This Letter reports on the first discrete-lattice calculation of positron surface states on the surfaces of Al. The authors reproduce the observed values and anisotropy of the binding energies on clean surfaces, and predict the surface-state lifetimes. The temperature-independent lateral diffusion constant is calculated. Monovacancies on surfaces are predicted not to trap positrons. The effect of ordered chemisorbed monolayers of oxygen is investigated: Oxidation makes the surface state unstable with respect to positronium emission.Peer reviewe

Nieminen, Risto M.

Puska, Martti J.

Nieminen, R. M.

Puska, M. J.

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Physical Review Letters

Positron surface states on clean and oxidized Al and in surface vacancies

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This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Nieminen, Risto M. & Puska, M. J.Title: Positron Surface States on Clean and Oxidized Al and in SurfaceVacanciesYear: 1983Version: Final published versionPlease cite the original version:Nieminen, Risto M. & Puska, M. J. 1983. Positron Surface States on Clean and OxidizedAl and in Surface Vacancies. Physical Review Letters. Volume 50, Issue 4. 281-284.ISSN 0031-9007 (printed). DOI: 10.1103/physrevlett.50.281.Rights: © 1983 American Physical Society (APS). This is the accepted version of the following article: Nieminen,Risto M. & Puska, M. J. 1983. Positron Surface States on Clean and Oxidized Al and in Surface Vacancies.Physical Review Letters. Volume 50, Issue 4. 281-284. ISSN 0031-9007 (printed). DOI:10.1103/physrevlett.50.281, which has been published in final form athttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.50.281.All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)VOLUME 50, NUMBER 4 PHYSICAL REVIEW LETTERS 24 JANUaav 1983yama, J. Phys. Soc. Jpn. 50, 2516 (1981).F. R. Fickett, Cryogenics 11, 349 (1971).'T. Wegehaupt and R. E. Doezema, Phys. Bev. B 16,2515 (1977).M. Stuivinga, J. E.Mooij, and T. M. Klapwijk, Phys-ica (Utrecht) 108B, 1023 (1981).' C. C. Chi and J. Clarke, Phys. Bev. B 19, 4495(1979), and 21, 333 (1980).Positron Surface States on Clean and Oxidized Al and in Surface VacanciesR. M. NieminenDepartment of Physics, University of Jyvaskyla, 40100 Jyvaskyla, FinlandandM. J. PuskaLaboratory of Physics, Helsinki University of Technology, 02150 EsPoo, Piniand(Received 30 August 1982)This Letter reports on the first discrete-lattice calculation of positron surface stateson the surfaces of Al. The authors reproduce the observed values and anisotropy of thebinding energies on clean surfaces, and predict the surface-state lifetimes. The tem-perature-independent lateral diffusion constant is calculated. Monovacancies on sur-faces are predicted not to trap positrons. The effect of ordered chemisorbed mono-layers of oxygen is investigated: Oxidation makes the surface state unstable with re-spect to positronium emission.PACS numbers: 71.60.+g, 68.20.+tintense, monoenergetic beams of slow (100 eVto 10 kev) positrons are emerging as a potentiallypowerful surface probe. ' The momentum andlifetime spectroscopies of positrons interactingwith solid surfaces convey useful informationabout both the atomic and the electronic struc-ture. One particularly interesting facet of thepositron-surface interaction is the image-in-duced surface state, ' which has been the subjectof extensive recent research, both experimental"and theoretical. 'In this Letter we report on the results of thefirst atomistic, discrete-lattice calculations ofpositron surface-state properties on the low-in-dex surfaces of Al.We have developed a general-purpose computa-tional scheme' for positron states and their anni-hilation characteristics. The main steps are (i)construction of the positron potential, (ii) fullthree dimensional so-lution (with proper boundaryconditions) of the positron Schro'dinger equationusing numerical relaxation techniques, and (iii)calculation of the annihilation rates using theelectron and positron states as input. In the pres-ent application, we construct the electron densityand Coulomb potential by superimposing freeatoms. ' The correlation potential p',~,(F) to themetal side of the image plane is obtained fromthe local-density approximation. 