Plasmonics in A omically Thin C ys alline
Sil e Films
Zaka ia M. Abd El-Fa ah,
†,‡,○
Vahagn Mkhi a yan,
†,○
Jens B ede,
§
Lau a Fe nandez,
∥
Cheng Li,
⊥
Qiushi Guo,
⊥
A nab Ghosh,
#
Al a o Rod íguez Echa i,
†
Do on Na eh,
#
Fengnian Xia,
⊥
J. En ique O ega,*
,§,¶
and F. Ja ie Ga cía de Abajo*
,†,∇
†
ICFO-Ins i u de Ciencies Fo oniques, The Ba celona Ins i u e o Science and Technology, 08860 Cas ellde els, Ba celona, Spain
‡
Physics Depa men , Facul y o Science, Al-Azha Uni e si y, Nas Ci y, E-11884 Cai o, Egyp
§
Donos ia In e na ional Physics Cen e , Paseo Manuel La dizabal 4, 20018 Donos ia, San Sebas ian,Spain
∥
Cen o de Física de Ma e iales CSIC-UPV/EHU and Ma e ials Physics Cen e , 20018 San Sebas ian, Spain
⊥
Depa men o Elec ical Enginee ing, Yale Uni e si y, New Ha en, Connec icu 06511, Uni ed S a es
#
Facul y o Enginee ing, Ba Ilan Uni e si y, Rama Gan 5290002, Is ael
∇
ICREA-Ins i ucioCa alana de Rece ca i Es udis A anca s, Passeig Lluís Companys 23, 08010 Ba celona, Spain
¶
Depa amen o de Física Aplicada I, Uni e sidad del País Vasco, E-20018 San Sebas ian, Spain
*
SSuppo ing In o ma ion
ABSTRACT: Ligh −ma e in e ac ion a he a omic scale
ules undamen al phenomena such as pho oemission and
lasing while enabling basic e e yday echnologies, includ-
ing pho o ol aics and op ical communica ions. In his
con ex , plasmons, he collec i e elec on oscilla ions in
conduc ing ma e ials, a e impo an because hey allow he
manipula ion o op ical fields a he nanoscale. The ad en
o g aphene and o he wo-dimensional c ys als has pushed
plasmons down o genuinely a omic dimensions, displaying
appealing p ope ies such as a la ge elec ical unabili y.
Howe e , plasmons in hese ma e ials a e ei he oo b oad
o lying a low equencies, well below he echnologically
ele an nea -in a ed egime. He e, we demons a e sha p
nea -in a ed plasmons in li hog aphically pa e ned wa e -scale a omically hin sil e c ys alline films. Ou measu ed
op ical spec a e eal na ow plasmons (quali y ac o o ∼4), u he suppo ed by a low shee esis ance compa able o
bulk me al in ew-a omic-laye sil e films down o se en Ag(111) monolaye s. Good c ys al quali y and plasmon
na owness a e ob ained despi e he addi ion o a hin passi a ing dielec ic, which ende s ou samples esilien o
ambien condi ions. The obse a ion o spec ally sha p and s ongly confined plasmons in a omically hin sil e holds
g ea po en ial o elec o-op ical modula ion and op ical sensing applica ions.
KEYWORDS: 2D plasmonics, ul a hin plasmonics, 2D ma e ials, a omically hin sil e , c ys alline me al films
The con ol o ligh a he nanoscale is a esea ch
on ie wi h applica ions in a eas as di e se as
biosensing,
1,2
op oelec onics,
3
nonlinea op ics,
4,5
quan um op ics,
6,7
and nano obo ics.
8
Me allic nanos uc u es
play a pi o al ole in his con ex because hey hos collec i e
elec on oscilla ions, known as plasmons, which can in e ac
s ongly wi h ligh . This enables a la ge confinemen o op ical
ene gy down o nanome e -sized egions, he eby enhancing
he associa ed elec omagne ic fields by se e al o de s o
magni ude ela i e o ex e nally inciden fields.
9
Such appealing
p ope ies and he pu sue o he no ed applica ions ha e ueled
in ense esea ch wo k in o plasmonics o be e unde s and
and con ol hese collec i e elec onic exci a ions and co e a
b oad spec al ange om he ul a iole o he e ahe z
egimes. P og ess has mainly elied on ad ances in nano-
ab ica ion and colloid chemis y, which allow he p oduc ion
o enginee ed me allic nanos uc u es wi h on-demand
plasmonic esponse.
10,11
Plasmons in a omic-scale sys ems ha e eme ged as a sou ce
o ex ao dina y p ope ies esul ing om he ac ha hey a e
Recei ed: Feb ua y 28, 2019
Accep ed: June 4, 2019
Published: June 4, 2019
A icle
www.acsnano.o g
Ci e This: ACS Nano 2019, 13, 7771−7779
© 2019 Ame ican Chemical Socie y 7771 DOI: 10.1021/acsnano.9b01651
ACS Nano 2019, 13, 7771−7779
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sus ained by a compa a i ely small numbe o cha ge ca ie s.
Elec on ene gy-loss spec oscopy has been ins umen al in
e ealing plasmons in sys ems such as C60 molecules,
12
ca bon
and bo on-ni ide single-wall nano ubes,
13,14
a omic gold wi es
g own on icinal silicon su aces,
15
ew-a omic-laye sil e
films,
16
monolaye DySi2,
17
ul a hin indium
18
and silicide
19
wi es, and g aphene.
20
Addi ionally, ul a hin TiN films ha e
been demons a ed o e ac o y plasmonics,
21,22
which
con ibu e o configu e he eme ging field o ansdimen ional
pho onics.
23
Among hese ma e ials, high-quali y g aphene has
been ound o sus ain low-ene gy plasmons when i is highly
doped, exhibi ing la ge elec o-op ical unabili y,
24,25
long
li e imes,
26
and s ong confinemen compa ed wi h con en-
ional plasmonic me als.
