signal, ensu ing ha
he e we e no unwan ed eflec ions in he se up. In he config-
u a ions p esen ed in Figu e 4, i was assumed ha bo h he sam-
ple and he subs a e we e anspa en . I he subs a e was no
anspa en , he sample could be placed di ec ly a he posi ion o
he M4 mi o o eflec ion measu emen s, wi hou equi ing
addi ional adjus men s.
4. Single-B anch Analysis
As explained ea lie , al hough he sys em is based on an in e -
e ome e , in e e ome y will no be used o ex ac he esul s.
Ins ead, we will only use signals om one b anch, co esponding
o he fi s ow and fi s column configu a ions in Figu e 4. The
main objec i e o his wo k is o demons a e ha he sys em can
be used o cha ac e ize subs a es and 2D samples. The op ical
beam pa h is essen ially he same as ha in he con en ional
ansmission se up desc ibed in e . [22], bu in his se up, we
include a mi o (M4) behind he sample ha eflec s he beam,
causing i o pass h ough he sample again be o e being mea-
su ed. I is impo an o no e ha he ecei ing an enna is no
posi ioned behind he sample, as i would be in he ansmission
se up. The simplified ay diag am o signals passing h ough he
e e ence (ai ) channel, S0ωðÞ, he channel wi h a single
subs a e, Ssub ωðÞ, and he channel con aining bo h laye s,
S2D ωðÞ, is shown in Figu e 5. Two addi ional pa hs,
co esponding o he Fab y–Pé o ’sfi s eflec ions, a e ep e-
sen ed by do ed lines. These beams a e pa o he Ssub ω
ðÞ
signal
and occu in o wa d and backwa d di ec ions. I mus be no ed
ha hese signals a i e a exac ly he same ime o he unca-
ion o he empo al signals, as explained la e .
Each signal can be exp essed in he equency domain
(ω¼2π ) as he p oduc o he Fou ie ans o m o he pulse
a i ing a in e ace 1, which is common o all measu emen s, by
he channel ans e unc ion, which depends on he ma e ials
being cha ac e ized. F om he ay diag am in Figu e 5, ans e
unc ions o he e e ence channel, H0ωðÞ, and o he signal
passing h ough he subs a e, Hsub ωðÞ, can be seen in
Equa ion (1) and (2), espec i ely. These exp essions ha e been
de i ed simila ly o he one-pass case in he con en ional ans-
mission se up.
[39,40]
H0ωðÞ¼p02dδþ2dsub
ðÞ (1)
Hsub ωðÞ¼p02dδ
ðÞ 0;sub psub dsub
ðÞ sub;0X
NFP
m¼0
p
m
sub
"#
2
(2)
whe e he NFP alue in he summa ion ep esen s he numbe o
Fab y–Pé o eflec ions, p
sub, occu ing wi hin he subs a e, as
defined in Equa ion (3), and he p opaga ion, ansmission, and
eflec ion coe ficien s a e specified in Equa ion (4)–(6), espec-
i ely, and depend on he complex e ac i e indices o he ma e-
ials a each in e ace. I is impo an o no e ha common
p opaga ion pa hs, such as hose be ween in e aces 2 and 3
shown in Figu e 5, a e excluded om any ans e unc ion.
p
sub ωðÞ¼
˜
nsub 1
˜
nsub þ1
2
exp 2i
˜
nsubωdsub
c
(3)
paω,dðÞ¼exp i
˜
naωd
c
(4)
a;bωðÞ¼ 2˜
na
˜
naþ˜
nb
(5)
a;bωðÞ¼
˜
na˜
nb
˜
naþ˜
nb
(6)
Con e sely, he ans e unc ion o he signal passing
h ough he comple e sample, ˆ
H2D ωðÞ, is p esen ed in
Equa ion (7). This exp ession assumes ha he 2D ma e ial laye
se es as a bounda y condi ion on he subs a e (dδ≪λ) wi h a
su ace conduc i i y σ2D, ollowing he me hod p oposed by Liam
e al. in
[40]
o measu ing 2D ma e ials using a con en ional
ansmission se up.