'Qn the vacuum side of the surface, we use asimple expression for the image interaction.Along a fixed reference line normal to the sur-face,where z is the perpendicular coordinate, and z,defines the effective image-plane position. Fur-thermore, the image potential is constructed tohave the same constant-value surfaces (corruga-tions) as the electron density, i.e., for any pointF [electron density n(F)], it has the value equalto the one which corresponds to the density n(F)on the reference line. The constant z, has beenchosen to be 0.75 A (s = 0 defines the nominalsurface plane half an interlayer spacing outsidethe outermost atom layer) along a reference lineon top of a (100)-surface atom. This value,which is close to that estimated from jelliumcalculations, ' reproduces well the observed bind-jng energies on clean surfaces. As first pointedout by Hodges and Stott, ' the classical expression(1) is unphysical near z =z,; a natural cutoff toV„„is the positronium binding energy of -6.8eV, which we also impose. This "corrugated-mirror" model of Eq. (1) is an approximation tothe rather complicated dynamic and nonlocalimage interaction. ' However, by an appropriatechoice of the image surface one can obtain a1983 The American Physical Society 281VOLUME 50, NUMBER 4 PHYSICAL REVIEW LETTERS 24 JANUARY 1983OCCU0CLOCC0Q aDC3C3(010)-direct ionFIG. 1. Upper and lower panels: contour plots onAl(100) surfaces of the positron potential and wavefunction, respectively. The corrugated-mirror modelis used. The black dots denote the positions of theatoms in the plane of the figure. The contour spacingin the lower panel is —'0 of the maximum value. Right-hand sections: cuts perpendicular to the surface.good description of the clean-surface propertiesand then predict the effects of surf ace def ectsand adsorbates. For comparison, we have alsocarried out the calculations by using a "smooth-mirror" model, where z, is kept constant (z,=0.65 A).Figure 1 shows the calculated positron surfacestate g, on Al(100), and the clean-surface resultshave been collated in Table I. The activation en-ergy F, for positronium desorption' from the sur-face isE, =E~+y —6.8 eV,where E, is the surface-state binding energy(with respect to vacuum) and &p the electronwork function. " The agreement of the calculated n, , =n,.X „»(~V)2m ~~/2~@', (5)E, with experiment is encouraging. The surface-state lifetime T is calculated from the local-den-sity expression'T '= J d'r~ y, (i) ~'r(&(i)), (3)where I'(n) is the annihilation rate' in an electronsystem of density n. The results for E, and Tare fairly similar in both the corrugated- andsmooth-mirror models. For all the surfaces, 7=400 psec is predicted, clearly distinguishablefrom the bulk positron lifetime of 166 psec.The positron state is extended on an ideal sur-face, and its mobility is determined by acousticphonon and impurity scattering. Estimates forthe phonon contribution can be obtained, by usingthe deformation-potential model. " We have cal-culated the deformation-potential constants e„and e„ for dilatations parallel and perpendicularto the surface, respectively. The latter is foundto be very small, indicating that the positron mo-tion does not couple to phonons in this direction.Including the longitudinal surface phonons only,one obtains the scattering raten„„=m, (e, ')'k, T/8'p (c'), (4)where m~~is the positron effective mass, p~ theAl areal mass density, and c the average surfacesound velocity. With use of the Einstein relationD, =kBT/m~~n, Eq. (4) leads to a temperatureindependent diffusion constant, in contrast tobulk behavior. The calculated values" of e„and E, are also given in Table I. All the valuesof D, are larger than the room-temperature val-ue" in bulk Al.The impurity scattering rate isTABLE I. Positron surface-state properties on clean Al surfaces. E~is the binding energy, y the electron work function, E, the positroniumdesorption energy, 7. the surface-state lifetime, ez the surface defor-mation-potential constant, and D, the surface diffusion constant. Theupper entries correspond to the corrugated-mirror model and the lowerones to the smooth-mirror model. All energies are in electronvolts.