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Field emission spectroscopy of gold on tungsten
SURFACE SCIENCE 44 (1974) 268-274 0 North-Holland Publishing Co.
FIELD
EMISSION
SPECTROSCOPY
OF
GOLD
ON
TUNGSTEN
Received 20 February 1974 Field emission spectroscopy has been applied to a number of adsorption systemsI), including metals like Ba and Th on W for which there is a net electron transferfrom the adsorbate, as shown by work function decreases. We have examined Au on W, for which there is a work function increase, i.e. electron transfer to the adsorbate, and find evidence for a broad resonance which can be attributed to the Au 6s’ orbital. The apparatus used consisted of a differential analyzer, described previousIy2). The Au source consisted of a heatable tungsten loop bearing a gold bead. This assembly had been previously outgassed in a separate system before incorporation into the apparatus; care was taken to outgas it in situ until no traces of 0 contamination were found on the emitter. Detailed experiments were carried out on the (111) plane, and consisted of taking Fowler-Nordheim data, i.e. current [from the (111) plane] versus voltage, and total energy distributions at fixed voltage. There is very little structure in the distributions (fig. l), but there is a marked increase in FowlerNordheim pre-exponential relative to the clean plane. Writing the Fowler-
Fig. 1. Energy distributions for Au adsorbed on the (I 11) plane of W; curves arbitrarily displaced for ease of viewing. Ordinates of clean curve should be mu~tipIied by 1.8. Numbers refer to number of doses of Au. 268
FIELD
Nordheim
equation
EMISSION
SPECTROSCOPY
269
OF GOLD ON TUNGSTEN
in the form ln(i/P)
= InA - 6.8 x 1074*/cV-,
where A is the Fowler-Nordheim B is defined as
pre-exponential
(1)
and c = F/ V, the quantity
B = In (A,/A),
(2)
where A,, refers to the clean surface. Thus in the present experiments negative B values were obtained (fig. 2). The work function changes as function of relative coverage, also shown in fig. 2, agree qualitatively with the results of Jones3) on the brightly emitting regions of a field emitter.
.a 2
.6
;3” .4 .2 1
2
3
Numter
Fig. 2.
4
5
7
6
of Doses
Work function increments and Fowler-Nordheim
pre-exponential
Energy distributions can be related to the local density adsorbate by the relationsd-6)
ratios B.
of states pa at the
pa = &lx,
where Gi, is the imaginary
(3)
part of the Green’s function
uated with respect to the adsorbate
matrix element eval-
state la) and
R (co) = 47c2r,i1, W,G;, x (5.12 x 107/F) j~#‘~ [l + (5.12 x 107n ~~~3’2/F)1’2]2 (1~1 + Wm)112 [l + (5.12 x 10’ (cj3/2/rrF)‘/2] x exp [2 (2rn7~~)‘/~ hz011/2x, - 4 (2m/k2y2
~op2 (1 - v (w)/F)]
) (4)
where R(o) is the enhancement, defined as [j(o)-j,, the density in energy of emitted electrons at energy
(w)]/& (w), withj(o) w eV (measured from
270
P.L.YOUNG
AND
R.GOMER
vacuum) and j,(w) the (hypothetical) density which would result if there were no adsorbate present but 4 were the same as with adsorbate. n, is the adsorbate density in particles/cm2, ra the adsorbate radius, W, the metal band width (in eV), F the applied field in V/cm, X, the metal-adsorbate
5 doses
Fig. 3.
CL, versus energy for various coverages, calculated on the basis of eq. (4) and assumed values of xa = 1.5 and 2.0 A.
distance and u(w) an image correction; y=3.810e4 Ff/lol. Fig. 3 shows plots of Gi, versus energy E measured from the Fermi level, for assumed nAu was taken as values of xAU of 1.5 and 2.0 A. In these calculations 5 x 1014 atoms/cm2 at the work function maximum, based on the data of Jonesa) which include (111). This value is not likely to be in serious error. rAu was taken as 1.5 A, j,, was determined by drawing the best straight line through the linear portions of the distributions. The slopes obtained in this way agree within experimental error with the prediction of the free electron model l) j(c) = (Jo/d) e-“*, with J, the total probe current l/d=
(5)
and (10.2 x lO’/F)@“.
