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Surface plasmon satellites in x-ray photoemission from core states of adsorbed atoms
Solid State CommunicationsYol. 16, pp. 671—673, 1975.
Pergamon Press.
Printed in Great Britain
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION FROM CORE STATES OF ADSORBED ATOMS J. Harris Institut für Festkorperforschung der KFA Jllhich, D-5 17 Julich, Germany (Received 25 November 1974 by L. Hedin)
It is shown that the kinetic energy spectrum of electrons emitted from core levels of atoms adsorbed on metal surfaces should exhibit surface plasmon satellites. At sufficiently high energies, the satellites arise only via the socalled “intrinsic” mechanism, namely, screening of a suddenly created hole by the metal electrons. Their observation for a suitable adsorption system would thus constitute the first unequivocal evidence for the “intrinsic” effect. IN A RECENT review, Langreth1 has discussed the observation of satellite structure in the kinetic energy spectrum of core electrons excited into the continuum via X-ray absorption. One general conclusion of this paper was that where a core level of the bulk solid is involved, it is not possible to distinguish between socalled “intrinsic” and “extrinsic” satellites. Briefly, “intrinsic” structure arises from the scrçening of the suddenly created core hole by the conduction electrons
surface. In this case, there should be both “intrinsic” and “extrinsic” satellites, the former arising from the screening of a core hole suddenly created just outside the surface, the latter from the excitation of surface plasmons by the outgoing electron. The qualitative form of the satellite structure due to these two effects can be determined via the Hamiltonian H= ~ k
while “extrinsic” structure is due to energy loss of the escaping electron via plasmon excitation. These processes are not normally independent, but become so in the limit that the energy of the escaping electron is very large. Since the coupling of a fast-electron to plasmons 2/hv, where v is the velocity, it is proportional to that e the height of the “extrinsic” might be thought peaks decreases with increasing v. Owing to life-time effects, however, the electrons one observes originate from a depth within the crystal which depends on their kinetic energy. Decrease of the coupling and increase of the mean-free-path complement each other and the strength of the “extrinsic” satellites approaches a constant as v -÷
11 ~ 1b~11 + g(k11, Z0)[bk11+ b~11]} (1) which describes the coupling of an external point charge located at Z = Zo outside a surface (Z = 0),
to a gas of independent surface plasmons of frequency C~)k11.For free electrons the coupling parameter is given by 1 2ir2e2n (2) g(k 11, Z0) = e exp (— k11Z0) _________
,J
where 11 is the bulk conduction electron density of the metal. If I iJi~>is the complete set of states for the Hamiltonian (I) and ~o>the initial state of the metal (i.e. the surface-plasmon “vacuum” state) the required photoemission spectrum due to the “intrinsic” process alone is
°°.
In the present paper, it is suggested that the mean-free-path effect can be circumvented by studying the satellite structureof peaks due to the excitation of core levels of suitable atoms adsorbed on a metal
=
671
I
I i’,> 12 6(1 —
+ E0
—
E1)
(3)
672
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION
where 1
=
hiS’ — ~
is the energy one would observe
if the metal were to remain in a “frozen” state following emission of the electron. Since (1) can be simply diagonalized it is straight forward to show that F(e)
=
exp
~
J
~k11’~ ~ —j--~
k11 ~
~
di’ exp (i(X — e + L~E)t
Wk
11 =
Vol. 16, No.5
wo + Ak~1+...
