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Chemisorptive emission and luminescence
605
Surface Science 107 (1981) 605-624 North-Holland Publishing Company
C~~SO~~E EMISSION AND L~I~SCENCE I. Chlorine/zirconium
R.H. PRINCE ofPhysics, York University, Toronto, CanadaM3J lP3
and R.M. LAMBERT and J.S. FOORD Department of Physical Chemistry, Universityof Cambridge, Cambridge CB2 lEP, UK Received 27 August; accepted for publication 23 January 1981
Experimental data for electron and photon emissions during the chemisorption of chlorine on pure and sodium-doped zirconium are presented, and a quantitative model is given which adequately describes the gross features of the electron emission process. The model is based on invoking a tunnelling mechanism and relaxation by a radiationless (Auger) process, and draws heavily on previous successful theories for Auger ion neutralization to predict the energy distribution functions for subsequent emissions. For a high electron affinity species such as chlorine, the observed chemisorptive emission yields are strongly dependent on work function varying from 10d to 10s2 electrons per incident atom, and following a cubic dependence on the excess energy available. Chemiso~tive luminescence is also observed, at levels of -10m8 photons per incident atom in accordance with previous estimates. A self-consistent kinetic analysis is presented to describe the rapid decay of these emission processes following the onset of chemisorption.
1. Introduction Adsorbing species of high electron affinity are expected to chemisorb into at least a partly ionic state, and the dissipation of the large chemisorption energies involved is usually considered to occur by means of phonon excitation of the solid. However, for adsorbing systems in which atoms of very high effective electron affmity EL are involved (the free atom affinity .f$~is enhanced considerably by the final state interaction) it becomes energetically possible for much faster relaxation to occur, p~a~y rad~tio~ess processes of the Auger type. In these cases, in which the initial coupling is to the solid eEec&ons, there will always be produced a non-equilibrium distribution of internal electrons, some of which may by virtue of their momenta surmount the surface barrier and escape as externally observable electrons. Such particles therefore offer diagnostic capability, and the parallel between the present case. of tunnelling to an adsorbate afftity level and Auger ion
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neutralization [l-3] is clear. These transitions do not involve diredy the translational energy of the incoming particle, although Hagstrum’s very successful adiabatic model [l] requires modifications to take into account that for higher velocities the Auger transitions take place closer to the surface and produce broadening effects. In Auger ion neutr~ization (INS), the dominant parameters of the problem are the effective ionization potential El and the surface work function Qt, the electronic emission yield being strongly dependent on the excess energy (Ei - 245). An analytical model is presented in the appendix which adequately describes the data obtained on the emission processes from chlorine and oxygen reactions on pure and sodium-doped zirconium surfaces. It shows that at least at small surface concentrations for which the effective electron affinity Ei is assumed constant, the electron yield per incident atom, y, scales as the cube of the excess energy (EL - 24). Using current literature convention, these emitted electrons are terms “exo-electrons” (i.e. the “Kramer effect”), even though this term implies a the~ally exoergic mechanism as was initially believed [4]. We prefer the terms “chemisorptive emission” (CSE) and “chemisorptive luminescence” [CSL] to describe the electron and photon emissions involved, and contend as proposed earlier [S] that this Auger or “potential” ejection mechanism has been responsible for a large number of reported phenomena, few of which have been adequately described quantitatively. These include early works in which emission was observed during the adsorption of oxygen on Ni, Cu, W, e.g. ref. [6], in the anomalous high background rates of fres~y-manufactured Geiger-Miiller counters [7], in the mechanical deformation of metals /8], and in the more recent work of McCarroll 191 and Kasemo et al. [lo-l 31 on optical emission during chemisorption. All of these reports involve the presence of high electron affinity gases, usually oxygen either free or in a combination which chemisorbs dissociatively, and the exposure of a clean surface either by evaporation, bulk phase change [ 141 or even mechanically by deliberate abrasion or the onset of fatigue microcracks [S] ; an extensive review may be found in ref. [ 151. The correlation between ~~~~~onyield and work function has been previously indicated by Anderson and Klemperer [4] and by Gesell and Arakawa ]16] using a parallel photoelectric measurement, and by Kasemo [ 111. The relationship between photon yield and work function has been discussed separately [ 13,171. Although the Auger process is dominant, the probability of radiative relaxation is small but non-zero, being of the order of the ratio of the time which a thermal particle spends within the tunnelling separation at the surface (-1O-‘3 S) and the typical lifetime for radiation (*lo-’ s), that is, the photon yield is expected to be about 10e5 times the yield of excited i~~er~ul electrons (the external yield of electrons is reduced by a suitable escape probability). It is thus reasonable to normalize the distribution function of internal electrons to one per incident chemisorbing atom in the subsequent model. Although the ratio of the electron yield to the photon yield is known to vary over several orders of magnitude for different systems, the typical maximum electron and photon yields in the present work are -10e4 and 10e9 per incident atom respectively, in keeping with these estimates, and are obtained using an
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atom of highest electron affinity feasible for such studies (Cl) on a very electropositive metal surface (Zr). In view of the difficulties of handling chlorine in conventional molecular beam configurations with adequate flux levels for measurement of such yields, a highly efficient electrolytic cell method is used, providing surface intensities of typically 1014/cm2 s-l. The quantitative treatment of these processes has been primarily confined to the photon emission aspect [ 13,171, and while the details of the variation of the affinity level Ei of the incident particle are not precisely known, it is generally accepted that near the surface the final state of the reaction can be regarded as the atomic affinity level, since only the atomic halogen affinity is large enough to produce the high energy photons observed for these systems. The advantages of chemiluminescence experiments in measuring the surface density of states function without the necessity for the deconvolution problems of INS have been already stated [ 171. However, the experimental difficulties in achieving an adequate photon flux are formidable, hence the present paper mainly addresses the experimentally more accessible electron emission process.
2. Experimental The present experiments were carried out in a conventional UHV chamber previously used for studying scattering of chlorine from metal surfaces [ 181, and utilized the electrolytic cell method of chlorine generation described earlier [18,19]. Typical base pressures were -3 X 10-r’ mbar rising to -1 X lo-’ mbar during sodium deposition. By operating the AgCl cell in a constant current mode (typically ice11= 10 to 100 /LA), the chlorine flux is accurately determined. However, the fraction ~1which strikes the specimen must be inferred from geometric considerations which take into account the degree of focussing achieved by recessing the cell anode within the silica support tube and the source-to-target separation. By using a high proximity configuration for the chemisorptive emission measurements, once having completed specimen diagnostics and calibrations, an efficiency factor p = 0.5 is believed appropriate, although additional corroboration is available from a kinetic analysis which follows. The specimen (99.99+ %), Goodfellow Metals) was polycrystalline foil, spot welded to 0.25 mm diameter Ta wires, which were themselves spot-welded to 2.0 mm diameter Ta rods. This configuration avoided end effects in heating and tended to eliminate support effects during thermal desorption experiments. Temperature measurement was by means of a Pt-Pt/l3% Bh thermocouple attached directly to the specimen, and the sample was resistively heated. After baking of the system, the polycrystal was annealed and ion bombarded at 1000 K with neon, usually at 300 eV for 12 h at 10m6 A cm-‘. Auger electron spectra obtained after
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this procedure showed satisfactory removal of chlorine and carbon contamination, and no evidence of bulk sulphur diffusion due to annealing. Electron diffraction indicated some quite sharp diffraction features with high background intensity, indicating an appreciable crystallite size after annealing cycles 1201. Sodium doping was derived from heating sodium alumina silicate (molecular sieve) suspended on a platinum substrate, drawing the ions so produced to the specimen, biased negatively at 9 V. Although such sources are known to emit neutral atoms as well as ions, the ratio of neutrals to ions in the present case has been determined by work function measurements at various substrate temperatures and bias conditions. The correction for neutral sodium has been determined to be less than 5 nA at the usual deposition level of 150 nA, so that dosage levels were determined by current integration. Work function changes following dosages up to -500 &C[cm2 were obtained in the usual manner by observing shifts in the characteristic current-voltage curves of a low energy electron gun. By means of sample rotation, thermal desorption spectra for dosages up to 180 /.&!/cm2 (--monolayer coverage) were obtained by a direct beaming con~guration into a residual gas analyzer (EAT Quad 1SO). Electron emission from the sample was recorded by monitoring the target current using an electrometer amplifier biased at -9 V, being the same arrangement used for Na deposition, for convenience. Optical emission was recorded by attaching a light-tight photomultiplier housing to the single quartz viewport; a Bendix BX 75005303 photon counting tube with S-20 response was used without filters and direct-coupled to a conventional single channel analyzer combination. The dark count rate for this photomuliplier was usually 2-5 cps, corresponding to an estimated sensitivity of ~lO-g photons per reacting atom, based on an isotropic distribution and the maximum cell current used (100 MA).Chemisorptive emission using oxygen was performed in the usual manner by direct admission of research grade gas to pressures required to produce surface flux levels comparable to those obtained by the chlorine cell (i.e. -3 X lo-’ mbar).
