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00 Jrii FILE COP POFFICE OF NAVAL RESEARCH 0 Contract N00014-80-K-0852 CR&T Code 0 Technical Report No. 45 N Understanding Core Level Decay Processes In the High-Temperature Superconductors By D. E. Ramaker, N. H. Turner and F. L. Hutson Prepared for Publication in the Physical Review B George Washington University Department of Chemistry Washington, D.C. 20052 December, 1988 Reproduction in whole or in part is permitted for any purpose of the United States Government This document has been approved for public release and sale; its distribution is unlimited. DTIC 0ELECTE &7 D

Transcript of Jrii 0 - DTIC · 2011. 5. 15. · 00 Jrii FILE COP 0POFFICE OF NAVAL RESEARCH Contract...

  • 00 Jrii FILE COPPOFFICE OF NAVAL RESEARCH0

    Contract N00014-80-K-0852

    CR&T Code0 Technical Report No. 45N

    Understanding Core Level Decay ProcessesIn the High-Temperature Superconductors

    By

    D. E. Ramaker, N. H. Turner and F. L. Hutson

    Prepared for Publication

    in the

    Physical Review B

    George Washington UniversityDepartment of Chemistry

    Washington, D.C. 20052

    December, 1988

    Reproduction in whole or in part is permitted forany purpose of the United States Government

    This document has been approved for public releaseand sale; its distribution is unlimited.

    DTIC0ELECTE

    &7 D

  • SECURITY CLASS,FIZCATION OF fZ. Ao au

    REPORT DOCUMENTATION PAGE1&. REPORT SECURITY CLASSIFICATION bRETITVEMAmG

    2a. SECURITY CLASSIFICATION AUTH4ORITY J. OISTRISUTIOF4IAVAILASIUITY OF REPORTApproved for Public Release, distribu-

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    60. NAME OF PERFORMING ORGANIZATION 6bA OFFICI SYMBOL ?a. NAME OF MONITORING ORGANIZATION

    Dept. of Chemistry (f#k& office of Naval Research (Code 413)George Washington Univ.I

    6r- ADDRESS (Oly. State. W ZIP Cod) 7b. ADORESS (Oty. Scam, &Md ZRP Cof.)

    Washington, D.C. 20052 Chemistry Program800 N. Qumncy StreetArlinaton. VA 22217

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    OfcofNaval Research Contract N00014-80-R-0852

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    Chemistry Program ELEMENT No. ~N OPP JACCEssION No800 North QUINCY, Arlington, VA 22217 61153 N N3080 CN 0566

    11. TITLE (Inrclude Socunty 0CUSSiaJiofl)Understanding Core Level Decay Procespes in the High-Temperature Super-conductors (Unci.) /I

    12. PERSONAL AUTH4OR(S)D. E. Ramaker, N. H. Tur er, and F. L . Hutson

    13a. TYPE OF REPORT li b_ TIME COVERED 1 14. DATE OF REPORT (Yar Moonth, Day) IS. PAGE COUNTinterim Technical( FROM ____ O December 1988 '0

    6. SUPPLEMENTARY NOTATION

    repared for publication in Physical 2view B

    17 COSATI CODES IW UJC E (Cont"'..e on ,W~iR* of necerrjry and identify by block '15o.,)

    E L GROUP 1SUB-CROuP Superconductivity, Asiger

    Spectroscopy, X 1 ray

    Emission Spectroscopy, HubbardMoe

    A XACT (Convnu# on mieerr. if I.enary and .doniify by block number)

    A highly correlated CuOq cluster model is utilized to intprpret the corelevel Auger and xray emission decay spectra for YBa?"O" and CLIO. Theevidence indicates that the initial-state shakeup stitei ?efax to states ofthe same symmetry before the core level decay, provided they have a shakeupexcitation energy much greater than the core level width.

    .0 DISTRIBUTION/AVAiLASIUITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION( UNCLASSIFIEO/UNLIMITED )Q SAME AS RPT 0OVIC USERS Unclassified

    220 NAME OF RESPONSIBLE INO01VIDUAL 22b. TELEPHONE (1IcUde Ale& Cotle) 122c. OFFiC- SYMBOL

    Dr. Davi L. Nelson (202 6-4410DO FORM 1473, SAMAR E3 APR f,t'n my " ud util tumausd. SECURITY CLASSIFICATIC4 OF THIS '.01

    All 11'rA ,Mo~I. Unclassified

  • 2

    Previously reported (1,21 core level Auger (AES) and x-ray emission

    (XES) data are interpreted within a highly correlated CuOs cluster model for

    the high-temperature superconductors (HTSC's), YSaCu,07.j and Lat.

