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Plasma excitations in LiF
Solid State Communications Vol. 4, pp. 159-163, 1966. Pergamon Press Ltd. Printed in Great Britain.
PLASMA EXCITATIONS IN LiF* David W. Lynch Institute for Atomic Research and Department of Physics, Iowa State University, Ames, Iowa, 50010 (Received 20 January 1966 by B.N. Brockhouse)
The absorption data of Milgram and Givens on LiF films have been analyzed by means of dispersion integrals. From the plot of Im( ~) vs. energy the characteristic electron energy loss at 25. 3 eV can be identified as a plasmalike excitation very close to a one-electron excitation peak at 23. 9 eV. Other possible plasma loss peaks are at 13. 4 eV, 45 eV and —50 eV. .-.
THERE has been recent discussion in the literature concerning andpeak excitons in LiF. 1 found anplasmons energy loss at 25.3 eV Sueoka with the appropriate dispersion for a plasma excitation. Creuzberg and Raether2 made similar measurements and found very little dispersion for the 25 eV loss peak and for the loss peaks at lower energy. ~ They attributed all of these loss peaks to one-electron excitations. More recent measurements5 confirmed earlier resuits,2 but a comparison with optical data6 lead Creuzberg5 to associate the 25 eV loss with a plasmon in a tightly bound system. There is no absorption coefficient peak at 25 eV. Miyakawa7 proposed a two- exciton mechanism for the nearby absorption peak at 24.3 eV, while Milgram and Givens6 ascribe this to excitation of 2s electrons on the F ions. To investigate this further we have taken the absorption coefficients of Ref. 6 and used the dispersion integral8 n(E)
=
1
+
~c
P
5
0
~ (Et ~dE’ E E2 -
(1)
stant, £ = £2, and plasma loss function, Im (Ci), can be found. The results are shown in Fig. 1. The integrand in equatIon (1) for E’ > 110 eV contributes negligibly for E <80 eV, assuming no large absorption peaks occur just beyond 110 eV. The curves of Fig. 1 are accurate to the extent that the data of Ref. 6 are accurate. The data in Ref. 6 have been obtained on evaporated films. No single crystal data exist in most of this wavelength region. Kato9 measured the reflectivity of single crystal LiF, but only to a maximum photon energy of 14. 5 eV. His dispersion analysis of the data produced spectra similar to the low energy regions of Fig. 1, but with different magnitudes. For comparison, we list the peak values of some of the optical constants in the first peak at 12. 8 eV, ours first, then Kato’s: reflectivity 19%, 36%; absorption coefficient 13.8 x 10~cm~’8 22 x 10~cm~ ~2, 3.74, 6.3. Part of the discrepancy may arise from Kato’s adjustment of the computed phases to account for the limited range of integration, and part is undoubtedly to differences between evaporated films anddue single crystal surfaces. Mllgrain -
and Givens8 point out that their films may be porous. This would lead to erroneously low absorption coefficients, an error which would give low values for the three peak quantities compared above. The shapes of Kato’s spectra agree with those of Fig. 1, and both are probably correct.
to compute the refractive index n (E) at energy E from the absorption coefficients The P indicates “principal value”. From the measured .t and computed n, the complex dielectric con~.
___________
*Work was performed in the Ames Laboratory of the U. S. Atomic Energy Commission. Contribution No. 1844.
A partial test of the data can be made by 159
160
PLASMA EXCITATIONS IN LiF
Vol. 4, No. 4
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Vol. 4, No. 4
PLASMA EXCITATIONS IN LIF
161
TABLE 1 Energy loss peaks in LiF (eV) Ref. I
Ref. 2
Ref. 3
Ref. 4 9a
Peak 1) In Im(C
Peak C in 2
12.9 13.3
13.6
13.4 14. 25(step)
15.3 17.8
15.4 ~18
14.3
14.7
14.9
15.2
14.5
15.2
15.6
17.0
16.3 18.0
17.7
17.5
20,8 21,3 22.8 25.3 42.6 51.4 62.9 68, 5
25
24.9
25 ~ 5a
43.2 50.6c
42a
62.0 68. 5
58 62.5
(a) Interpreted as involving a colour center. (b) Not resolved as peaks, very broad. (c) Interpreted in Ref. 3 as due to excitation of the 25 eV plasmons. (d) Very weak, broad.