3. Results and discussion 3.1. Characterization ofsodium dosing Thermal desorption spectra for Na dosing levels up to 180 @C/cm’ are shqwn in fig. 1. At least two binding states for Na on Zr are evident, with desorption maxima at temperatures of -470 and -600 K, corresponding to desorption activation energies of -112 and -140 KJfmole respectively, assu~g first order kinetics and a pre-exponential factor of 10 l3 s-l [21]. The heating rate was not uniform at all times (typically -100 K s-r), and these binding energies are regarded as tentative. Clearly the lower temperature state initially flus more rapidly, and although the peak locations are not always reproduced, the areas under the desorption curves,
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(4
45
6
7 Sample
8
45
Temperature
6 (K)
Fig. 1. Sodium thermal desorption spectra from Zr polycrystal at (a) low and (b) intermediate coverage levels, for sodium dosages from 5 to 180 PC cmm2 as indicated. Heating rate -100 K s-1.
which are presumed proportional to sodium uptake, are well-behaved, as may be seen in fig. 2. The curve is highly linear at small coverages, up to 30 pC/cm2. and highly correlated to the work function change which is also shown in this figure. If the initial sticking probability is taken to be unity, then the uptake is known, and the slope of the uptake curve may be used to scale the sticking probability as a function of surface coverage. This is shown in fig. 3, again with work function change for convenience. The behaviour of the sticking coefficient suggests that the departure from Langmuir atomic adsorption kinetics is not large. It is noted that for a 1 X 1 structure on the (lOi0) plane (a = 3.23 A, c/a = 1.59 for hcp Zr [22] a coverage of 6.028 X 10r4 cmm2 would be expected, increasing to 1.1 X 10” cm-? on the (0001) plane. The results shown in fig. 3 are consistent with these estimates, the (1010) plane being favoured by the Langmuir model. Clearly the asymptotic approach of Aq5 to the metallic sodium value A@ = @zr - @Na= 1.7 eV [23] is slow; the data shown extends to 3.4 X 10” atoms cmd2 incident, but inaccuracies in measured sticking coefficients beyond monolayer coverage make a precise determination of coverage difficult, although it must be in excess of 3 monolayers incident to achieve the metallic value.
610
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120 Sodium Dose ( pC percm? Fig. 2. Sodium uptake and uro~k function change as functions assuming an initiat sticking probability of unity. 60
P of integrated
sodium dose,
Sodium Coverage fatoms per cm3 Fig. 3. Coverage dependence of the sticking probability and work function change for Na on the Zr polycrystalline sample, assuming an initial probability of unity, A Langmuir functian with monolayer coverage urn = 6 X 10” 4 cm-l is shown dotted.
R.H. Prince et al, / Chemisorptive
3.2. The kinetics
ofthe
where 0 4 (_!?a - 24)
&- 0 [(I$, -
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elech-on and photon yields
Using the cubic approximation
y(f) =
emission and luminescence. 1
for the electron yield developed in the appendix
then by setting 4 = $zr - A@(t),
29zr) + W(f>13.
The pure Zr system marginally satisfies the excess energy criterion, such that (EX - 24~~) = A_!?is small with respect to the sodium induced term, as will be seen later, but aE may be retained here as a subsequent fitting parameter. This simple cubic dependence will clearly only be valid if the effective electron affinity I?i remains constant during adsorption. This might be expected to be true during the initial stages of chemisorption, possibIy up to monolayer coverage, beyond which changes in the tunnelling barrier itself will occur. We now consider the sodium sites as “active sites”, and further limit the surface concentration to values sufficiently low that A@4 0.3 eV. This condition not only ensures linearity between sodium coverage and work function change A@ (see figs. 2 and 3) which is a most useful relationship for simplification of the kinetic equations, but also that (EL - 24) is maintained at sufficiently small values to justify the linearization of the escape function and the validity of a cubic yield function. If the initial sodium fractional coverage is denoted t?$,, and the initial work function shift A$‘, then for small BN,,,, A4/A#’ = &&t$&. A number of possible dissociative adsorption models then may be proposed, in order to calculate the time dependence of y_ Each model leads to a characteristic electron emission decay with time, only the third model being in accord with experiment. (i) Dissociative adsorption with no short range order at sites where two neighbouring vacancies exist. Such sites may be either dual Na or Zr sites, or mixed Na/ Zr sites. (ii) Langmuir kinetics with complete order and repulsive nearest neighbour interactions. (iii) Langmuir kinetics with high order and attractive nearest neighbour interactions d&,/dt
= (l/7) (1 - @a),
~~~~~~ = expf-t/r),
whence for AZ? = 0, i(t) = i(O) {exp(-t/7)}3
= i(0) exp(-3t/r)
i.e. an exponential decay for aE = 0, or at all times such that aE < 2 A#, with an apparent time constant which is one third the kinetic time T-= (Aa,/,S,,@) where
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I \ - I
\
8- \ \ \
0
2
4
6
8
$0
12
14
Time (seconds)
Fig. 4. Time dependence of electron emission current for three chlorine flux levels corresponding to electrolytic cell currents of (A) 100 JLA,(B) 50 @A, (C) 10 MA. An extrapolation to zero time is shown (dotted) based on the non-dimensional decay curve of fig. 5.
(T, is the monolayer surface coverage (atoms/cm’), A the irradiated sample area (cm2), and !.i the fraction of the atomic chlorine flux F (atoms/s) which strikes the sample with initial sticking probab~ty So_ Transient exoelectron yields i(f) are displayed in fig. 4 for three values of F (Le. cell current), for A@’= 0.3 eV corresponding to a sodium dose of 45 &‘cm2. Due to the extremely rapid decay at short times, the finite response of the electrometer/ recorder combination prevents an adequate representation of the early portion of each curve. In addition, the rapid rate of change of surface potential (up to 1 V/s) will induce sign&ant displacement currents unless efforts are made to reduce stray target capacitance by means of guarding techniques, for example. In order to verify that proper kinetic scaling has been achieved, and to effectively extend the observations to shorter times, the curves of fig. 4 are replotted in fig. 5 using universal variables i/&n and dose D = ice11t (C/cm2), where these parameters are related to the previously defined kinetic parameters by z-(O)/i,,r,= p?(O),
D = Fet = (eAu&&)
t/T.
There is ample proof in fig. 5 that such a universal decay curve exists, and that it
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x1o-4
Fig. 5. Normalized emission current as a function of chlorine dose D at the electrolytic ceil for the three cases shown in fig. 7. (A) ice11= 100 &A f -1; (B) ieel = 50 PA f- - -1; (C) ice11= lOpA (. - . - .>.A universal decay curve exp(-0.54 X 104Df is shown dotted (* * * 1* .).
,o-7/ 2
5
10 20 Dose (pC percm22) Fig. 6. Theoretical variation of the electron emission coefficient with sodium dose (solid curves) for various values of AE = (EL - %$z,). Experimental points are shown for four assumed valued of the cell efficiency factor it = 1 (01, 0.5 (u), 0.31 (o), 0.17 (0). Error bars are shown for only the case or = 1. Sodium
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is adequately represented by the function i/&r1 = (10e4) exp(-0.54 X 104D), from which it is determined (Au,/@,) = 3.5 X 10”. For hcp Zr, we expect u, = 6 X 1014/cm2 for a 1 X 1 structure on the (1010) plane, and 1.1 X 1015/cm2 on the (0001) plane. Taking Se = 1, these values correspond to p = 0.31 respectively for the sample size used, whence the measured values of r(O) for these cases is in the range from 3.2 to 5 9 X 10T4. These values of I-1are in reasonable accord with values computed on geometrical grounds. By repeating this experiment at various sodium dosings up to 45 PC/cm*, the dependence of y(O) on the initial work function shift AGo is shown in fig. 6. Although at the largest dose (2A$, = 0.6 eV) the effect of a small value of AE is clearly minimal, it is used at this point as a fitting parameter, having considerable influence at the lowest dosings. Thus we show a family of calculated curves for y(O) based various p, for AE = 0, 0.05, 0.1, 0.15 eV, values AE = 0.1 eV, /J - 0.5 appearing to best reconcile this admittedly crude theoretical model to the observed variation in yield. This implies that Ei = 8.1 eV for the chlorine/zirconium system, and that the value a = 0.3 eV_’ used in this model is consistent with a purely Coulombic shift of the affinity level and previous insight from the Auger neutralization results. Thus only electrons within about 1 eV of the Fermi edge are active in the electron emission process, and there is little value to be gained by using more realistic band models. This does not apply to the photon emission process, however, in which only the lower third of the conduction band is excluded from participating in the process. 3.3. Chemisorptive luminescence A sample decay curve for photon emission is shown in fig. 7 in which a photomultiplier with S-20 response is used in the counting mode. In this particular example, 45 PC cm-* Na was added to the pure Zr sample, and in view of the weak dependence of photon yield y* on work function discussed in the appendix, little change in total photon emission would be expected for this case. Since (EL - I$) for pure Zr is estimated to be 4.1 eV, a value large compared to the change A@’ = 0.3 eV, the change in y* is only 4% using the previous kinetic model. The actual decay observed in fig. 7 is believed due to failure of the cell to operate at the high currents used (-200 PA) for periods greater than 20 s, since the decay time is at least one order of magnitude too large to be related to the adsorption kinetics discussed earlier. If the emission is isotropic, the total photon yield is calculated.to be -low8 photons/atom incident, a value which is quite reasonable on the basis of characteristic times for optical and electronic processes, and the normalization to one excited internal electron per incident atom. Preliminary experiments on the oxygen-zirconium system were as follows. No electron emission was seen at any Na-doping level (2.8 < $ G 4.0 eV), whence EL for oxygen must be G5.6 eV. However, photon emission at a level of twice the background rate (-lo-’ photons/atom) was detected for Na levels >135 PC cm-’
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t Cell On
Time(s)
615
5 cps
t Cell Off
Fig. 7. Chemisorptive luminescence signal observed for Zr + 45 PC cmd2 Na and i,,ll = 200 PA. The signal clearly persists at times approaching 100 s which exceeds the kinetic time constant by nearly two orders of magnitude. The decay after t = 10 s is believed due to cell instability.