    &BaCuO4 (herein referred as 123 and La), The Lu s4V Auger lineshape is

    reported here for the first time and is interpreted consistently with the LVV

    lineshape and XES data. This work clearly indicates, contrary to previous

    reports [1,31, that the initial-core shake-up (ICSU) states do not directly

    decay, but rather relax to the primary core-state before decay. The XES data

    dramatically reveal the change of character of the valence band (VB) states

    between CuO and 123.

    The basic electronic structure of the HTSC's can be described by an

    extended Hubbard model, characterized by the transfer or hopping integral t,

    the Cu and 0 orbital energies ca and cv, the core polarization energy Qi, the

    intra-site Coulomb repulsion energies U, and Up, and the inter-site repulsion

    energies U., and U, •* (i.e. between neighboring Cu-O and 0-0 atoms). The

    extended Hubbard model is most appropriate when the U's are large relative to

    the band widths [3], i.e. when correlation effects dominate covalent or

    hybridization effects. A CuO.( a4-1 ) cluster model, which is also reasonably

    valid when U >) t, simplifies the model [3). Both La and CuO contain CuO.

    groups (41, having 4 short and 2 long Cu-a bonds. The 123 HTSC contains

    CuOs and planar CuO4 groups [4]. The different n may alter the relative

    intensities of various features, but similar features are present in each case.

    The different bond lengths may increase the widths of the spectral features,

    but little else since correlation dominates.

    The CuO.(20- 2 )- cluster has one hole shared between the Cu 3d and 0

    2p shells in the ground state, which we term the v (valence) states. The

    spectroscopic final states reflect multi-hole states, e.g. v I , cv (c = core) etc.

  • 3

    We indicate the location of the v holes by d (Cu 3d) or p (0 2p). In the case

    of two holes on the oxygens, we distinguish two holes on the same 0 (ps), on

    ortho neighboring 0 stoms (pp'), or on pars 0 atoms (ppv) of the cluster.

    Furthermore, neighboring pla holes can dimerize [51, so we distinguish

    between two holes in bonded (pp%) and antibonded (pp*.) 0 pairs. Most of

    the 0 atoms actually participate in two CuOs clusters. Consistent with

    previous work [6], we account for this by defining the effective parameter, ¢p

    = cp' + UP,, where U,. includes the interaction of a hole in an 0 p orbital

    with its environment. In general U,. will be less than U.p due to

    polarization.

    The v states, as reflected by the theoretical DOS [1], can be described

    as having the Cu-0 bonding (*b) and antibonding (+&) orbital@ centered at 4

    and 0 eV and the nonbonding Cu and 0 orbitals at 2 eV. The 0 features each

    have a width 21- = 4 eV due to the 0-0 bonding and antibonding character

    and the Cu-0 dispersion. The +b and +a wavefunctions can be expressed as

    [31,

    +. = d cosO, - p sindt (la)

    +b = d sind, + p cosO,, (Ib)

    where 0, = 0.5 tan-'(2t/A). We also define the Cu-0 hybridization shift 61

    0.5 sqrt(A2+4t2) - A/2, which is utilized in Table I to give the energies. In

    this picture, the ground state of an average CuOs cluster is located at 1 eV

    having the energy c4 -8 1 +r 2 = cs-, which we use as a reference energy for 3r

    the excited v2, v3, and cv states reflected in the core level spectra. In CuO,

    the hybridization shift r is smaller, and we shall see below that Atc p-cd has C1

    increased to I eV. C1

    Recently (8] we consistently interpreted the VB photoelectron spectra

    (UPS and XPS). Most of the features in the UPS and XPS are also reflected

    .dbLzlty Codes

    Avail and/orSpecial

    • ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 man +ED niml miN• -

  • 4

    in the AES and XES, so that we review these assignments here. In 123, the

    states were assigned as indicated in Table I [8,101. Calculated photoemission

    intensities, their variation with 6, and photon energy dependencies confirm

    these assignments (8]. In CuO [9], we have previously assigned a feature at

    5.5 eV to ppea and ppo and at 3 eV to dp. The character switch of state 1

    from mostly dp to pp, and vice versa for state 2 between CuO and 123 arises

    because A decreases from I eV in CuO to 0 eV in 123. The reduction in a as

    indicated by the UPS data is consistent with the Cu 2p XPS data and with the

    XES data to be discussed below.