-2 O(shoulder) 20.75 22.6 23. 9
25.3 45b
62.5 69.2 75
68. 5d 75d
—83
82d
162
PLASMA EXCITATIONS IN LiF
i~ntegrating £2 with various weighting functions: E max E L(E) 2(E )dE
2e2 2 rrt~2 Neff m
—
(2)
and 9(E)clE E ______
=
rr 2 (c
—
-
1)
(3)
or E
2N £2(E)dE EL’(E)
=
2
ii
eff a
(3’)
Here Neff is the effective density of electrons contributing to the absorption below energy Emax~ 10 In ecluation (2) L(E) is the local field correction and can vary from 1, as in equation (3), to the full Lorentz-Lorenz local field correction, L’(E)
values of £ and a. Equation (2) with L = 1 gives an oscillator strength of 0. 4/molecule for the first band in the ~ spectrum. This agrees well The withprincipal Sueoka’s characteristic value. 1 energy loss peaks given in Tableloss 1 along with the peaks in the are computed plasma function, Im(e’), and in the peaks in the computed 62. The loss
E max
S0
= [(~~
+
2)2
+
£82
j/9
(4)
as in equation (3’). c is the optical dielectric constant, if reststrahl contributions to 62 are omitted in equation (3). a is the ionic or molecular optical polarizability. If L (E) = 1, equation (3) should be satisfied when E — L’ (E) is appropriate, equation (3’r~ouldbe correct as E — =, with a the Tessman, Kahn and Sho~I~y molecular polarizability, computed in Ref. ii using such a local field correction. At Emax = 80 eV equation (1) gives Neff = 7. 95 electrons/molecular volume when L = 1 and 7. 80 electrons/molecule when L’ (E) is used. Integrating equation (3) to 80 eV gives a computed of 1. 72 instead of the actual 1. 92. However, at this energy only about 8 of the 12 electrons have contributed to . Integrating (3’) to 80 eV gives a = 0. 742 x i0~ cm3 instead of the actual 0. 91 x 10~’cm3. Integrating to larger values of Emax would improve agreement but one would anticipate8 that by 80 eV, Neff should be close to 10 electrons/molecular volume. Any film porosity tends to reduce the integrands in equations (1) (3’), giving low -
peaks thatexcitations correspondto £2 peaks are oneelectron whilethe those in region of small ~1 and £ 2, with d £1/dE> 0 and dc2/dE<0, are probably plasma excitations. ~° On this basis the peak at at 25.13.4 3 eVeV is and a plasma The loss sharp peak broad excitation. peaks at —45 and -50 eV maybe plasma peaks. The peak at 13. 4 eV lies between the first strong £3 peak at 12.8 eV and the step in 62 at 14.2 eV. For a free electron valence band of 6 or 8 electrons per ion pair, the plasma excitation energy would be 22.4 or 25. 8 eV. In a crystal the plasma loss peaks can be reduced and shifted considerably if there are nearby one-electron excitations. 12 If there is strong overlap of freeelectron plasma excitation and one-particle excitation there may be no plasma loss peak at all. The 25.3 eV loss peak overlaps the high energy part of the 23. 9 eV peak in £2. Thus it is not a pure plasma resonance. The lack of dispersion noted by Creuzberg and Raether2’ ~ probably arises from the hybrid character of the excitation. One cannot obviously assign the loss peak to a plasma resonance in the F2p band alone or to the combined F2p and 2s bands, although the latter may be more nearly correct. The 13. 4 eV loss peak is probably also a hybrid resonance. Phillips12 has analyzed the u. v. spectra of several alkali halides into interband and exciton components. The spin-orbit splitting is of considerable value in the analysis but for LiF the splitting is less than 0. 05 eV, not resolvable in Fig. 1. Previous work8” has made the identification of the ~2 structure below 22 eV with F2p (valence band) to conduction band transitions, the 23 eV structure to F2s to conduction band transitions, and the 60-100 eV structure to Li~is electron excitations.
