Plasmonics in atomically thin crystalline silver films

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 Downloaded ia UNIV POLITECNICA DE CATALUNYA on May 3, 2021 a 07:23:16 (UTC). See h ps://pubs.acs.o g/sha ingguidelines o op ions on how o legi ima ely sha e published a icles. 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. ACS Nano A icle DOI: 10.1021/acsnano.9b01651 ACS Nano 2019, 13, 7771−7779 7772 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 DOI: 10.1021/acsnano.9b01651 ACS Nano 2019, 13, 7771−7779 7773 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. ACS Nano A icle DOI: 10.1021/acsnano.9b01651 ACS Nano 2019, 13, 7771−7779 7774 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). REFERENCES (1) Anke , J. N.; Hall, W. P.; Lyand es, O.; Shah, N. C.; Zhao, J.; Van Duyne, R. P. Biosensing wi h Plasmonic Nanosenso s. Na . Ma e . 2008,7, 442−453. 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