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Inelastic electron scattering in nickel
Solid State Communications, Vol. 27, pp. 1255—1257. © Pergamon Press Ltd. 1978. Printed in Great Britain.
0038—1098/78/0915—1255 $02.00/O
INELASTIC ELECTRON SCATTERING IN NICKEL A.E. Meixner, R.E. Dietz, G.S. Brown and P.M. Platzman Bell Laboratories, Murray Hill, NJ 07974, U.S.A. (Received l4March 1978 byA.G. Chynoweth) Using a 200 keV electron spectrometer, with an energy resolution of —~0.25 eV and a momentum resolution of 0.2 A’, we have measured the energy loss spectra for transmission of electrons through thin (‘~600 A) Ni films. These results address the general question of the validity of momentum transfer estimates in electron loss scattering. Using low.energy electron backscattering, we have observed the dipole forbiddenM, transition at 112 eV. For high.energy scattering, we have observed this transition only at high momentum transfer (q ~ 2 A-’). These results indicate sizable contributions from high momentum transfer collisions in the low-energy experiments. THE INELASTIC electronic scattering spectrum da/d~2dw,for fast electrons scattering weakly from a thin solid, is given by do 4r2 d~ld = ~ S(q, ~,) (1) w ~q ~inc where, within the framework of the Born approximation,
/ S(q,w)
=
~
\2
~ e~r
~ 6(E~—E
1—-w). (2) / Historically, high-energy electron scattering ~ and low-energy electron backscattering [2] have been employed to measure the long wavelength (q -÷ 0) limit of equation (2) which is proportional to Im (lie). The low-energy backscattering experiments were believed to be dominated by forward inelastic processes preceded or followed by large-angle diffraction, and hence represented by the q 0 limit of (2). In this paper, we compare high-energy electron transmission data for singlecrystal Ni with low-energy backscattering data to obtain a measure of the mean momentum transfer in the backscattering experiments. We have studied the scattering of 200 keV electrons from a single-crystal 600 A Ni foil. The q = 0 inelastic spectrum is shown in Fig. 1 [3]. Three important features may be discerned, as well as subsidiary structure at low energy which we will not discuss, (1) atE = 0, the elastic and the quasi-elastic peak, corresponding to unresolved scattering from the lattice vibrations are both present; (2) at E = 20 eV, a double-humped plasmon interband excitation which changes in shape but does not disperse as q increases, and (3) an edgelike structure corresponding to 3p112 312—3d(M11,11) transition [2]. Conspicuously absent in this spectrum is the 3s—3d (M,) transition at 112 eV, which is dipole i,f
\
—~
i
forbidden and therefore absent in U.V. absorption spectroscopy and q = 0 electron scattering. However, when we examine the q-dependence of the spectrum in the energy range 50—130eV (Fig. 2)we see the expected appearance of this transition. The relative strength of the 3s transition (Fig. 3), after correcting for multiple scattering [4], follows the formula S(3s) a 2 R
=
=
\pJ with a = 0.28 and q,. = 2.55 A-’. The strength S(3s) of the 3s line was measured as the peak height above background and the strength, S(3p) of the 3p line was taken to be the dip-to.peak height. Here, q. is taken to be the reciprocal of the 3s core radius [5] of Ni and the factor 1/3 takes into account the multiplicity of the s and p electrons, a was chosen to fit the observed intensity ratio. These spectra are compared to the low-energy electron backscattering spectrum in Fig. 2. Electrons of 1000 eV energy were directed at normal incidence on a Ni single crystal (100) surface, and the backscattered electrons collected at 42.5°from the normal were energy-analyzed with a double-pass cylindrical mirror analyzer. One may assume, as is usually done [6] that inelastic reflection of electrons of a few hundred eV kinetic energy is mainly due to an elastic backscattering followed or preceded by a forward-scattering inelastic event. Since electrons at 1000eV have a wavevector k 15 A-’, this cannot be true for the core excitations in Ni reported here unless a higher order Born approximation is required to describe the forward inelastic scattering from a Ni atom. The other alternative, of course, is to think of the reflection scattering as a weighted sum of inelastic events at different momentum
1255
1256
INELASTIC ELECTRON SCATTERING IN NICKEL
Vol. 27, No. ii
(J~ F—
o
-
0
ENERGY LOSS (eV)
Fig. 1. The q
=
0 transmission inelastic electron scattering spectrum from a single crystal Ni foil.