(8)
whence, for example the first satellite gives a contribution Pj(e)
=
—~--0[(~ —e)sgnA] e 12z0 2w0 xpk~~~(e~ (9)
Here 0(x) is the unit step-function and e~ X + ~E g; + ~—~—
(4)
e—~’~’kItt)
k11Wk11
where L~E
0k ~k -~ 11 ~ 11
is the lowering of the energy of the metal due to the screening of the core hole on the adsorbed atom. A~ important difference between (4) and the equivalent expression for bulk plasmon satellites is the weighting factor exp expresses [— 2k11Z0 I which appears in all k11 charge -sums, and which the fact that an external at Z 0 can couple strongly only to surface plasmons of wavelength Z0. Thus one might expect surface plas. mon satellites to be sharper than the corresponding bulk satellites, where large-k plasmons have a relatively larger weighting. Under the assumption of dispersionless surface plasmons, Wk11 = w0 the spectrum (4) consists of 6-function peaks located at energies 1+ /~E— nco0, having weights given by the usual Poisson distribution 2’-~ ~y =
—
(6)
e7
In this approximation, ~E is just the classical image 2/4Z energy e 0, so that the relative strength of the first satellite is a 0
=
[“Image” Energy of Adsorbed Ion] [Surface Plasmon Energy]
For many chemisorbed species, Z0 a few A so that the image energy can be a few eV. The parameter 7 may therefore be comparable with the corresponding value for bulk satellites. It is, of course, independent of the energy of the outgoing electron, provided only that this energy is large enough to ensure the validity of the sudden approximation (1). To study the effect of surface plasmon dispersion wewrite
coo. The observation of asymmetry in the satellites would thus constitute evidence concerning the sign
—
ofA, an experimentally elusive quantity. In the work 2 who measured the satellite structure of the Al(2p) line from bulk aluminium, asymof Baer and Busch, metry due to the dispersion of bulk plasmons is clearly visible. Whether these satellites arise from an “intrinsic” or “extrinsic” mechanism is, however, not known. We turn now the the “extrinsic” and note, 3 that the effect probability that following ~unjiá lose and Lucas, the fast electron energy in transit from crystal to detector is
w(e)
=
1< ~(t
—~oC~)I
~)
2 ~ (~—
e-).
(10)
Here the states I~,>,e~,are the eigenstates and energies of the free-plasmon Hamiltonian, while the state I ~!i(t)) is the solution of the Schrodinger equation I ~(t)) = H(t) I iji(t)> (11)
where H(t) is given by (1) and (2) with Zo replaced by the trajectory of Zthe outgoing electron 0-÷Z0+vt0(t) (12) Following precisely the analysis of reference 3, one concludes that for fast electrons emitted normally, V = VZ,
W()
=J ~
where (2
Mt)
=
W0 exp —
f
M~t)
~
~
(13)
I
~-2k~Z0 ~_ic~~~9tt
w~,+14i4 j o with W0 a normalising factor. The relative weight of the one surface plasmon loss line is thus 2~° 13I — e~w0 ~ k~e +w2 4twz 0/4 (14)
J~
Vol. 16, No.5
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION
and is inversely proportional to VZ, as expected. Electrons emitted non-normally have a greater chance of exciting surface plasmons since, for a given lvi, they spend more time close to the surface. At grazing angles one can expect strong extrinsic multiple surface plasmon peaks even at high energy. We may conclude, therefore, that while the strength of the “intrinsic” surface plasmon satellites is independent of the energy of the emitted electrons, that of the “extrinsic” satellites varies as 1 f’~.,/e,at least for normal emission. The excitation ofcore levels of atoms adsorbed on metal surfaces by X-rays of sufficiently large energy [i.e. such that j3~is negligible] thus provides a possible experimental test for the existence of an intrinsic effect. For a definitive experiment, the metal must support sharp surface plasmons [Al, Mg or even Ag are possible candidates] and the adsorbed atom must sit fairly close to the surface in order that the parameter ~ be appreci&~ble.Yates and Erickson4 have recently studied the Xe (3d5/2) and O(ls) lines for Xe and 0 adsorbed on W. Their spectra
show considerable tailing on the low energy side, part of which may be accounted for by mechanisms similar to those discussed above. Of course, in a metal like W the redistribution of charge is not described by a simple Hamiltonian of the form (1) and one would not expect to observe sharp structure below the main peak. It is interesting to note, however, that, in agreement with the above discussion, the tailing is considerably more pronounced in the case of the .oxygen adsorbate, which, being chemi- rather than physisorbed, sits closer to the tungsten surface. The electrons observed in this experiment, had a kinetic energy [~720 eV for O(ls)] which is not large enough to permit separation of intrinsic and extrinsic effects. The parameter ~ determining the relative height of the first surface plasmon loss peak, becomes negligible only for kinetic energies in excess of 3 keV [in which case 0.06]. Whether at such energies the background in the region of interest can be kept small enough to allow observation of satellite structure is perhaps questionable. ,
REFERENCES
2.
Theory of plasmon effects in high energy spectroscopy by LANGRETH D.C. in Nobel Syposia, Vol. 24, Academic Press, New York and London. BAER Y. and BUSCH G., Phys. Rev. Lett. 30, 280 (1973).
3.
~UNJI~ M. and LUCAS A.A.,Phys. Rev. 3,719(1971).
4.
YATES J.T. and ERICKSON N.E., Surf Sd. 44,489(1974).