(A$ - 0.65 eV, @- 3.35 eV) using the Bendix tube (hve - 2 eV) which implies that (EL - I$) > hve, or EL 2 5.35 eV. The gas phase value f$ is -1.46 eV for O- (15), whence a Coulomb shift of 4.1 eV is required for this system, an amount very similar to that for Cl- in the present experiment. If the molecular ion were similarly shifted the effective value of electron affinity for 0; would be about 1 eV lower, so that molecular adsorption would result in near infrared emission. It is of interest to note that if the cubic emission yield is applied to the oxygen-magnesium system [ 161, excellent agreement is obtained for EL = 5.6 eV. The value of $Ms at emission threshold is 2.8 eV, as expected, and the cubic law is verified over a range A$ = 0.7 eV, corresponding to monolayer coverage. In addition, a secondary maximum in electron yield is shown to exist at larger coverages, an effect recently observed for the chlorine/Hf system [24]. Thus for oxygen reacting with fresh aluminum films (4 N 4.2 eV), as reported by Kasemo et al. [ 121, the excess energy available for photon emission is (EL - 4,& 1.4 eV which is only marginally higher than the red cut-off of the EM19659 photomultiplier used by this group. Furthermore, the tube was apparently used in analogue mode, without correction for photocathode response. For an exponential change in work function, as used in the present kinetic discussion, the equation for observed total photon yield then may be shown to contain two exponential terms, the second of which is a “superexponential”, such that the decay curve appears to
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represent that expected for parallel fast and slow reactions, which was the mechanism invoked by the latter authors. We wish to indicate that an alternative interpretation exists, which does not negate the concept of “active” (e.g. Na) sites or a single reaction, but does reject the use of a constant photon emission probability during the reaction, and the necessity to consider two types of sites. The fast initial decay occurs as a result of small changes in work functions; pre-exposure of the Al fnms to methane may then “passivate” the Na sites. Using the estimated parameters for the O?--Al system, a change in work function of only 0.05 eV is sufficient to reduce the observed photon yield by more than one order of magnitude, a sensitivity to coverage which is certainly “not credible” [ 121 if the photon emission probability is assumed constant. The effects of patches in a polycrystalline sample cannot be ignored in such situations, just as for other forms of emission which show a strong functional dependence on work function. This effect may also account for the observations of Kasemo et al. [ 121, since a small patch of reduced work function may dominate the emission process. They estimate that a frequency shift of
Acknowledgement R.H.P. and R.M.L. acknowledge the support of the North Atlantic Treaty Organization (Grant 103.80). J.S.F. thanks the Science Research Council for the award of a Research Studentship.
Appendix:
A model of emission processes
As indicated schematically in fig. 8, the affinity level is lowered and broadened as the molecule approaches the surface. The high affinity of the halogen molecules
617
Fig. 8. Energy level diagram of the atom-metal surface system, illustrating negative Auger ionization of the atom and the effect of the ion-surface interaction potential on the final state energy.
makes electron transfer from the substrate to the adsorbate possibIe even at large adsorbate-surface separations, so that while the details of the variation are unknown, for much of the approach the effective potential must be governed by the image potential [ 171. In addition, the resonance width increases, ~thou~ for the case of the halogens, the absence of a high energy tail in the experimental emission spectra indicates a much narrower resonance than in the case of the broad oxygen 2p resonance [ 131. In the present treatment, state broadening is ignored in view of this and in the absence of experimental energy distribution functions for exo-electrons, although a “broadened Auger transform” [l] could readily be introduced into the subsequent development. It is to be noted that the model considers a twoelectron, pure Auger process, being one of two mech~isms proposed by Kasemo et al. [ 131, the alternative choice being resonance tunnelling and the subsequent filling of a valence band hole. Both offer the possibility of an electron cascade process, i.e. “hot-hole injection” [32] which may lead to an enhanced energy distribution above fF. However, while this mechanism was invoked to explain the anomalous energy distribution above fF of field-emitted electrons [32], the strong (quadratic) dependence of the high energy tail on the hole creation rate implies that in view of the fast electronic relaxation rate it is unhkely that a non-equ~ibrium valence band distribution is sampled by the incident halogen atom at the flux levels used (-lOi cm-’ s-l). This is generally not the case for field emission experiments where the equivalent hole creation rates are typically three orders higher. In any event, cascade effects will not influence the high energy photons and electrons externaily observed since these arise from direct transitions to an essentially atomic affinity level [ 133, but will rather contribute to tailing at the low energy limit of the internal excited electron distribution Ni(eK), where the escape probability is
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small [ 1] . While it is true that the observed electron yield varies rapidly with work function, it will be adequately explained below without the necessity of invoking a non-equilibrium electron distribution function arising from the cascade model such as that due to Ritchie [33]. As an aid in gaining insight into the dependence of the process on the physical parameters involved, we adopt two approaches previously used for the analogous process of Auger ion neutralization. The first is based on an analysis by Propst [3] in which the radiation field set up by the first electron when it falls into the atomic level is regarded as the perturbation that excites the second electron. This model has as virtues a simpler analytical form, and, by regarding the photon absorption as incomplete, the ability to also predict the behaviour of the photon emission process. The second method adopts the alternative perturbation theory approach of Hagstrum [I] in which it is assumed that the Coulomb interaction between the two participating electrons is the perturbation that causes the transition. In the nonrelativistic limit, Burhop [25] has shown that these two approaches yield the same result. Although Hagstrum’s method incorporates the effects of incident particle motion as a lifetime broadening of the electron enery distribution functions, both models must be regarded as adiabatic theories; an attempt to intrinsically incorporate the particle motion is found in the quanta1 model of Wenaas and Howsmon [26]. Using a purely Cuulombic interaction potential, and numerical integration of the WKB transmission probability, Propst [3] finds that the probability of the initial electronic transition from initial state E, when the atom is at separation x, is
where B and a are functions of the atom-surface separation, and thus correlated with the energy shift of the negative ion affinity level A.!?, = (EL - El), where Ei is the effective electron affinity at separation x, and PA is the value at infinite separation. For the case of a purely Coulombic interaction the parameters EL and a effectively become a single fitting parameter, the former determining the maximum energy of ejected electrons (Ei - 2@), the latter being correlated to Ei through their mutual dependence on x, as shown in fig. 2 of the paper by Propst [3]. Note that since the final state of the present system is now shifted by the Coulomb field, (E&= is larger than that based on values at infinite separation, in contrast to the ion neutralization process, and further, since the atomic well is now much more shallow, the reduced tunnelling probability is likely to result in a reduced mean value of x,. Values yielding best tit for the ion neutralization case were generally a = 0.4 eV_‘, x, - 2.3 a, pi - 2 eV. For the present data, values - 4.5 eV are appropriate, as will be seen later, and this a--O.3 eV_‘, x,-2AAEA separation will be taken as that for which the process (which is isoelectronic with Ar’ neutralization) Cl t n e, + Cl- + (n - 2) e, t ek t AE
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is energetically favourable, where a = Ei t e1 t ~2 - 2ee ranges from (EL - 2~) for both electrons from the bottom of the conduction band, to (EL - 24) for both electrons from the top of the band (el = e2 = EF). For El = 3.6 eV [27], the fact that the yield for clean Zr (4 = 4.05 eV [28] is marginally detectable whereas that for small Na doping (4 = 4.1 eV) is observable, implies that Ei N 2& = 8.1 eV, hence A_E’*= 4.5 eV. A value of eF for Zr is also required. Skinner et al. [29] indicate that the band width for all transition metals is -6 eV. This value is consistent with calculated band spectra by Altmann and Bradley [30] and experimental data of Fomichev et al. [31]. Two peaks are evident at about 1 and 2.5 eV below the Fermi edge. The energy released by the initial electron transition as a virtual photon is
and the probability
that a photon of energy hv, is produced as
p(x,, hv,) = B exp [-a(Ea
- 4 - hv,)] .
This form would also be a reasonable a priori assumption for the variation in tunnelling probability through the band. This maximum photon energy is thus for the case E = eF, for which (hv,),, = (Ei - 4) as expected. For the subsequent photon absorption process, it is assumed that the density of states in the conduction band N,(e) is constant, and that the probability of absorption is independent of the initial state of the absorbing electron. The former assumption is justified on the grounds that for the values of $ for clean and Na-doped Zr, only electrons near the band edge are externally observable. Further, the so-called “Auger Transform” [l] tends to eliminate much of the structure in N,-(E) that can appear in the distribution function of external electrons N,,(Ek); additional smoothing will occur in the emission coefficient itself, following integration over No(Ek). We now calculate Ni(ek), the energy distribution function for electrons inside the metal excited by the Auger process, where the kinetic energy of such electrons has the allowed range ek> eF; states fk
= J”
Nc(EI)N~(Ez)P(x~,
~1) de1
de2
.
band
This former is similar to the Auger Transform T(e) used by Hagstrum, with the additional point that the process is weighted by the state-dependent probability p(x,, ei). The present result for constant density of states and variable transition probability is then very similar to that using Hagstrum’s theory for the case NC 0: e1’2 and an energy-independent transition probability, as may be seen in fig. 9. Integration over the conduction band, subject to energy conservation, El + es = 2E = fk + ee - Ea ,
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Prince e? ai. ,/ ~~ernisor~~~ve emission and Iuminescence.
.2
.6
E$"]
I
,
.8
4x1o-2
3
P,
2T LEA CL?
1
i
i
4
~
IO
0
11
E,
L[eV]
Fig. 9. Computed electron energy distribution functions Ni(ek) andNo using the methods of Propst () and Hagstrum for constant density of states Nc (* - . - .) and NC oi e1’2 (- - -1. An escape probability function Pe(ek) appropriate to an isotropic distribution of electron velocities inside the metal is used in each case. Values used are EL = 8 eV, Q = 3.7 eV (corresponding to 45 r.lC cm-’ Na on Zr), EF = 6 eV. The function Nr(ek) has been normalized to one electron per incident atom.
yields Ni(Ek) =;
{ 1 - exp [+!?a
Since the probability
+ fF - a, - Ek)] } , of external
photon
emission
is very low, we normalize
R.H. Prince et al. / Chemisorptive emission and luminescence.
Ni(ek) to one electron per incident
621
I
Cl atom, i.e.