    The "shakeup" or "many-particle" features at 9.5, 12.5, and 16 eV have

    also been assigned as Indicated in Table 1 [8]. The pp% state has been

    assigned to the "mystery" feature at 9.5 eV. Such a feature also appears for

    CuO [9,11] so that this feature is not unique to the HTSC's. This feature

    cannot arise from the p2 final state because U, is around 12-13 eV, much too

    large to cause a feature at 9.5 eV. In fact we have found evidence (8] for

    the existence of the p2 feature around 16 eV in 123. Finally the d2 state is

    known to cause the 12.5 eV feature [12).

    Cu_2p and 0 Is core level XPS. In order to understand the XES and

    AES data, we first characterize the initial state, which is reflected directly in

    the Cu 2p and 0 Is XPS data. The primary and satellite features seen in the

    Cu 2p XPS spectrum for CuO [131 and 123 or La [1,14] are known to arise

    from the cp and cd states, respectively (3], having the energies given in

    Table 1. The relative satellite intensity, I(cp)/I(cd) decreases from 0.55 in

    CuO to 0.37 in 123 as determined from the experimental data [1). The energy

    separation, E(cd) - E(cp) increases from 8.7 eV in CuO to 9.2 in 123 (1].

    The primary (cp) and satellite (cd) wavefunctions can be written similar

    to eq. (1), with hybridization angle 6 = 0.5 tan-t(2t/(-Qd)) [3]. In the

    i

  • 5

    sudden approximation, the Intensities are proportional to the overlap between

    the ground state wavefunction, #, and the final states, so that I(dp) -

    cos(,&-3) and I(cd) - sins(O.-O) (3). Thus the satellite intensity increases

    with change in the hybridizhtion angles between the v and cv states. In the

    ground v state, the hole is shared equally in the p and d orbitals since J1 ?

    450, in the primary cv state it is mostly in the p orbital since jc ? 780. The

    changes between CuO and 123 noted above are just that expected for a

    decrease in a and reflect an increased covlency in 123 (151.

    The large width of the primary cp peak is believed to arise from the

    mixing with the cd state [3,15). The cd state has a large width due to the

    large core-hole, valence-hole interaction, indeed, the satellite actually reveals

    the cd multiplet structure. Evidence that the primary cp peak width arises

    from the cd interaction comes from the Cu halide data [3], which show a direct

    correlation of the primary cp peak width with the satellite cd peak intensity.

    We do not believe that the primary peak width arises from the 0 p band width

    as proposed by others (161.

    The 0 Is spectra have been reported by many authors; however, it is

    seriously altered by impurities such as 011- and CO" on the sample surface

    [171. Recent data (181 from single crystal samples of the La material cleaved

    in-situ are expected to be reasonably free of impurity effects. The cp- and

    cpP states listed in Table 1 are believed to account for the tailing off of the

    spectra seen in these spectra (this will be positively identified upon

    examination of the XES data). Consistent with the sudden approximation, the

    cp state is not seen in the 0 Is XPS because now both the v and cv states

    have similar hybridization angles, i.e. the valence hole is mostly in the d

    orbital in both cases.

  • We will find below that the ISSU process, which is responsible for the

    satellites in the XPS noted above, does not produce satellites in the AES or

    XES data, because the ISSU states generally "relax" to the primary states of

    the same symmetry before the core level decay. Such a relaxation is expected

    when the ISSU excitation energy is larger than the core level width (191.

    Previously, vanderLaan et al t31 suggested the intensity of these ISSU

    states in the XPS should be quantitatively reflected in the intensity of the

    Auger satellites found in the LsVV lineshapes for the Cu halides. The data

    do not indicate this however. While I(cd)/I(cp) increases from 0.45 for CuBra

    to 0.8 for CuFa, the Auger satellites do not increase (3]. We previously [1]

    indicated that a fraction of these ISSU states probably resulted in Auger

    satellites for the HTSC's, and that this fraction increased with the increasing

    covalency of the HITSC material. Evidence presented here indicates rather that

    the ISSU states relax before the core level decay to states of the same

    symmetry, provided they have a ISSU excitation energy much greater than the

    core level width. We believe this to be a general result, at least in the Cu*'

    materials.

