Optical Origin of Subnanometer Resolution in Tip-Enhanced Raman Mapping

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1 Artcle pubs.acs.org/jpcc Optcal Orgn of Subnanometer esoluton n Tp-Enhanced aman Mappng Chao Zhang, Bao-Qn Chen, and Zh-Yuan L* Laboratory of Optcal Physcs, Insttute of Physcs, Chnese Academy of Scences, P.O. Box 63, Bejng 9, Chna ABSTACT: aman spectroscopy and magng at the snglemolecular level n both sgnal senstvty and spatal resoluton have been a long dream. A recent expermental study of snglemolecule aman mappng wth a subnanometer resoluton by usng a tp-enhanced aman scatterng (TES) technque s a great step closer to ths great dream. However, how the subnanometer spatal resoluton s possble wth a aman exctaton lght spot ( hot spot ) of dameter over nm formed between the tp substrate nanogap to excte and probe the molecule stll remans mysterous. Here we present an optcal theory of aman scatterng that accounts for the strong near-feld self-nteracton of molecule wth the plasmonc nanogap due to multple elastc scatterng of lght by the molecule. The result shows that the self-nteracton effect strongly modulates the aman exctaton and radaton n both the sgnal ntensty and spatal senstvty, leadng to a super-hot spot and subnanometer lateral resoluton of aman mappng. The optcal theory can help to uncover the full pcture of lght-matter nteracton of atoms and molecules wth plasmonc nanostructures and explore unknown fronters of physcs and chemstry at nanoscale. I. INTODUCTION aman spectroscopy offers a powerful means to observe vbratonal, rotatonal, and other low-frequency modes n molecules, and has become a popular and useful technology for molecular dentfcaton. A fundamental dream of aman spectroscopc scence and technology s to probe aman sgnal wth ultrahgh spectroscopc senstvty down to sngle-molecule detecton level and ultrahgh spatal resoluton down to the sngle-molecule sze scale. Ths would allow people to dentfy, montor, and manpulate sngle molecules both n temporal and spatal doman. As the cross secton of aman scatterng s extremely low under usual condtons of laser exctaton, many methods have been explored to advance the power of aman spectroscopy to the fundamental sngle-molecule lmt. Among them, surface plasmon resonance (SP) effect n metallc nanostructures has been a promsng means. SP would allow gant enhancement of the nteracton between laser and molecules adsorbed n specally desgned and prepared metallc nanostructures under the scheme of surface-enhanced aman spectroscopy (SES) to the level of sngle-molecule detecton lmt.,5 When aman spectroscopy works together wth varous mature scannng probe mcroscopy technologes under the scheme of tp-enhanced aman spectroscopy (TES), the spatal resoluton of aman probng and montorng can be greatly upgraded to a level far below the dffracton-lmt scale (about half the laser wavelength, usually several hundred nanometers). 6 5 The metal tp n ether atomc force mcroscopy (AFM) or scannng tunnelng mcroscopy (STM) can nduce a hghly concentrated electrc feld focus spot wth greatly enhanced feld ntensty n the vcnty of the tp apex due to SP effect. In addton to aman scatterng, the SP effect can enhance many other physcal processes, such as fluorescence, 6 catalyss, 3 nonlnear optcs and other nteractons. 5 7 The focus spot, wth a sze as small as nm, wll excte molecules sgnfcantly only wthn ts landscape. As a result, both hgh-senstvty and hgh spatal resoluton of aman spectroscopy can be acheved by TES. 6 Although many methods lke coherent ant-stokes aman scatterng, 3 chemcal,5 and physcal contact 9 have been used to mprove the spatal resoluton and other performances of TES, the ultrahgh vacuum (UHV) TES 8,,,5 provdes a general and relable system to have hgh spatal resoluton for many molecules. It s generally beleved that the spatal resoluton of TES s nearly the same as the focus spot sze of the metallc AFM or STM tp, whch strongly depends on many factors, such as the molecule-tp vertcal dstance, the curvature radus of tp, the exctaton wavelength, and the substrate composton, but at best s n the order of nm. Therefore, t s generally expected that the purely optcal aman sgnal probe can only acheve a spatal resoluton n the order of nm, whch s far away from a sngle-molecule crteron ( nm), although both AFM and STM can map the surface tomography of mcroscopc objects at the subangstrom resoluton level. The stuaton s smlar to the conventonal optcal mcroscope, where the resoluton s the same as the focus spot sze of lght formed by the objectve lens and subject to the aylegh dffracton lmt of lght. eceved: March 9, 5 evsed: Aprl 7, 5 Publshed: Aprl 3, 5 5 Amercan Chemcal Socety 858 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

2 The Journal of Physcal Chemstry C ecently, ths general rule of wsdom has been broken down n a recent work by Dong and co-workers. The team has bult a TES system based on sophstcated ultrahgh vacuum and low temperature STM technologes as well as adoptng a double-resonance enhancement scheme for both aman exctaton and emsson. Although the sze of hot spot around the STM tp s stll n the order of nm, the team has been able to acheve an ultrahgh spatal resoluton of aman spectroscopy suffcent for chemcal mappng of the subnanometer nteror detals of a sngle HTBPP organc molecule adsorbed on the Ag() surface. Ths beautful experment has opened a new wndow to perform chemcal magng at the sngle-molecule level. Nonetheless, the physcal mechansm underlyng ths surprsng expermental observaton s stll unclear. Obvously there s a huge gap between the conventonal wsdom ( nm) and the expermental observaton ( nm) n regard to the spatal resoluton of aman mappng. What can act as the brdge to connect ths order of magntude huge gap? In ths work we offer a soluton to ths puzzlng problem. We wll show that the strong near-feld self-nteracton of the molecule wth the plasmonc nanogap n the TES system wll make the molecule tself an ndspensable part of the strongly correlated tp-molecule substrate nanosystem and sgnfcantly enhance both the sgnal ntensty and spatal resoluton of aman mappng. The paper s organzed as follows. In secton II, we present a bref ntroducton to the conventonal theory for plasmon enhanced aman scatterng. In secton III, we use the conventonal theory to calculate the spatal resoluton of TES system n ref, and fnd that the old theory yelds a spatal resoluton far larger than the expermental observaton. In secton IV, we derve a new theory for aman enhancement consderng molecule self-nteracton. In secton V, we use our theory to calculate the spatal resoluton of TES system and fnd that the new theory