References 1. SUEOKA 0.,
J. Phys. Soc. Japan, 19, 2239 (1964).
2. CREUZBERG M. and RAETHER H., 3. BEST P.E., 4.
Vol. 4, No. 4
Proc. Phys. Soc.
Solid State Comm. 2, 175 (1964).
74, 133 (1962).
PRADAL F. and GOUT C., C.R. Acad. Sci. Paris,
256, 1267 (1963).
Vol. 4, No.
4
PLASMA EXCITATIONS IN LiF
5. CRETJZBERG M., J. Phys. Soc. Japan, 20, 1745 (1965). 6. MILGRAM A. and GWENS M. P., 7. MIYAKAWA T.,
Phys. Rev. 125, 1506 (1962).
J. Phys. Soc. Japan,
19, 1989 (1962).
8. STERN F., Solid State Physics 15, 299 (1963), p. 331. 9. KATO R.,
J. Phys. Soc. Japan,
16, 2525 (1961); 17, 413 (1962).
10. PHILIPP H.R. and EHRENREICH H., 11. TESSMAN J.R.,
KAHN A.H. and SHOCKLEY W., Phys. Rev. 92, 890 (1953).
12. NOZIERES P. and PINES D., 13. PHILLIPS J.C.,
Phys. Rev. 131, 2016 (1963).
Phys. Rev.
Phys. Rev. 113, 1254 (1959). 136, A1705 (1964).
Die Absorptionsdaten fir LiF-Schichten von Milgram und Givens sind 1)vs mittels worden. Electron-energieverlust Von der Kurve Im( c Energie Dispersionsintegrale ergibt sich, dass deranalysiert charakteristische bei 25. 3 eV etne plasma-ã]mllche Anregung nahezu der bei 23.9 eV liegenden Einelektronenanregung entspricht. Andere m~$glichePlasmaverlustmaxima liegen bei 13.4 eV, -~45eV und —50 eV.
163
PLASMA EXCITATIONS IN LiF* David W. Lynch Institute for Atomic Research and Department of Physics, Iowa State University, Ames, Iowa, 50010 (Received 20 January 1966 by B.N. Brockhouse)
The absorption data of Milgram and Givens on LiF films have been analyzed by means of dispersion integrals. From the plot of Im( ~) vs. energy the characteristic electron energy loss at 25. 3 eV can be identified as a plasmalike excitation very close to a one-electron excitation peak at 23. 9 eV. Other possible plasma loss peaks are at 13. 4 eV, 45 eV and —50 eV. .-.
THERE has been recent discussion in the literature concerning andpeak excitons in LiF. 1 found anplasmons energy loss at 25.3 eV Sueoka with the appropriate dispersion for a plasma excitation. Creuzberg and Raether2 made similar measurements and found very little dispersion for the 25 eV loss peak and for the loss peaks at lower energy. ~ They attributed all of these loss peaks to one-electron excitations. More recent measurements5 confirmed earlier resuits,2 but a comparison with optical data6 lead Creuzberg5 to associate the 25 eV loss with a plasmon in a tightly bound system. There is no absorption coefficient peak at 25 eV. Miyakawa7 proposed a two- exciton mechanism for the nearby absorption peak at 24.3 eV, while Milgram and Givens6 ascribe this to excitation of 2s electrons on the F ions. To investigate this further we have taken the absorption coefficients of Ref. 6 and used the dispersion integral8 n(E)
=
1
+
~c
P
5
0
~ (Et ~dE’ E E2 -
(1)
stant, £ = £2, and plasma loss function, Im (Ci), can be found. The results are shown in Fig. 1. The integrand in equatIon (1) for E’ > 110 eV contributes negligibly for E <80 eV, assuming no large absorption peaks occur just beyond 110 eV. The curves of Fig. 1 are accurate to the extent that the data of Ref. 6 are accurate. The data in Ref. 6 have been obtained on evaporated films. No single crystal data exist in most of this wavelength region. Kato9 measured the reflectivity of single crystal LiF, but only to a maximum photon energy of 14. 5 eV. His dispersion analysis of the data produced spectra similar to the low energy regions of Fig. 1, but with different magnitudes. For comparison, we list the peak values of some of the optical constants in the first peak at 12. 8 eV, ours first, then Kato’s: reflectivity 19%, 36%; absorption coefficient 13.8 x 10~cm~’8 22 x 10~cm~ ~2, 3.74, 6.3. Part of the discrepancy may arise from Kato’s adjustment of the computed phases to account for the limited range of integration, and part is undoubtedly to differences between evaporated films anddue single crystal surfaces. Mllgrain -
and Givens8 point out that their films may be porous. This would lead to erroneously low absorption coefficients, an error which would give low values for the three peak quantities compared above. The shapes of Kato’s spectra agree with those of Fig. 1, and both are probably correct.