    The Cu L2 3 and 0 K XES data. The 0 K XES data (21 in Figure la confirms

    our assignment of the 0 XPS, and clearly shows the dependency of the rSSU

    state relaxation on the excitation energy and symmetry. The principal XPS

    peak arises from the cd state, and it decays to the dp state since the x-ray

    emission process is intra-atomic in nature. Therefore the principal 0 XES

    peak aligns with the dp feature in the UPS as shown in Fig. 1. The cp- state

    does not mix with the primary cd state; therefore, it does not relax before the

    decay, but decays directly to the ppe% (and perhaps a little also to the ppa)

    state. This accounts for the feature around 6.5 eV in the XES, just 3 eV

    above the ppo feature in the UPS. The shift of 3 eV matches the energy

  • difference between the cps and cd core hole states. The cpv state can m x

    with the cd state, therefore it can relax to the cd state, but it does this

    slowly because of the small excitation energy of 0.5 eV. Therefore, the cpP

    state decays either directly to the ppP state, or relaxes to the cd state, which

    then decays to the dp state. This explains the photon energy dependence

    seen (21 in the data of Fig. Is. At high photon energy, the sudden

    approximation is more valid, creating a larger intensity for the cpr state, and

    consequently a larger ppo contribution around 2.5 eV in the XES.

    The Cu Lt3 XES data t2,201 shown In Figure lb dramatically reveals the

    switch in character of the I and 2 v2 states between CuO and 123. Again, the

    satellite cd initial state relaxes to the cp state before the decay so that the

    XES reflects primarily the dp DOS. In CuO the XES spectrum peaks at 3 eV,

    in 123 it falls around 4.2 eV, very near where we indicated the dp states fall

    in the UPS data. The large intensity in the CuO XES extending above the

    Fermi level is believed to be an experimental artifact [20].

    The Cu L23VV and L33M23V Auger data. Comparison of the L3VV data

    for CuO [11] end 123 [11 are shown in Fig. 2. The data reveal features at 7

    (the two-center feature), 15, and 19 eV, which we previously [l] attributed to

    dp, d2, and d3 final states, utilizing a vi final state model. The d3 states

    were attributed to a combination of 3 different processes; I) initial state

    shakeoff (ISSO) followed by Auger decay (g.e. + hu - L3V - d3), 2) Coster-

    Kronig (CK) decay followed by Auger decay (g.e. + hv - Lu - Liv - di), and

    3) ISSU followed by Auger decay (g.s. + hv - Live -. Liv -. d3, where e

    denotes the excited electron). The ISSO and CK processes accounted for all of

    the ds component in CuO, and the ISSU process was believed, as mentioned

    above,to account for the increasing d component in La and 123 [1].

    We report and interpret here, for the first time, the LzsMI:V Auger

  • lneshapes for the 123 SC. The sample preparation, treatment, and instrument

    utilized were described previously (1). Fig. 2 compares the LtsMlgV spectra

    for CuO [241 and 123 , and Identifies the various features. The L23Ms3V

    lineshapes reflect the cv2 DOS# the main features arising from the cdp final

    state, and the satellite from the cd'p state apparently resulting from the

    similar ISSO, CK, and ISSU processes defined above. However, Fig. 2 reveals

    a most interesting point; although 123 shows an increased satellite in the

    L23VV relative to CuO, It is not increased in the LssMfV. This Indicates

    strongly that the ISSU process is not responsible for the increased satellite in

    the L3VV, because then it should Increase the satellite in both 123 lineshapes.