yelds a subnanometer spatal resoluton that agrees wth the expermental observaton. In secton VI, we make an estmate of near-feld self-nteracton contrbuton to aman enhancement. Fnally, n secton VII, we summarze ths paper and make our conclusons. II. CONVENTIONAL THEOY FO PLASMON-ENHANCED AMAN SCATTEING aman scatterng nvolves nteracton of optcal feld wth quantum states of aman molecules. Therefore, the enhancement of aman sgnal contrbutes from the electromagnetc factor and the chemcal factor. The electromagnetc enhancement factor s closely related wth the local electrc feld enhancement. Accordng to the tradtonal surface enhanced aman scatterng (SES) and tp-enhanced aman scatterng (TES) theory, the ntensty of spontaneous aman radaton s nearly proportonal to the fourth power of the local fled enhancement and lnear to the exctaton ntensty I., Although that s an approxmate result, t always shows good agreement wth experment for general stuatons. Some more accurate calculatons for the enhancement factor of SES that are based on optcal recprocty theorem and specfc expermental condtons have been made, 8 and some more accurate defnton for sngle molecule SES enhancement factor has also been dscussed. 9 In the scalar phenomenologcal theory that we adopt n the current work, the aman enhancement could owe to the separate contrbuton from the exctaton and radaton enhancement process. In the dpole approxmaton the Stokes (ant-stokes) lght radated by the vbraton molecule could be expressed as the radaton by the nduced dpole μ( ). In the plasmonc nanostructure envronment, μ( ) s gven by μ( ) = α(, ) Er (, ) = α (, )[ E( r, ) + Es( r, )] (.) where s the frequency of exctaton radaton, s the Stokes (ant-stokes) frequency of aman sgnal, and r s the molecule s ste. The polarzablty α(, ) (called aman tensor n general) descrbes the transton ntensty of aman frequency shft process that connects the exctaton frequency and the vbraton shft frequency, and t s closely related wth the molecular quantum states nvolved wth the aman process. The local feld E(r, ) conssts of the ncdent feld E (r, ) and the greatly enhanced scatterng feld E s (r, ) from the nanostructure upon the ncdent feld. In usual aman experments, the total local feld s a lnear functon of the exctaton feld. The local feld enhancement factor due to plasmonc nanostructures f () sdefned by E(r, ) = f () E (r, ). For nanostructures wth complcated geometrc confguraton, ths local feld enhancement factor does not have a smple analytcal formulaton, but nstead must be determned numercally. When the molecule s placed n vacuum and s excted by E(r, ), the correspondng dpole moment would be μ ( ) = α(, ) E ( r, ) (.) Obvously, we have f () =E(r, )/E (r, ) = μ( )/ μ ( ). The aman radaton far feld from the nduced dpole μ( ) s gven by the followng formula Er ( =, ) Gr (, r, ) μ( ) εc = [ G ( r +, r, ) Gs( r, r, )] μ( ) εc (.3) In comparson, the aman radaton far feld by the dpole μ( ) placed n vacuum would be smply E = ( r, ) G ( r, r, ) μ( ) Artcle (.) The total Green functon G (r, r, ) (a second rank tensor descrbed by a 3 3 matrx) could splt nto the free space Green functon G (r, r, ) and the scatterng Green functon G s (r, r, ), whch descrbes the nfluence, n partcular, enhancement due to plasmonc nanostructures. We can defne another enhancement factor to descrbe ths mprovement of the radaton power of a dpole asssted by ts plasmonc nanostructure envronment, namely, f ( )= E(r, )/E (r, ). Notce that the Green functon exactly descrbes the power of a gven dpole to radate ts optcal energy from near feld to far feld n a partcular electromagnetc envronment. Accordng to eqs.3 and., f ( ) s equal to the quantty of the total Green functon projected to the dpole moment μ( ) orentaton (unt vector n) over that of the free space Green functon, f ( )=G (r, r, ) n/g (r, r, ) n, whch can be approxmated by f ( ) Tr[G (r, r, )]/Tr[G (r, r, )]) when averagng over the dpole orentaton. Here Tr[...] means the trace of a matrx. For 859 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

3 The Journal of Physcal Chemstry C nanostructures wth complcated geometrc confguraton, ths enhancement factor also must be determned numercally. Combnng eqs.., the aman radaton far feld of a molecule placed n the plasmonc nanostructure s gven by E( r = α, ) (, ) G( r, r, ) E( r, ) (.5) In comparson, the aman radaton far-feld for the molecule placed n vacuum s smply E = α vac( r, ) (, ) G ( r, r, ) E ( r, ) εc (.6) Comparson between eq.5 and eq.6 yelds the aman radaton power enhancement factor as Artcle Ths fundamental result of tradtonal SES theory has long been the physcal bass for descrbng all SES and TES phenomena, ncludng the spatal resoluton of aman mappng. 8 = I( r, ) = Er (, ) G Ivac( r, ) Evac( r, ) = Gr (, r, ) Er (, ) G ( r, r, ) E( r, ) Tr Gr [ (, r, )] Er (, ) Tr[ G ( r, r, )] E ( r, ) [ f ( )] [ f ( )] = G ( ) G ( ) E (.7) where G E () and G ( ) are the enhancement factor n the aman exctaton and radaton processes, respectvely. Combnng eq.5.7 the total enhanced aman ntensty s I( r, ) = [ f ( )] [ f ( )] α G (, ) ( r, r, ) n I ( r, ) (.8) Here I (r, ) s the ntensty of the ncdent lght actng at the aman molecule. It has been well-establshed that plasmonc nanostructures not only can enhance the ncdent feld to a greatly ntensfed local feld va varous physcal processes lke surface plasmon resonance effect or near-feld scatterng effect, t also can sgnfcantly enhance the radaton power of molecular aman sgnal from the near feld regon to the far feld regon (where the detector s placed) through varous physcal processes such as surface plasmon resonance effect or optcal antenna effect. In fact, the exctaton and radaton enhancement s closely connected wth each other (almost equal to each other) as they follow the electromagnetc recprocty prncple. Generally speakng, f a nanostructure can enhance accumulaton of the far-feld ncdent lght to the local feld, t can equally enhance the emsson of local feld to the far-feld radaton lght. As a result, f () =E(r, )/E (r, ) E(r, )/E (r, ) = f ( ) due to the small shft of aman radaton frequency relatve to the exctaton frequency. In ths stuaton, the overall aman sgnal enhancement factor s approxmately equal to the fourth power of the local feld enhancement factor, namely G( r ) = E( r, ) / E ( r, ) (.9) Fgure. Local electrc feld profle n the gap regon of TES system calculated by FDTD. (a) The schematc confguraton of TES system used for aman mappng of molecule. The radus of the tp head s 5 nm, the gap between the tp head wth the substrate s nm, the exctaton lght s at wavelength 53 nm, ncdence angle 6, and p- polarzaton. The ntensty profle