(6)
The field F was obtained from eq. (1) and the slope of the Fowler-Nordheim plot In (Jo/V”) versus l/V, and the value 4 =4.50 eV for the (111) plane. Allowance for the change in Fowler-Nordheim pre-exponential was made by multiplying j(e) by A/A,.
FIELD
EMISSION
SPECTROSCOPY
OF GOLD
271
ON TUNGSTEN
At all coverages there seems to be a broad resonance apparently to zero at a= - 1.4 eV. It is not possible of course to say whether represents
its termination
decaying this truly
or whether
there is further local density below the probed energy region. For n < 5 x 1Or4 atoms/cm2 a small peak at E= - 1.1 eV is superimposed on this broad resonance. The fine structure in Gt, other than the peak at - 1.1 eV is of dubious validity because of the smallness of the variations inj(s); the salient feature, namely a broad resonance, is well outside of experimental error. It is interesting to compare the result obtained here with the situation for hydrogen an tungsten. Photoemission results7) indicate a narrow peak at - 5.5 eV (relative to the Fermi level), while field emission & g, shows a narrow peak at - 1 eV, similar to that seen with Au in the present work. On the other hand H adsorption leads to a decrease in Fowler-Nordheim preexponentialis). In the case of H the photoemission results indicate rather convincingly that a localized bond is formed, corresponding to the resonance seen at - 5.5 eV, with the peak at - 1 eV the result of structure in the tungsten surface density of states. The localized bond, very simply speaking, results because the hydrogen 1s’ level lies 13.6 eV below vacuum. In the case of alkali metals, for instance Cs or K the relevant s1 levels lie much higher, and for this reason bonding is delocalized; pa is broad and 1s largely above the Fermi level, so that there is considerable electron deficiency on the adsorbatell). Au represents an intermediate case. The 6s1 level in Au is located 9.22 eV below vacuum, intermediate between H and the alkalis. Although definitive conclusions must await photoemission data we believe that the present results indicate that bonding of Au is nonlocalized with the broad resonance observed by us constituting the essential part of pa. The small peak seen at - 1.1 eV undoubtedly constitutes fine structure resulting from the shape of the surface density of state curve. The principal reason for this interpretation is the increase in Fowler-Nordheim pre-exponential. It is worth noting that such increases are also observed with alkali metalsii), probably for the same reason, namely appreciable pa near the Fermi level. In this connection it is interesting that Hagstrum and Becker is) were unable to see a sharp 6s level for Hg adsorbed on Ni. On the basis of the simplest theoretical modella), Gi, is given by
G:, =
A (E - E; - A)” + A2'
where al = 8, + (n> Ue, + Vi,. E, is the adsorbate
level, here - 9.22 eV relative to vacuum,
(8) (n> is the average
272
population
P. L. YOUNG
of electrons
AND R.GOMER
of given spin,
Vi, = (3.6/x,)
Vi, is an image interaction
eV-Angstrom
and U,, is an effective intra-atomic
Coulomb
u.?i,, = u-
energy
units,
(9)
repulsion’j),
given by
2vi,,
(10)
where U is the free atom Coulomb repulsion. The term Vi, in ELarises cause the effective ionization energy of the adsorbate is decreased near metal by the resultant image interaction of the ion core with the surface; factor 2 Vi, in CJ,, comes about because the adsorbate level E, is pushed by Vi, while the affinity level, E, + U is pulled down by Vi,. A and n are imaginary and real parts of the self energy respectivelyrs),
bethe the up the
(11) 1 A= n
mA(4
s& -
(12)
dE,
E’
’
-0c
with V,, the hopping integral coupling a metal state Ik) to the adsorbate via the adsorbate potential V. To a crude approximation V,, can be transformed by changing to an atomic basis Ii)
v~k= C Ki Ci 1k,
FZ nO
I/aio
CiO1k,
(13)
3
where (i,) is the specific orbital (say a tungsten dZ2) with which the adsorbate interacts most strongly and no the number of such bonds. Then, calling Vai,=Bb
A z
TC
I&l’ 12;c i(io ) k>126 (E- Ed).
(14)
k
To a very crude approximation the sum over k, which is the surface density of states, is of order 11W,, where W, is the band width, since (i,/k)-l/N
and
C~(E--sk)-N/W,,,, k
N
being the number
of substrate
atoms in the bulk substrate.