27,28
Topological insula o s
29
and black
phospho us
30
ha e also been shown o display wo-dimen-
sional (2D) plasmons. Un o una ely, unlike noble-me al
s uc u es, he plasmons epo ed in hese sys ems a e ei he
a he b oad o lying a mid-in a ed o lowe equencies, a
om he echnologically appealing nea -in a ed (NIR) egime.
As a po en ial solu ion o his p oblem, elec ochemically
unable plasmons ha e been e ealed h ough op ical spec-
oscopy in small polycyclic a oma ic hyd oca bons,
31,32
al hough hei in eg a ion in as commu a ion de ices emains
a challenge.
A omically hin noble-me al films appea as a iable solu ion
o achie e la ge elec o-op ical unabili y
33,34
wi hin he NIR
spec al ange. Howe e , c ys alline quali y is equi ed o lowe
op ical losses o he p omised le el o hese ma e ials in he
plasmonic spec al egion. Indeed, he p esence o mul iple
ace s in ew-nanome e nanopa icles
35,36
and spu e ed
films
37
p oduce b oad plasmons cha ac e ized by a quali y
ac o (Q= a io o peak equency o spec al wid h) o he
o de o ∼1, which a e s hei use in cu ing-edge plasmonic
applica ions.
In his A icle, we epo on he ab ica ion and he excellen
plasmonic and elec ical p ope ies o wa e -scale a omically
hin c ys alline sil e films composed o only a ew a omic
laye s. We use ad anced su ace-science echniques o ab ica e
and cha ac e ize Ag(111) films consis ing o 7−20 a omic
monolaye s (MLs) on a clean Si(111) subs a e, which we
hen co e wi h ∼1.5 nm o Si o passi a e hem om ai . The
high a omic quali y o he samples, which we confi m h ough
scanning unneling mic oscopy (STM), angle- esol ed pho o-
elec on spec oscopy (ARPES), high- esolu ion ansmission
elec on mic oscopy (HRTEM), and low-ene gy elec on
diff ac ion (LEED), allows us o esol e sha p elec onic
e ical quan um-well s a es (QWs) and measu e e y low
shee esis ances o hin films down o 7 ML Ag(111) (1.65
nm hick, ∼20 Ω/sq, jus a ac o o 2 highe han he bulk
es ima e). We ob ain spec al e idence o confined plasmons
by using elec on-beam (e-beam) nanoli hog aphy o pa e n
ibbons on he sil e films, esul ing in measu ed plasmons
wi h quali y ac o s nea ing Q≈4 o 10 ML (∼2.4 nm) films.
These esul s e eal he abili y o la e ally pa e ned ew-
a omic-laye a omically fla sil e o confine plasmons wi h
simila li e imes as bulk sil e , hus ex ending 2D plasmonics
in o he echnologically appealing NIR egime.
Like in g aphene,
38
me al films o small hickness din he
ew a omic-laye ange allow us o d ama ically educe he in-
plane su ace-plasmon wa eleng h λp. In he D ude model (see
he Me hods sec ion), we find λp o scale linea ly wi h dand
quad a ically wi h he ligh wa eleng h λ0as
λ
λ
=d
L
p0
2
1
2(1)
(see Figu e 1b), whe e L1is a cha ac e is ic leng h ha
depends on he combina ion o me al and subs a e ma e ials
(e.g.,L1≈205 nm o Ag on Si). The confinemen in he
e ical di ec ion is cha ac e ized by a symme ic exponen ial
decay o he associa ed elec ic field in ensi y away om he
film, ex ending a dis ance ∼λp/4π ega dless o he choice o
ma e ials and me al hickness (Figu e 1a). The compa a i ely
small numbe o elec ons ha suppo he plasmons in
a omically hin films makes hem mo e suscep ible o he
en i onmen , so ha elec ical ga ing wi h a ainable ca ie
densi ies can p oduce significan plasmon shi s in single-a om-
laye noble me als,
33
while he addi ion and elec ical ga ing o
a g aphene film esul s in d ama ic modula ion o hicke films
up o a ew nanome e s.
34
Likewise, he p esence o an analy e
can shi he plasmon esonance and in oduce molecule
spec al finge p in s enhanced by he nea field o he
plasmons, simila o wha has been obse ed wi h g aphene.
2
Howe e , besides such plasmon shi s, all o hese applica ions
Figu e 1. P ope ies o plasmons in a omically hin me al films. (a) The plasmon wa eleng h λpis small compa ed wi h he ligh wa eleng h
λ0, while he associa ed elec ic field ex ends a dis ance λp/4πaway om he film ( o 1/edecay in field in ensi y), symme ically on bo h
sides o he in e ace (see he Me hods sec ion) ega dless o dielec ic en i onmen and film composi ion. The ske ch shows a c oss sec ion
o an ex ended film (pe mi i i y ϵ< 0) and subs a e (pe mi i i y ϵs> 0) in a plane pe pendicula o he su ace, along wi h he in-plane
ha monic oscilla ion o he plasmon field (sine p ofile) and exponen ial ou -o -plane decay o i s in ensi y ( igh plo ). (b) The plasmon
wa eleng h scales linea ly wi h me al hickness dand quad a ically wi h λ0as λp=d(λ0/L1)2, whe e L1depends on he choice o ma e ials
and is a he la ge (L1≈205 nm) o Ag on Si. A ibbon o wid h Wexhibi s ans e se dipola esonances (i.e., wi h in-plane pola iza ion
ac oss he ibbon) de e mined by W≈0.37 λp. (c) In ibbon a ays, he plasmon wid h has a adia i e componen ha scales linea ly wi h
bo h he me al hickness and he in e se o he pe iod- o-wid h a io (see Me hods), and depends on he choice o me al and subs a e
pe mi i i y (see labels), he e o e affec ing he quali y ac o Qas shown he e o 10 ML me al a λ0= 1.55 μm wa eleng h. Do ed
ho izon al lines deno e he long pe iod limi o Ag and Au. The do ed e ical line shows he a io used in his wo k.
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equi e spec ally na ow plasmons, so ha spec al modula ion
esul s in s ong changes in ligh ansmission o sca e ing, and
his, in u n, demands he ab ica ion o high-quali y films.