ˆ
H2D ωðÞ¼
ˆ
0;sub psub 2dsub
ðÞ sub;0 0;sub ˆ
sub;0X
NFP
m¼0
p
m
b
!
2
(7)
p
bωðÞ¼
˜
nsub 1
˜
nsub þ12˜
nsubX1ðÞexp 2i
˜
nsubωdsub
c
(8)
X1¼1þ˜
nsub þσ2DZ0(9)
Figu e 5. Ray diag am o THz beams passing h ough he ai , he ba e
subs a e, and he en i e sample.
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ˆ
0;sub ωðÞ¼ 2
1þ˜
nsub þσ2DZ0
(10)
ˆ
sub;0ωðÞ¼ 2˜
nsub
1þ˜
nsub þσ2DZ0
(11)
He e, p
bis defined in Equa ion (8) and (9); Z0¼120πΩ ep-
esen s he ee-space impedance. The ansmission coe ficien s
ˆ
0;sub and ˆ
sub;0, which co espond o he ai –sample in e ace
(deno ed as 1 in Figu e 5), a e specified in Equa ion (10) and (11),
espec i ely.
In o he wo ds, due o symme y, he esul o each channel
essen ially ep esen s he squa e o he ans e unc ion o a
single pass h ough he sample. The common pa be o e each-
ing he fi s su ace is no included in he analysis, as i can be
ea ed as pa o he THz pulse wa e o m. Based on hese ans-
e unc ions, new complex ansmission coe ficien s a e defined
o cha ac e ize he subs a e (see Equa ion 12). Once he complex
e ac i e index is de e mined, he su ace conduc i i y o he
sample can be calcula ed (Equa ion 13).
[40,41]
Tsub ωðÞ¼
Ssub ωðÞ
S0ωðÞ¼16 ˜
nsub
ðÞ
2
˜
nsub þ1ðÞ
4e2i
˜
nsub1
ðÞ
ωdsub
cX
NFP
m¼0
p
m
sub
!
2
(12)
ˆ
T2D ωðÞ¼
S2D ωðÞ
S0ωðÞ¼16X2˜
nsub
ðÞ
2
˜
nsub þ1ðÞ
2e2i
˜
nsub1
ðÞ
ωdsub
cX
NFP
m¼0
p
m
b
!
2
(13)
Fo analyzing each sample, eflec ion- ee Fab y–Pé o mod-
els can be applied by selec ing sho ime windows in he meas-
u emen s. This app oach elimina es he summa ion e ms,
educing he ansmission coe ficien o he o m shown in
Equa ion (14).
ˆ
T2DðωÞFP ¼0¼16X2˜
nsub
ðÞ
2
˜
nsub þ1ðÞ
2e2i
˜
nsub1
ðÞ
ωdsub
c(14)
Al e na i ely, one can selec ime windows ha a e su ficien ly
long o ensu e ha all eflec ions a e e ec i ely included. This
allows he summa ions o he con e gen geome ic se ies o
be eplaced by hei esul , as shown in Equa ion (15).
ˆ
T2DðωÞFP!∞
¼16X2˜
nsub
ðÞ
2
˜
nsub þ1ðÞ
2e2i
˜
nsub1
ðÞ
ωdsub
c1
1 p
bωðÞ
2
(15)
I should be no ed ha he Fab y–Pé o eflec ions be ween
in e aces 2 and 3 in Figu e 5 ha e no been conside ed in
he analysis. This is because, on he one hand, we used
dx>20dsub, and, on he o he hand, he e ac i e index o
he subs a es used is less han 2, meaning ha a leas 10 eflec-
ions occu be ween he walls o he subs a e be o e any a e p o-
duced be ween he subs a e and he mi o .
[42]
I he dxdis ance
is educed o imp o e spa ial esolu ion, a mul ilaye model
mus be used o accoun o hese Fab y–Pé o eflec ions.
The same applies i a much hicke subs a e o one wi h a highe
e ac i e index is used, as his limi s he a ailable ime window
be o e addi ional eflec ions a e obse ed. Howe e , since he
eflec ions a e mo e a enua ed, sho e ime windows can be
employed.