I.
673
Pergamon Press.
Printed in Great Britain
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION FROM CORE STATES OF ADSORBED ATOMS J. Harris Institut für Festkorperforschung der KFA Jllhich, D-5 17 Julich, Germany (Received 25 November 1974 by L. Hedin)
It is shown that the kinetic energy spectrum of electrons emitted from core levels of atoms adsorbed on metal surfaces should exhibit surface plasmon satellites. At sufficiently high energies, the satellites arise only via the socalled “intrinsic” mechanism, namely, screening of a suddenly created hole by the metal electrons. Their observation for a suitable adsorption system would thus constitute the first unequivocal evidence for the “intrinsic” effect. IN A RECENT review, Langreth1 has discussed the observation of satellite structure in the kinetic energy spectrum of core electrons excited into the continuum via X-ray absorption. One general conclusion of this paper was that where a core level of the bulk solid is involved, it is not possible to distinguish between socalled “intrinsic” and “extrinsic” satellites. Briefly, “intrinsic” structure arises from the scrçening of the suddenly created core hole by the conduction electrons
surface. In this case, there should be both “intrinsic” and “extrinsic” satellites, the former arising from the screening of a core hole suddenly created just outside the surface, the latter from the excitation of surface plasmons by the outgoing electron. The qualitative form of the satellite structure due to these two effects can be determined via the Hamiltonian H= ~ k
while “extrinsic” structure is due to energy loss of the escaping electron via plasmon excitation. These processes are not normally independent, but become so in the limit that the energy of the escaping electron is very large. Since the coupling of a fast-electron to plasmons 2/hv, where v is the velocity, it is proportional to that e the height of the “extrinsic” might be thought peaks decreases with increasing v. Owing to life-time effects, however, the electrons one observes originate from a depth within the crystal which depends on their kinetic energy. Decrease of the coupling and increase of the mean-free-path complement each other and the strength of the “extrinsic” satellites approaches a constant as v -÷
11 ~ 1b~11 + g(k11, Z0)[bk11+ b~11]} (1) which describes the coupling of an external point charge located at Z = Zo outside a surface (Z = 0),
to a gas of independent surface plasmons of frequency C~)k11.For free electrons the coupling parameter is given by 1 2ir2e2n (2) g(k 11, Z0) = e exp (— k11Z0) _________
,J
where 11 is the bulk conduction electron density of the metal. If I iJi~>is the complete set of states for the Hamiltonian (I) and ~o>the initial state of the metal (i.e. the surface-plasmon “vacuum” state) the required photoemission spectrum due to the “intrinsic” process alone is
°°.
In the present paper, it is suggested that the mean-free-path effect can be circumvented by studying the satellite structureof peaks due to the excitation of core levels of suitable atoms adsorbed on a metal
=
671
I
I i’,> 12 6(1 —
+ E0
—
E1)
(3)
672
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION
where 1
=
hiS’ — ~
is the energy one would observe
if the metal were to remain in a “frozen” state following emission of the electron. Since (1) can be simply diagonalized it is straight forward to show that F(e)
=
exp
~
J
~k11’~ ~ —j--~
k11 ~
~
di’ exp (i(X — e + L~E)t
Wk
11 =
Vol. 16, No.5
wo + Ak~1+...
(8)
whence, for example the first satellite gives a contribution Pj(e)
=
—~--0[(~ —e)sgnA] e 12z0 2w0 xpk~~~(e~ (9)
Here 0(x) is the unit step-function and e~ X + ~E g; + ~—~—
(4)
e—~’~’kItt)
k11Wk11
where L~E
0k ~k -~ 11 ~ 11
is the lowering of the energy of the metal due to the screening of the core hole on the adsorbed atom. A~ important difference between (4) and the equivalent expression for bulk plasmon satellites is the weighting factor exp expresses [— 2k11Z0 I which appears in all k11 charge -sums, and which the fact that an external at Z 0 can couple strongly only to surface plasmons of wavelength Z0. Thus one might expect surface plas. mon satellites to be sharper than the corresponding bulk satellites, where large-k plasmons have a relatively larger weighting. Under the assumption of dispersionless surface plasmons, Wk11 = w0 the spectrum (4) consists of 6-function peaks located at energies 1+ /~E— nco0, having weights given by the usual Poisson distribution 2’-~ ~y =
—
(6)
e7
In this approximation, ~E is just the classical image 2/4Z energy e 0, so that the relative strength of the first satellite is a 0
=
[“Image” Energy of Adsorbed Ion] [Surface Plasmon Energy]
For many chemisorbed species, Z0 a few A so that the image energy can be a few eV. The parameter 7 may therefore be comparable with the corresponding value for bulk satellites. It is, of course, independent of the energy of the outgoing electron, provided only that this energy is large enough to ensure the validity of the sudden approximation (1). To study the effect of surface plasmon dispersion wewrite
coo. The observation of asymmetry in the satellites would thus constitute evidence concerning the sign
—
ofA, an experimentally elusive quantity. In the work 2 who measured the satellite structure of the Al(2p) line from bulk aluminium, asymof Baer and Busch, metry due to the dispersion of bulk plasmons is clearly visible. Whether these satellites arise from an “intrinsic” or “extrinsic” mechanism is, however, not known. We turn now the the “extrinsic” and note, 3 that the effect probability that following ~unjiá lose and Lucas, the fast electron energy in transit from crystal to detector is
w(e)
=
1< ~(t
—~oC~)I
~)
2 ~ (~—
e-).