RESULTS AND DISCUSSION
We epi axially g ow high-quali y c ys alline Ag(111) films on a
Si(111)-o ien ed wa e subs a e
39
wi h a con olled numbe o
a omic monolaye s unde ul ahigh- acuum (UHV) condi ions
(see he Me hods sec ion). Th ough fine uning o he g ow h
pa ame e s, we achie e films consis ing o a single c ys al
domain on a cm2chip scale, as e ealed by STM wi h a omic
esolu ion (see Figu es 2a and S2). The o iginal 7 ×7
econs uc ion o a omically fla Si (Figu e 2c, whe e he uppe
and lowe hal es a e emp y and filled s a e images acqui ed
wi h bias ol ages o +2 V and −2 V, espec i ely) is emo ed
upon Ag deposi ion, lea ing an a omically fla Ag su ace
(Figu e 2e) ha p ese es c ys al la ice o ien a ion (c . Figu e
2b,d). We app oach he a ge ed numbe o Ag(111)
monolaye s (10 ML in Figu e 2a) wi h jus a ∼5% ac ion
o egions diffe ing by 1 ML hickness. We comple e s uc u al
cha ac e iza ion by imaging a c oss sec ion o he film using
HRTEM, which e eals a p ese a ion o de ec - ee o de ing
o a omic Ag(111) monolaye s (Figu e 2k,l) on he Si c ys al
subs a e.
Because plasmons a e sus ained by conduc ion elec ons, we
s udy he elec onic band s uc u e o he films, he small
hickness o which p oduces disc e iza ion in o a cha ac e is ic
se o s anding wa es, encompassing e ical QWs
40−42
(labeled by n=1,··· in he ske ch o Figu e 2 ) and a
su ace-bound s a e (SS). Each o hese QWs defines a band
wi h nea ly ee pa abolic dispe sion (effec i e mass o ∼1), as
e ealed by ARPES (Figu e 2g), which also show na ow
lineshapes. We passi a e ou films wi h Si (1.5 ML nominal
hickness) o p o ec hem du ing handling and pa e ning
using e-beam nanoli hog aphy (see below). We no e ha high-
quali y unpassi a ed Ag(111) films a e s able du ing hou s
when b ough om UHV o ambien condi ions wi hou
pa e ning;
43,44
howe e , s ain in he Ag−Si in e ace
e en ually leads o film dewe ing (wi hin days), ini ia ed by
pinholes
44
and leading o sil e oxides and o ma ion o ough
films. The p o ec i e Si laye is apidly oxidized upon exposu e
o ai , while he unde lying Ag film is unaffec ed o weeks (see
Figu e S1). We ema k ha he addi ion o he hin Si capping
laye causes he SS o disappea bu does no affec he QW
s a es (Figu e 2h,i). Con ol o e hickness and high-quali y o
he films u he allows us o expe imen ally obse e a ∼1/d
scaling o he QW binding ene gies wi h inc easing film
hickness d(Figu e 2j), ypical o a 1D pa icle-in-a-box
sys em. We esol e QWs in all samples used in he p esen
s udy, yielding an unambiguous de e mina ion o he numbe
o laye s in each Ag film. The p esence and quali y o he Ag
film in he samples is u he co obo a ed by ellipsome y
measu emen s compa ed wi h ba e Si subs a es (see Figu e
S4).
I is a widely acknowledged ac ha ul a hin me al films
mus expe ience s ong su ace sca e ing, and he e o e, see
hei elec ical esis ance sha ply inc eased, as p e ious s udies
ha e indica ed.
45−49
In con as , he high c ys al quali y o ou
films p oduces e y low le els o he shee esis ance (Figu e
Figu e 2. Fab ica ion and cha ac e iza ion o a omically hin c ys alline sil e films. (a) Scanning unneling mic oscopy (STM) image o 10
ML Ag(111) on Si. The his og am (uppe inse ) e eals he nea -comple ion o he 10 h laye (95% a ea) wi h a small p esence o 9 ML (4%,
da ke ea u es) and 11 ML (1%, b igh e ea u es) islands (see colo scale o ou -o -plane dis ance). (b−d) Low-ene gy elec on diff ac ion
(LEED) o (b) he ba e Si(111) (7 ×7 econs uc ion) subs a e and (d) a e deposi ion o 10 ML Ag(111), along wi h a omic-scale STM
de ails o bo h su aces (panels c and e, espec i ely). Fou ie ans o ms o he STM images a e shown in he lowe -le co ne s. ( ) Ske ch
o a Ag(111) film deposi ed on Si(111), along wi h i s su ace-s a e (SS) and he h ee lowes e ical quan um-well-s a e (n=1−3) wa e
unc ions, he e p obed h ough angle- esol ed pho oemission spec oscopy (ARPES). (g−i) ARPES in ensi y as a unc ion o elec on
ene gy ela i e o he Fe mi ene gy ( e ical scale) and pa allel wa e ec o o (g) a 10 ML Ag (111)/Si sample, and (h, i) a e co e age
wi h 1 and 2 MLs o Si. (j) E olu ion o he no mal-emission ARPES in ensi y as a unc ion o sil e film hickness o 8−16 ML Ag(111) on
Si. Dashed cu es a e guides o he eye, co esponding he he op h ee s a es, wi h he s a e index n(see ) a ying wi h he numbe o
laye s Nas indica ed by labels. (k, l) High- esolu ion ansmission elec on mic oscopy (HRTEM) images o he ans e sal c oss-sec ion o
a 14 ML Ag(111)/Si sample, showing he sil e a omic planes and hei 0.236 nm sepa a ion. (m) Measu ed oom- empe a u e shee
esis ance o sil e films consis ing o N=7−20 ML Ag(111)/Si (symbols), compa ed wi h he 293 °C bulk es ima e o ∼(68.7/N)Ω/sq
(solid cu e). A o al o h ee diffe en de ices ha e been measu ed o each alue o N, and one o hem is shown in he mic og aph inse .
ACS Nano A icle
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2m), as e ealed by ou -p obe measu emen s (see Figu e S3).
