High-resolution temperature-dependent photoemission data from Na 2p  core levels reveal substantially larger phonon broadening in the first  atomic layer of Na(110) than in the bulk. We show that the enhanced  width is due primarily to the excitation of relatively soft phonon modes  perpendicular to the surface. Soft surface-phonon modes also account  for previously reported but uninterpreted broadening of transition-metal  surface-atom core levels

Citrin, P. H.

Riffe, D. Mark

Wertheim, G. K.

English

DigitalCommons@USU

VOLUME 67, NUMBER 1 PHYSICAL REVIEWW LETTERS 1 JUL+ 1991Enhanced Vibratiional Broadening of Core-L evel Photoemission fromn the Surface of Na(110)D. M. RiA'e, ' G. K W d P. H. Citrinertheim ande a oratories, Murra H'' ay Hill, Ne~ Jersey 07974eceived 10 December 1990)High-resolution ternmperature-dependent hotoy larger phonon broad ening in the firsten p emission data from N 2}1 d id}li da p core levelels reveal substantial-is ue primarily to the excita than in the bulk. Wesurface. Soft surface- hone ation of relatively soft hshow that thetransition-metal surf~ ~ace-p on modes also account for previousl re dy t p onon modes erp pendicular to theace-atom core level s.y ported but uninter t d'rpre e roadening ofPACS numbers: 79.60.CnThe cou linp g of vibrations to electronic tf fie y o solid-state s stemsthe classic example of of"" """php e optical excitation fo oemission of core electr1't"' 'nd 't'1' Mface have been ha oms an molecules adsorbed on the sur-s own to exhibit similarh' "b"nic ""1adsorbate-substrat b ' th eoup ing is to the vibrational}lo of ha e on rathere intriguing question naturall y arises re-w'th'n th' frst atom~ ~e o t e vibronic cs o tc layer of a solid. Alface-atom core-level d hi . though sur-indeed been re orted 've wi t s exceedin g bulk values havep rte in several s stemsof the extra width hy s, the magnitudei as generall~ been sgin, which could lie in tmall, and its ori-e core-hole lifetimHerenei ies, as generally been obscure.r , we re ortp on surface-sensitiveemission from th 2e p levels of a (}}0~'e core-level photo-e ig -resolution s ectraween 7 and 250 K costrate a sub t ' lls antially enhanced vibra, nclusively demon-for atoms at therational broadeninge surface relative toThis extra width isthose in the bulk.i argued to arise from tthe core-excited at.ie relaxation ofom normal to the surthe excitation of 1face, resulting in'n re atively soft surfac-polarized in that dia irection. The rocee-phonon modespn ri utions of phonons inlevel data, as well as outhe surface core-t r' of th' 'nh'nc d br conclusions re ardapplicable to a widance roadenin itseg lf, are generallye range of systems.Data were obtained on beam line U4ASynchrotron Light Sat the Nationalource using hotonp o go eV. Photoelectronopemispherical anal zion, giving a total instrumg po p oomeV, dependinsamp es were rowstrate at 77 K b de ' commy position fromA d ' d 'h(LEED), th f M dine wit low-ener esurface orientation ofe res y eposited sam 1p es exhibited (110)a ion several domains. I h' s. n omogeneousNa(11 =45 eVRaw DatI—COZ'.LLlI—Spin-Orbit StrippedI31.5 31.0 30.5BINDING ENERGY (eV)30.0FIG. 1. To: Rawp: a data of 2p core-levelo) ob i ddaa =80 K. Bottom: Sta showing only thepin-orbit-strippedsmoothed represent ty e py2 corn onenta ions of the data.p . Solid li nes ar ebroadening from atoms at dom bdb 1 thain oundarback down to 77 K. Thg e samples to -200 K and coolingd d ' 1 dis resulted in- omain surfaces with si n'LEED patterns andi gnificantly sharpers somewhat shar er cThe temperatu -dre- epen ent data w -ep ore-level spectraphotons as tha ere taken with 45 Vs e sample warmed u coiqui - 2 cooling. Thed uisi ion of a single 200-typically 5 K. At theg e sec spectrum wase end of a tern eraturh"k for 'h'n hanges in t e spectrum due tfrom the ambiento contaminationn vacuum of —1&10 ' Tchanges were observed.orr. No suchANa2 sp pectrum from a sinshown in the ugle-domain sample ise pper part of Fig. 1. Th e three distinct116 1991 The American Phri ysical SocietyVovUMv 67, NUM~vR 1 P H YS I CA L R EV I E%' LETTER S 1 JUL+ 1991peaks observed are the result of two overlapping spin-orbit doublets, one from bulk and one from surfaceatoms. The well-resolved peak at 30.6 eV is the bulk2@3~2 component and that at 30.95 eV is the surface2pl~2 component. The feature between these peaks