    Since only the primary cp core-hole state Auger decays, and this

    process is also known to be strictly intra-atomic, the L2WV lineshape in our

    current v3 final state model, reflects the d'p DOS, as it is distributed among

    the vs states listed in Table 1. Thus the features at 7, 15, and 19 eV arise

    naturally from the dppP, d2p, snd dpZ final states. The ISSO and CK

    processes also contribute to the "satellite" contribution at 19 eV just as in

    CuO. The dppo state does not appear in the LVV lineshape because it does

    not have the same symmetry possessed by all the other vs final states and

    the cv initial state. The increased "satellite" feature at 19 eV in the HTSC's

    arises apparently because of increased configuration mixing between the dZp

    and dp2 states. Its intensity is increased in 123 relative to CuO because the

    energy separation (before hybridization) between d2p and dp2 has decreased

    from 3.8 eV in CuO to 2.5 eV in 123. We have indicated this mixing in Table I

    by adding the hybridization shifts 62 to the energy expressions for these two

    states.

    The L,3M 23V lineshape reflects the cdp DOS. The mixing of the other

    states (cd', cppP, cpp%, and cpp%; the latter three are not listed in Table 1)

  • 9

    with the cdp state is small because of the large energy separations involved.

    The cp' state Is close to cdp; however, it falls in between the 3L and IL

    multiplets of the cdp state. Although it may have some intensity, It surely

    does not contribute to the CK + SU satellite around 25 eV in either CuO or

    123. The exchange splitting (2K) between the 3p and d holes is known to be

    very large [3), so we include it explicitly in Table I to account for the haL

    multiplets.

    The 0 KVV lineshape is severely altered by impurities on the sample

    surfaces, and no single crystal lineshape data have been reported. The 0 KVV

    lineshapes for CuO and CuaO have been reported (111, and they have the

    primary dp2 or pt features, respectively, around 19 eV. A very small satellite

    appears around 7 eV in CuaO which we attribute to the ppP state. A much

    larger and broader satellite around 7 to 14 eV in CuO appears, which we

    attribute to the dp state around 14 eV as well as a smaller amount to the

    dpp state around 7 eV. Thus the d~p and dps states appear in both the Cu

    L2jVV and 0 Auger lineshapes for Cu"* oxides, except their primary and

    satellite roles are reversed.

    In summary, we have interpreted XES and AES data utilzing a highly

    correlated CuO. cluster model. Both the XES data and the previously

    interpreted UPS data reveal the reversal in character of the VB states

    between CuO and the ITSC's. We have also shown that the initial-state shake-

    up states evident in core level XPS, do not generally produce satellites in the

    core emission spectra, because they relax to the primary core states of the

    same symmetry, provided the ISSU excitation energy is greater than the core

    level width.

  • TABLE I Summary of hole states revealed in the spectroscopicdata, and estimated energies using the following optimal valuesfor the Hubbard parameters in eVa:

    6, = 2 to = 2 Up - 12, 13 UP =9.5,10.26a = 0.5,0.8 to = 2, 3 UP,* = 4.5, 4 U4 , =1" = 2 Upp : 0. Uo z 2 Q4 =9a a 1, 0.5 A a 0, 1. K: 4

    Stateb Energy expression Calc. E. Exp. I. RemarkeVe.4 eVe

    G.S. and IPRS. v*.) d ce - a, * r 0 : 2 - heavily+6) p cp + a, * r 4 : 2 - mixed

    UPS and XES. vs1)0 ppP c + A - 62 + a 2.5 2.5 heavily2)" dp c, UP, +dr +a 4.5 4.2 mixed3) pp*. c,+ A +Ut,, -r'+a 5.5 5.4) ppeb tp+ A *U,," +fla 9.5 9.5 mystery peak5) d' to + U, + a 12.5 12.5 Cu sat.6) pt C + A + Up + ,a 15 16

    Cu 2p IPS, evCP cc + A + a cc, +1 ES maincd C. + Q4 + a C. + 10 BP+9.2 sat.

    0 In IPS, CvCd cc + a cc4 I Eta maincpP cc + A + a cc + I BE. maincpO cc + A + Ue +a c, + 3 Ej.+2 ? tailcp c. + A + Q, + a ? not obs

    Cu LIVV ARS. v2dppP 2c, + 2UdP * a 7 7 2 cent. featuredppo 2cp+Uepo+2U.p+ 11.5 - no mixingdip td+c,+U+2U.p-6,+a 16 15.5 main featuredpi 2cp+Up+2Up+6+a 19.5 18-25 sat. feature

    Cu LIMisV ARS. cvs

    cdp cC+cp+Q+U.p.X+a Ce +9 E3,+l0 main, ILc.+17 Ejp+18 main, 3L

    CpR cC +Cp +A +Up + a c. + 15 - not observedcdi cc"cd+U*+2Qe +a cc+30.5 - not observed

    *PSrameters for 123 indicated first, those for CuO serond.The dominant character in the hybridized states is given.

    eThe Calc. E and Exp. E columns indicate the results for 123.dThe calculated E is defined relative to the ground vi (d) state energy = C -a. The vIld) energy defines the Fermi level relative to the vacuum level atzero.*The dominant character switches an described in the text, and thus the signin front of 82 in the opposite for CuO.