In pa icula , we find he esis ance o be only a ac o o ∼2
highe han he es ima e based on he bulk esis i i y o sil e
o films as hin as 7 ML Ag(111) (1.65 nm hickness).
Because he film quali y does no open new channels o
inelas ic collisions compa ed wi h he bulk, we a ibu e his
ac o o 2 o de ec s in oduced by he capping Si laye , which
has educed c ys allini y (see op o Figu e 2l), al hough some
film damage du ing de ice ab ica ion canno be uled ou . We
hus a ibu e he la ge educ ion o esis ance in ou films
compa ed wi h p e ious s udies, in which films had a
polyc ys alline mo phology, o he high c ys allini y and
absence o g ain bounda ies ob ained by ou ollowed epi axial
p ocedu e (see he Me hods sec ion). The p esen esul s hus
es ablish a much lowe bound o he ole played by su ace
sca e ing in he elec ical esis ance o high-quali y c ys alline
sil e films.
Plasmons in a omically hin films a e confined exci a ions
wi h la e al wa e ec o 2π/λpg ea ly exceeding he ligh wa e
ec o 2π/λ0, which p e en s di ec ligh -plasmon coupling. An
addi ional sou ce o la e al momen um is needed o b eak his
op ical momen um misma ch, such as ha p o ided by a
pa e n in he films. In his wo k, we use e-beam nano-
li hog aphy (see he Me hods sec ion) o ca e ibbons wi h
he desi ed ange o wid hs W∼50−500 nm, which allow us
o explo e plasmon wa eleng hs λp≈2.7 W(Figu e 1b and he
Me hods sec ion). The s uc u e unde conside a ion is
ske ched in Figu e 3a, while scanning elec on mic oscopy
(SEM) images o some o he ac ual s uc u es a e shown in
Figu e 3b. The esul ing measu ed op ical spec a o diffe en
Figu e 3. Plasmons in a omically hin c ys alline sil e nano ibbons. (a) Ske ch o he ibbon a ays ab ica ed o his s udy. (b) Scanning
elec on mic oscopy (SEM) images o some o he s uc u es in a 10 ML Ag(111)/Si sample, wi h he a ge ed ibbon wid h (da k a eas)
indica ed in each case. (c) No malized op ical ex inc ion as expe imen ally measu ed o fixed ibbon wid h W= 70 nm and a ious me al
film hicknesses (see labels). (d) The same as panel c o fixed me al hickness (10 ML) and a ying ibbon wid h. Ve ical a ows in panels c
and d co espond o he analy ical p edic ion o eq 2 o he colo -coo dina ed plasmon wa eleng hs.
Figu e 4. Enginee ing he wa eleng h and quali y ac o Qo plasmons in a omically hin c ys alline sil e films. (a) Plasmon ene gy ( igh
scale) and co esponding ligh wa eleng h (le scale) as a unc ion o ibbon wid h. Expe imen (symbols) is compa ed wi h simple
analy ical heo y (dashed cu es, eq 2). (b) Plasmon spec al wid h ℏγas a unc ion o plasmon ene gy ℏω. Measu ed da a om samples
wi h a ious sil e hicknesses a e plo ed using diffe en symbols, wi h he ibbon wid h encoded in he colo scale. The uppe dashed
ho izon al line is a guide o he eye. The lowe dashed line shows he adia i e con ibu ion o he damping ℏγ ad acco ding o eq 5 o 10
ML. (c) Quali y ac o (peak ene gy di ided by whm spec al wid h, Q=ω/γ) as p edic ed by he D ude model o sil e films using
diffe en inpu alues o he damping a e γ(see he main ex ) compa ed wi h he expe imen al da a aken om panel b.
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film hicknesses and ibbon wid hs a e p esen ed in Figu e
3c,d, whe e plasmon edshi s a e clea ly obse ed when
educing he hickness o inc easing he wid h, in quali a i e
ag eemen wi h he analy ical o mula
λ
≈LWd2.7 /
01 (2)
( e ical a ows in Figu e 3c,d), which p edic s he ligh
wa eleng h associa ed wi h he plasmon o scale linea ly wi h
he squa e oo o he wid h- o- hickness aspec a io W/d.
This exp ession, which ollows om he D ude model
combined wi h he ela ion be ween λpand W(see he
Me hods sec ion),
50
is in excellen ag eemen wi h a quan um-
mechanical desc ip ion o ew-laye Ag films based upon he
andom-phase app oxima ion combined wi h a ealis ic
desc ip ion o QWs in he films (see Figu e S10). Analy ically
calcula ed spec a (see he Me hods sec ion) ha e a simila
le el o ag eemen wi h measu emen s and nea ly coincide
wi h ull elec omagne ic simula ions (see Figu es S8 and S9).
Addi ionally, he spec a o Figu e 3c,d e eal an inc ease in
plasmon b oadening wi h inc easing ibbon wid h (see below).
These plasmon cha ac e is ics a e consis en ly co obo a ed
upon inspec ion o diffe en samples (see Figu es S5 and S6),
he wa eleng hs and spec al wid hs o which a e summa ized
in Figu e 4. In pa icula , when plo ing he obse ed plasmon
wa eleng h as a unc ion o ibbon wid h, we ob ain a good
ag eemen wi h eq 2 despi e de ia ions in indi idual s uc u es,
which we a ibu e o a a iabili y in he ac ual wid h o he
pa e ned ibbons. Addi ionally, we find a oughly cons an
plasmon wid h ℏγ≈230 meV, which gi es ise o a linea
inc ease in Q=ω/γwi h plasmon ene gy ℏω(see Figu e 4b,c
and he quali y- ac o ex ac ion p ocedu e in Figu e S7). In
ou expe imen s, we find alues o Qapp oaching 4 a plasmon
ene gies nea 1 eV. These spec ally na ow plasmons a e made
possible by he small hickness o ou me al films combined
wi h hei c ys alline quali y. Indeed, polyc ys alline films in he
ew nanome e ange ha dly each Q≈1.