to compute the refractive index n (E) at energy E from the absorption coefficients The P indicates “principal value”. From the measured .t and computed n, the complex dielectric con~.
___________
*Work was performed in the Ames Laboratory of the U. S. Atomic Energy Commission. Contribution No. 1844.
A partial test of the data can be made by 159
160
PLASMA EXCITATIONS IN LiF
Vol. 4, No. 4
w -
—Q -0-
-
QC~
0
_0 V.. -~
Cl)’
— •,_ C~o
-
Cl) Cl)
-
-~ —
-
,, -
-
—?
-0 N
—
.
c~ —
-o .‘Q
-~ —
I
I
I
0
0
0
2
2 0 ~ 0
0 VO
0 ~ 0
0 0 N
>
—
8
0
—~
WI
-
—
~..
~
-
______________________
I
o 0
in
0 ~
0 0 ~
0 1) N
0 Q N
I
I
0
8
g~
-~
I 0 0
0 0 0
~
=
—
~•0 -~
z —~
-
0 ~
8
~
~
in
0
0
In
C~J
0 0 N I;
-~
8 —
~
Vol. 4, No. 4
PLASMA EXCITATIONS IN LIF
161
TABLE 1 Energy loss peaks in LiF (eV) Ref. I
Ref. 2
Ref. 3
Ref. 4 9a
Peak 1) In Im(C
Peak C in 2
12.9 13.3
13.6
13.4 14. 25(step)
15.3 17.8
15.4 ~18
14.3
14.7
14.9
15.2
14.5
15.2
15.6
17.0
16.3 18.0
17.7
17.5
20,8 21,3 22.8 25.3 42.6 51.4 62.9 68, 5
25
24.9
25 ~ 5a
43.2 50.6c
42a
62.0 68. 5
58 62.5
(a) Interpreted as involving a colour center. (b) Not resolved as peaks, very broad. (c) Interpreted in Ref. 3 as due to excitation of the 25 eV plasmons. (d) Very weak, broad.
-2 O(shoulder) 20.75 22.6 23. 9
25.3 45b
62.5 69.2 75
68. 5d 75d
—83
82d
162
PLASMA EXCITATIONS IN LiF
i~ntegrating £2 with various weighting functions: E max E L(E) 2(E )dE
2e2 2 rrt~2 Neff m
—
(2)
and 9(E)clE E ______
=
rr 2 (c
—
-
1)
(3)
or E
2N £2(E)dE EL’(E)
=
2
ii
eff a
(3’)
Here Neff is the effective density of electrons contributing to the absorption below energy Emax~ 10 In ecluation (2) L(E) is the local field correction and can vary from 1, as in equation (3), to the full Lorentz-Lorenz local field correction, L’(E)
values of £ and a. Equation (2) with L = 1 gives an oscillator strength of 0. 4/molecule for the first band in the ~ spectrum. This agrees well The withprincipal Sueoka’s characteristic value. 1 energy loss peaks given in Tableloss 1 along with the peaks in the are computed plasma function, Im(e’), and in the peaks in the computed 62. The loss
E max
S0
= [(~~
+
2)2
+
£82
j/9
(4)
as in equation (3’). c is the optical dielectric constant, if reststrahl contributions to 62 are omitted in equation (3). a is the ionic or molecular optical polarizability. If L (E) = 1, equation (3) should be satisfied when E — L’ (E) is appropriate, equation (3’r~ouldbe correct as E — =, with a the Tessman, Kahn and Sho~I~y molecular polarizability, computed in Ref. ii using such a local field correction. At Emax = 80 eV equation (1) gives Neff = 7. 95 electrons/molecular volume when L = 1 and 7. 80 electrons/molecule when L’ (E) is used. Integrating equation (3) to 80 eV gives a computed of 1. 72 instead of the actual 1. 92. However, at this energy only about 8 of the 12 electrons have contributed to . Integrating (3’) to 80 eV gives a = 0. 742 x i0~ cm3 instead of the actual 0. 91 x 10~’cm3. Integrating to larger values of Emax would improve agreement but one would anticipate8 that by 80 eV, Neff should be close to 10 electrons/molecular volume. Any film porosity tends to reduce the integrands in equations (1) (3’), giving low -