of local electrc feld as calculated by 3D FDTD method s dsplayed wthn the gap, showng a hghly localzed hot spot centered rght below the tp apex. (b) D profle of electrc feld ntensty versus the horzontal x-axs coordnate at the mddle of the gap, where the tp apex s located at x = nm. The fwhm of the gap mode hot spot s about nm. III. CONVENTIONAL THEOY APPLIED TO TES SYSTEM The schematc confguraton of the TES system used to pontby-pont map the aman mage of a sngle HTBPP organc molecule adsorbed on Ag() surface s llustrated n Fgure a. We frst use the three-dmensonal fnte-dfference tmedoman (3D FDTD) method to smulate the local electrc feld ntensty profle of nanogap plasmonc mode excted by a p- polarzed ncdent plane-wave lght. A strong enhancement of electrc feld s seen clearly n Fgure b, whch corresponds to the exstence of a hot spot located wthn the nanogap. The full-wdth at half-maxmum (fwhm) of the plasmonc hot spot s about nm, whch s substantally larger than the lateral sze of the HTBPP molecule ( nm). Accordng to the conventonal plasmon enhanced aman scatterng theory, a molecule located n the vcnty of plasmonc nanostructures wll be excted by strongly enhanced local electrc feld E(r, ), whch has an ampltude enhancement factor f () =E(r, )/E (r, ) over the 86 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

4 The Journal of Physcal Chemstry C ncdent feld E (r, ), and jump from ts ground level to hgher ntermedate quantum states wth greatly ncreased transton probablty. Then the molecule subsequently makes spontaneous transtons from these ntermedate excted states to lower Stokes or ant-stokes levels. The emtted photon at frequency wll be scattered away by the plasmonc nanostructures to far-feld regon wth a great enhancement factor defned as f ( )=E(r, )/E (r, ), where E(r, ) and E (r, ) are the far-feld radaton of molecule (modeled as an electrc dpole) wth and wthout the assstance of plasmonc nanostructures. Thus, the aman enhancement n TES and SES nvolves contrbuton from exctaton enhancement and radaton enhancement. As both factors are approxmately equal to the enhancement factor of local feld ntensty E(r, ) /E (r, ), altogether the aman sgnal enhancement factor s gven by G( r) = [ f ( )] [ f ( )] E( r, ) / E ( r, ) (3.) The strong enhancement and tght localzaton of nanogap plasmonc mode naturally brng even more drastc enhancement of aman sgnal. Besdes, the aman sgnal s hghly senstve to the gap mode profle and decays drastcally when leavng the center of the hot spot. Numercal smulaton based on eq 3. reveals the spatal resoluton (defned as the fwhm) of aman mappng s about 7. nm (Fgure b). Ths value s much larger than the lateral scale of the HTBPP molecule. It s thus expected that TES should not be able to resolve a sngle HTBPP molecule, not to say ts nternal subtle structure such as the central molecular skeleton. Such a predcton made by the conventonal aman scatterng theory obvously s at odd wth the expermental observaton reported n ref, whch clearly llustrated subnanometer lateral spatal resoluton n TES suffcent to map the nternal structure of the HTBPP molecular skeleton. How to brdge the huge theory-experment gap n the TES mappng, whch s sub- nm versus subnanometer? There must be somethng crtcal mssng n the conventonal aman scatterng theory n applcaton to the current TES system and the mysterous observaton. IV. THEOY FO AMAN ENHANCEMENT CONSIDEING MOLECULE SELF-INTEACTION Before we go nto the detals for constructng a new aman scatterng theory that can fully account for the major physcs of aman processes nvolved n the UHV-TES system, we stress here (although t s not a nave thng) that the conventonal theory for aman enhancement as dscussed n secton II only consders the nfluence of plasmonc nanostructure neghborng or surroundng a molecule upon the ncdent feld (exctaton enhancement) and the radaton power of the molecule (radaton enhancement). The molecule tself only serves as a passve probe to sense and apperceve the local feld ntensty. The counteractve nfluence of the molecule tself upon the surroundng electrc feld envronment has been completely neglected, perhaps because so far ths thng has not been recognzed by the SES and TES communty over the last fve decades. We wll make a thorough analyss over ths brand new unknown terrtory of aman scatterng physcs and chemstry. The result wll show that the molecule tself can mpose a tremendous counteractve nfluence over ts electromagnetc envronment at nanoscale through electromagnetc near-feld self-nteracton n both the exctaton and radaton enhancement processes, and ths has a pvotal mplcaton and meanng for the spatal resoluton of aman mappng va a TES system. As mentoned above, the molecule has a aman tensor connectng the exctaton lght at frequency and the Stokes or ant-stokes scatterng lght at frequency. When the molecule sze s comparable to the gap sze and the dstance to the metal surface, ts scatterng to the lght wthn small gap s so strong that we have to consder the molecule response to the exctaton electrc feld and the Stokes (ant-stokes) electrc feld. Ths s called the electromagnetc self-nteracton process of the molecule, whch can be characterzed as the phenomenologcal parameter of electrc polarzablty β() under the dpole approxmaton, namely p(r, ) =β()e(r, ). Accordng to the tradtonal spontaneous aman enhancement theory descrbed n the last secton, we can also attrbute the overall contrbuton upon the modfcaton of molecule polarzaton to the exctaton and radaton process separately. Frst, n the exctaton process the near-feld self-nteracton of molecule wth ts envronment s characterzed by the modfcaton of molecule to the local feld. Ths self-nteracton s va the elastc scatterng of molecule upon lght (ether the drect ncdent lght or scatterng lght) mpngng on t. In correspondence to eq., the new local feld could be expressed as E( r, ) = E ( r, ) + E( r, ) + E ( r, ) s m, s (.) where E m,s (r, ) s the radaton feld by the nduced dpole p(r, ) at the exctaton wavelength of the molecule. It wll be scattered and modfed by the surroundng nanostructure and ts quantty wll be determned self-consstently n a way that wll be descrbed later on n ths secton. In the radaton process the self-nteracton of molecule can also be characterzed by the modfcaton to the nduced dpole radatng at. The new radaton fled n the far-feld aman sgnal detecton regon could be expressed as Artcle Er ( =, ) Gr (, r) [ μ( r, ) + p ( r, )] εc = [ G ( r +, r ) Gs( r, r )] [ μ( r, ) + p ( r, )] (.) where p (r, ) s the modfed nduced dpole. As the wavelength of both the exctaton and aman scatterng radaton s much larger than the sze we care about n the TES system (ncludng the molecular sze, the gap sze, and the molecule to substrate and tp surface dstances), we can utlze the quas-electrostatc approxmaton to descrbe ths near-feld self-nteracton of molecule wth ts envronment. We could use the method of mage n electrostatcs to calculate the above modfcaton quantty. 3 Frst, E m,s (r, ) could be consdered as the local feld generated by a set of mage dpoles of the nduced dpole p(r, ) relatve to the slver substrate and tp. Smply speakng, the slver substrate nfluence to the molecule near-feld radaton s approxmately (but wth suffcently hgh accuracy) descrbed by the radaton from an mage dpole p mag, (r, ) located n the mage poston of r, and the slver tp nfluence to the molecule near-feld radaton s approxmately (but wth suffcently hgh accuracy) descrbed by the radaton from another mage dpole p mag, (r, ) located n the mage poston 86 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