Thus
On the basis of eq. (7), A can be found from the half width at half maximum of Gi, and, in principle at least, from the amplitude at maximum. The latter
FIELD
is probably
EMISSION
SPECTROSCOPY
much less reliable
OF GOLD
since it depends
ON TUNGSTEN
on the quantitative
273
validity
of expression
(4) for R(E), as well as on x,. Very roughly the widths shown really in fig. 3 indicate A values of - 1 eV, assuming that the resonances vanish at - 1.5 eV, while the amplitudes give values of - 3 eV, with exception of 0 = 5 x 1014 atoms/cm* where - 1 eV is found. It is possible that the discrepancies are due to changes in location of Au atoms at various coverages, so that different effective X, values would have to be used. Further, no correction for the effective polarizability of the adsorbate complex has been made. The latter leads to a decrease in Brr), so that the values to be used for the computation of GL, should be larger than the observed B values. This would lead to a reduction in Gi, calculated from the amplitudes. Considering all these uncertainties, the agreement between values of A obtained from widths and amplitudes is not unreasonable. Very roughly then, AZ 1 eV, so that /I’ - (1.7/n,) eV which seems reasonable. The criterion of validityra) for Hartree-Fock calculations of the kind leading to eq. (7), CL, is TEA/U,, > 1 (16) and it is therefore interesting to see if this criterion is met in the present case. U can be estimated by the method of Edlenrs) to be 6.45 eV. Assuming a classical image potential, an Au radius of 1.4 A and a screening length of 0.6 A, we find Vi,,,g 3.612 = 1.8 eV or Ll,,=2.85 eV. Consequently we see that for A> 1 eV the Hartree-Fock criterion is met. Finally we can obtain some idea of the position of the center of the resonance from EL, given by eq. (8). From the coverage estimate of Jones3) and the work function increase we can estimate the dipole moment per Au atom and, using 2 8, for the dipole length, the effective charge. This turns out to be 1.06 electron charges, so that (n) = 0.503, i.e. very close to 3. Consequently, the image terms in .si cancel and its position is given by .s,+$U or by - 9.22 + + x 6.45 = - 6.0 eV, i.e. roughly 0.7 to 1 eV below the Fermi energy. The center of the resonance will be shifted downward by /1, and thus the center will lie even farther below sr, since n is presumably positive. It is interesting that the charge value
s
pa ds = (n)
.
--m
This means that the actual shape of pa is considerably distorted from a simple Lorentzian, which is, of course, what a more detailed theory would predict.
214
P. L. YOUNG
We wish to thank drawings.
AND R. GOMER
Mr. Lee Richter
This work was supported
for help with the computations
in part by NSF Grant
and
GP 32848X.
PETER L. YOUNC;“’ and ROBERT GOMER
James Franck Institute ard Department of’ Chemistry, The University of Chicago, Chicago, Illinois 60637, U.S.A. References 1) 2) 3) 4) 5) 6) 7) 8) 9) IO) 11) 12) 13) 14) 15)
J. W. Gadzuk and E. W. Plummer, Rev. Mod. Phys. 45 (1973) 487. P. 1. Young and R. Comer, Phys. Rev. Letters 30 (1972) 955; J. Chem. Phys., in press. J. P. Jones, S.C.I. Monograph No. 28 (1967) 263. D. Penn, R. Gomer and M. H. Cohen, Phys. Rev. B 5 (1972). 768. D. Penn, Phys. Rev. B4 (1974) 844. R. Comer, CRC Critical Rev. in Solid State 4 (1974) 274. E. W. Plummer, to be published. E. W. Plummer and W. E. Bell, J. Vacuum Sci. Technol. 9 (1972) 583. P. L. Young and R. Gomer, unpublished. R. Wortman, R. Comer and R. Lundy. J. Chem. Phys. 26 (1957) 1333. L. 0. Schmidt and R. Comer, J. Chem. Phys. 45 (1966) 1605. H. D. Hagstrum and G. E. Becker, to be published. D. M. Newns, Phys. Rev. 178 (1969) 1123. J. R. Schrieffer and D. C. Mattis, Phys. Rev. 140 (1965) 1412. B. Edlen, J. Chem. Phys. 33 (1960) 98.
* Present address: 14830, U.S.A.