con-tains the unresolved surface 2p3~2 and bulk 2plg2 lines.Apart from the qualitative observation that the 2pl~2surface component is broader than the 2p3~2 bulk line,quantitative information can be obtained only from moredetailed analysis. A straightforward approach is to ap-ply a subtractive stripping technique to remove the con-tribution of the 2plg2 components. This procedure in-volves no assumptions about the line shape and requiresonly the spin-orbit splitting and intensity ratio. We ob-tain satisfactory results for splittings between 155 and165 meV and ratios between 0.48 and 0.58. Belo~ theraw data in Fig. 1 we show a stripped version of thesame spectrum using a splitting of 160 meV and a ratioof 0.52.Several conclusions can be drawn from the strippedspectrum. First, the success of the procedure (as seen bythe lack of oscillations in the tail at high binding energy)indicates that the lifetime width of the 2pl~2 componentis not greatly altered by the L2L3Ml Coster-Kronig de-cay process. Second, the spin-orbit parameters of thebulk and surface components are identical, rather thandiA'erent as reported in an analysis of polycrystalline Nadata. Third, the surface-atom core-level shift is 1905meV, a value 30 meV smaller than the polycrystallineaverage. 'The most significant observation to emerge from thestripping procedure is that the width of the surface line is—50 meV wider than the bulk line. Crystal-field split-ting cannot explain this result because it broadens onlythe p3y2 component, and would yield an oscillating high-binding-energy tail in the stripped spectrum, which is notobserved. Enhanced lifetime broadening of the 2p sur-face core levels, which are dominated by core-valence-valence (CVV) Auger transitions, is also not a viable ex-planation. In W(110), whose valence-band density ofstates (DOS) is significantly modified at the surface,only a 40% increase in the CVV Auger decay rate is ob-7served. Not only would such an effect be even smallerin the alkali metals because their surface DOS are moresimilar to those of the bulk, but the 2p lifetime width ofbulk Na is only 10.15+ 1 meV, clearly too small to ac-count for the large observed diff'erence. An increasedsingularity index e at the surface would make the linemore asymmetrical, but would not aff'ect its peak.Analysis of our data as a function of photon energyshows only minor variation of a with relative surfacestrength, confirming a recent theoretical calculationwhich predicts identical e's for bulk and surface Na.This leaves inhomogeneous andjor phonon broadeningas possible sources of the extra surface width. Both areexpected to produce Gaussian contributions to the lineNa(110)T ~ T1 f r'I I j 1 f I Thv=45 eV3OOC)t-(f) 2LLII—Z'I1g -2—II I I ) I& I IfI~.IIjjI tIttt, le!Itic.|I! ILI & w,"j,"IjlIjlIII1II IjtII jul jg I p~~ II jt!J '1' j tIII 1 I! Ill)ltltlj I t(IjIpfg31.5 31.0 30.5 30.0BIND ING ENE RG Y (eV)FIG. 2. Least-squares analysis of data from Fig. 1. Surfacespectrum is Gaussian-broadened version of bulk spectrum.Note only statistical deviations in residuals.shape. In order to establish that the extra surface widthis indeed Gaussian requires least-squares analysis of thedata. Figure 2 shows the result of such a fit to the datafrom Fig. 1. Averaged over all measured photon ener-gies for 77-K samples, the surface peaks are character-ized by an extra Gaussian width of 92 ~ 12 meV (addedin quadrature to the bulk Gaussian width). The spin-orbit parameters obtained from the stripping procedureare reaffirmed by the fits. In addition, we obtain a singu-larity index a of 0.190+0.016, in good agreement withan earlier value of 0.198+ 0.015, and a Lorentzian life-time width of 13 ~ 3 meV, consistent with absorption-and emission-edge results.To distinguish between inhomogeneous and phononbroadening, we have performed temperature-dependentmeasurements of the 2p photoemission. Figure 3 showsspin-orbit-stripped and smoothed spectra obtained atthree diff'erent temperatures. The increasing width withtemperature of both the bulk and surface components isapparent. Moreover, the surface width increases at afaster rate than the bulk as seen by the decrease of thepeak height of the surface line relative to the bulk. (Ashift in binding energy with temperature due to expan-sion of the lattice is also evident. )A guide to quantitative