37
Addi ionally,
spa ially confined NIR plasmons in noble me als equi e he
use o high aspec a ios W/d≈20; be o e he p esen s udy,
high-quali y s uc u es could only be ob ained o much hicke
films, he e o e in ol ing la ge W, and in consequence
p oducing subs an ially b oade plasmons due o coupling o
adia ion. Likewise, NIR plasmons in me allic colloids demand
la ge pa icle aspec a ios, o which he obse ed quali y
ac o s a e significan ly smalle han 4 due o adia i e losses as
well,
51
while in con as o ou films, he s a egy o b inging
he pa icle size o he ew-nanome e ange in oduces
addi ional plasmon quenching o igina ing in fini e-size effec s
36
and he eby limi ing he achie able Q.
The plasmon quali y ac o s in ou ibbon a ays a e pa ially
limi ed by adia i e losses (see Figu e 1c). Indeed, as shown in
he Me hods sec ion, he o al plasmon damping a e γ=γin +
γ ad is he sum o an in insic componen γin and a geome y-
dependen adia i e componen γ ad =Γ×Wd/a, whe e ℏΓ≈
88 meV/nm o Ag(111) films on silicon. Fo ou expe imen s,
we ab ica e ibbons wi h a pe iod- o-wid h a io a/W= 1.5,
which yields ℏγ ad ≈137 meV o 10 ML films. This alue is
shown in Figu e 4b as a lowe dashed line; so we a e le wi h
an in insic damping ℏγin ≈93 meV, which is s ill o e 4 imes
la ge han he bulk alue o 21 meV de i ed om he
measu ed pe mi i i y o bulk sil e .
52
We no e ha adia i e
losses should be negligible o a ays o la ge pe iod- o-wid h
a io, hus sugges ing a di ec way o imp o e he quali y ac o
wi h he same film quali y (see Figu e S8).
The excess o in insic damping is p esumably o igina ing in
sample damage incu ed du ing he e ching p ocesses used o
e-beam nanoli hog aphy (see he Me hods sec ion). Now, he
ques ion a ises, how high can Qbe o confined plasmons
based upon high-quali y me al films consis ing o a ew a omic
laye s (e.g., < 2 nm o 8 ML Ag(111))? We add ess his
ques ion by compa ing ou measu ed Q’s wi h diffe en
es ima es based upon he D ude exp ession Q=ω/γin
neglec ing adia i e losses (Figu e 4c). Assuming he alue
ℏγAC = 21 meV ob ained by fi ing he measu ed Ag
pe mi i i y
52
o a D ude ail in he <1 eV spec al egion,
we find Q> 40 (an o de o magni ude la ge han hose
obse ed he e), in ag eemen wi h p edic ions based on he
es ima e o Qgi en by −Im{ϵ}/Re{ϵ}.
53
This is also in good
ag eemen wi h bo h he quali y ac o s o spec a calcula ed in
he long-wa eleng h limi (spec al fi ) and he es ima e
ob ained o m he measu ed bulk DC conduc i i y (ℏγDC,N≫1
≈17 meV). We no e ha he shee esis ance measu ed om
ou films (Figu e 2m) leads acco ding o he D ude model o
p edic ed alues Q> 20 o 10 ML Ag(111) films (see he
Me hods sec ion) in he absence o adia i e losses.
CONCLUSIONS
In b ie , we epo well-defined plasmons in a omically fla
Ag(111) films g own on Si(111), wi h hickness as low as 8
ML (∼1.9 nm). The measu ed quali y ac o s each alues o
∼4. Fu he imp o emen o hese esul s should include he
explo a ion o hinne films down o 1−3 ML, which a e,
howe e , challenging because o he s ain associa ed wi h he
Ag−Si(111) in e ace. Following a wo-s ep p ocess (i.e.,
deposi ion a low empe a u e o ∼100 K ollowed by
annealing o 300 K), we find he lowes hickness needed o
p oduce a omically fla films using his p ocedu e o be 6 ML.
Ne e heless, 2 ML Ag(111) films ha e been ecen ly epo ed
by employing a Ga/Si buffe laye ,
54
showing a he fla
su aces and well-defined quan um-well s a es.
55
In ou films,
he c ys alline quali y o he ab ica ed Ag(111) films, which
exhibi a clean elec onic band s uc u e consis ing o
quan ized QWs, combined wi h he c ys alline quali y o he
subs a e, pe mi uling ou inelas ic elec on and plasmon
sca e ing due o impe ec ions. Howe e , he nonc ys alline
p o ec ing capping laye can in oduce inelas ic coupling
channels. Addi ionally, he e ching p ocesses used du ing e-
beam li hog aphy can cause sample damage, o which we
a ibu e he educ ion by hal in film elec ical conduc ance
and by a ac o o ∼5 in op ical quali y ac o wi h espec o
he maximum es ima e in he s udied spec al ange, while
ano he ac o o >2 in quali y ac o can be gained by educing
adia i e losses (e.g., by inc easing he pe iod- o-wid h a io o
he ibbon a ays). Fu he imp o emen in nano ab ica ion
could he e o e inc ease he achie ed plasmon quali y ac o s.
Ne e heless, he plasmons he e obse ed should be al eady
sufficien ly na ow o p oduce la ge elec o-op ical modula ion
in he NIR,
34
while hei educed e ical and la e al size
(down o ∼20 and ∼50 nm a 0.8 eV, see Figu es 1a and 4a)
a e ideally sui ed o enhancing he in e ac ion wi h
neighbo ing molecules, hus holding g ea po en ial o op ical
sensing.