5 The Journal of Physcal Chemstry C of r. The substrate and tp nfluences to these two secondary mage dpoles can be further descrbed by more secondary mage dpoles p mag, (r, ) located n the mage poston of r. The quantty of these mage dpoles, ther postons, and ther nfluences can all be calculated analytcally. 3 A typcal example s depcted n Fgure. where Artcle p (, r ) = M p( r, ) mage, (.) and M are the mage matrx that descrbes the polarzaton, ampltude and phase change of each mage dpole. As has been sad above, the overall nduced dpole of molecule s proportonal to the overall local feld, namely p( r, ) = β( ) E( r, ) (.5) As the local feld and the nduced dpole are nterrelated, we can use the self-consstent method that has been extensvely used n near-fled optcs By substtutng eqs.,.3, and. nto eq.5, we can get Fgure. Electromagnetc self-nteracton of molecule (modeled as a dpole) wthn the Ag tp substrate nanogap. The poston and polarzaton of a seres of mage dpole are llustrated when the molecule s at 5 nm lateral dsplacement away from the tp apex and at nm vertcal dsplacement from the substrate. The hghly localzed hot spot around the nanogap s also shown. Under ths mage dpole methodology, the overall modfed near feld could be expressed as Ems( =, r, ) G ( r, r, ) p ( r, ) mage, (.3) p( r = β, ) ( ) E( r, ) + Es( r, ) + G ( r, r, ) M p( r, ) From eq.6 we drectly fnd (.6) p( r = β β, ) ( ) I ( ) G ( r, r, ) M [ E( r, ) + Es( r, )] (.7) Here I s the unt matrx. Accordng to eq.5, the correspondng effectve local feld s gven by E = β NE, ( r, ) I ( ) G ( r, r, ) M [ E( r, ) + Es( r, )] = I β ( ) G ( r, r, ) M E( r, ) (.8) The denotaton [...] n eqs.7 and.8 means matrx nverson operaton. Comparng eq.8 wth eq., the new local feld E N,E (r, ) when consderng the near-feld selfnteracton of molecule wth ts plasmonc envronment n the aman exctaton process s now subject to a modfcaton factor over the orgnal local feld E(r, ) wthout consderng ths effect. The modfcaton factor s descrbed by the followng second rank tensor: β g ( r, ) = I ( ) G ( r, r, ) M (.9) Generally the quantty of the modfcaton factor s proportonal to the trace of the matrx, whch means that the near-feld self-nteracton modfcaton factor s gven by g ( r, ) = E ( r, )/ E( r, ) Tr[ g ( r, )] NE, 3 (.) Now we turn to the aman radaton process. Followng a very smlar physcal argument and mathematcal dervaton procedure, we also have p ( r, ) = β( ) E( r, ) (.) Accordng to eq. the local feld at the aman radaton frequency could be expressed as Er ( =, ) Gr (, r, ) [ μ( r, ) + p ( r, )] εc = G s( r, r, ) [ μ( r, ) + p ( r, )] (.) The mage dpole method under the quas-electrostatc approxmaton model can also enable the local feld calculaton smlar to the case of exctaton process. We can wrte drectly 86 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

6 The Journal of Physcal Chemstry C G s( r, r, ) p ( r, ) = G ( r, r, ) p mage, ( r, ) (.3) and p mage, (, r ) = M p ( r, ) (.) By the self-consstent approach we can get from eqs.. the followng formula p ( r = β, ) ( ) [ G( r, r, ) μ( r, ) s + G ( r, r, ) M p ( r, )] whch drectly yelds Artcle (.5) β β = p ( r, ) ( ) I ( ) G ( r, r, ) M [ G( r, r, ) μ( r, )] s β β = ( ) I ( ) G ( r, r, ) M [ G( r, r, ) μ( r, )] (.6) Accordng to eq.5, the local feld related wth ths nduced polarzaton n the aman radaton process s β = E N, ( r, ) I ( ) G ( r, r, ) M [ G( r, r, ) μ( r, )] (.7) From eq. we can fnd that the total nduced dpole s μ β r = I (, ) ( ) G ( r, r, ) N, M μ( r, ) (.8) and the far feld of aman radaton s gven by E( r =, ) G( r, r, ) μ ( r, ) N, (.9) Comparng eqs.8 and.9 wth eq.3, we can fnd that there exsts a modfcaton factor for the aman radaton process that orgnates from the near-feld self-nteracton of molecule wth ts plasmonc envronment durng ths aman radaton process. Smlar to the aman exctaton process, ths modfcaton factor s also descrbed by the followng second rank tensor: β g r = I (, ) ( ) G ( r, r, ) M (.) The quantty of ths modfcaton factor, g ( ), whch s defned as g (r, ) =μ N, (r, )/μ(r, ), s also proportonal to the trace of the matrx g ( ), namely g ( r, ) = μ ( r, )/ μ( r, ) N, Tr[ g ( r, )] 3 (.) Takng nto account the above analyss of aman exctaton and radaton processes and followng the procedure to derve eq.7, we can derve the followng formula for the modfed overall aman ntensty enhancement factor when the nearfeld self-nteracton of the molecule wth ts electromagnetc envronment s fully consdered: = I( r, ) = Er (, ) G r S( ) I ( r, ) E ( r, ) vac vac [ f ( )] [ g ( r, )] [ f ( )] [ g ( r, )] = G ( ) G ( r, ) G ( ) G ( r, ) = G( r ) [ GES, ( r, ) GS, ( r, )] (.) For a usual aman process the shft of aman radaton frequency relatve to the exctaton frequency s small. As a result, g (r, ) g (r, )=g(r, ). In ths stuaton, the modfed aman sgnal enhancement factor s also approxmately equal to the fourth power of the rato of the modfed local feld E N (r, ) when consderng the near-feld selfnteracton effect of molecule wth respect to the ncdent feld E (r, ), whch s E E, S, S GS( r) = EN( r, ) / E( r, ) = g ( r, ) E( r, ) / E ( r, ) (.3) In the above, we have adopted a sphercal-tp flat-surface model to descrbe the TES geometrc confguraton, from whch the near-feld self-nteracton of the molecule wth ts envronment s calculated analytcally by a multple-mage dpole theory. Yet, the concept of near-feld self-nteracton s applcable to any other geometrc confguraton n a wde range of plasmon-molecule nteracton problems ncludng TES, SES, and plasmon enhanced fluorescence. In these cases, the near-feld self-nteracton of molecules can be wrtten nto the followng general form = β gr (, ) [ I ( ) Gr (, r, )] (.) 863 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