5. Expe imen al Resul s
In his sec ion, he single-b anch analysis is used o cha ac e ize
a ew-laye WS
2
sample on a used qua z subs a e. P elimina y
measu emen s and calib a ions using he 00 configu a ion e eal
ha he maximum ampli ude o he pulses is educed by mo e
han 95%, sugges ing ha he delays in b anches A and B a e
simila and ha he beam dis ibu ion on each b anch is close
o 50%. The analysis con inues by measu ing he bulk ma e ials
in he ime domain o e i y ha he new se up is sui able o
ex ac ing he subs a e’s p ope ies. Two ypes o used qua z
subs a es om di e en supplie s a e used: he fi s is he same
used qua z as he one suppo ing he WS
2
sample, wi h a hick-
ness o 1.00 5% mm, and he second is a 20% hicke used
qua z (1.20 5% mm) wi h a ec angula su ace a ea o 300
mm
2
.Figu e 6 shows he ime-domain wa e o ms o he wo
ai e e ences (ob ained wi h X0 and 0X configu a ions), he ba e
subs a e signals (ob ained wi h X1 and 1X configu a ions) and
he comple e WS
2
/qua z sample signal (ob ained wi h he 2X
configu a ion). Figu e 6 also includes he coo dina es ( ime
and ampli ude) o he main peaks’maximums, which we e used
o p elimina y hickness and e ac i e index es ima ions. All
measu emen s in b anch B ha e been mul iplied by 1 o com-
pensa e o he in e ing e ec o lens L2 (see Figu e 2). While
he wo e e ence signals a e aligned in peak iming, hey di e
sligh ly in he shape; howe e , his disc epancy is no significan
he e since da a ex ac ion in each b anch is done ela i e o i s own
e e ence. The hickness di e ence be ween he subs a es is
appa en in he ela i e delay o 1.05 ps, which inc eases o 3.4
ps o he fi s Fab y-Pé o eflec ions. Rega ding ampli ude educ-
ion due o he subs a es and sample, i is no able ha he fi s
Fab y–Pé o eflec ions a e s ongly a enua ed. This sugges s ha
he esul s ob ained using he app oxima ions in Equa ion (14)
and (15) should be simila , making i unnecessa y o use e y long
ime windows o alida e he app oxima ion in Equa ion (15).
As wi h he ansmission se up, a e ac i e index es ima e o
each subs a e can be ob ained di ec ly om he ime-domain
wa e o ms, conside ing he ay diag am o he beams (see
Figu e 5) and he educed speed due o he subs a e hickness,
dsub. The fi s Fab y–Pé o eflec ion was also used o de i e an
addi ional equa ion o es ima ing he subs a e hickness and
confi ming he consis ency o he alues. Equa ion (16)–(18)
show he ela ionships be ween pulse imes, e ac i e index,
and subs a e hickness.
0¼2dsub
cþ e (16)
1¼2dsubnsub
cþ e (17)
2¼4dsubnsub
cþ e (18)
whe e 0is he a i al ime o he e e ence S0ωðÞpulse, 1is he
a i al ime o he fi s Ssub ωðÞsignal pulse, 2is he ime o he
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fi s Fab y–Pé o eflec ion, and e is an a bi a y delay due o ai
p opaga ion, common o all measu emen s.
Thickness and e ac i e index es ima es o bo h subs a es
can hen be ob ained om he ime di e ences, as shown in
Equa ion (19) and (20).
Δ 10 ¼ 1 0¼2dsub
cnsub 1ðÞ (19)
Δ 21 ¼ 2 1¼2dsubnsub
c(20)
F om he da a in Figu e 6, we ob ained ha he fi s
used qua z sample has a hickness o dsub ≈1.022 mm and
a e ac i e index o nsub ≈1.966. The hicke used qua z shows
a hickness o dsub2≈1.216 mm and a e ac i e index o
nsub2≈1.943. Bo h e ac i e index alues a e consis en wi h
li e a u e
[43]
o his equency ange, and he hicknesses ag ee
wi h he specifica ions p o ided by he manu ac u e s as well as
wi h expe imen al measu emen s.