(10)
Here the states I~,>,e~,are the eigenstates and energies of the free-plasmon Hamiltonian, while the state I ~!i(t)) is the solution of the Schrodinger equation I ~(t)) = H(t) I iji(t)> (11)
where H(t) is given by (1) and (2) with Zo replaced by the trajectory of Zthe outgoing electron 0-÷Z0+vt0(t) (12) Following precisely the analysis of reference 3, one concludes that for fast electrons emitted normally, V = VZ,
W()
=J ~
where (2
Mt)
=
W0 exp —
f
M~t)
~
~
(13)
I
~-2k~Z0 ~_ic~~~9tt
w~,+14i4 j o with W0 a normalising factor. The relative weight of the one surface plasmon loss line is thus 2~° 13I — e~w0 ~ k~e +w2 4twz 0/4 (14)
J~
Vol. 16, No.5
SURFACE PLASMON SATELLITES IN X-RAY PHOTOEMISSION
and is inversely proportional to VZ, as expected. Electrons emitted non-normally have a greater chance of exciting surface plasmons since, for a given lvi, they spend more time close to the surface. At grazing angles one can expect strong extrinsic multiple surface plasmon peaks even at high energy. We may conclude, therefore, that while the strength of the “intrinsic” surface plasmon satellites is independent of the energy of the emitted electrons, that of the “extrinsic” satellites varies as 1 f’~.,/e,at least for normal emission. The excitation ofcore levels of atoms adsorbed on metal surfaces by X-rays of sufficiently large energy [i.e. such that j3~is negligible] thus provides a possible experimental test for the existence of an intrinsic effect. For a definitive experiment, the metal must support sharp surface plasmons [Al, Mg or even Ag are possible candidates] and the adsorbed atom must sit fairly close to the surface in order that the parameter ~ be appreci&~ble.Yates and Erickson4 have recently studied the Xe (3d5/2) and O(ls) lines for Xe and 0 adsorbed on W. Their spectra
show considerable tailing on the low energy side, part of which may be accounted for by mechanisms similar to those discussed above. Of course, in a metal like W the redistribution of charge is not described by a simple Hamiltonian of the form (1) and one would not expect to observe sharp structure below the main peak. It is interesting to note, however, that, in agreement with the above discussion, the tailing is considerably more pronounced in the case of the .oxygen adsorbate, which, being chemi- rather than physisorbed, sits closer to the tungsten surface. The electrons observed in this experiment, had a kinetic energy [~720 eV for O(ls)] which is not large enough to permit separation of intrinsic and extrinsic effects. The parameter ~ determining the relative height of the first surface plasmon loss peak, becomes negligible only for kinetic energies in excess of 3 keV [in which case 0.06]. Whether at such energies the background in the region of interest can be kept small enough to allow observation of satellite structure is perhaps questionable. ,
REFERENCES
2.
Theory of plasmon effects in high energy spectroscopy by LANGRETH D.C. in Nobel Syposia, Vol. 24, Academic Press, New York and London. BAER Y. and BUSCH G., Phys. Rev. Lett. 30, 280 (1973).
3.
~UNJI~ M. and LUCAS A.A.,Phys. Rev. 3,719(1971).
4.
YATES J.T. and ERICKSON N.E., Surf Sd. 44,489(1974).
I.
673