7 The Journal of Physcal Chemstry C where G (r, r, ) represents the near-feld self-nteracton of the molecule wth ts envronment. The exact form and magntude of G (r, r, ) usually request extensve numercal smulatons. The above dscussons more or less focus on the mathematcal formalsm of the new aman scatterng theory assocated wth the UHV-TES system. In the followng we further present a more comprehensve dscusson on the physcal mechansm nvolved n the molecular self-nteracton n TES, wth a hope to offer an easy-to-understand general physcal pcture about the puzzlng problem of subnanometer resoluton n aman mappng. As s well-known, lght-matter nteracton n plasmonc nanostructures nvolves two aspects. On the one hand, many plasmonc nanostructures, such as nanoantenna and nanogap could generate huge feld enhancement and large photon densty of states to have large mpact on matter, for nstance, greatly enhance aman, fluorescence, nonlnear optcal and other types of lght-matter nteracton. On the other hand, matter could counteract and have mpact on the optcal feld n plasmonc nanostructures. For example, the SP effect s senstve to the tny refractve ndex change of surroundng envronment, leadng to promnent effects lke shft n the SP peak, whch could be used to buld hghly senstve bochemcal sensors. 3,35 Careful analyss ndcates that both aspects of lght-matter nteracton are present n the TES system under study and could play a crtcal role n achevng huge aman scatterng enhancement and hgh spatal resoluton smultaneously. Thus, t s necessary to consder the complcated near-feld self-nteracton of molecules wth ts plasmonc nanostructure envronment. In our new theory, there exst two modfcaton factors nduced by the near-feld self-nteracton of the molecule wth ts plasmonc envronment, one to the local feld n the aman exctaton process, and the other to the radaton dpole moment n the aman radaton process. For the sake of clarty and convenence of magnaton and thnkng about the physcs, we schematcally llustrate n Fgure 3 the major physcal pcture nvolved n the conventonal aman scatterng theory and our new aman scatterng theory. The smlarty and dfference of the two theores can be seen clearly: eq.3 wth eq 3. shows that the new theory adds a supplemental term equal to the fourth power of the near-feld self-nteracton modfcaton factor to the conventonal aman enhancement factor. A plenty of new physcs are nvolved n ths theory. In the tradtonal aman scatterng theory, the molecule s purely passve n both the exctaton and radaton processes as t does not change the propertes of ts plasmonc envronment. In contrast, n the new theory, the molecule not only probes the local electrc feld shaped by ts plasmonc envronment n both the exctaton and radaton processes, but also change the propertes of such a plasmonc envronment va elastc scatterng so that t s dfferent from a bare envronment wthout the molecule. Besdes, such a change wll nversely counteract upon and modfy the aman exctaton and radaton processes. In some sense, ths s a hghly nonlnear phenomenon. It wll become clear that the effect s dependent on the near-feld selfnteracton strength, and wll brng many new characterstcs ncludng the subnanometer spatal resoluton of TES. V. NEW AMAN ENHANCEMENT THEOY APPLIED TO TES SYSTEM For the UHV-TES setup used n ref, the near-feld selfnteracton modfcaton factor g(r, ) s approxmately Artcle Fgure 3. Schematc dagram for normal spontaneous aman enhancement and molecule self-nteracton asssted aman enhancement. (a) Exctaton process of normal spontaneous aman enhancement, where the ncdent lght s scattered by the Ag tp substrate gap to form hghly localzed plasmonc gap mode wth greatly enhanced electrc feld ntensty. E and E s (yellow arrows) are the ncdent and scatterng electrc feld at frequency, summng up to the local feld E. (b) Exctaton process of spontaneous aman enhancement when consderng the molecule self-nteracton wth the Ag tp substrate gap through multple elastc scatterng (whte arrows, abbrevated by E.S.) for the ncdent lght. E m,s s the modfed exctaton feld due to the E.S. mechansm and p s the nduced dpole moment descrbng the molecule response to the exctaton lght. (c) adaton process of normal spontaneous aman enhancement, where the aman sgnal at frequency emtted by the molecule s scattered by the Ag-substrate gap to have greatly enhanced far-feld ntensty. G μ and G s μ (blue arrows) are the drect aman radaton of molecule (descrbed by the dpole moment μ) and greatly enhanced scatterng aman radaton by the tp substrate gap, where G and G s are free-space and scatterng dyadc Green s functon. (d) adaton process of spontaneous aman enhancement when consderng the molecule self-nteracton wth the Ag tp substrate gap through multple elastc scatterng for the aman radaton sgnal. The multple E.S. mechansm (whte arrows) strongly modfes the molecule dpole moment to a value μ N,. descrbed by nteracton of the molecule dpole wth ts mage dpoles wth respect to the flat Ag substrate and the Ag tp, as well as nteracton among the mage dpoles, reflectng the multple elastc scatterng of molecule radaton wthn the deep subwavelength nanogap regon. Several factors are nvolved n the UHV-TES setup to enhance the molecule near-feld selfnteracton modfcaton factor g(r, ). Frst, the HTBPP organc molecule has a lnear sze n the order of nmso that ts polarzablty β() s on a suffcently large level. Second, the aman radaton of molecule s resonantly excted by lght wth wavelength matched well wth the drect aman transton band, and ths further greatly ncreases the molecular polarzablty β(). Thrd, the wdth of Ag-substrate Ag-tp nanogap s n the order of several nanometers so that the molecule dstance to the nanogap lower and upper surface s both n the order of nm and comparable to the molecule sze. Ths makes the near-feld dpole dpole nteracton strength G (r, r, ) (nversely proportonal to the thrd power of dpole dpole dstance) to take a hgh level. Fnally, as the molecule s placed wthn the nanogap, ts radaton s subject to an effcent multple reflecton effect and the molecule dpole can nteract wth all of ts mage dpoles for many tmes, whch further greatly enhances the near-feld self- 86 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