Ek+q+ Ni(Ek)
s
dek = 1
3
EF
whence the normalized 1 - exp
Ni(ek) =(Ea -
energy distribution
[-&!?A + eF
function
is
4 - ek)]
-
$) - u-l { 1 - exp [-a(Ea
- @)I } *
The energy distribution function for exo-electrons excited by the Auger process, Ne@k), is now computed, using an escape function Pe(ek) for the case of an isotropic angular distribution and a planar surface barrier [ 1,3]
Pe(Ek) =
i
ii1 - (%/#2 ,
ek> 63 ,
0,
ek <
co a
such that NO(Ek)
I
=Ni(Ek)Pe(Ek)
where the energy scales for interior electrons (fk), referred to the bottom of the conduction band, and exo-electrons (Ek), referred to the vacuum level, are related by the barrier height eo, where Ek =
(Ek
-
Eo)
,
EO = (EF
+ 4)
o
2
Sample distribution functions for the case of lightly doped Zr are shown in fig. 9, together with a calculation based on Hagstrum’s analysis, for the cases NC(e) = constant and NC(e) 0: ~r’~. Since the model of Propst gives extra weight to initial transitions from electrons near eF (i.e. larger er), Hagstrum’s model will similarly agree if a half-power density of states function is used with an energy-independent tunnelling probability. In the present paper, the overall yield per incident atom, y, is of greater interest, and the analytically simpler form due to Propst is preferable. Thus eo+Ei-2@
Ek--2@ -r=
No(Ek)
s
ak
=
0
s
Ni(Ek)
Pe(Ek)
dEk
.
EO
It is desirable to obtain an analytical expression for y, at least for a restricted range of (Ei - 2@), the energy excess for the process. For negative ion formation, unlike Auger ion neutralization, the energy excess is small, typically less than 1 eV, where eo - 10 eV SO that (ek - ee) Q EOand the escape function may be linearized 2Pe(fk)=
1 -
(1 +%$q+s.=
1 _ [1 -$%$q
. ..I&$
.
622
R.H. Prince et al. / Chemisorptive emission and luminescence.
Then putting C = (Ea - @) - a-l { 1 - exp [-a(Ea -1 (EA;2@)2_(EA;2Q) y - 4cee [
+f
- @)I },
(1 -exp[-@&2@)]}
Expanding the exponential term in series, valid for a(Ei terms of power three and less, yz &
(Ea - 2$)3
EL - 24
for
I
= 3.5 eV
1
- 24) < 1, and retaining
,
0
where the “constant” C has a weak dependence on 4, partly cancelled by a dependence of the barrier height e. = (EF + @), such that the product varies only 5% over the range 3.7 < $Jd 4 eV for the implied value Ei = 8 eV. This simple cubic expression will be seen to be of considerable use in any discussion of reaction kinetics, but clearly overestimates the yield when the inequality is not properly satisfied, the values for a pure Na surface (# = 2.3 eV) being y = 1.08 X 10m2 by numerical integration and y = 1.99 X 10e3 using the approximate cubic expression. The strong dependence of y on $I makes the correlation between these parameters a sensitive one, and offers attractive diagnostic possibilities since the electron current is readily detected. The external photon yield may be deduced in a similar fashion. The absorption of the virtual photon was assumed to be independent of the initial state of the absorbing electron and the photon energy hv, thus the total photon yield y* is proportional to the integral of p(xa hv) i.e. Ek-@ Y*a s
p(x,,
hv) dhv =5
{
1 - exp[-a(Ea
- @)I} ,
(E&@>O,
hv=O
where B and a are previously tion x,. Thus y* = A { 1 - exp [-a(Ei
defined constants
depending
on the transition
separa-
- @)I},
where the constant A is unknown, but would be expected to reflect the characteristic transition rates for optical and electronic processes, consistent with the normalization of the internal electron energy distribution function Nt(ek) for 1 electron per incident atom, i.e. A < lo-‘. If the photon emission process is detected by a non-wavelength-discriminating device such as a photomultiplier operating in a photon-counting mode with adequate threshold immunity, then y* is reliably related to 4, though with low sensitivity, since even for the Cl/Zr system, (Ei - 4) = 4 eV. In fact, one would expect photon emission from any metal/Cl system, although the photon wavelengths may pose detection difficulties. It is important to note, however, that in general one cannot assume that the photon yield y* is time-independent during a surface reaction, and furthermore, if a wavelength sensitive detector is used, such as
R.H. Prince et al. / Chemisorptive
emission and luminescence.
I
623
a photomuliplier
operating in the conventional (analogue) mode, there is an additional variation in output signal due to the shifting of the wavelength distribution to the red, for systems in which, as usual, adsorption increases the work function. This is tantamount to reformulating the previously-discussed Auger electron ejection yield, since the photon is now transformed at a photocathode with maximum wavelength sensitivity hve to a photoelectron for subsequent detection. For photocathodes operating near the photoelectric threshold, the conversion efficiency 5 is highly linear, such that on including this effect the experimental output varies as ~~~~=A’{(E~-~-hv~)-a-‘{l
-exp[-a@‘~-@-hve)]}}.
Provided that hv,, = (I$, - $) is far from the threshold value hv,-,,the dependence on q5is weak, but extremely large changes can occur if this is not the case.
References [l] [2] [3] [4]
H.D. Hagstrum, Phys. Rev. 96 (1954) 336, and references to earlier work cited therein. H.D. Hagstrum, Phys. Rev. 119 (1960) 940. F.M. Propst, Phys. Rev. 129 (1963) 7. J.S. Anderson and D.F. Klemperer, Proc. Roy. Sot. (London) A258 (1960) 350, and references cited therein. The use of the term “Kramer Effect” to describe structure dependent electron emission was internationally agreed at a meeting of the Austrian Physical Society, Innsbruck, Sept. 1956, see W. Hanle, Acta Phys. Austriaca 10 (1957) 339. [S] T.F. Gesell, E.T. Arakawa and T.A. Callcott, Surface Sci. 20 (1970) 174. [6] T.A. Delchar, J. Appl. Phys. 38 (1967) 2403. [7] L. Grunberg, Brit. J. Appl. Phys. 9 (1958) 85. [8] W.B. Lewis and W.E. Burchan, Proc. Cambridge Phil. Sot. 32 (1936) 503. [9] B. McCarrol, J. Chem. Phys. 50 (1969) 4758, and references cited therein, particularly the USSR literature. [lo] B. Kasemo, Phys. Rev. Letters 32 (1974) 1114. [ll] B. Kasemo and L. Wallden, Solid State Commun. 15 (1974) 571; Surface Sci. 53 (1975) 393; 75 (1978) L379. [12] J. Harris, B. Kasemo and E. Tomqvist, Chem. Phys. Letters 52 (1977) 538. [ 131 B. Kasemo, E. Tornqvist, J.K. N$rskov and B.I. Lundqvist, Surface Sci. 89 (1979) 554. [ 141 F. Futschik, K. Lintner and E. Schmid, Z. Physik 145 (1956) 48. [15] L. Himmel and P. Kelly, Comments Solid State Phys. 7 (1976) 81. [16] T.F. Gesell and E.T. Arakawa, Surface Sci. 33 (1972) 419. [17] J.K. Ngrskov, D.M. Newns and B.J. Lundqvist, Surface Sci. 80 (1979) 179. [18] R.H. Prince and R.M. Lambert, Chem. Phys. Letters 67 (1979) 388. [19] P. Goddard, K. Schwaha and R.M. Lambert, Surface Sci. 71 (1978) 35. 1201 J.S. Foord, P.J. Goddard and R.M. Lambert, Surface Sci. 94 (1980) 339. [21] P.A. Redhead, Vacuum 12 (1962) 203. [22] C.S. Barret, Structure of Metals, 2nd ed. (McGraw Hill, New York, 1952) p. 646. [23] R.J. Maurer, Phys. Rev. 57 (1940) 653. [24] R.H. Prince, R.M. Lambert, J.S. Foord and M.P. Cox, unpublished. [ 251 E.H.S. Burhop, The Auger Effect and Other Radiationless Transitions (Cambridge Univ. Press, 1952). [26] E.P. Wenaas and A. Howsmon, in: The Structure and Chemistry of Solid Surfaces, Ed. G.A. Somorjai (Wiley, New York, 1969) p. 13-1.
624
R.H. Prince et al. / Chemisorptive emission and luminescence.
[ 271 B.L. Moiseiwitsch,
I
in: Advances in Atomic and Molecular Physics, Vol. 1, Ed. D.R. Bates (Academic Press, London, 1965) p. 6 1. [ 281 D.E. Eastman, Phys. Rev. B2 (1970) 1. [29] H.W.B. Skinner, T.G. Bullen and J.E. Johnston, Phil. Mag. 45 (1954) 1070. [30] S.L. Astmann and C.J. Bradley, in: Soft X-Ray Band Spectra and the Electronic Structure of Metals and Materials, Ed. D.J. Fabian (Academic Press, London, 1968) p. 265. [31] V.A. Fomichev, T.M. Zimkina, A.V. Rudnev and S.A. Nemnonov, in: Band Structure Spectroscopy of Metals and Alloys, Eds. D.J. Fabian and L.M. Watson (Academic Press, London, 1973) p. 273. [32] J.W. Gadzuk and E.W. Plummer, Phys. Rev. Letters 26 (1971) 92. [33] R.H. Ritchie, J. Appl. Phys. 37 (1966) 2276.