METHODS
Fab ica ion o A omically-Thin Sil e Films. Ou Ag/Si(111)
samples we e p epa ed inside an UHV chambe a 1.0 ×10−10 mba
base p essu e. We used 4 mm ×12 mm n-doped Si(111) chips wi h
ACS Nano A icle
DOI: 10.1021/acsnano.9b01651
ACS Nano 2019, 13, 7771−7779
7775

specific esis ance 120−340 Ωcm as ba e subs a es. The dopan
concen a ion o Si (1.3−3.7 ×1013 cm−3) was chosen o gua an ee
he elec ical conduc ion equi ed by su ace science echniques while
no influencing he plasmonic pe o mance o he sil e films. Once
inside he UHV chambe , he Si(111) chips we e degassed o e nigh
a 900 K and subsequen ly flashed o 1400 K o 20−30 s o emo e
he na i e silicon oxide. The sample empe a u e was slowly educed
o 600 K, main ained a his empe a u e o 30 min, and hen cooled
o oom empe a u e. This esul ed in he o ma ion o a de ec - ee,
a omically clean Si(111) su ace wi h a 7 ×7 econs uc ion. Sil e
a oms we e sublima ed om an elec on-bomba dmen e apo a o ,
which was calib a ed o submonolaye accu acy using a qua z
mic obalance moni o in combina ion wi h p obing o he dis inc 1−
2 ML Ag/Cu(111) su ace s a es by pho oemission.
56
Sil e films
we e g own on Si(111) ollowing his wo-s ep p ocess. The Si(111)
subs a e was kep a 100−120 K du ing Ag deposi ion and slowly
annealed o oom empe a u e a e wa d.
57
The deposi ion a e was
∼0.3 ML/min, al hough a simila film quali y was ob ained wi hin he
0.1−0.5 ML/min ange; he c ucial pa ame e he e is he deposi ion
empe a u e, which was equi ed o be ∼100 K.
Su ace-Science Cha ac e iza ion. The a omic and elec onic
s uc u e o he Si subs a e and he g own Ag films we e
cha ac e ized by LEED, STM, and ARPES. STM da a we e collec ed
using an Omic on VT se up ope a ing a oom empe a u e. ARPES
measu emen s we e pe o med using a SPECS Phoibos 150 elec on
analyze equipped wi h a monoch oma ized He gas discha ge lamp
ope a ing a he He Iαexci a ion ene gy (21.2 eV), wi h an elec on
ene gy and angula esolu ion o 30 meV and 0.1°, espec i ely. The
diame e o he UV ligh beam was ∼0.5 mm a he sample su ace.
Sample ans e be ween STM and ARPES se ups was made wi hou
b eaking UHV condi ions. P io o a mosphe e exposu e, he samples
we e capped by a Si p o ec ion laye (1.5 nm nominal hickness),
e apo a ed by di ec hea ing o a Si chip wi h he same doping le el as
he subs a e. The obus ness and aging o he films was moni o ed by
X- ay pho oemission spec oscopy (XPS; see Figu e S1).
HRTEM Cha ac e iza ion. Elec on- anspa en (<50 nm hick-
ness) c oss-sec ional lamellas o he samples we e p epa ed by fi s
spu e ing a pla inum laye o p o ec ion, ollowed by ca ing using a
FEI Helios NanoLab 600 dual beam SEM/ ocused-ion-beam (FIB)
sys em. A e he ans e o he lamellas o a coppe g id, hey we e
imaged using a JEOL JEM-2100 high- esolu ion ansmission elec on
mic oscope ope a ed a 200 kV.
Shee Resis ance Measu emen s. Ul a hin sil e films we e
e ched in o a Hall-ba s uc u e by a gon plasma using an Ox o d
Plasmalab 100 eac ion-ion e ching (RIE) sys em. A poly(me hyl
me hac yla e) (PMMA) laye was used as he e ch mask. Con ac
elec odes we e o med by deposi ing a C /Au/Al (3/60/190 nm)
laye ollowed by li -off. All s uc u es we e pa e ned by a Rai h
EBPG 5000+ elec on-beam li hog aphy sys em. A ou -p obe
scheme
58
(Figu e S3) was used o ex ac he shee esis ance. The
elec ical cha ac e iza ion was pe o med in a Lakesho e p obe s a ion
ope a ing a 7 ×10−5mba . An Agilen B1500A semiconduc o
pa ame e analyze was used o all elec ical measu emen s.
Elec on-Beam Nanoli hog aphy. Passi a ed sil e -film chips
we e uni o mly spin-coa ed wi h ∼100 nm ZEP520A esis o 1 min
a 6000 pm. Ribbons we e hen w i en using a RAITH150-Two
elec on-beam li hog aphy sys em ollowed by de elopmen in amyl
ace a e and eac i e-ion e ching o ∼1 min wi h an A and CHF3
mix u e in a RIE Ox o d Plasmalab 80 Plus sys em. Pe iodic a ays o
50−1000 nm wide ibbons we e ab ica ed wi h a oo p in o 200 μm
×200 μm pe sample and a ∼1.5 pe iod- o-wid h a io. Impo an ly,
al hough s anda d p ocedu es usually in ol e baking a 150−180◦C
a e spin-coa ing o induced a phase ansi ion o glass in he esis ,
we skipped his s ep o a oid Ag film damage, a he expense o ha ing
a mo e agile esis ha equi ed ca e ul calib a ion o he RIE gas
mix u e and e ching ime o p ese e he e ching mask.
Op ical Cha ac e iza ion. We used a SOPRA GES-5E sys em o
pe o m ellipsome y (Figu e S4) o incidence angles in he 60−75°
ange o e he UV-NIR pho on ene gy egion (1.5−5 eV). Op ical
ansmission/ eflec ance spec a (Figu es S5 and S6) we e collec ed
using a B uke Hype ion Fou ie - ans o m in a ed (FTIR)
spec ome e ope a ing in he 1.3−17 μm ange.
Analy ical Simula ions. The plasmon dispe sion ela ion
(pa allel wa e ec o k∥as a unc ion o equency ω)o a
homogeneous hin film is gi en in he quasis a ic limi by
38
ω
πσ
=ϵ+ϵ
ki( )
4
12
whe e ϵ1and ϵ2a e he pe mi i i ies o he media on ei he side o
he film, while σis he 2D conduc i i y. Assuming local esponse, we
w i e he la e as
σωπ=−ϵ
d
(i /4 )(1 )
which is p opo ional o he film hickness dand whe e ϵs ands o
he me al pe mi i i y; his is an excellen app oxima ion o he
ma e ials and film hicknesses unde conside a ion e en when
compa ed wi h quan um-mechanical simula ions (see Figu e S10).