8 The Journal of Physcal Chemstry C nteracton strength (namely, dpole-mage dpole nteracton) descrbed by G (r, r, ). Consderng all these factors, the near-feld self-nteracton term β()g (r, r, ) can have a magntude close to, and thus g(r, ) has a magntude much larger than. Ths means that the near-feld self-nteracton of a large-sze aman resonant molecule wth ts plasmonc envronment can become very sgnfcant and cannot be neglected, whch s just the stuaton n the UHV-TES aman mappng experment n ref. In such a stuaton, the tradtonal SES and TES theory as descrbed n eq 3. s no longer accurate and must be subject to a sgnfcant modfcaton as descrbed n eq.3. Further notes can be made for the usual SES and TES experments nvolvng small molecules such as hodamne 6G (h6g). These small molecules have a sze far below one nanometer and a very small polarzablty n the order of atom unt,.e.,.65 C m /V. In a usual TES setup, the nanogap wdth s order of magntude larger than the molecule sze. As a result, the near-feld self-nteracton term β()g (r, r, ) has a magntude far below, and thus, g(r, ) has a magntude close to. Ths means that the self-nteracton of a usual small molecule wth ts plasmonc envronment s very small and can be neglected. In these stuatons, the tradtonal SES and TES theory hold wth hgh accuracy. Because of the strong self-nteracton of molecule wth ts envronment of plasmonc resonant nanocavty, the modfcaton factor s very senstve to the overall geometrc confguraton and physcal consttuton of the strongly coupled nanosystem of metal nanogap and molecule. One sgnfcant thng s that the molecule tself s an ndspensble part of the coupled system, therefore, any change to the molecule should change the property of the coupled system. Ths change should nclude the spatal locaton shft of molecule relatve to the metal nanogap along both the horzontal and vertcal drectons n the geometrc confguraton. Ths geometrc change wll nduce sgnfcant change to the aman scatterng ntensty of molecule, and ths s the physcal orgn of ultrahgh senstvty of aman sgnal to the TES tp scannng poston and the correspondng subnanometer spatal resoluton n aman mappng. Ths concluson can also be made based on a more mathematcal argument. Note that when the near-feld selfnteracton term β()g (r, r, ) s close to n magntude, the modfcaton factor g(r, ) can be hghly nonlnear wth respect to the molecule poston r, leadng to ultrahgh senstvty of aman sgnal upon the relatve poston of molecule to the metal nanogap, namely the Ag tp. The above theoretcal analyss s largely qualtatve. The next step s to estmate quanttatvely to what extent the physcal mechansm of sgnfcant near-feld self-nteracton can enhance the senstvty and spatal resoluton of aman mappng by usng UHV-TES setup. The frst mportant parameter that needs to establsh s the molecule polarzablty. Here the Clausus Mossott relaton 3 s used to estmate the parameter. Assume that the molecules form a macroscopc perfect, homogeneous and sotropc delectrc wth the constant about ε = 3, and the average volume of one molecule s about the value of a sphere of radus r m = nm due to ts bg atomc number. Then the polarzablty of sngle molecule s about β() =πε (ε )/(ε +)r m 3 =.5 37 C m /V). Yet, the precse value of ths molecular polarzablty depends on several factors, such as the exctaton wavelength and the orentaton angle of the molecule skeleton. The second mportant parameter s the lateral and longtudnal poston of Artcle the molecule relatve to the TES tp, denoted as x and d. After these parameters are establshed, the near-feld selfnteracton modfed aman sgnal as a functon of the molecule lateral dsplacement wth respect to the Ag tp can be calculated to reveal the spatal resoluton of aman mappng. The calculaton for the aman sgnal from the hybrd system ncludng the Ag tp substrate nanogap and molecule starts from determnaton of the unmodfed local feld profle by usng the 3D FDTD method, whch has been dsplayed n Fgure. Then the unmodfed and modfed aman scatterng theory are adopted to calculate the aman sgnal wthout and wth consderaton the near-feld self-nteracton of molecule wth ts plasmonc envronment, respectvely. A typcal result s dsplayed n Fgure for β =.5 37 C m /V) and d = Fgure. Local feld profle and aman sgnal when consderng the electromagnetc self-nteracton of molecule wth the tp and substrate. (a) Calculated ntensty profle of local feld confned wthn the gap nvolvng the molecule n self-nteracton va multple elastc scatterng wth the Ag tp substrate gap. The molecular polarzablty s β =.5 37 C m /V), the lateral and longtudnal dsplacement of molecule to substrate are x = nm and d =. nm. The fwhm of the hot spot s about.3 nm. (b) aman sgnal ntensty versus the lateral dsplacement of molecule x, as predcted by the unmodfed (red) and modfed (black) theory. The fwhm of the aman sgnal s 7. and. nm for the unmodfed and modfed theory, respectvely.. nm. Fgure a clearly shows that the strong self-nteracton would sgnfcantly reduce the hot spot sze to about.3 nm, order of magntude smaller than the value wthout selfnteracton ( nm). As a result, the resoluton of aman mappng, whch s assumed to equal the fwhm of the aman response curve, can reach. nm, more than 3 tmes smaller than the unmodfed value of 7. nm. The above result has ndcated the formaton of super-hot spot due to strong couplng of the molecule wth the tp 865 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

9 The Journal of Physcal Chemstry C Artcle Fgure 5. Super-hot spot formaton and ultrahgh resoluton n aman mappng. (a) Local feld ntensty versus the horzontal coordnate-x as calculated by modfed theory and 3D FDTD method for dfferent lateral dsplacement of molecule (the molecular polarzablty s β =.5 37 C m /V), the lateral and longtudnal dsplacement of molecule to substrate are x = nm and d =. nm). The dashed black curve represents the unmodfed local feld calculated by 3D FDTD method. (b) Local feld ntensty versus the horzontal coordnate-x as calculated by 3D FDTD method for dfferent lateral dsplacement of molecule (the molecule s modeled by a delectrc sphere wth radus nm, relatve delectrc constant 3, the lateral and longtudnal dsplacement of sphere to substrate are x = nm and d =. nm). (c) aman mappng resoluton at dfferent values of the longtudnal dsplacement of molecule to the substrate d and molecular polarzablty β. (d) Local feld ntensty versus the lateral dsplacement of molecule at β =. 