M~,
1~j
M1 1
0.3
-
02
-
q~45A
‘~
~
N ~
W
~
q,3A~
“~‘-. ,.
2
•\\\ BACK EINC SCATTERING~~~. ~ \ I I 1000eV I I ~ 50 70 ENERGY90LOSS (eV) 110 I
130
Fig. 2 The upper curves show the transmission inelastic electron scattering spectrum in the vicinity of the M, and M 11 ~ transitions for q = 4.5, 3.0, 2.0, and 0.0 A-’, respectively. The lowest curve shows the backscattering inelastic electron scattering spectrum at Ej~~ = 1000eV. transfer preceded or followed by elastic scattering. In fact, a preliminary analysis of backscattering data at 250 and 500 eV indicates a decreasing 3s/3p ratio with increasing energy, a result consistent with both models posed above. The correct interpretation of the electron back-scattering results awaits a detailed calculation of
o. 0Fig. 3. The M
R Oq2(~2>
~
~q I/q >2 20
a = 0.28.from trans1/M,1 Ill transition2,strengths, mission electron scattering, vs q the multiple scattering contributions using existing LEED techniques, or perhaps careful absolute crosssection measurements. There is at least one other point worth noting about the data presented in Fig. 2. The shape of the M1111, edge [2] has been described as a Fano interference effect between transitions to the empty 3.d state and excitations of the 3-d electrons into the f continuum. One sees this effect if one makes a smooth background interpolation to the data (see dashed curve
Vol. 27, No. 11
INELASTIC ELECTRON SCATTERING IN NICKEL
on back-scattering data, [2]). The shape of the transmission electron beam spectrum from 50—80eV depends on the momentum transfer. In principle, this is due to the variation of two quite distinct effects. If we could turn off the Coulomb interactions between valence and core electrons, then the spectrum would simply be the sum of these two independent contributions, both of which would depend on momentum transfer. In particular, the valence electron part centered at the plasmon energy at low momentum transfers would evolve to a Compton-like peak at the highest momentum transfers
1.
1257
reported here [7]. The difference between this sum and the actual spectrum represents the so-called interference or interaction effect [2] which itself could be q-dependent. A detailed analysis of this kind of data requires a one-electron spectrum plus a formulation of the interference phenomenon as a function of momentum transfer. Acknowledgement We would like to acknowledge Robert Kirsch, who grew the single crystal Ni film used in the transmission experiments. —
REFERENCES DANIELS J., FESTENBERG C.V., RAETHER H. & ZEPPENFELD K., Springer Tracts in Modern Physics 54, 77(1970).
2.
DIETZ R.E., McRAE E.G., YAFET Y. & CALDWELL C.W.,Phys. Rev. Lett. 33, 1372 (1974); Similar spectra have also been reported by:
3.
MISELL D.L. & ATKINS A.J., Phil. Mag. 27,95 (1973); DAVIS L.C. & FELDKAMP L.A., Solid State Commun. 19,413 (1976).
4.
The single crystal sample transmitted 25% of the incident 200 keV electrons in the forward direction. Almost all of the remaining electrons were elastically scattered into Bragg peaks or into a broad thermal diffuse background. The data at finite q was corrected for multiple scattering by subtracting the required amount of the q = 0 inelastic spectrum. The correction was of the order of 10% for the largest q values. No corrections were made in this data for multiple inelastic scattering processes.
5,
HERMAN F. & SKILLMAN S.,Atomic Structure Calculations. Prentice Hall, New Jersey (1963).
6.
Such an assumption was made in [2] (above). Other recent studies are listed in the review article by McRAE E.G. & HAGSTRUM H.D., Treatise ofSolid State Chemistry, Vol. 6A, Chap. 2, pp. 57—163. Plenum, New York (1976). It is necessary that q = 0 (i.e. forward-scattering) in the inelastic step if the energy-loss spectrum is to be closely described by the optical dielectric function.
7.
PLATZMAN P.M. & EISENBERGER P.,Phys. Rev. Lett. 33, 152 (1974); EISENBERGER P., & PLATZMAN P.M.,Phys. Rev. Lett. 31, 311 (1973).