Adop ing he D ude model,
59
we app oxima e ϵ≈1−ωbulk
2/ω(ω+
iγin) in e ms o he bulk plasma equency ωbulk and he in insic
damping a e γin (assuming ω≪ωbulk), which leads o he dispe sion
ela ion k∥d≈(ϵ1+ϵ2)ω(ω+iγin)/ωbulk
2, and his in u n allows us o
w i e he in-plane plasmon wa eleng h defined by λp=2π/Re{k∥}as
λp=d(λ0/L1)2(i.e.,eq 1 in he main ex ), whe e
πω
=ϵ+ϵ
L
c
2( )
112
bulk
and λ0is he ee-space ligh wa eleng h. Fo Ag films (ℏωbulk ≈9.17
eV
52
) deposi ed on silicon (ϵ1≈12) and coa ed wi h ZEP502A esis
(ϵ2≈2.4), we find L1≈205 nm, which ende s λp≪λ0a ligh
wa eleng hs below ∼5μm when dspans a ew a omic laye s (below
∼15 ML), he eby jus i ying ou using he quasis a ic limi , al hough
e a da ion effec s can become appa en o longe wa eleng hs and
hicke films. Inciden ally, he esis is no emo ed om he samples
be o e plasmon measu emen s, bu he pene a ion dep h λp/4πis
smalle han he esis hickness (∼100 nm), hus jus i ying he use o
he esis pe mi i i y in he abo e exp ession o L1.
We ema k ha he abo e esul s assume a small film hickness d
compa ed wi h he plasmon wa eleng h λp, while he educ ion o he
me al film esponse o a su ace conduc i i y is alid i dis also small
compa ed wi h he skin dep h λ0/(2πIm{ ϵ}) ≈c/ωbulk ∼20 nm in
Ag. Addi ionally, in he quasis a ic limi , he elec ic field Eis
longi udinal (∇×E= 0) and di e genceless (∇·E= 0), he e o e
displaying a symme ic pa e n ela i e o he negligibly hick film (we
e e o a ecen s udy
60
o mo e de ails). In pa icula , he elec ic
field associa ed wi h he plasmon has symme ic (an isymme ic) in-
plane (ou -o -plane) componen s wi h espec o he no mal
coo dina e zand admi s he exp ession
60
∝[x+ i sign(z)z]ek∥(ix−|z|)
o p opaga ion along he in-plane di ec ion x, om which an
exponen ial decay away om he film is p edic ed wi h a 1/e all in
in ensi y a a dis ance λp/4π om he film (see Figu e 1a in he main
ex ). We no e ha he field is howe e asymme ic i he film
hickness is no small compa ed wi h bo h he plasmon wa eleng h
and he me al skin dep h. The abo e exp ession o he field also
allows us o w i e he in-plane plasmon p opaga ion dis ance ( o 1/e
decay in in ensi y) as Lp= 1/2Im{k∥}. Using he dispe sion ela ion
no ed abo e, we find Lp=λpL2/λ0, whe e L2=c/2γin (e.g., aking ℏγin
= 21 meV o Ag, as ob ained om op ical da a,
52
we ha e L2= 4.7
μm); he p opaga ion dis ance is hen L2/λ0(independen o me al
hickness) imes he plasmon wa eleng h (p opo ional o me al
hickness). Inciden ally, a plasmon li e ime 1/γin is di ec ly inhe i ed
om he D ude model in he absence o adia i e losses (a good
app oxima ion o λp≪λ0) and subs a e abso p ion (Si losses a e
negligible in he s udied spec al ange wi hin he λp/4πplasmon
pene a ion dep h), leading o a plasmon quali y ac o ( equency- o-
wid h a io) Q=ω/γin. This ela ion is used in Figu e 4c o he main
ex wi h a ious es ima es o γin (see below as well). We also find
use ul o w i e he p opaga ion dis ance as Lp=λpQ/4π.
Fo ibbon a ays, plasmons a e exci ed unde ans e se pola -
iza ion (i.e., wi h he elec ic field o ien ed ac oss he wid h o he
ACS Nano A icle
DOI: 10.1021/acsnano.9b01651
ACS Nano 2019, 13, 7771−7779
7776
ibbons, see Figu e 1b in he main ex ), whe eas a ea u eless weak
abso p ion is p oduced when he inciden ligh field is pa allel o he
ibbons. Consequen ly, we concen a e on he o me in wha ollows
and adop a p e iously epo ed model
38
o calcula e he no mal-
incidence ans e se-pola iza ion ansmission coefficien as
α
=

+∼−
−
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
n
S
G
11i
1(3)
whe e

=+ϵn(1 )/2
Si is he a e age e ac i e index o he media
abo e (ai , neglec ing he esis laye in he coupling o adia ion) and
below (Si) he me al laye , αis he ibbon pola izabili y pe uni
leng h, S=4π2/aλ0ndesc ibes adia i e coupling, ais he la ice
pe iod, G=2π2/3a2ϵ+iSaccoun s o in e - ibbon in e ac ions in he
dipola app oxima ion, and ϵ=(1+ϵSi)/2 is he a e age pe mi i i y
o he su ounding media. We exp ess he pola izabili y as
α
ζηω σ
∼≈− ϵ
+ϵ

W
W
1
1/ i /
21
2
1
in e ms o he 2D conduc i i y o he me al σand only conside he
dominan con ibu ion o he dipola plasmon esonance co espond-
ing o pa ame e s
61
η1≈−0.0921 + 0.0233 e−8.9 d/Wand ζ1≈0.959−
0.016 e−39 d/W, which depend on he ibbon hickness- o-wid h aspec
a io d/W. Finally, he 2D conduc i i y is ela ed o he me al
pe mi i i y as σ=(iω/4π)[(1 −ϵAg)d+(1−ϵc)dc], whe e we
app oxima e he capping laye o hickness dc= 1.5 nm as an
addi ional e m in σwi h ϵc= 2. We use abula ed op ical da a o
sil e
52
(ϵAg) and c ys alline silicon
62
(ϵSi). Reassu ingly, he analy ical
heo y jus p esen ed p oduces spec a in nea ly ull ag eemen wi h
nume ical elec omagne ic simula ions (see Figu es S8 and S9).