Surface Science 107 (1981) 605-624 North-Holland Publishing Company
C~~SO~~E EMISSION AND L~I~SCENCE I. Chlorine/zirconium
R.H. PRINCE ofPhysics, York University, Toronto, CanadaM3J lP3
and R.M. LAMBERT and J.S. FOORD Department of Physical Chemistry, Universityof Cambridge, Cambridge CB2 lEP, UK Received 27 August; accepted for publication 23 January 1981
Experimental data for electron and photon emissions during the chemisorption of chlorine on pure and sodium-doped zirconium are presented, and a quantitative model is given which adequately describes the gross features of the electron emission process. The model is based on invoking a tunnelling mechanism and relaxation by a radiationless (Auger) process, and draws heavily on previous successful theories for Auger ion neutralization to predict the energy distribution functions for subsequent emissions. For a high electron affinity species such as chlorine, the observed chemisorptive emission yields are strongly dependent on work function varying from 10d to 10s2 electrons per incident atom, and following a cubic dependence on the excess energy available. Chemiso~tive luminescence is also observed, at levels of -10m8 photons per incident atom in accordance with previous estimates. A self-consistent kinetic analysis is presented to describe the rapid decay of these emission processes following the onset of chemisorption.
1. Introduction Adsorbing species of high electron affinity are expected to chemisorb into at least a partly ionic state, and the dissipation of the large chemisorption energies involved is usually considered to occur by means of phonon excitation of the solid. However, for adsorbing systems in which atoms of very high effective electron affmity EL are involved (the free atom affinity .f$~is enhanced considerably by the final state interaction) it becomes energetically possible for much faster relaxation to occur, p~a~y rad~tio~ess processes of the Auger type. In these cases, in which the initial coupling is to the solid eEec&ons, there will always be produced a non-equilibrium distribution of internal electrons, some of which may by virtue of their momenta surmount the surface barrier and escape as externally observable electrons. Such particles therefore offer diagnostic capability, and the parallel between the present case. of tunnelling to an adsorbate afftity level and Auger ion
0039-6028/8 l/0000-0000/$02.50
0 North-Holand Publishing Company
606
R.H.
Prince
et al. / ~~lemisor~~ive emission und luminescence.
I
neutralization [l-3] is clear. These transitions do not involve diredy the translational energy of the incoming particle, although Hagstrum’s very successful adiabatic model [l] requires modifications to take into account that for higher velocities the Auger transitions take place closer to the surface and produce broadening effects. In Auger ion neutr~ization (INS), the dominant parameters of the problem are the effective ionization potential El and the surface work function Qt, the electronic emission yield being strongly dependent on the excess energy (Ei - 245). An analytical model is presented in the appendix which adequately describes the data obtained on the emission processes from chlorine and oxygen reactions on pure and sodium-doped zirconium surfaces. It shows that at least at small surface concentrations for which the effective electron affinity Ei is assumed constant, the electron yield per incident atom, y, scales as the cube of the excess energy (EL - 24). Using current literature convention, these emitted electrons are terms “exo-electrons” (i.e. the “Kramer effect”), even though this term implies a the~ally exoergic mechanism as was initially believed [4]. We prefer the terms “chemisorptive emission” (CSE) and “chemisorptive luminescence” [CSL] to describe the electron and photon emissions involved, and contend as proposed earlier [S] that this Auger or “potential” ejection mechanism has been responsible for a large number of reported phenomena, few of which have been adequately described quantitatively. These include early works in which emission was observed during the adsorption of oxygen on Ni, Cu, W, e.g. ref. [6], in the anomalous high background rates of fres~y-manufactured Geiger-Miiller counters [7], in the mechanical deformation of metals /8], and in the more recent work of McCarroll 191 and Kasemo et al. [lo-l 31 on optical emission during chemisorption. All of these reports involve the presence of high electron affinity gases, usually oxygen either free or in a combination which chemisorbs dissociatively, and the exposure of a clean surface either by evaporation, bulk phase change [ 141 or even mechanically by deliberate abrasion or the onset of fatigue microcracks [S] ; an extensive review may be found in ref. [ 151. The correlation between ~~~~~onyield and work function has been previously indicated by Anderson and Klemperer [4] and by Gesell and Arakawa ]16] using a parallel photoelectric measurement, and by Kasemo [ 111. The relationship between photon yield and work function has been discussed separately [ 13,171. Although the Auger process is dominant, the probability of radiative relaxation is small but non-zero, being of the order of the ratio of the time which a thermal particle spends within the tunnelling separation at the surface (-1O-‘3 S) and the typical lifetime for radiation (*lo-’ s), that is, the photon yield is expected to be about 10e5 times the yield of excited i~~er~ul electrons (the external yield of electrons is reduced by a suitable escape probability). It is thus reasonable to normalize the distribution function of internal electrons to one per incident chemisorbing atom in the subsequent model. Although the ratio of the electron yield to the photon yield is known to vary over several orders of magnitude for different systems, the typical maximum electron and photon yields in the present work are -10e4 and 10e9 per incident atom respectively, in keeping with these estimates, and are obtained using an
R.H. Prince et al. / Chemisorptive
emission and luminescence.
I
601
atom of highest electron affinity feasible for such studies (Cl) on a very electropositive metal surface (Zr). In view of the difficulties of handling chlorine in conventional molecular beam configurations with adequate flux levels for measurement of such yields, a highly efficient electrolytic cell method is used, providing surface intensities of typically 1014/cm2 s-l. The quantitative treatment of these processes has been primarily confined to the photon emission aspect [ 13,171, and while the details of the variation of the affinity level Ei of the incident particle are not precisely known, it is generally accepted that near the surface the final state of the reaction can be regarded as the atomic affinity level, since only the atomic halogen affinity is large enough to produce the high energy photons observed for these systems. The advantages of chemiluminescence experiments in measuring the surface density of states function without the necessity for the deconvolution problems of INS have been already stated [ 171. However, the experimental difficulties in achieving an adequate photon flux are formidable, hence the present paper mainly addresses the experimentally more accessible electron emission process.
2. Experimental The present experiments were carried out in a conventional UHV chamber previously used for studying scattering of chlorine from metal surfaces [ 181, and utilized the electrolytic cell method of chlorine generation described earlier [18,19]. Typical base pressures were -3 X 10-r’ mbar rising to -1 X lo-’ mbar during sodium deposition. By operating the AgCl cell in a constant current mode (typically ice11= 10 to 100 /LA), the chlorine flux is accurately determined. However, the fraction ~1which strikes the specimen must be inferred from geometric considerations which take into account the degree of focussing achieved by recessing the cell anode within the silica support tube and the source-to-target separation. By using a high proximity configuration for the chemisorptive emission measurements, once having completed specimen diagnostics and calibrations, an efficiency factor p = 0.5 is believed appropriate, although additional corroboration is available from a kinetic analysis which follows. The specimen (99.99+ %), Goodfellow Metals) was polycrystalline foil, spot welded to 0.25 mm diameter Ta wires, which were themselves spot-welded to 2.0 mm diameter Ta rods. This configuration avoided end effects in heating and tended to eliminate support effects during thermal desorption experiments. Temperature measurement was by means of a Pt-Pt/l3% Bh thermocouple attached directly to the specimen, and the sample was resistively heated. After baking of the system, the polycrystal was annealed and ion bombarded at 1000 K with neon, usually at 300 eV for 12 h at 10m6 A cm-‘. Auger electron spectra obtained after
608
R.H. Prince et al. / ~~em~sor~tive emission and luminescence. I
this procedure showed satisfactory removal of chlorine and carbon contamination, and no evidence of bulk sulphur diffusion due to annealing. Electron diffraction indicated some quite sharp diffraction features with high background intensity, indicating an appreciable crystallite size after annealing cycles 1201. Sodium doping was derived from heating sodium alumina silicate (molecular sieve) suspended on a platinum substrate, drawing the ions so produced to the specimen, biased negatively at 9 V. Although such sources are known to emit neutral atoms as well as ions, the ratio of neutrals to ions in the present case has been determined by work function measurements at various substrate temperatures and bias conditions. The correction for neutral sodium has been determined to be less than 5 nA at the usual deposition level of 150 nA, so that dosage levels were determined by current integration. Work function changes following dosages up to -500 &C[cm2 were obtained in the usual manner by observing shifts in the characteristic current-voltage curves of a low energy electron gun. By means of sample rotation, thermal desorption spectra for dosages up to 180 /.&!/cm2 (--monolayer coverage) were obtained by a direct beaming con~guration into a residual gas analyzer (EAT Quad 1SO). Electron emission from the sample was recorded by monitoring the target current using an electrometer amplifier biased at -9 V, being the same arrangement used for Na deposition, for convenience. Optical emission was recorded by attaching a light-tight photomultiplier housing to the single quartz viewport; a Bendix BX 75005303 photon counting tube with S-20 response was used without filters and direct-coupled to a conventional single channel analyzer combination. The dark count rate for this photomuliplier was usually 2-5 cps, corresponding to an estimated sensitivity of ~lO-g photons per reacting atom, based on an isotropic distribution and the maximum cell current used (100 MA).Chemisorptive emission using oxygen was performed in the usual manner by direct admission of research grade gas to pressures required to produce surface flux levels comparable to those obtained by the chlorine cell (i.e. -3 X lo-’ mbar).
3. Results and discussion 3.1. Characterization ofsodium dosing Thermal desorption spectra for Na dosing levels up to 180 @C/cm’ are shqwn in fig. 1. At least two binding states for Na on Zr are evident, with desorption maxima at temperatures of -470 and -600 K, corresponding to desorption activation energies of -112 and -140 KJfmole respectively, assu~g first order kinetics and a pre-exponential factor of 10 l3 s-l [21]. The heating rate was not uniform at all times (typically -100 K s-r), and these binding energies are regarded as tentative. Clearly the lower temperature state initially flus more rapidly, and although the peak locations are not always reproduced, the areas under the desorption curves,
R.H. Prince et al. / Chemisorptive emission and luminescence.