  • Figure Captions

    Fig. 181 Comparison of 0 K XES data for 123 taken at the indicated

    photon excitation energies (from Ref.2).

    lb) Comparison of Cu Lu XIS data for 123 (Ref. 2) and CuO

    (Ref. 20).

    Ic) UPS data for 123 (h' z 74 eV from Ref. 10).

    Fig. 2) Comparison of Auger data for the materials indicated. Cu

    L2VV data for CuO and 123 from refs. 25 and 1. Cu

    Lz3 M2aV data for CuO from ref. 24 and for 123, this work.

    The Ls2VV data is on a 2-hole binding energy scale = ELZ-

    Ek,, and the L:3M22V on a 1-hole scale = ELi-EI-EN,, where

    E.3 = 933.4 and Em3 = 77.3 eV (9,11].

  • 0OK (a)XES

    123

    *570hog=535

    CuCuO (b)

    .0 1231I'

    65

    zI

    z

    . . . . . . . . . . . . .

    15 10 5 0BINDING ENERGY (eV)

  • sat. L3

    co

    123

    c/z/

    CuO

    sat. L 3 LL

    3228 2420 16 128 4 0 -4 -8BINDING ENERGY (eV rel. L,3)

  • References

    1. D.E. Ramaker at &l., Phys. Rev. 36, 5672 (1987).

    2. K.L. Tuang at &l., Phys. Rev. 337, 2293 (1988).

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    Phys. Rev. B37, 1123 (1988).

    4. J.E. Greedan at al., Phys. Rev. B35, 8770 (1987).

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    451 (1987); W. Folkerts et al., J. Phys. C: Solid State Phys. 20,

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    Rev. B37, 3734 (1988).

    6. J.E. Hirsch et al., Phys. Rev. Letters 60, 1168 (1988).

    7. J. Redinger et al., Phys. Lett. 124, 463 and 469 (1987).

    8. D.E. Ramaker, N.H. Turner, and F.L. Hutson, submitted.

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    (1982).

    10. N.G. Stoffel et al., Phys. Rev. B37, 7952 (1988); also preprint.

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    12. R. Kurtz et al., Phys. Rev. B35, 8818 (1987).

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    14. P. Steiner et al., 2. Phys. B- Condensed Matter 67, 497 (1987).

    15. D.E. Ramaker et al., Phys. Rev. 36, 5672 (1987).

    16. D.D. Sarma, Phys. Rev. B37, 7948 (1988).

    17. S.L. Qiu et al., Phys. Rev. B37, 3747 (1988); W.K. Ford et al., Phys.

    Rev. B37, 7924 (1988); D.E. Ramaker, N.H. Turner, and F.L. Hutson,

    In Thin Film Processing and Characterization of Hibh Temperature

  • Superconductors, J.M.Harper, J.H. Colton, and L.C. Feldman ads.,

    AVS Series No. 3 (American Institute Physics, New York, 1988), p

    284.

    18. T. Takahashi et ml., Phys. Rev. D37, 9788 (1988).

    19. J.W. Gadzuk and M. Sunjic, Phys. Rev. 312, 524 (1975).

    20. A.S. Koeter, Mole. Phys. 26, 625 (1973).

    21. D. van der Marel et &l., Phys. Rev. B37, 5136 (1988).

    22. Y. Chang et &l., Phys. Rev. B (In press).

    23. N. Nucker et al., Z. Phys. B: Cond. Matter 67, 9 (1987); Phys. Rev.

    37, 5158 (1988).

    24. L. Fiermans, R. Hoogewijs, and J. Vennik, Surf. Sci. 47, 1 (1975).

    25. P.E. Larson, J. Electron Spectroec. Related Phenom. 4, 213 (1974).

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