analysis of the extra surfacewidth versus temperature is obtained by considering thecoupling of the core-hole excitation to a longitudinal De-bye phonon spectrum. Such coupling, first studied byOverhauser and later refined by Hedin and Rosen-10llgren, expresses the core-hole excitation of phonons bya Gaussian broadening whose FWHM value, G, l ~h, at117VOLUME 67, NUMBER 1 PH YSICAL REVIEW LETTERS 1 JULY 1991IIi I I I 1 I I I I I I 5040CI—COZ',LLII—30ECO~I 20(31000I100 200TEMPERATURE (K)3008.5I9.5 10.09.0KINETIC ENERGY (eV)FIG. 3. Smoothethree tern eratureso he and spin-orbit-strip ed 2 dponent.p ures normalized to the height of th b le uk com-temperature T is given byC 1+ 8 TZ- i/2BD 3 BDHere 6 is ht e Debye temperature and C is awhich de ends uparameterpe s pon the valence-band structure do e solid. Since contributions to the totalmeasured Gaussian width G addT in quadrature, we may2+C8 T 1 3 HD3@D 2 8 Twhere G, and G;„h are widths from the inresolution and inhomo eneoe strumentale square of the phonon width has beenive y.large (T/8 ) .i expanded forTle )0, hNote that in thD .8, the is limit (actually forp onon contribution is ver lineo is igh-temperature linear regime simply yields thesum of the instrumental and inhtions.a omogeneous contribu-Using a least-squares analysis of the terndependent data, values oe mperature-a, ues f GT for the surface and bu1 tt d' F 4 L fitface data arean to all of the sur-diff'a also shown. Most notabl herence in slope between the teistelaregqe wo curves; the s uarees faster than that ofe u . e linearity at the highest temperatures indi-FiG. 4. Square of' the total Gaussian wfor 2 bulk da idth vs temperaturep an surface components. Note verperature dependens. e y diferent tem-en ence o surface line. Both least-s ustraight lines extrapol t h ua awidth.apoae to t e so q re of the instrumentalcates that anharmoonic eftects are not importantthe surface. Bothan, even ate. 'inear extrapolations cross thtern eraturep axis at nearly the same point. Si nificantlss e zero-this point is close to the r me esolution determined fro thermi-ed e cuteanal sis. Tg to, thereby confirming th 1 de va i ity of thisy . he slightly higher value for the fcates that a small ame surface indi-ount of inhomogeneous broadeninmay contribute at the surface, but this iared te, is s negligible com-p o the inherent vibrational broadenin g-..V., 80 K ~we e uce bulk vibrational width f 7and 124~10 meV at 300 K. Thesecompare favorabl with ey ar ier, less precise determina-tions of bulk phonon widths in Na, 90+ 20 meV at 80 Kand 160+40 meV at 300 K. B coy ntrast, the surface201 ~ 2010 meV at 80 K and extrapolates tomeV at room temperature.What accounts for the extra surface width? In thebulk, because of symmetr th ' ae-ry, e vi rational motion ccompanying the excitation of a core ele trn an in c ron resi es sole-y e surrounding atoms of th 1 tte a ice. onsiderinjust the nearest neighbors (NN) the', t eir relaxation to anew equilibrium distance around the bulk ce ore-excitedns rained by their bonds with other NN's.e, e same is true of relaxations in-uce parallel to the surface and 0 dis re ected in parallelDebye temperatures H~~ for bcc (110) surfaces whicese N motions at the surface th ' dcan relax normal to the interfe excite atom itsel~ ~r ace. ecause the new e ui-i rium distance between the dq ithe undere excited surface atom ande layer atoms is restrained to first order onl bsur ace atoms rf- en ing orces between it and otheerthan the re ae axation of surface atoms fs is ar greatere laxation of neighboring atoms. This ease of118VOLUME 67, NUMBER 1 PHYSICAL REVIEW LETTERS 1 JUr v 1991C 8 1 1 1Gel- h + +3 3 (3)motion normal to the surface is reflected in perpendicu-lar Debye temperatures 6& that are calculated to bemuch smaller than bulk values ' and lead to theenhanced vibrational broadening at the surface.To express this broadening, Eq. (1) can be easily ex-tended to the surface since G,f-ph comes from a weightedsum of mean-square displacements of appropriate pho-non modes. ' ' For (T/8O )» 1, we obtainIn summary, enhanced vibrational broadening at aclean metal surface has been observed and characterizedfor the first time. The phenomenon is dominated by ex-citation of phonons polarized perpendicular to themetal-vacuum interface. The results of this study shouldnow enable a much more complete