0038—1098/78/0915—1255 $02.00/O
INELASTIC ELECTRON SCATTERING IN NICKEL A.E. Meixner, R.E. Dietz, G.S. Brown and P.M. Platzman Bell Laboratories, Murray Hill, NJ 07974, U.S.A. (Received l4March 1978 byA.G. Chynoweth) Using a 200 keV electron spectrometer, with an energy resolution of —~0.25 eV and a momentum resolution of 0.2 A’, we have measured the energy loss spectra for transmission of electrons through thin (‘~600 A) Ni films. These results address the general question of the validity of momentum transfer estimates in electron loss scattering. Using low.energy electron backscattering, we have observed the dipole forbiddenM, transition at 112 eV. For high.energy scattering, we have observed this transition only at high momentum transfer (q ~ 2 A-’). These results indicate sizable contributions from high momentum transfer collisions in the low-energy experiments. THE INELASTIC electronic scattering spectrum da/d~2dw,for fast electrons scattering weakly from a thin solid, is given by do 4r2 d~ld = ~ S(q, ~,) (1) w ~q ~inc where, within the framework of the Born approximation,
/ S(q,w)
=
~
\2
~ e~r
~ 6(E~—E
1—-w). (2) / Historically, high-energy electron scattering ~ and low-energy electron backscattering [2] have been employed to measure the long wavelength (q -÷ 0) limit of equation (2) which is proportional to Im (lie). The low-energy backscattering experiments were believed to be dominated by forward inelastic processes preceded or followed by large-angle diffraction, and hence represented by the q 0 limit of (2). In this paper, we compare high-energy electron transmission data for singlecrystal Ni with low-energy backscattering data to obtain a measure of the mean momentum transfer in the backscattering experiments. We have studied the scattering of 200 keV electrons from a single-crystal 600 A Ni foil. The q = 0 inelastic spectrum is shown in Fig. 1 [3]. Three important features may be discerned, as well as subsidiary structure at low energy which we will not discuss, (1) atE = 0, the elastic and the quasi-elastic peak, corresponding to unresolved scattering from the lattice vibrations are both present; (2) at E = 20 eV, a double-humped plasmon interband excitation which changes in shape but does not disperse as q increases, and (3) an edgelike structure corresponding to 3p112 312—3d(M11,11) transition [2]. Conspicuously absent in this spectrum is the 3s—3d (M,) transition at 112 eV, which is dipole i,f
\
—~
i
forbidden and therefore absent in U.V. absorption spectroscopy and q = 0 electron scattering. However, when we examine the q-dependence of the spectrum in the energy range 50—130eV (Fig. 2)we see the expected appearance of this transition. The relative strength of the 3s transition (Fig. 3), after correcting for multiple scattering [4], follows the formula S(3s) a 2 R
=
=
\pJ with a = 0.28 and q,. = 2.55 A-’. The strength S(3s) of the 3s line was measured as the peak height above background and the strength, S(3p) of the 3p line was taken to be the dip-to.peak height. Here, q. is taken to be the reciprocal of the 3s core radius [5] of Ni and the factor 1/3 takes into account the multiplicity of the s and p electrons, a was chosen to fit the observed intensity ratio. These spectra are compared to the low-energy electron backscattering spectrum in Fig. 2. Electrons of 1000 eV energy were directed at normal incidence on a Ni single crystal (100) surface, and the backscattered electrons collected at 42.5°from the normal were energy-analyzed with a double-pass cylindrical mirror analyzer. One may assume, as is usually done [6] that inelastic reflection of electrons of a few hundred eV kinetic energy is mainly due to an elastic backscattering followed or preceded by a forward-scattering inelastic event. Since electrons at 1000eV have a wavevector k 15 A-’, this cannot be true for the core excitations in Ni reported here unless a higher order Born approximation is required to describe the forward inelastic scattering from a Ni atom. The other alternative, of course, is to think of the reflection scattering as a weighted sum of inelastic events at different momentum
1255
1256
INELASTIC ELECTRON SCATTERING IN NICKEL
Vol. 27, No. ii
(J~ F—
o
-
0
ENERGY LOSS (eV)
Fig. 1. The q
=
0 transmission inelastic electron scattering spectrum from a single crystal Ni foil.