Figu e 7 p esen s he spec a co esponding o he signals in
Figu e 6. All spec a show s ong molecula abso p ion peaks due
o wa e apo a 557, 752, and 988 GHz.
[44,45]
Be ween 100 and
300 GHz, he e e ence spec um om b anch B is clea ly highe
han ha om b anch A, bu abo e 1 THz, he opposi e end is
obse ed. In he in e media e egion, he spec a a e simila ,
hough no iden ical. The spec a ob ained o he sample and
he ba e subs a es a e consis en wi h he e e ence spec a
o each espec i e b anch. Compa ed o he spec a om he
Figu e 6. Time-domain elec ic field pulse o he ansmi ed THz wa e h ough he wo e e ences (ai ), he ba e subs a es ( used qua z), and he WS
2
sample.
Figu e 7. Elec ic field ampli ude spec a o he ansmi ed THz wa e h ough he wo e e ences (ai ), he ba e subs a es ( used qua z), and he WS
2
sample.
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ansmission configu a ion using he same an ennas,
[22]
he band-
wid h is sligh ly na owe . Abo e 1 THz, subs a e signals become
highly a enua ed, esul ing in a low signal- o-noise a io (SNR).
Figu e 8 shows he ansmi ance o he subs a es and he
comple e sample wi hin he ange o 0.2–1.2 THz. No ably, all
ansmi ances in Figu e 8 ep esen a single pass h ough he
sample, calcula ed based on he ac ha he ansmission coe -
ficien s o his configu a ion a e he squa e o hose o a single-
pass ansmission configu a ion. The ansmi ance alues
and beha io align wi h hose measu ed ia he ansmission
me hod:
[42]
subs a e ansmi ances dec ease om ≈95% o
70%, and he WS
2
sample shows a nea ly cons an ansmi ance
a ound 90% o e he measu ed ange. Al hough one o he sub-
s a es is 20% hicke , he ansmi ance emains nea ly he
same, indica ing ha he ex inc ion coe ficien κsub is close o
ze o, as seen in Figu e 9. In o he wo ds, he ampli ude educ-
ion is mainly a ibu able o he ansmission coe ficien s o
eflec ions a he ai –subs a e in e aces a he han o p opaga-
ion h ough he ma e ial i sel . Figu e 9 also shows ha he
e ac i e index o he subs a e is nsub ¼1.960 0.009 om
300 GHz o 1 THz. Specifically, a 500 GHz, he measu ed alue
is nsub ¼1.962, which ma ches he alue epo ed by M. Na aly
and R. E. Miles a his equency.
[46]
The e ac i e index also
ag ees wi h he es ima e de i ed om he ime-domain analysis.
Figu e 8. T ansmi ance ob ained om he ampli ude spec a o he ba e subs a es ( used qua z), he WS
2
laye , and he en i e sample in he
ange [0.2, 1.2] THz.
Figu e 10. Real pa o he shee conduc i i y o WS
2
ob ained using single-b anch analysis, compa ed o he alues ob ained om a ansmission
THz–TDS configu a ion o WS
2
and single-laye (SL) g aphene in a p e ious s udy.
[22]
Figu e 9. Complex e ac i e index o he used qua z subs a e in he
ange [0.2, 1.2] THz.
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The eal pa o he shee conduc i i y o he WS
2
sample,
ob ained om Equa ion (15) (assuming all eflec ions a e
included), is shown in Figu e 10. The WS
2
shee conduc i i y
emains s able be ween 2.2 and 2.6 mS sq1. Fo compa ison,
Figu e 10 also includes shee conduc i i y o an SL g aphene
sample and ew-laye WS
2
sample on a simila subs a e,
p oduced using he same echnique, and measu ed using a
ansmission se up in a p e ious s udy.