Corning Research Laboratories,
Sullivan Park, Corning, New York
FIELD
EMISSION
SPECTROSCOPY
OF
GOLD
ON
TUNGSTEN
Received 20 February 1974 Field emission spectroscopy has been applied to a number of adsorption systemsI), including metals like Ba and Th on W for which there is a net electron transferfrom the adsorbate, as shown by work function decreases. We have examined Au on W, for which there is a work function increase, i.e. electron transfer to the adsorbate, and find evidence for a broad resonance which can be attributed to the Au 6s’ orbital. The apparatus used consisted of a differential analyzer, described previousIy2). The Au source consisted of a heatable tungsten loop bearing a gold bead. This assembly had been previously outgassed in a separate system before incorporation into the apparatus; care was taken to outgas it in situ until no traces of 0 contamination were found on the emitter. Detailed experiments were carried out on the (111) plane, and consisted of taking Fowler-Nordheim data, i.e. current [from the (111) plane] versus voltage, and total energy distributions at fixed voltage. There is very little structure in the distributions (fig. l), but there is a marked increase in FowlerNordheim pre-exponential relative to the clean plane. Writing the Fowler-
Fig. 1. Energy distributions for Au adsorbed on the (I 11) plane of W; curves arbitrarily displaced for ease of viewing. Ordinates of clean curve should be mu~tipIied by 1.8. Numbers refer to number of doses of Au. 268
FIELD
Nordheim
equation
EMISSION
SPECTROSCOPY
269
OF GOLD ON TUNGSTEN
in the form ln(i/P)
= InA - 6.8 x 1074*/cV-,
where A is the Fowler-Nordheim B is defined as
pre-exponential
(1)
and c = F/ V, the quantity
B = In (A,/A),
(2)
where A,, refers to the clean surface. Thus in the present experiments negative B values were obtained (fig. 2). The work function changes as function of relative coverage, also shown in fig. 2, agree qualitatively with the results of Jones3) on the brightly emitting regions of a field emitter.
.a 2
.6
;3” .4 .2 1
2
3
Numter
Fig. 2.
4
5
7
6
of Doses
Work function increments and Fowler-Nordheim
pre-exponential
Energy distributions can be related to the local density adsorbate by the relationsd-6)
ratios B.
of states pa at the
pa = &lx,
where Gi, is the imaginary
(3)
part of the Green’s function
uated with respect to the adsorbate
matrix element eval-
state la) and
R (co) = 47c2r,i1, W,G;, x (5.12 x 107/F) j~#‘~ [l + (5.12 x 107n ~~~3’2/F)1’2]2 (1~1 + Wm)112 [l + (5.12 x 10’ (cj3/2/rrF)‘/2] x exp [2 (2rn7~~)‘/~ hz011/2x, - 4 (2m/k2y2
~op2 (1 - v (w)/F)]
) (4)
where R(o) is the enhancement, defined as [j(o)-j,, the density in energy of emitted electrons at energy
(w)]/& (w), withj(o) w eV (measured from
270
P.L.YOUNG
AND
R.GOMER
vacuum) and j,(w) the (hypothetical) density which would result if there were no adsorbate present but 4 were the same as with adsorbate. n, is the adsorbate density in particles/cm2, ra the adsorbate radius, W, the metal band width (in eV), F the applied field in V/cm, X, the metal-adsorbate
5 doses
Fig. 3.
CL, versus energy for various coverages, calculated on the basis of eq. (4) and assumed values of xa = 1.5 and 2.0 A.
distance and u(w) an image correction; y=3.810e4 Ff/lol. Fig. 3 shows plots of Gi, versus energy E measured from the Fermi level, for assumed nAu was taken as values of xAU of 1.5 and 2.0 A. In these calculations 5 x 1014 atoms/cm2 at the work function maximum, based on the data of Jonesa) which include (111). This value is not likely to be in serious error. rAu was taken as 1.5 A, j,, was determined by drawing the best straight line through the linear portions of the distributions. The slopes obtained in this way agree within experimental error with the prediction of the free electron model l) j(c) = (Jo/d) e-“*, with J, the total probe current l/d=
(5)
and (10.2 x lO’/F)@“.