I
609
(4
45
6
7 Sample
8
45
Temperature
6 (K)
Fig. 1. Sodium thermal desorption spectra from Zr polycrystal at (a) low and (b) intermediate coverage levels, for sodium dosages from 5 to 180 PC cmm2 as indicated. Heating rate -100 K s-1.
which are presumed proportional to sodium uptake, are well-behaved, as may be seen in fig. 2. The curve is highly linear at small coverages, up to 30 pC/cm2. and highly correlated to the work function change which is also shown in this figure. If the initial sticking probability is taken to be unity, then the uptake is known, and the slope of the uptake curve may be used to scale the sticking probability as a function of surface coverage. This is shown in fig. 3, again with work function change for convenience. The behaviour of the sticking coefficient suggests that the departure from Langmuir atomic adsorption kinetics is not large. It is noted that for a 1 X 1 structure on the (lOi0) plane (a = 3.23 A, c/a = 1.59 for hcp Zr [22] a coverage of 6.028 X 10r4 cmm2 would be expected, increasing to 1.1 X 10” cm-? on the (0001) plane. The results shown in fig. 3 are consistent with these estimates, the (1010) plane being favoured by the Langmuir model. Clearly the asymptotic approach of Aq5 to the metallic sodium value A@ = @zr - @Na= 1.7 eV [23] is slow; the data shown extends to 3.4 X 10” atoms cmd2 incident, but inaccuracies in measured sticking coefficients beyond monolayer coverage make a precise determination of coverage difficult, although it must be in excess of 3 monolayers incident to achieve the metallic value.
610
.6
I
120 Sodium Dose ( pC percm? Fig. 2. Sodium uptake and uro~k function change as functions assuming an initiat sticking probability of unity. 60
P of integrated
sodium dose,
Sodium Coverage fatoms per cm3 Fig. 3. Coverage dependence of the sticking probability and work function change for Na on the Zr polycrystalline sample, assuming an initial probability of unity, A Langmuir functian with monolayer coverage urn = 6 X 10” 4 cm-l is shown dotted.
R.H. Prince et al, / Chemisorptive
3.2. The kinetics
ofthe
where 0 4 (_!?a - 24)
&- 0 [(I$, -
611
elech-on and photon yields
Using the cubic approximation
y(f) =
emission and luminescence. 1
for the electron yield developed in the appendix
then by setting 4 = $zr - A@(t),
29zr) + W(f>13.
The pure Zr system marginally satisfies the excess energy criterion, such that (EX - 24~~) = A_!?is small with respect to the sodium induced term, as will be seen later, but aE may be retained here as a subsequent fitting parameter. This simple cubic dependence will clearly only be valid if the effective electron affinity I?i remains constant during adsorption. This might be expected to be true during the initial stages of chemisorption, possibIy up to monolayer coverage, beyond which changes in the tunnelling barrier itself will occur. We now consider the sodium sites as “active sites”, and further limit the surface concentration to values sufficiently low that A@4 0.3 eV. This condition not only ensures linearity between sodium coverage and work function change A@ (see figs. 2 and 3) which is a most useful relationship for simplification of the kinetic equations, but also that (EL - 24) is maintained at sufficiently small values to justify the linearization of the escape function and the validity of a cubic yield function. If the initial sodium fractional coverage is denoted t?$,, and the initial work function shift A$‘, then for small BN,,,, A4/A#’ = &&t$&. A number of possible dissociative adsorption models then may be proposed, in order to calculate the time dependence of y_ Each model leads to a characteristic electron emission decay with time, only the third model being in accord with experiment. (i) Dissociative adsorption with no short range order at sites where two neighbouring vacancies exist. Such sites may be either dual Na or Zr sites, or mixed Na/ Zr sites. (ii) Langmuir kinetics with complete order and repulsive nearest neighbour interactions. (iii) Langmuir kinetics with high order and attractive nearest neighbour interactions d&,/dt
= (l/7) (1 - @a),
~~~~~~ = expf-t/r),
whence for AZ? = 0, i(t) = i(O) {exp(-t/7)}3
= i(0) exp(-3t/r)
i.e. an exponential decay for aE = 0, or at all times such that aE < 2 A#, with an apparent time constant which is one third the kinetic time T-= (Aa,/,S,,@) where
612
R.H prince et al. / Chemisorptive emission and luminescence. I IO-\ I
I \ - I
\
8- \ \ \
0
2
4
6
8
$0
12
14
Time (seconds)
Fig. 4. Time dependence of electron emission current for three chlorine flux levels corresponding to electrolytic cell currents of (A) 100 JLA,(B) 50 @A, (C) 10 MA. An extrapolation to zero time is shown (dotted) based on the non-dimensional decay curve of fig. 5.
(T, is the monolayer surface coverage (atoms/cm’), A the irradiated sample area (cm2), and !.i the fraction of the atomic chlorine flux F (atoms/s) which strikes the sample with initial sticking probab~ty So_ Transient exoelectron yields i(f) are displayed in fig. 4 for three values of F (Le. cell current), for A@’= 0.3 eV corresponding to a sodium dose of 45 &‘cm2. Due to the extremely rapid decay at short times, the finite response of the electrometer/ recorder combination prevents an adequate representation of the early portion of each curve. In addition, the rapid rate of change of surface potential (up to 1 V/s) will induce sign&ant displacement currents unless efforts are made to reduce stray target capacitance by means of guarding techniques, for example. In order to verify that proper kinetic scaling has been achieved, and to effectively extend the observations to shorter times, the curves of fig. 4 are replotted in fig. 5 using universal variables i/&n and dose D = ice11t (C/cm2), where these parameters are related to the previously defined kinetic parameters by z-(O)/i,,r,= p?(O),
D = Fet = (eAu&&)
t/T.
There is ample proof in fig. 5 that such a universal decay curve exists, and that it
R.H. Prince et al. / Chemisorptive emission and luminescence.
I
613
x1o-4
Fig. 5. Normalized emission current as a function of chlorine dose D at the electrolytic ceil for the three cases shown in fig. 7. (A) ice11= 100 &A f -1; (B) ieel = 50 PA f- - -1; (C) ice11= lOpA (. - . - .>.A universal decay curve exp(-0.54 X 104Df is shown dotted (* * * 1* .).
,o-7/ 2
5
10 20 Dose (pC percm22) Fig. 6. Theoretical variation of the electron emission coefficient with sodium dose (solid curves) for various values of AE = (EL - %$z,). Experimental points are shown for four assumed valued of the cell efficiency factor it = 1 (01, 0.5 (u), 0.31 (o), 0.17 (0). Error bars are shown for only the case or = 1. Sodium
614
R.H. Prince et al. / Chemisorptive emission and luminescence.
I
is adequately represented by the function i/&r1 = (10e4) exp(-0.54 X 104D), from which it is determined (Au,/@,) = 3.5 X 10”. For hcp Zr, we expect u, = 6 X 1014/cm2 for a 1 X 1 structure on the (1010) plane, and 1.1 X 1015/cm2 on the (0001) plane. Taking Se = 1, these values correspond to p = 0.31 respectively for the sample size used, whence the measured values of r(O) for these cases is in the range from 3.2 to 5 9 X 10T4. These values of I-1are in reasonable accord with values computed on geometrical grounds. By repeating this experiment at various sodium dosings up to 45 PC/cm*, the dependence of y(O) on the initial work function shift AGo is shown in fig. 6. Although at the largest dose (2A$, = 0.6 eV) the effect of a small value of AE is clearly minimal, it is used at this point as a fitting parameter, having considerable influence at the lowest dosings. Thus we show a family of calculated curves for y(O) based various p, for AE = 0, 0.05, 0.1, 0.15 eV, values AE = 0.1 eV, /J - 0.5 appearing to best reconcile this admittedly crude theoretical model to the observed variation in yield. This implies that Ei = 8.1 eV for the chlorine/zirconium system, and that the value a = 0.3 eV_’ used in this model is consistent with a purely Coulombic shift of the affinity level and previous insight from the Auger neutralization results. Thus only electrons within about 1 eV of the Fermi edge are active in the electron emission process, and there is little value to be gained by using more realistic band models. This does not apply to the photon emission process, however, in which only the lower third of the conduction band is excluded from participating in the process. 3.3. Chemisorptive luminescence A sample decay curve for photon emission is shown in fig. 7 in which a photomultiplier with S-20 response is used in the counting mode. In this particular example, 45 PC cm-* Na was added to the pure Zr sample, and in view of the weak dependence of photon yield y* on work function discussed in the appendix, little change in total photon emission would be expected for this case. Since (EL - I$) for pure Zr is estimated to be 4.1 eV, a value large compared to the change A@’ = 0.3 eV, the change in y* is only 4% using the previous kinetic model. The actual decay observed in fig. 7 is believed due to failure of the cell to operate at the high currents used (-200 PA) for periods greater than 20 s, since the decay time is at least one order of magnitude too large to be related to the adsorption kinetics discussed earlier. If the emission is isotropic, the total photon yield is calculated.to be -low8 photons/atom incident, a value which is quite reasonable on the basis of characteristic times for optical and electronic processes, and the normalization to one excited internal electron per incident atom. Preliminary experiments on the oxygen-zirconium system were as follows. No electron emission was seen at any Na-doping level (2.8 < $ G 4.0 eV), whence EL for oxygen must be G5.6 eV. However, photon emission at a level of twice the background rate (-lo-’ photons/atom) was detected for Na levels >135 PC cm-’
R.H. Prince et al. / Chemisorptive emission and luminescence. I
I
t Cell On
Time(s)
615
5 cps
t Cell Off
Fig. 7. Chemisorptive luminescence signal observed for Zr + 45 PC cmd2 Na and i,,ll = 200 PA. The signal clearly persists at times approaching 100 s which exceeds the kinetic time constant by nearly two orders of magnitude. The decay after t = 10 s is believed due to cell instability.