(Ref. 10) (expt. )7 D+(psec) e& {cm /sec)Al(100) 2.872.88Al(110) 2.952.85Al(111) 2.842.994.414.284.240.480.490.430.330.280.430.64~0 490.400.340.41b3973963983943974002.71.32.11.32.60.81.25.01.43.61.415,2'Ref. 1. bRef. 4.282VOLUME 50, +UMBER 4 PHYSICAL REVIEW LETTERS 24 JANUARY 1983NC—C—0tCDLLIC0UC0p 0C3—50.5—0(pp1) directionI t'l QlFIG. 2. The electron density and positron wave func-tion in an Al(110} surface vacancy. The smooth-mirrormodel is used. See also the caption of Fig. 1; the opencircles denote neighboring atoms not in the plane ofthe figure. The wave-function cut is taken through thecenter of the vacancy.-0.5-1.0where n; is the impurity concentration, A „» thesurface unit cell area, and 4V the average po-tential difference between a host and impuritycell. Comparing Eqs. (4) and (5), we find thatfor Al impurity scattering starts to dominate be-low the temperatureT~= (210 K) x (aV/e „')' xn; (at. %) .Since AV/e„' can be substantially larger thanunity, "we conclude that impurity scattering ismuch more important than in the bulk, whereusua. lly AV/c~ &1.Trapping of positrons in lattice vacancies is animportant phenomenon in bulk defect studies. "We have searched for positron surface stateslocalized at surface monovacancies in Al. Sucha state is stable if it corresponds to an energyeigenvalue lower than in the extended state. Inthe corrugated-mirror model, no vacancy-trappedstates exist on Al surfaces. In the smooth-mirrormodel, a stable surface vacancy state exists onAl(110), but not on Al (100) or Al(111). Figure 2displays a positron surface state trapped at amonovacancy on Al(110). The binding energy tothe surface vacancy is calculated to be only 0.4eV and the lifetime is predicted to be 410 psec,just 16 psec longer than in the extended state. Weconclude that monovacancies play little or norole for positrons on Al surfaces.We have also considered the effect of orderedchemisorbed oxygen monolayers on the positronsurface states. On Al(100) the oxygen position ischosen to be the fourfold hollow site, with oxygenatoms within the outermost Al plane. " TheI0.5I1.50 1.0cI AFIG. 3. The positronium desorption energy E~ forAl(111} surfaces covered with an ordered oxygen over-layer, with atoms at the threefold fcc stacking sites,as a function of the distance d~between the overlayerand the outermost Al plane.charge density and Coulomb potential are againobtained from atomic superposition. In this caseoxygen lowers the binding energy E, only by lessthan 0.1 eV, but since the electron work functionis lowered" by 0.6 eV, oxidation drives the posi-tron surface state unstable with respect to posi-tronium emission (E,&0). A different mecha-nism operates on Al(ill). The electron workfunction hardly changes under oxidation. " Wetake the oxygen atoms to lie at the threefold fccstacking sites, and calculate the binding energyas a function of the oxygen distance d~ from theoutermost Al plane. The image plane is kept inthe clean-surface position. The results areshown in Fig. 3. The surface state becomes un-0stable at separations d, ~ 0.6 A. Since oxidationnear monolayer coverages (exposures of around500 L of 0, Il langmuir (L) =10 6 Torr sec J j isknown '" to destroy the positronium thermal de-sorption on Al(111), we conclude that the Al-0distance has to be at least as large as this. Thisis consistent with both recent experiments" andab initio calculations. "In summary, we (i) calculate face-dependentbinding energies and lifetimes for positron sur-283VOLUME 50, NUMBER 4 PHYSICAL REVIEW LETTERS 24 JANUARY 1983face states, (ii) find