(6)
The field F was obtained from eq. (1) and the slope of the Fowler-Nordheim plot In (Jo/V”) versus l/V, and the value 4 =4.50 eV for the (111) plane. Allowance for the change in Fowler-Nordheim pre-exponential was made by multiplying j(e) by A/A,.
FIELD
EMISSION
SPECTROSCOPY
OF GOLD
271
ON TUNGSTEN
At all coverages there seems to be a broad resonance apparently to zero at a= - 1.4 eV. It is not possible of course to say whether represents
its termination
decaying this truly
or whether
there is further local density below the probed energy region. For n < 5 x 1Or4 atoms/cm2 a small peak at E= - 1.1 eV is superimposed on this broad resonance. The fine structure in Gt, other than the peak at - 1.1 eV is of dubious validity because of the smallness of the variations inj(s); the salient feature, namely a broad resonance, is well outside of experimental error. It is interesting to compare the result obtained here with the situation for hydrogen an tungsten. Photoemission results7) indicate a narrow peak at - 5.5 eV (relative to the Fermi level), while field emission & g, shows a narrow peak at - 1 eV, similar to that seen with Au in the present work. On the other hand H adsorption leads to a decrease in Fowler-Nordheim preexponentialis). In the case of H the photoemission results indicate rather convincingly that a localized bond is formed, corresponding to the resonance seen at - 5.5 eV, with the peak at - 1 eV the result of structure in the tungsten surface density of states. The localized bond, very simply speaking, results because the hydrogen 1s’ level lies 13.6 eV below vacuum. In the case of alkali metals, for instance Cs or K the relevant s1 levels lie much higher, and for this reason bonding is delocalized; pa is broad and 1s largely above the Fermi level, so that there is considerable electron deficiency on the adsorbatell). Au represents an intermediate case. The 6s1 level in Au is located 9.22 eV below vacuum, intermediate between H and the alkalis. Although definitive conclusions must await photoemission data we believe that the present results indicate that bonding of Au is nonlocalized with the broad resonance observed by us constituting the essential part of pa. The small peak seen at - 1.1 eV undoubtedly constitutes fine structure resulting from the shape of the surface density of state curve. The principal reason for this interpretation is the increase in Fowler-Nordheim pre-exponential. It is worth noting that such increases are also observed with alkali metalsii), probably for the same reason, namely appreciable pa near the Fermi level. In this connection it is interesting that Hagstrum and Becker is) were unable to see a sharp 6s level for Hg adsorbed on Ni. On the basis of the simplest theoretical modella), Gi, is given by
G:, =
A (E - E; - A)” + A2'
where al = 8, + (n> Ue, + Vi,. E, is the adsorbate
level, here - 9.22 eV relative to vacuum,
(8) (n> is the average
272
population
P. L. YOUNG
of electrons
AND R.GOMER
of given spin,
Vi, = (3.6/x,)
Vi, is an image interaction
eV-Angstrom
and U,, is an effective intra-atomic
Coulomb
u.?i,, = u-
energy
units,
(9)
repulsion’j),
given by
2vi,,
(10)
where U is the free atom Coulomb repulsion. The term Vi, in ELarises cause the effective ionization energy of the adsorbate is decreased near metal by the resultant image interaction of the ion core with the surface; factor 2 Vi, in CJ,, comes about because the adsorbate level E, is pushed by Vi, while the affinity level, E, + U is pulled down by Vi,. A and n are imaginary and real parts of the self energy respectivelyrs),
bethe the up the
(11) 1 A= n
mA(4
s& -
(12)
dE,
E’
’
-0c
with V,, the hopping integral coupling a metal state Ik) to the adsorbate via the adsorbate potential V. To a crude approximation V,, can be transformed by changing to an atomic basis Ii)
v~k= C Ki Ci 1k,
FZ nO
I/aio
CiO1k,
(13)
3
where (i,) is the specific orbital (say a tungsten dZ2) with which the adsorbate interacts most strongly and no the number of such bonds. Then, calling Vai,=Bb
A z
TC
I&l’ 12;c i(io ) k>126 (E- Ed).
(14)
k
To a very crude approximation the sum over k, which is the surface density of states, is of order 11W,, where W, is the band width, since (i,/k)-l/N
and
C~(E--sk)-N/W,,,, k
N
being the number
of substrate
atoms in the bulk substrate.