37 C m /V and d =.6 nm. The nsert fgure s the correspondng aman ntensty versus the lateral dsplacement, showng the fwhm of aman sgnal (equal to the resoluton) of.9 nm. substrate nanogap and ths super-hot spot s responsble for the much mproved aman mappng resoluton. On the other hand, the property of the super-hot spot could be dependent on the relatve poston (longtudnal and lateral) of the molecule wth respect to the tp apex. Ths feature s nvestgated n detals by usng the modfed self-nteracton theory. The result of local feld ntensty profle at each value of molecule lateral dsplacement,.e., x, s dsplayed n Fgure 5a. The molecule s excted at 53 nm and located at d = nm. To confrm the accuracy of the theoretcal result, the 3D FDTD method s also used to reexamne the problem by modelng the molecule as a delectrc sphere wth radus nm and relatve delectrc constant 3. The numercal result s dsplayed n Fgure 5b, whch agrees well wth the theoretcal result n regard to the lne-shape of the curve and the peak ntensty and poston. For the sake of comparson, the unmodfed local feld ntensty profle wthout consderng self-nteracton s also plotted n Fgure 5, parts a and b. At x =, the super-hot spot has the greatest enhancement and narrowest lne wdth. When x ncreases, the self-nteracton nduced feld profle curve gets lower and wder, as a result of whch the aman mappng resoluton does not obey the relaton predcted by the conventonal theory that the aman mappng resoluton s about half the super-hot spot sze. Such a stuaton has already been llustrated n Fgure 3. A systematc exploraton on the key ssue of aman mappng resoluton s made n a broad space of parameters β and d by usng the trusty self-nteracton modfed theory, and the calculaton results are summarzed n Fgure 5c. A sgnfcant pont s that n some certan parameter space where the molecule s closer to the tp than to the substrate, the aman mappng resoluton could be below nm. A typcal example s llustrated n Fgure 5d, where the super-hot spot feld ntensty profle at varous values of the lateral dsplacement of molecule are dsplayed. Here the molecule polarzablty s at a modest value of β =. 37 C m /V and located at the poston of d =.6 nm. Note that ths molecule polarzablty s substantally smaller than the value estmated for a sphere nm at radus, β =.5 37 C m /V, and s closer to the value of flat HTBBP molecule whch has a horzontal scale of nm and vertcal scale of below nm. At x =, the super-hot spot has the greatest enhancement factor n peak ntensty of 36 and the narrowest lne wdth of.8 nm, whch are 7 tmes larger and 3 tmes smaller respectvely than the correspondng values for the bare hot spot n Fgure wthout consderng molecule self-nteracton. emarkably, the peak ntensty of the super-hot spot rapdly decays down to about / when x ncreases to nm. The decay s much more volent than the stuaton at Fgure 5, parts a and b, whch ndcates that the aman sgnal could be hghly senstve to the molecule lateral dsplacement leadng to an ultrahgh spatal resoluton n aman mappng. Subsequent calculaton based on the selfnteracton modfed theory s made and the result s dsplayed n the nset of Fgure 5d. The aman sgnal response curve has a fwhm of.9 nm, whch mples a.9 nm resoluton n aman mappng, justfyng the above expectaton. Further calculaton shows that ths resoluton s fne enough to dscrmnate two dentcal molecules nm n lateral dstance by aman mappng (Fgure 6). VI. ESTIMATE OF NEA-FIELD SELF-INTEACTION CONTIBUTION TO AMAN ENHANCEMENT In the last few sectons, we have developed a new optcal theory of aman scatterng of molecules nteractng not only wth the ncdent lght, whch s subject to great enhancement n both aman exctaton and radaton strengths, but also wth ts 866 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

10 The Journal of Physcal Chemstry C Fgure 6. aman mappng of two molecules n the TES system. Calculated aman ntensty versus the horzontal coordnate-x for two dentcal molecules n lateral dstance of nm. Both molecules have polarzablty β =. 37 C m /V) and they are located d =.6 nm above the Ag substrate. The result s calculated by the modfed theory consderng molecule self-nteracton. The two molecules are dscernble by the aman mappng. complex near-feld self-nteracton wth the plasmonc nanostructure envronment. Accordng to our numercal smulatons, Artcle the new theory appled to TES system can well explan the expermental observaton of subnanometer spatal resoluton n aman mappng. In ths secton we further present an analyss to estmate the near-feld self-nteracton contrbuton to aman scatterng, n order to better understand the new aman scatterng theory assocated wth varous TES systems under a broad range of geometrc parameters and operatonal condtons. The new theory nvolves contrbutons from two new modfcaton factors g (r, ) and g (r, ), n addton to the factors descrbed by the tradtonal aman scatterng theory. It s thus pvotal to make deep quanttatve analyses on the roles played by these modfcaton factors on our current problem of subnanometer resoluton n the aman mappng usng TES, among whch ther magntude and spatal senstvty needs specal attenton. Let us take a closer look at the near-feld self-nteracton modfcaton-factor tensor g (r, ) = [I β()( /ε c ) G (r, r, )M ]. Let k = /c be the free-space wavenumber, the free space Green functon G (r, r, ) s gven by k r r e G = + = + ( r, r, ) IG ( r, r, ) I k π k r r + k x k x y k x z k r r e = + π k y x k y k y z r r + k z x k z y k z 3( x x) 3( x x)( y y) x x z z 3( )( ) r r r r r r y y x x y y y y z z 3( )( ) 3( ) 3( )( ) kr r e πk 3 r r r r r r r r 3( z z)( x x) 3( z x)( z y) 3( z z) r r r r r r = πk k r r e r r 3 B (6.) Here n dervng the fnal equaton of eq 6., we have adopted the quas-statc approxmaton based on the fact that n the deep-subwavelength near-feld regon, ths model works very well. The matrx B reflects the orentaton of near-feld dpole radaton, and ts magntude s n the order of the unt matrx I. We can see that n the deep-subwavelength near-feld regon, the free space Green functon s nversely proportonal to cubc power of the dpole-mage dpole dstance r r. Now let us look at the matrx M, whch s a tensor descrbng the self-nteracton of the molecule dpole wth ether the lowersde flat Ag substrate or the upper-sde Ag curved tp modeled by a Ag sphere. In the deep-subwavelength near-feld regon, ths self-nteracton effect can be approxmated wth hgh accuracy by nteracton of the dpole wth an mage dpole located ether wthn the substrate or wthn the sphercal tp. As a result, M are called mage matrx. Accordng to refs 3 and 33, we can get the explct analytcal form of ths mage matrx. The recurson relaton for the mage matrx relatve to the lower-sde flat substrate s M =((ε m )/(ε m + ))( n x n x n y n y + n z n z )M, wth n x, n y, and n z beng the three unt vectors n the Cartesan coordnates relatve to the metal substrate. Smlarly, the mage matrx relatve to the upper-sde metal sphere has a recurson relaton as M = ((ε m )/(ε m + ))( n θ n θ n φ n φ + n r n r )M by referrng to the sem-nfnte delectrc and the conductng sphere. n θ, n φ, and n r are the three unt vectors n the sphercal coordnates relatve to the metal 867 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,