and physical interpre-tation of surface core-level data.The data were taken at the National SynchrotronLight Source, Brookhaven National Laboratory, which issupported by the U.S. Department of Energy, Division ofMaterials Sciences and Division of Chemical Sciences.where 8& is the Debye temperature for phonon modespolarized normal to the surface and 6~~; are the two De-bye temperatures for in-plane vibrations. CombiningEqs. (1) and (3) and approximating 8~~; by 8D, wedetermine from the data in Fig. 4 that 8&/8o=0.41+ 0.03 for Na(110), provided C is the same inbulk and surface. ' This is somewhat larger than thetheoretical estimate of 0.32 for Na(110), ' but like thatestimate it is well below an average theoretical value of—0.6 for a set of five bcc (110) transition-metal sur-faces. ' Our experimentally determined value of8~/8D =0.41 for Na(110) implies that as much as 75%of the Gaussian width (in quadrature) comes from theexcitation of perpendicular modes. Data obtained fromK(110) and Rb(110) surfaces also yield quantitativelysimilar behavior. 'Since perpendicular Debye temperatures at metal sur-faces are, in general, expected to be smaller than thebulk value, it is no surprise that broadened surface lineshave been reported for other metals. If Eq. (3) doesindeed have general validity, it should account for theseother results as well. The reported broadenings have in-variably remained uninterpreted because of experimentalinadequacies and/or the lack of a suitable theoretical for-malism. As an example, bcc (110) transition-metal sur-face atoms have 8&=0.68D, and so should exhibit [for(T/8o)» I] phonon widths that are —30/0 larger thanatoms in the bulk. This is, in fact, consistent with dataobtained on W(110). For low-index bcc (100) and bcc(111) surfaces, which are calculated to have 8& andboth 8~~'s of =0.68', ' the high-temperature surface-phonon widths are predicted be —1.65 times larger thanthe bulk value. Photoemission data on Ta(111) havebeen previously analyzed to have room-temperatureGaussian widths of 220 and 320 meV for the bulk andsurface atoms, respectively. ' ' Subtracting the instru-mental resolution in that work of -150 meV yields 160and 238 meV, or a ratio of 1.77, which is close to oursimple estimate of 1.65." Present address: Department of Physics, The Universityof Texas, Austin, TX 78712.'See, e.g. , D. B. Fitchen, in Physics of Color Centers, editedby W. B. Fowler (Academic, New York, 1968), p. 293.2P. H. Citrin, P. Eisenberger, and D. R. Hamann, Phys. Rev.Lett. 33, 965 (1974).P. H. Citrin, G. K. Wertheim, and Y. Baer, Phys. Rev. B16, 4256 (1977).4A. Nilsson and N. Martensson, Phys. Rev. Lett. 63, 1483(1989);Solid State Commun. 70, 923 (1989).~R. Kammerer, J. Barth, F. Gerken, C. Kunz, S. A.Floodstrom, and L. J. Johansson, Phys. Rev. B 26, 3491(1982).6This last result is not surprising since the (110) surface isthe most close packed, and hence most bulklike, of the bcc sur-faces. See, e.g. , the shifts of low-index surfaces of Ta and W:D. Spanjaard, C. Guillot, M.-C, Desjonqueres, G. Treglia, andJ. Lecante, Surf. Sci. Rep. 5, 1 (1985).7D. M. RiA'e, G. K. Wertheim, and P. H. Citrin, Phys. Rev.Lett. 63, 1976 (1989).8T. A. Calcott, E. T. Arakawa, and D. L. Ederer, Phys. Rev.B 18, 6622 (1978).9M. Kato, Phys. Rev. B 38, 10915 (1988).' A. H. Overhauser, as reported by L. G. Parratt, Rev. Mod.Phys. 31, 616 (1959), and A. J. McAlister, Phys. Rev. 186, 595(1969).' 'L. Hedin and A. Rosengren, J. Phys. F 7, 1339 (1977).'2N. F. Mott and H. Jones, The Theory of the Properties ofMetals and Alloys (Dover, New York, 1958), p. 14.'3This value is obtained from the linear-fit value (64~ 5meV) using the (eo/T) term in Eq. (2) with 6o =150 K.'4D. P. Jackson, Surf. Sci. 43, 431 (1974).'~To test whether C is the same for bulk and surface wouldrequire data extending to T—Bo/10'6D. M. Riffe, G. K. Wertheim, and P. H. Citrin (unpub-lished).' J. F. van der Veen, F. J. Himpsel, and D. E. Eastman, Phys.Rev. B 25, 7388 (1982).' G. K. Wertheim, P. H. Citrin, and J. F. van der Veen, Phys.Rev. B 30, 4343 (1984).119

Enhanced Vibrational Broadening of Core-Level Photoemission from the Surface of Na(110)

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Enhanced Vibrational Broadening of Core-Level Photoemission from the Surface of Na(110)

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