(A$ - 0.65 eV, @- 3.35 eV) using the Bendix tube (hve - 2 eV) which implies that (EL - I$) > hve, or EL 2 5.35 eV. The gas phase value f$ is -1.46 eV for O- (15), whence a Coulomb shift of 4.1 eV is required for this system, an amount very similar to that for Cl- in the present experiment. If the molecular ion were similarly shifted the effective value of electron affinity for 0; would be about 1 eV lower, so that molecular adsorption would result in near infrared emission. It is of interest to note that if the cubic emission yield is applied to the oxygen-magnesium system [ 161, excellent agreement is obtained for EL = 5.6 eV. The value of $Ms at emission threshold is 2.8 eV, as expected, and the cubic law is verified over a range A$ = 0.7 eV, corresponding to monolayer coverage. In addition, a secondary maximum in electron yield is shown to exist at larger coverages, an effect recently observed for the chlorine/Hf system [24]. Thus for oxygen reacting with fresh aluminum films (4 N 4.2 eV), as reported by Kasemo et al. [ 121, the excess energy available for photon emission is (EL - 4,& 1.4 eV which is only marginally higher than the red cut-off of the EM19659 photomultiplier used by this group. Furthermore, the tube was apparently used in analogue mode, without correction for photocathode response. For an exponential change in work function, as used in the present kinetic discussion, the equation for observed total photon yield then may be shown to contain two exponential terms, the second of which is a “superexponential”, such that the decay curve appears to
616
R.H. Prince et al. / Chemisorptive emission and luminescence.
I
represent that expected for parallel fast and slow reactions, which was the mechanism invoked by the latter authors. We wish to indicate that an alternative interpretation exists, which does not negate the concept of “active” (e.g. Na) sites or a single reaction, but does reject the use of a constant photon emission probability during the reaction, and the necessity to consider two types of sites. The fast initial decay occurs as a result of small changes in work functions; pre-exposure of the Al fnms to methane may then “passivate” the Na sites. Using the estimated parameters for the O?--Al system, a change in work function of only 0.05 eV is sufficient to reduce the observed photon yield by more than one order of magnitude, a sensitivity to coverage which is certainly “not credible” [ 121 if the photon emission probability is assumed constant. The effects of patches in a polycrystalline sample cannot be ignored in such situations, just as for other forms of emission which show a strong functional dependence on work function. This effect may also account for the observations of Kasemo et al. [ 121, since a small patch of reduced work function may dominate the emission process. They estimate that a frequency shift of
Acknowledgement R.H.P. and R.M.L. acknowledge the support of the North Atlantic Treaty Organization (Grant 103.80). J.S.F. thanks the Science Research Council for the award of a Research Studentship.
Appendix:
A model of emission processes
As indicated schematically in fig. 8, the affinity level is lowered and broadened as the molecule approaches the surface. The high affinity of the halogen molecules
617
Fig. 8. Energy level diagram of the atom-metal surface system, illustrating negative Auger ionization of the atom and the effect of the ion-surface interaction potential on the final state energy.
makes electron transfer from the substrate to the adsorbate possibIe even at large adsorbate-surface separations, so that while the details of the variation are unknown, for much of the approach the effective potential must be governed by the image potential [ 171. In addition, the resonance width increases, ~thou~ for the case of the halogens, the absence of a high energy tail in the experimental emission spectra indicates a much narrower resonance than in the case of the broad oxygen 2p resonance [ 131. In the present treatment, state broadening is ignored in view of this and in the absence of experimental energy distribution functions for exo-electrons, although a “broadened Auger transform” [l] could readily be introduced into the subsequent development. It is to be noted that the model considers a twoelectron, pure Auger process, being one of two mech~isms proposed by Kasemo et al. [ 131, the alternative choice being resonance tunnelling and the subsequent filling of a valence band hole. Both offer the possibility of an electron cascade process, i.e. “hot-hole injection” [32] which may lead to an enhanced energy distribution above fF. However, while this mechanism was invoked to explain the anomalous energy distribution above fF of field-emitted electrons [32], the strong (quadratic) dependence of the high energy tail on the hole creation rate implies that in view of the fast electronic relaxation rate it is unhkely that a non-equ~ibrium valence band distribution is sampled by the incident halogen atom at the flux levels used (-lOi cm-’ s-l). This is generally not the case for field emission experiments where the equivalent hole creation rates are typically three orders higher. In any event, cascade effects will not influence the high energy photons and electrons externaily observed since these arise from direct transitions to an essentially atomic affinity level [ 133, but will rather contribute to tailing at the low energy limit of the internal excited electron distribution Ni(eK), where the escape probability is
618
R.H. Prince et al. / Chemisorptive emission and
luminescence. I
small [ 1] . While it is true that the observed electron yield varies rapidly with work function, it will be adequately explained below without the necessity of invoking a non-equilibrium electron distribution function arising from the cascade model such as that due to Ritchie [33]. As an aid in gaining insight into the dependence of the process on the physical parameters involved, we adopt two approaches previously used for the analogous process of Auger ion neutralization. The first is based on an analysis by Propst [3] in which the radiation field set up by the first electron when it falls into the atomic level is regarded as the perturbation that excites the second electron. This model has as virtues a simpler analytical form, and, by regarding the photon absorption as incomplete, the ability to also predict the behaviour of the photon emission process. The second method adopts the alternative perturbation theory approach of Hagstrum [I] in which it is assumed that the Coulomb interaction between the two participating electrons is the perturbation that causes the transition. In the nonrelativistic limit, Burhop [25] has shown that these two approaches yield the same result. Although Hagstrum’s method incorporates the effects of incident particle motion as a lifetime broadening of the electron enery distribution functions, both models must be regarded as adiabatic theories; an attempt to intrinsically incorporate the particle motion is found in the quanta1 model of Wenaas and Howsmon [26]. Using a purely Cuulombic interaction potential, and numerical integration of the WKB transmission probability, Propst [3] finds that the probability of the initial electronic transition from initial state E, when the atom is at separation x, is
where B and a are functions of the atom-surface separation, and thus correlated with the energy shift of the negative ion affinity level A.!?, = (EL - El), where Ei is the effective electron affinity at separation x, and PA is the value at infinite separation. For the case of a purely Coulombic interaction the parameters EL and a effectively become a single fitting parameter, the former determining the maximum energy of ejected electrons (Ei - 2@), the latter being correlated to Ei through their mutual dependence on x, as shown in fig. 2 of the paper by Propst [3]. Note that since the final state of the present system is now shifted by the Coulomb field, (E&= is larger than that based on values at infinite separation, in contrast to the ion neutralization process, and further, since the atomic well is now much more shallow, the reduced tunnelling probability is likely to result in a reduced mean value of x,. Values yielding best tit for the ion neutralization case were generally a = 0.4 eV_‘, x, - 2.3 a, pi - 2 eV. For the present data, values - 4.5 eV are appropriate, as will be seen later, and this a--O.3 eV_‘, x,-2AAEA separation will be taken as that for which the process (which is isoelectronic with Ar’ neutralization) Cl t n e, + Cl- + (n - 2) e, t ek t AE
R.H. Prince et al. / Chemisorptive
emission and luminescence.
I
619
is energetically favourable, where a = Ei t e1 t ~2 - 2ee ranges from (EL - 2~) for both electrons from the bottom of the conduction band, to (EL - 24) for both electrons from the top of the band (el = e2 = EF). For El = 3.6 eV [27], the fact that the yield for clean Zr (4 = 4.05 eV [28] is marginally detectable whereas that for small Na doping (4 = 4.1 eV) is observable, implies that Ei N 2& = 8.1 eV, hence A_E’*= 4.5 eV. A value of eF for Zr is also required. Skinner et al. [29] indicate that the band width for all transition metals is -6 eV. This value is consistent with calculated band spectra by Altmann and Bradley [30] and experimental data of Fomichev et al. [31]. Two peaks are evident at about 1 and 2.5 eV below the Fermi edge. The energy released by the initial electron transition as a virtual photon is
and the probability
that a photon of energy hv, is produced as
p(x,, hv,) = B exp [-a(Ea
- 4 - hv,)] .
This form would also be a reasonable a priori assumption for the variation in tunnelling probability through the band. This maximum photon energy is thus for the case E = eF, for which (hv,),, = (Ei - 4) as expected. For the subsequent photon absorption process, it is assumed that the density of states in the conduction band N,(e) is constant, and that the probability of absorption is independent of the initial state of the absorbing electron. The former assumption is justified on the grounds that for the values of $ for clean and Na-doped Zr, only electrons near the band edge are externally observable. Further, the so-called “Auger Transform” [l] tends to eliminate much of the structure in N,-(E) that can appear in the distribution function of external electrons N,,(Ek); additional smoothing will occur in the emission coefficient itself, following integration over No(Ek). We now calculate Ni(ek), the energy distribution function for electrons inside the metal excited by the Auger process, where the kinetic energy of such electrons has the allowed range ek> eF; states fk
= J”
Nc(EI)N~(Ez)P(x~,
~1) de1
de2
.
band
This former is similar to the Auger Transform T(e) used by Hagstrum, with the additional point that the process is weighted by the state-dependent probability p(x,, ei). The present result for constant density of states and variable transition probability is then very similar to that using Hagstrum’s theory for the case NC 0: e1’2 and an energy-independent transition probability, as may be seen in fig. 9. Integration over the conduction band, subject to energy conservation, El + es = 2E = fk + ee - Ea ,
620
RX.
Prince e? ai. ,/ ~~ernisor~~~ve emission and Iuminescence.
.2
.6
E$"]
I
,
.8
4x1o-2
3
P,
2T LEA CL?
1
i
i
4
~
IO
0
11
E,
L[eV]
Fig. 9. Computed electron energy distribution functions Ni(ek) andNo using the methods of Propst () and Hagstrum for constant density of states Nc (* - . - .) and NC oi e1’2 (- - -1. An escape probability function Pe(ek) appropriate to an isotropic distribution of electron velocities inside the metal is used in each case. Values used are EL = 8 eV, Q = 3.7 eV (corresponding to 45 r.lC cm-’ Na on Zr), EF = 6 eV. The function Nr(ek) has been normalized to one electron per incident atom.
yields Ni(Ek) =;
{ 1 - exp [+!?a
Since the probability
+ fF - a, - Ek)] } , of external
photon
emission
is very low, we normalize
R.H. Prince et al. / Chemisorptive emission and luminescence.