11 The Journal of Physcal Chemstry C sphere. In wave optcs, the mage matrces just represent the reflecton of dpole radaton from the flat Ag substrate and curved Ag sphere. As we have seen n secton II, these radaton felds are subject to multple reflecton wthn the gap by the lower and upper Ag-ar nterfaces, leadng to the exstence of a seres of mage dpoles and mage matrces. Although the magntude of each mage matrx M s n the order of unt matrx I, all these mage matrces that represent the nteracton among these mage dpoles could sum up to a sgnfcant magntude, and n some specal stuatons could trgger resonance nteracton of the molecule dpole wth ts plasmonc envronment, namely the lower and upper Ag substrates. The fnal factor s the molecular polarzablty, β(), whch relates the molecule dpole moment p wth the exctaton electrc feld by p = β()e. Bascally, ths factor s proportonal to the volume of the molecule V m n the macroscopc aspect and the dpole transton probablty denoted as d m (usually wth a magntude n the order of, unless at condton of aman resonance) between lower and upper molecule quantum states n the mcroscopc aspect. The molecule volume V m s related wth ts lnear sze r m va V m =πr m 3 /3. Therefore, β() πε r m 3 d m /3. Now the near-feld self-nteracton modfcaton-factor tensor s approxmately wrtten as d g ( r, ) = I 3 m 3 rm e k r r 3 r r BM (6.) Equaton 6. tells us many thngs. Note that for a usual small molecule, the sze s below one nanometer, and the polarzablty s always very small and s n the order of au = C m /V). When ths molecule s placed close to usual plasmonc nanostructures, the dstance of the molecule to the surface s n the order of several nanometers or more, order of magntude larger than the molecule lnear sze. Besdes, the molecule radaton nteracts wth the plasmonc nanostructure only once. As a result, the term (d m /3) ((r m 3 e k r r )/( r r 3 ))B M has a magntude far below, and thus g (r, ) has a magntude close to. Ths means that the self-nteracton of a usual small molecule wth ts plasmonc envronment s very small and can be neglected. In these stuatons, the tradtonal SES and TES theory hold wth hgh accuracy. It can also be clear from eq 6. what can be done to greatly enhance the molecule near-feld self-nteracton modfcaton factor, g (r, ) (/3)Tr[g (r, )]. Several schemes can be adopted to acheve ths. Frst, ncrease the molecule sze r m and make the molecule very close to the metal surface so that r m s comparable wth the dpole-mage dpole dstance r r. Second, ncrease the molecule dpole transton probablty d m, for nstance by adoptng the condton of aman resonance. Thrd, ncrease the number of mage dpoles wth nonneglgble contrbuton, for nstance by adoptng a plasmonc resonant cavty nanostructure wth effcent multple reflecton effects, so as to make the overall self-nteracton much larger than a sngle dpole-mage dpole nteracton. When all the enhancement schemes are nvolved wthn a sngle system, ther contrbutons can be summed up to a large magntude. Ths s just the stuaton n the current UHV-TES aman mappng experment by Dong and co-workers, n whch the HTBPP organc molecule has a lnear sze n the order of nm, t s placed wthn the Ag-substrate Ag-tp nanogap so that ts radaton s subject to an effcent multple reflecton effect. Besdes, the gap s on the order of several Artcle nanometers, so that the molecule dstances to the lower and upper surface are both on the order of nm. In addton, the aman radaton of molecule s excted under the resonance condton n whch the exctaton wavelength matches well wth the drect aman transton band nstead of the usual transton asssted by vrtual photons. Consderng all these factors, the term (d m /3) ((r m 3 e k r r )/(r r 3 ))B M can have a magntude close to, and thus g (r, ) has a magntude much larger than. Ths means that the near-feld self-nteracton of a large-sze aman resonant molecule wth ts plasmonc envronment can be sgnfcant and cannot be neglected. In the stuaton, the tradtonal SES and TES theory s no longer accurate and must be subject to a sgnfcant modfcaton. Yet, the precse quanttatve value of ths nearfeld self-nteracton modfcaton factor must be determned numercally. Because of the strong self-nteracton of molecule wth ts envronment of plasmonc resonant nanocavty, the modfcaton factor should be very senstve to the overall geometrc confguraton and physcal consttuton of the strongly coupled system of metal nanogap and molecule. One sgnfcant thng s that the molecule tself s an ndspensble part of the coupled system, therefore, any change to the molecule should change the property of the coupled system. Ths change should nclude the spatal locaton shft of molecule relatve to the metal nanogap along both the horzontal and vertcal drectons n the geometrc confguraton. Ths geometrc change wll nduce a sgnfcant change to the aman scatterng ntensty of molecule, and that s the physcal orgn of ultrahgh senstvty of aman sgnal to the TES tp scannng poston and the correspondng subnanometer spatal resoluton n aman mappng. Ths concluson can also be made based upon a more mathematcal argument. Note that when the term (d m / 3) ((r m 3 e k r r )/(r r 3 ))B M s close to n magntude, the modfcaton factor g (r, ) and ts magntude g (r, ) (/3)Tr[g (r, )] can be hghly nonlnear wth respect to the molecule poston r. And ths leads to ultrahgh senstvty of aman sgnal upon the relatve poston of molecule to the metal nanogap, namely the Ag tp. Now we can use ths general physcal pcture to understand the UHV-TES system that we study n ths work. The Ag tp has a small curvature radus as 5 nm, thus when the tp s dsplaced away from the center of the HTBPP organc molecule along the horzontal drecton, the vertcal dstance of the tp to the center of the molecule s ncreased, leadng to an ncrease n the dstance between the molecular dpole wth ts mage dpoles nsde the Ag tp and thus a sgnfcant reducton n ther nteracton strengths as well as the magntude of the self-nteracton modfcaton factor g (r, ). Ths means that the aman sgnal would reach the maxmum value when the Ag tp s rght at the top of the molecular center, and rapdly reduces when the tp s dsplaced n the lateral drecton from the molecular center. As a result, the spatal resoluton of aman mappng s much fner than the hot spot of nanogap mode can support. Besdes, notce that ths reducton of selfnteracton strength would become more volent when the molecule s vertcally closer to the tp, because now the molecule would sense a more curved surface of the tp and ts nteracton wth the mage dpoles would change much rapdly when the tp s laterally dsplaced. Therefore, the spatal resoluton of aman mappng s ncreased n ths stuaton. All these qualtatve arguments overall agree well wth our 868 DOI:./acs.jpcc.5b653 J. Phys. Chem. C 5, 9,