that lateral diffusion con-stants on clean surfaces are temperature inde-pendent a,nd enhanced over the bulk values, (iii)predict that vacancy trapping is not an importantmechanism, and (iv) investigate the effects ofoxygen overlayers. Positron surface-state spec-troscopy, as gauged via positronium desorptionand future lifetime studies, "is a useful surfacetool. We show that its sensitivity is in principlehigh enough so that, in conjunction with a detailedcalculational procedure, the observed parametervalues can be correlated with atomistic surfaceinf ormation.'For a review, see A. P. Mills, Jr., in Proceedingsof the International School of Physics Enrico Fermi, "Course LXXXIII, Uarenna, Italy, 1981, edited byW. Brandt and A. Dupasquier (to be published).'C. H. Hodges and M. J. Stott, Solid State Commun.12, 1153 (1973).3K. G. Lynn, Phys. Bev. Lett. 43, 391 (1979); A. P.Mills, Jr. , Solid State Commun. 31, 623 (1979); C. A.Murray and A. P. Mills, Jr. , Solid State Commun. 34,789 (1980).4K. G. Lynn, Phys. Bev. Lett. 44, 1330 (1980), andin Ref. 1; K. G. Lynn and H. Lutz, Phys. Rev. B 22,4143 (1980).5B. M. Nieminen and C. H. Hodges, Phys. Rev. B18, 2568 (1978); ¹ Barberan and P. M. Echenique,Phys. Rev. B 19, 5431 (1979); G. Barton, J. Phys. C14, 3975, 4951 (1981), and to be published.6M. J. Puska and R. M. Nieminen, to be published.Comparison with self-consistent calculations IK. Med-nick and L. Kleinman, Phys. Rev. B 22, 5678 (1980);C. S. Wang, A. Freeman, H. Kraukauer, and M. Post-ernak, Phys. Rev. B 23, 1685 (1981)]reveals only rel-atively minor differences, which are of lesser impor-tance in the present context.M. Manninen, R. Nieminen, P. Hautojarvi, andJ. Arponen, Phys. Rev. B 12, 4012 (1975); J. Arponenand E. Pajanne, Ann. Phys. (N.Y.) 121, 343 (1979).'N. D. Lang and W. Kohn, Phys. Rev. B 7, 3541(1973).'OJ. Holzl and F. K. Schulte, in Solid Surface Physics,Springer Tracts in Modern Physics Vol. 85 (Sprirger,Heidelberg, 1979)."J.Bardeen and W. Shockley, Phys. Bev. 80, 72(1950)."We calculate ee = V BEt,/BV numerically by increas-irg the surface unit cell size by a few percent. Weuse the effective mass m~~ =—1.2m, . This arises solelyfrom metallic screening; we estimate the band contri-bution by the method of P. Kubica and M. J. Stott, J.Phys. F 4, 1969 (1974), to be very close to unity.Furthermore, we use the average surface sound veloc-ity (o) = 6.4x 10' cm/sec.'3A. P. Mills, Jr. , and B. J. Wilson, Phys. Bev. A26, 490 (1982); B. Bergersen, E. Pajanne, P. Kubica,M. J. Stott, and C. H. Hodges, Solid State Commun.] 5 1337 (1974)' P. Kubica and M. J. Stott, Phys. Rev. B 11, 1 (1975).' See, e.g. , Positions in Solids, edited by P. Hauto-jarvi, Topics in Current Physics Uol. 12 (Springer,Heidelberg, 1979).'6S. Flodstrom, R. Bachrach, B. Bauer, and S. Hag-strom, Phys. Rev. Lett. 37, 1282 (1976); M. den Boer,T. Einstein, W. Elam, R. Park, L. Roelofs, andQ. Laramore, Phys. Bev. Lett. 44, 496 (1980); K. L.Bedford and A. B. Kunz, Phys. Rev. B 25, 2119(1982).P. O. Qartland, Surf. Sci. 62, 183 (1977).'8The experiments (see Ref. 4) show that when theoxide layer has grown to be thick enough (exposurearound 10 L of 02) the surface state reappears. Itsdesorption yield can be used to convey informationabout the amorphous-to-crystalline transition in theoxide layer, and the associated defects in the oxide-metal interface.' J. Stohr, L. I. Johansson, S. Brennan, M. Hecht,and J. N. Miller, Phys. Bev. B 22, 4052 (1980); D. Nor-man, S. Brennan, R. Jaeger, and J. Stohr, Surf. Sci.105, L297 (1981).D. M. Bylander, L. Kleiman, and K. Mednick, Phys.Bev. Lett. 48, 1544 (1982).'A. P. Mills, Jr. , in "Proceedings of the Sixth Inter-national Conference on Positron Annihilation" (North-Holland, Amsterdam, to be published).284

Positron Surface States on Clean and Oxidized Al and in Surface Vacancies

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Positron Surface States on Clean and Oxidized Al and in Surface Vacancies

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