M~,
1~j
M1 1
0.3
-
02
-
q~45A
‘~
~
N ~
W
~
q,3A~
“~‘-. ,.
2
•\\\ BACK EINC SCATTERING~~~. ~ \ I I 1000eV I I ~ 50 70 ENERGY90LOSS (eV) 110 I
130
Fig. 2 The upper curves show the transmission inelastic electron scattering spectrum in the vicinity of the M, and M 11 ~ transitions for q = 4.5, 3.0, 2.0, and 0.0 A-’, respectively. The lowest curve shows the backscattering inelastic electron scattering spectrum at Ej~~ = 1000eV. transfer preceded or followed by elastic scattering. In fact, a preliminary analysis of backscattering data at 250 and 500 eV indicates a decreasing 3s/3p ratio with increasing energy, a result consistent with both models posed above. The correct interpretation of the electron back-scattering results awaits a detailed calculation of
o. 0Fig. 3. The M
R Oq2(~2>
~
~q I/q >2 20
a = 0.28.from trans1/M,1 Ill transition2,strengths, mission electron scattering, vs q the multiple scattering contributions using existing LEED techniques, or perhaps careful absolute crosssection measurements. There is at least one other point worth noting about the data presented in Fig. 2. The shape of the M1111, edge [2] has been described as a Fano interference effect between transitions to the empty 3.d state and excitations of the 3-d electrons into the f continuum. One sees this effect if one makes a smooth background interpolation to the data (see dashed curve
Vol. 27, No. 11
INELASTIC ELECTRON SCATTERING IN NICKEL
on back-scattering data, [2]). The shape of the transmission electron beam spectrum from 50—80eV depends on the momentum transfer. In principle, this is due to the variation of two quite distinct effects. If we could turn off the Coulomb interactions between valence and core electrons, then the spectrum would simply be the sum of these two independent contributions, both of which would depend on momentum transfer. In particular, the valence electron part centered at the plasmon energy at low momentum transfers would evolve to a Compton-like peak at the highest momentum transfers
1.
1257
reported here [7]. The difference between this sum and the actual spectrum represents the so-called interference or interaction effect [2] which itself could be q-dependent. A detailed analysis of this kind of data requires a one-electron spectrum plus a formulation of the interference phenomenon as a function of momentum transfer. Acknowledgement We would like to acknowledge Robert Kirsch, who grew the single crystal Ni film used in the transmission experiments. —
REFERENCES DANIELS J., FESTENBERG C.V., RAETHER H. & ZEPPENFELD K., Springer Tracts in Modern Physics 54, 77(1970).
2.
DIETZ R.E., McRAE E.G., YAFET Y. & CALDWELL C.W.,Phys. Rev. Lett. 33, 1372 (1974); Similar spectra have also been reported by:
3.
MISELL D.L. & ATKINS A.J., Phil. Mag. 27,95 (1973); DAVIS L.C. & FELDKAMP L.A., Solid State Commun. 19,413 (1976).
4.
The single crystal sample transmitted 25% of the incident 200 keV electrons in the forward direction. Almost all of the remaining electrons were elastically scattered into Bragg peaks or into a broad thermal diffuse background. The data at finite q was corrected for multiple scattering by subtracting the required amount of the q = 0 inelastic spectrum. The correction was of the order of 10% for the largest q values. No corrections were made in this data for multiple inelastic scattering processes.
5,
HERMAN F. & SKILLMAN S.,Atomic Structure Calculations. Prentice Hall, New Jersey (1963).
6.
Such an assumption was made in [2] (above). Other recent studies are listed in the review article by McRAE E.G. & HAGSTRUM H.D., Treatise ofSolid State Chemistry, Vol. 6A, Chap. 2, pp. 57—163. Plenum, New York (1976). It is necessary that q = 0 (i.e. forward-scattering) in the inelastic step if the energy-loss spectrum is to be closely described by the optical dielectric function.
7.
PLATZMAN P.M. & EISENBERGER P.,Phys. Rev. Lett. 33, 152 (1974); EISENBERGER P., & PLATZMAN P.M.,Phys. Rev. Lett. 31, 311 (1973).