Inciden ally, his analysis o ibbon a ays igno es he esis , which ou
nume ical simula ions (no shown) p edic o only cause mino
plasmon edshi s.
The ans e se dipola plasmon o a single ibbon is signaled by a
di e gence in α(i.e.,iωϵ/σ=−1/η1W), which combined wi h he
dispe sion ela ion o he ex ended film k∥=iωϵ/2πσ ≈2π/λpleads
o he condi ion
λ
πη λ=−≈W
4( ) 0.37
p
2
1
p
o d≪W. Adop ing his exp ession and neglec ing in e - ibbon
in e ac ions, we can use eq 1 o eadily ob ain eq 2 in he main ex . I
should be no ed ha in e - ibbon in e ac ion can p oduce a small
edshi co ec ion in he plasmon posi ion (see Figu e S8).
We find i con enien o a ange he abo e abo e exp essions by
neglec ing he capping laye and app oxima ing he sil e pe mi i i y
as ϵAg ≈1−ωbulk
2/ω(ω+iγin) o exp ess he ansmission coefficien
o he a ay (eq 3)as
ωγ
ωωωγ
=

+−+
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
n
11i
(i)
ad
p
2
whe e
ωω πη
πζ
=ϵ−−ϵ
d
W
Wd
a
1
4( ) 6
pbulk
1
1
2
2(4)
is he esul ing plasmon esonance o he a ay unde no mal
incidence, whe eas
γ
γγ=+
in a
d
is he o al plasmon damping a e, con ibu ed by he in insic
componen γin and a adia i e componen
γ
ζω
=

nc
Wd
a2
ad
1
2bulk
2
(5)
The fi s e m inside he squa e oo o eq 4 desc ibes he plasmon
equency o he isola ed ibbon, while he second e m accoun s o a
edshi due o in e - ibbon in e ac ion. We no e ha adia i e
damping (eq 5) dec eases wi h inc easing a ay pe iod a, so sha pe
plasmons a e expec ed in he limi o la ge sepa a ions, o which γ≈
γin (see Figu e 1c); inciden ally, we ha e neglec ed adia i e
con ibu ions o he damping o indi idual ibbons unde he
assump ion W≪λ0. When we speci y eq 5 o Ag(111) ibbons on
silicon, we find γ ad =Γ×Wd/a, whe e ℏΓ=ζ1
2ℏωbulk
2/(2nc)≈88
meV/nm.
D ude Damping Es ima ed om he Elec ical Resis ance.
We use he exp ession
ρπ ρ[]≈ × × × [Ω
]
−
s (4 8.854 10 ) m
0,CGS
12
0,SI
o con e DC esis i i ies om SI o CGS uni s. Then, we use he
D ude model o w i e he damping a e as
γ
πωρ=
−
(4 )
in
1bulk
2
0,CGS
Damping a es in Figu e 4c a e ob ained by applying hese o mulas o
he SI esis i i ies ρ0,SI = 1.62 ×10−8Ωm o bulk sil e (γDC,N≫1)
and ρSNd111 o sil e films consis ing o NAg(111) a omic laye s
(γDC,N), whe e d111 = 0.236 nm is he a omic laye spacing and ρSis
he a e age shee esis ance ( o each alue o N) ob ained om he
da a poin s p esen ed in Figu e 2m.
ASSOCIATED CONTENT
*
SSuppo ing In o ma ion
The Suppo ing In o ma ion is a ailable ee o cha ge on he
ACS Publica ions websi e a DOI: 10.1021/acsnano.9b01651.
Addi ional figu es showing he su ace quali y upon Si
capping and a e exposu e o ambien condi ions,
examples o cha ac e is ic su ace hickness dis ibu ions,
a mic og aph o a shee esis ance measu emen de ice,
ellipsome y measu emen s, measu ed ansmission
spec a, a desc ip ion o he me hod used o ex ac
he plasmon quali y ac o om he measu ed spec a, a
heo e ical s udy o he effec o ibbon a ay spacing, a
compa ison be ween quan um-mechanical and classical
heo e ical desc ip ions o plasmons in hin me al films,
and a compa ison o measu ed spec a wi h analy ical
and nume ical simula ions (PDF)
AUTHOR INFORMATION
Co esponding Au ho s
*E-mail: [email p o ec ed].
*E-mail: [email p o ec ed].
ORCID
Jens B ede: 0000-0002-4946-8160
A nab Ghosh: 0000-0003-1828-9837
Do on Na eh: 0000-0003-1091-5661
Fengnian Xia: 0000-0001-5176-368X
J. En ique O ega: 0000-0002-6643-806X
F. Ja ie Ga cía de Abajo: 0000-0002-4970-4565
Au ho Con ibu ions
○
Z.M.A. and V.M. con ibu ed equally o his wo k.
No es
The au ho s decla e no compe ing financial in e es .
ACKNOWLEDGMENTS
We hank Ma a Au o e, Josep Cane -Fe e , Raine Hill-
enb and, Johan Osmond, and F ede ik Schille o echnical
suppo and help ul discussions. V.M. and F.J.G.A. g a e ully
acknowledge gene ous help and hospi ali y om Luis Hueso
and Ralph Gay a CIC nanoGUNE, whe e nanoli hog aphy
ACS Nano A icle
DOI: 10.1021/acsnano.9b01651
ACS Nano 2019, 13, 7771−7779
7777
and FTIR we e pe o med. This wo k has been suppo ed in
pa by ERC (Ad anced G an 789104-eNANO), he Spanish
MINECO (g an nos. MAT2017-88492-R, SEV2015-0522,
PCIN-2015-155, and MAT2016-78293-C6-6-R), he Ca alan
CERCA P og am, he Basque Go e nmen (g an no. IT-
1255-19), FundacioP i ada Cellex, and he U.S. Na ional
Science Founda ion CAREER Awa d (g an no. 1552461).
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