[22]
The shee conduc i i y
o WS
2
measu ed wi h his double-pass configu a ion is
sligh ly highe bu emains wi hin he same o de o magni ude
as p e ious measu emen s wi h he ansmission se up. The
esul s a e consis en and show, as expec ed, ha he numbe
o laye s in he 2D ma e ial influences he conduc i i y o he
samples.
6. Conclusion
A se o configu a ions o THz–TDS based on a Michelson in e -
e ome e has been p esen ed. The p ima y ad an age o his
app oach lies in i s e sa ili y, enabling bo h in e e ome y as
well as ansmission and eflec ion measu emen s on he sample
wi h minimal adjus men s o he se up. Wi h a su ficien ly
ex ended delay line, he single-b anch configu a ion can, in ac ,
cap u e bo h ansmi ed and eflec ed pulses o semi anspa -
en samples in a single measu emen . When he signal om one
b anch is cancelled, measu emen s o 2D ma e ial samples,
subs a es, o ai e e ences can be conduc ed simila ly o a ans-
mission se up, bu wi h a double pass o e he sample. This
double-pass configu a ion has been shown o allow ansmi -
ance and su ace conduc i i y measu emen s in 2D ma e ials,
such as WS
2
on used qua z. The bandwid h ob ained wi h his
echnique is na owe compa ed o he ansmission configu a-
ion, and he a ailable ime window o measu emen s is sho e
due o he addi ional eflec ions in ol ed. Howe e , as he ampli-
udes o he Fab y–Pé o eflec ions a e educed, a sho e ime
window is also equi ed. Fo cha ac e izing samples wi h a la ge
su ace a ea, measu emen s can be aken om ei he b anch.
Howe e , he b anch wi h he lens (B) o e s highe spa ial eso-
lu ion, while he b anch wi hou he lens (A) a oids he Gouy
phase shi e ec . The empo al signals allow o an es ima ion
o he subs a es’ e ac i e indices, and i is e en possible o
ob ain an app oxima e measu emen o subs a e hickness
using he fi s Fab y–Pé o eflec ions. The equa ions p o ided
o he double-pass configu a ion ha e achie ed a high le el o
accu acy in ob aining he subs a es’complex e ac i e index
in he THz ange. Rega ding 2D ma e ial measu emen s, bo h
he su ace conduc i i y and ansmi ance ob ained om he
ew-laye WS
2
sample wi h his configu a ion a e consis en wi h
alues ob ained in p e ious s udies using a con en ional ans-
mission se up on simila samples, hough he conduc i i y is
highe han expec ed. The disc epancy in shee conduc i i y
could be a ibu ed o di e ences in he numbe o laye s, he
g ain size, o he e e ence subs a e used, among o he ac o s.
Fu he in es iga ion should be ca ied ou o ob ain mo e accu-
a e alues o he shee conduc i i y. Finally, as his echnique is
based on a noncon ac THz–TDS wi h low powe pulses, he
me hod is nondes uc i e.
Acknowledgemen s
This wo k has ecei ed unding om he CONFLOC g an (g an no.
PID2022-1377540B), unded by MCIN/AEI/10.13039/501100011033/
FEDER, UE, om he EU’s Ho izon Eu ope unde Ma ie Sklodowska-
Cu ie g an ag eemen no. 101073265 (EWOC), and om he Ca alan
Go e nmen Uni e si y and Resea ch Aid Managemen Agency
(AGAUR) h ough he Resea ch G oup g an 2021 SGR 01415. The au ho s
would like o hank he Scien ific and Technological Cen e a he
Uni e si a de Ba celona (CCiT-UB) o p o iding Raman spec oscopy
acili ies and he P o . J. Eom g oup om Sejong Uni e si y, Ko ea, o
p o iding he WS
2
sample.
Conflic o In e es
The au ho s decla e no conflic o in e es .
Da a A ailabili y S a emen
The da a ha suppo he findings o his s udy a e a ailable om he
co esponding au ho upon easonable eques .
Keywo ds
2D ma e ials, su ace conduc i i ies, e ahe z ime-domain spec os-
copies (THz-TDS), WS
2
Recei ed: June 29, 2024
Re ised: No embe 14, 2024
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