Ni(ek) to one electron per incident
621
I
Cl atom, i.e.
Ek+q+ Ni(Ek)
s
dek = 1
3
EF
whence the normalized 1 - exp
Ni(ek) =(Ea -
energy distribution
[-&!?A + eF
function
is
4 - ek)]
-
$) - u-l { 1 - exp [-a(Ea
- @)I } *
The energy distribution function for exo-electrons excited by the Auger process, Ne@k), is now computed, using an escape function Pe(ek) for the case of an isotropic angular distribution and a planar surface barrier [ 1,3]
Pe(Ek) =
i
ii1 - (%/#2 ,
ek> 63 ,
0,
ek <
co a
such that NO(Ek)
I
=Ni(Ek)Pe(Ek)
where the energy scales for interior electrons (fk), referred to the bottom of the conduction band, and exo-electrons (Ek), referred to the vacuum level, are related by the barrier height eo, where Ek =
(Ek
-
Eo)
,
EO = (EF
+ 4)
o
2
Sample distribution functions for the case of lightly doped Zr are shown in fig. 9, together with a calculation based on Hagstrum’s analysis, for the cases NC(e) = constant and NC(e) 0: ~r’~. Since the model of Propst gives extra weight to initial transitions from electrons near eF (i.e. larger er), Hagstrum’s model will similarly agree if a half-power density of states function is used with an energy-independent tunnelling probability. In the present paper, the overall yield per incident atom, y, is of greater interest, and the analytically simpler form due to Propst is preferable. Thus eo+Ei-2@
Ek--2@ -r=
No(Ek)
s
ak
=
0
s
Ni(Ek)
Pe(Ek)
dEk
.
EO
It is desirable to obtain an analytical expression for y, at least for a restricted range of (Ei - 2@), the energy excess for the process. For negative ion formation, unlike Auger ion neutralization, the energy excess is small, typically less than 1 eV, where eo - 10 eV SO that (ek - ee) Q EOand the escape function may be linearized 2Pe(fk)=
1 -
(1 +%$q+s.=
1 _ [1 -$%$q
. ..I&$
.
622
R.H. Prince et al. / Chemisorptive emission and luminescence.
Then putting C = (Ea - @) - a-l { 1 - exp [-a(Ea -1 (EA;2@)2_(EA;2Q) y - 4cee [
+f
- @)I },
(1 -exp[-@&2@)]}
Expanding the exponential term in series, valid for a(Ei terms of power three and less, yz &
(Ea - 2$)3
EL - 24
for
I
= 3.5 eV
1
- 24) < 1, and retaining
,
0
where the “constant” C has a weak dependence on 4, partly cancelled by a dependence of the barrier height e. = (EF + @), such that the product varies only 5% over the range 3.7 < $Jd 4 eV for the implied value Ei = 8 eV. This simple cubic expression will be seen to be of considerable use in any discussion of reaction kinetics, but clearly overestimates the yield when the inequality is not properly satisfied, the values for a pure Na surface (# = 2.3 eV) being y = 1.08 X 10m2 by numerical integration and y = 1.99 X 10e3 using the approximate cubic expression. The strong dependence of y on $I makes the correlation between these parameters a sensitive one, and offers attractive diagnostic possibilities since the electron current is readily detected. The external photon yield may be deduced in a similar fashion. The absorption of the virtual photon was assumed to be independent of the initial state of the absorbing electron and the photon energy hv, thus the total photon yield y* is proportional to the integral of p(xa hv) i.e. Ek-@ Y*a s
p(x,,
hv) dhv =5
{
1 - exp[-a(Ea
- @)I} ,
(E&@>O,
hv=O
where B and a are previously tion x,. Thus y* = A { 1 - exp [-a(Ei
defined constants
depending
on the transition
separa-
- @)I},
where the constant A is unknown, but would be expected to reflect the characteristic transition rates for optical and electronic processes, consistent with the normalization of the internal electron energy distribution function Nt(ek) for 1 electron per incident atom, i.e. A < lo-‘. If the photon emission process is detected by a non-wavelength-discriminating device such as a photomultiplier operating in a photon-counting mode with adequate threshold immunity, then y* is reliably related to 4, though with low sensitivity, since even for the Cl/Zr system, (Ei - 4) = 4 eV. In fact, one would expect photon emission from any metal/Cl system, although the photon wavelengths may pose detection difficulties. It is important to note, however, that in general one cannot assume that the photon yield y* is time-independent during a surface reaction, and furthermore, if a wavelength sensitive detector is used, such as
R.H. Prince et al. / Chemisorptive
emission and luminescence.
I
623
a photomuliplier
operating in the conventional (analogue) mode, there is an additional variation in output signal due to the shifting of the wavelength distribution to the red, for systems in which, as usual, adsorption increases the work function. This is tantamount to reformulating the previously-discussed Auger electron ejection yield, since the photon is now transformed at a photocathode with maximum wavelength sensitivity hve to a photoelectron for subsequent detection. For photocathodes operating near the photoelectric threshold, the conversion efficiency 5 is highly linear, such that on including this effect the experimental output varies as ~~~~=A’{(E~-~-hv~)-a-‘{l
-exp[-a@‘~-@-hve)]}}.
Provided that hv,, = (I$, - $) is far from the threshold value hv,-,,the dependence on q5is weak, but extremely large changes can occur if this is not the case.
References [l] [2] [3] [4]
H.D. Hagstrum, Phys. Rev. 96 (1954) 336, and references to earlier work cited therein. H.D. Hagstrum, Phys. Rev. 119 (1960) 940. F.M. Propst, Phys. Rev. 129 (1963) 7. J.S. Anderson and D.F. Klemperer, Proc. Roy. Sot. (London) A258 (1960) 350, and references cited therein. The use of the term “Kramer Effect” to describe structure dependent electron emission was internationally agreed at a meeting of the Austrian Physical Society, Innsbruck, Sept. 1956, see W. Hanle, Acta Phys. Austriaca 10 (1957) 339. [S] T.F. Gesell, E.T. Arakawa and T.A. Callcott, Surface Sci. 20 (1970) 174. [6] T.A. Delchar, J. Appl. Phys. 38 (1967) 2403. [7] L. Grunberg, Brit. J. Appl. Phys. 9 (1958) 85. [8] W.B. Lewis and W.E. Burchan, Proc. Cambridge Phil. Sot. 32 (1936) 503. [9] B. McCarrol, J. Chem. Phys. 50 (1969) 4758, and references cited therein, particularly the USSR literature. [lo] B. Kasemo, Phys. Rev. Letters 32 (1974) 1114. [ll] B. Kasemo and L. Wallden, Solid State Commun. 15 (1974) 571; Surface Sci. 53 (1975) 393; 75 (1978) L379. [12] J. Harris, B. Kasemo and E. Tomqvist, Chem. Phys. Letters 52 (1977) 538. [ 131 B. Kasemo, E. Tornqvist, J.K. N$rskov and B.I. Lundqvist, Surface Sci. 89 (1979) 554. [ 141 F. Futschik, K. Lintner and E. Schmid, Z. Physik 145 (1956) 48. [15] L. Himmel and P. Kelly, Comments Solid State Phys. 7 (1976) 81. [16] T.F. Gesell and E.T. Arakawa, Surface Sci. 33 (1972) 419. [17] J.K. Ngrskov, D.M. Newns and B.J. Lundqvist, Surface Sci. 80 (1979) 179. [18] R.H. Prince and R.M. Lambert, Chem. Phys. Letters 67 (1979) 388. [19] P. Goddard, K. Schwaha and R.M. Lambert, Surface Sci. 71 (1978) 35. 1201 J.S. Foord, P.J. Goddard and R.M. Lambert, Surface Sci. 94 (1980) 339. [21] P.A. Redhead, Vacuum 12 (1962) 203. [22] C.S. Barret, Structure of Metals, 2nd ed. (McGraw Hill, New York, 1952) p. 646. [23] R.J. Maurer, Phys. Rev. 57 (1940) 653. [24] R.H. Prince, R.M. Lambert, J.S. Foord and M.P. Cox, unpublished. [ 251 E.H.S. Burhop, The Auger Effect and Other Radiationless Transitions (Cambridge Univ. Press, 1952). [26] E.P. Wenaas and A. Howsmon, in: The Structure and Chemistry of Solid Surfaces, Ed. G.A. Somorjai (Wiley, New York, 1969) p. 13-1.
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R.H. Prince et al. / Chemisorptive emission and luminescence.
[ 271 B.L. Moiseiwitsch,
I
in: Advances in Atomic and Molecular Physics, Vol. 1, Ed. D.R. Bates (Academic Press, London, 1965) p. 6 1. [ 281 D.E. Eastman, Phys. Rev. B2 (1970) 1. [29] H.W.B. Skinner, T.G. Bullen and J.E. Johnston, Phil. Mag. 45 (1954) 1070. [30] S.L. Astmann and C.J. Bradley, in: Soft X-Ray Band Spectra and the Electronic Structure of Metals and Materials, Ed. D.J. Fabian (Academic Press, London, 1968) p. 265. [31] V.A. Fomichev, T.M. Zimkina, A.V. Rudnev and S.A. Nemnonov, in: Band Structure Spectroscopy of Metals and Alloys, Eds. D.J. Fabian and L.M. Watson (Academic Press, London, 1973) p. 273. [32] J.W. Gadzuk and E.W. Plummer, Phys. Rev. Letters 26 (1971) 92. [33] R.H. Ritchie, J. Appl. Phys. 37 (1966) 2276.