Thus
On the basis of eq. (7), A can be found from the half width at half maximum of Gi, and, in principle at least, from the amplitude at maximum. The latter
FIELD
is probably
EMISSION
SPECTROSCOPY
much less reliable
OF GOLD
since it depends
ON TUNGSTEN
on the quantitative
273
validity
of expression
(4) for R(E), as well as on x,. Very roughly the widths shown really in fig. 3 indicate A values of - 1 eV, assuming that the resonances vanish at - 1.5 eV, while the amplitudes give values of - 3 eV, with exception of 0 = 5 x 1014 atoms/cm* where - 1 eV is found. It is possible that the discrepancies are due to changes in location of Au atoms at various coverages, so that different effective X, values would have to be used. Further, no correction for the effective polarizability of the adsorbate complex has been made. The latter leads to a decrease in Brr), so that the values to be used for the computation of GL, should be larger than the observed B values. This would lead to a reduction in Gi, calculated from the amplitudes. Considering all these uncertainties, the agreement between values of A obtained from widths and amplitudes is not unreasonable. Very roughly then, AZ 1 eV, so that /I’ - (1.7/n,) eV which seems reasonable. The criterion of validityra) for Hartree-Fock calculations of the kind leading to eq. (7), CL, is TEA/U,, > 1 (16) and it is therefore interesting to see if this criterion is met in the present case. U can be estimated by the method of Edlenrs) to be 6.45 eV. Assuming a classical image potential, an Au radius of 1.4 A and a screening length of 0.6 A, we find Vi,,,g 3.612 = 1.8 eV or Ll,,=2.85 eV. Consequently we see that for A> 1 eV the Hartree-Fock criterion is met. Finally we can obtain some idea of the position of the center of the resonance from EL, given by eq. (8). From the coverage estimate of Jones3) and the work function increase we can estimate the dipole moment per Au atom and, using 2 8, for the dipole length, the effective charge. This turns out to be 1.06 electron charges, so that (n) = 0.503, i.e. very close to 3. Consequently, the image terms in .si cancel and its position is given by .s,+$U or by - 9.22 + + x 6.45 = - 6.0 eV, i.e. roughly 0.7 to 1 eV below the Fermi energy. The center of the resonance will be shifted downward by /1, and thus the center will lie even farther below sr, since n is presumably positive. It is interesting that the charge value
s
pa ds = (n)
.
--m
This means that the actual shape of pa is considerably distorted from a simple Lorentzian, which is, of course, what a more detailed theory would predict.
214
P. L. YOUNG
We wish to thank drawings.
AND R. GOMER
Mr. Lee Richter
This work was supported
for help with the computations
in part by NSF Grant
and
GP 32848X.
PETER L. YOUNC;“’ and ROBERT GOMER
James Franck Institute ard Department of’ Chemistry, The University of Chicago, Chicago, Illinois 60637, U.S.A. References 1) 2) 3) 4) 5) 6) 7) 8) 9) IO) 11) 12) 13) 14) 15)
J. W. Gadzuk and E. W. Plummer, Rev. Mod. Phys. 45 (1973) 487. P. 1. Young and R. Comer, Phys. Rev. Letters 30 (1972) 955; J. Chem. Phys., in press. J. P. Jones, S.C.I. Monograph No. 28 (1967) 263. D. Penn, R. Gomer and M. H. Cohen, Phys. Rev. B 5 (1972). 768. D. Penn, Phys. Rev. B4 (1974) 844. R. Comer, CRC Critical Rev. in Solid State 4 (1974) 274. E. W. Plummer, to be published. E. W. Plummer and W. E. Bell, J. Vacuum Sci. Technol. 9 (1972) 583. P. L. Young and R. Gomer, unpublished. R. Wortman, R. Comer and R. Lundy. J. Chem. Phys. 26 (1957) 1333. L. 0. Schmidt and R. Comer, J. Chem. Phys. 45 (1966) 1605. H. D. Hagstrum and G. E. Becker, to be published. D. M. Newns, Phys. Rev. 178 (1969) 1123. J. R. Schrieffer and D. C. Mattis, Phys. Rev. 140 (1965) 1412. B. Edlen, J. Chem. Phys. 33 (1960) 98.
* Present address: 14830, U.S.A.
Corning Research Laboratories,
Sullivan Park, Corning, New York