peaks thatexcitations correspondto £2 peaks are oneelectron whilethe those in region of small ~1 and £ 2, with d £1/dE> 0 and dc2/dE<0, are probably plasma excitations. ~° On this basis the peak at at 25.13.4 3 eVeV is and a plasma The loss sharp peak broad excitation. peaks at —45 and -50 eV maybe plasma peaks. The peak at 13. 4 eV lies between the first strong £3 peak at 12.8 eV and the step in 62 at 14.2 eV. For a free electron valence band of 6 or 8 electrons per ion pair, the plasma excitation energy would be 22.4 or 25. 8 eV. In a crystal the plasma loss peaks can be reduced and shifted considerably if there are nearby one-electron excitations. 12 If there is strong overlap of freeelectron plasma excitation and one-particle excitation there may be no plasma loss peak at all. The 25.3 eV loss peak overlaps the high energy part of the 23. 9 eV peak in £2. Thus it is not a pure plasma resonance. The lack of dispersion noted by Creuzberg and Raether2’ ~ probably arises from the hybrid character of the excitation. One cannot obviously assign the loss peak to a plasma resonance in the F2p band alone or to the combined F2p and 2s bands, although the latter may be more nearly correct. The 13. 4 eV loss peak is probably also a hybrid resonance. Phillips12 has analyzed the u. v. spectra of several alkali halides into interband and exciton components. The spin-orbit splitting is of considerable value in the analysis but for LiF the splitting is less than 0. 05 eV, not resolvable in Fig. 1. Previous work8” has made the identification of the ~2 structure below 22 eV with F2p (valence band) to conduction band transitions, the 23 eV structure to F2s to conduction band transitions, and the 60-100 eV structure to Li~is electron excitations.
References 1. SUEOKA 0.,
J. Phys. Soc. Japan, 19, 2239 (1964).
2. CREUZBERG M. and RAETHER H., 3. BEST P.E., 4.
Vol. 4, No. 4
Proc. Phys. Soc.
Solid State Comm. 2, 175 (1964).
74, 133 (1962).
PRADAL F. and GOUT C., C.R. Acad. Sci. Paris,
256, 1267 (1963).
Vol. 4, No.
4
PLASMA EXCITATIONS IN LiF
5. CRETJZBERG M., J. Phys. Soc. Japan, 20, 1745 (1965). 6. MILGRAM A. and GWENS M. P., 7. MIYAKAWA T.,
Phys. Rev. 125, 1506 (1962).
J. Phys. Soc. Japan,
19, 1989 (1962).
8. STERN F., Solid State Physics 15, 299 (1963), p. 331. 9. KATO R.,
J. Phys. Soc. Japan,
16, 2525 (1961); 17, 413 (1962).
10. PHILIPP H.R. and EHRENREICH H., 11. TESSMAN J.R.,
KAHN A.H. and SHOCKLEY W., Phys. Rev. 92, 890 (1953).
12. NOZIERES P. and PINES D., 13. PHILLIPS J.C.,
Phys. Rev. 131, 2016 (1963).
Phys. Rev.
Phys. Rev. 113, 1254 (1959). 136, A1705 (1964).
Die Absorptionsdaten fir LiF-Schichten von Milgram und Givens sind 1)vs mittels worden. Electron-energieverlust Von der Kurve Im( c Energie Dispersionsintegrale ergibt sich, dass deranalysiert charakteristische bei 25. 3 eV etne plasma-ã]mllche Anregung nahezu der bei 23.9 eV liegenden Einelektronenanregung entspricht. Andere m~$glichePlasmaverlustmaxima liegen bei 13.4 eV, -~45eV und —50 eV.
163