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Wavelength-modulated reflectivity of the noble metals
Solid State Communications, Vol. 9, PP. 2139—2142, 1971. Pergamon Press.
Printed in Great Britain
WAVELENGTH—MODULATED REFLECTIVITY OF THE NOBLE METALS* M. Welkowsky and R. Braunstein Department of Physics, University of California, Los Angeles, California 90024 (Received 19 September 1971 by A.A. Maradudin)
The interband transitions of evaporated films of the noble metals copper, gold, and silver have been studied in reflectivity in the energy region 2.~l— 5.0eV as a function of temperature, using wavelength modulation. In copper and gold, features have been observed in the imaginary part of the dielectric constant which support recent band theories as to their location in the Brillouin zone. In silver, new weak structure has been resolved near the onset of interband absorption. The surface plasmon in silver has been studied, and shown to possess a strong temperature dependence.
THE EXISTENCE of considerable disagreement between various band calculations and experiments, regarding the number and location of the interband transitions in the noble metals, has been of concern for some time. In an effort to illuminate the problem, we have used the sensitivity of wavelength modulation derivative spectroscopy to study the noble metals Cu, Au, and Ag, in the energy range 2.0 — 5.0 eV as a function of temperature. The logarithmic energy derivative of the reflectivity of each metal has been measured, and then transformed via a Kramers—Krönig analysis to yield the optical constants of the material. So that a direct comparison could be made to theoretical predictions, the imaginary part of the dielectric constant, E2~has been calculated; the Drude free electron distribution to E~ has been neglected at energies above the onset of interband absorption, where it is a rapidly decreasing function of energy. The sensitivity of modulation techniques is well known.’ However, not all have been successfully applied to metals.2 We have utilized a double beam, single detector wavelength modulation Work supported by U.S. Army Research Office, Durham
system, which allows photon shot-noise limited measurements with sensitivities of one part in 5 The depth of modulation is controllable iO. through an electro-mechanical device to a maximum value of AA/A 10~. Typical modulation amplitudes used are 5—8 A, r.m.s., yielding a spectral resolution of 0.003 eV. Depending on the spectral region, a tungsten—iodine lamp and a xenon arc are used as sources. The single detector is an EM! 9558QB photomultiplier. The system has been described in detail elsewhere.3 Measurements were taken on thick films evaporated on sapphire substrates at vacuums of 10~torr. Immediately after preparation, the samples were placed directly into a dewar which was held at 3 x 10~torr.The use of films in this study, as opposed to bulk samples, is supported by recent measurements4 of the d.c. resistivities of Au and Ag, which showed no significant difference between the bulk and evaporated film samples. The experimental derivative reflectivity data was transformed with a Kramers—Krönig program utilizing the method of trapezoidal integration. Above the 5 eV cutoff of our spectrometer high
*
energy data to 20 eV for use in the program was taken from the reflectivity studies of Ehrenreich 2139
2140
REFLECTIVITY OF THE NOBLE METALS
Cu
0
,_.~ r
__
&oo
Ag
Co
•~
lHi~Li
23~5:~
Vol. 9, No. 23
/
energy (eV)
0.00
FIG. 1. The logarithmic derivatives of the reflectivities of Cu, Au and Ag, at 80°K.
0.00 I
5 and Cooper, Ehrenreich and and Philipp, Philipp.6 For energies above 20eV, the extrapolation procedure chosen is amodification of the Drude formula for reflectivities above the bound plasma energy.
~nF~
____________________
2
ener:y ~V)
~
80°Kby a Kramers—Kronig analysis of the derivative data.
L R(E)
R
(Em\ m
\E
/
(1)
where is theexperimental reflectivity at energy , the highestRm energy data point.E,7~ The exponent p is varied so as to give a best fit to known optical constants at low energy.5’6 The logarithmic derivatives of the reflectivities of the noble metals at 80°K are presented in Fig. 1. The large negative structures of the derivatives, which correspond to a large drop in the reflectivity, can be correlated with the sharp rises in 2, shown in Fig. 2, and are characteristic of the onset of interband absorption in the metals. In Cu, this absorption occurs at 2.18eV. This large negative peak in the derivative of the reflectivity does not show any significant ternperature dependence. It is attributed to d-band — Fermi surface transitions: A ~ -n A 1(E,) and L3(Q~)—~ E1(L2’). The band nomenclature 7 The rapid riseisin due to Mueller and Phillips. 2 is due to the flatness of the L3 d-band, which permits a large number of interband transitions to the Fermi surface, within a narrow energy range. The first peak in ~2 is seen at 2.53eV and corresponds to the transition L3(Q_) .-~ E~ (L2’). The second peak, 3.75eV is associated 1. The thirdatpeak, at 4.74eV, is with X5 —nto X4 assigned the conduction-band transition
2’ .-~ L1. In addition to these major structures, the Kramers—Krönig inversion of the derivative spectrum has revealed a very weak feature at 3.26eV in ~ This small with to 7’8 peak and isagrees attributed theoretical predictions volume effects near X and L. There has been some diagreement among the various band calculations over the assignment of 3.75eV and 4.74eV transitions in Cu? The failure of previous experiments5’9 to resolve the second of the three major peaks seen here in 2 added to the controversy. Recent wavelength modulation data ‘° on bulk Cu at 7°Kshows structure similar to that reported here, but no attempt was made to use the reflectivity derivative results to obtain an 2 spectrum as was done in the present work. The results of the present study, supported with the symmetry analysis of piezo-optical data,’’ conclusively differentiates between the X and L transitions.
The large negative peak in the derivative of the with reflectivity Au occurstoatL 2.49eV at 80°K. As Cu, it isof attributed
3 (Q~).-n E1 (L2’).
Unlike Cu, this Au peak shifts with temperature; at 300°K ii is located at 2.44 eV. Furthermore, a comparison of the major structures of Cu and Au in Fig. 1 indicates that the onset of interband transitions in Au is not as abrupt as in Cu. This may be which correlated with the toelectron—phonon interaction, is expected be stronger in Au than in Cu.6 The first peak in the 2 spectrum of
Vol. 9, No. 23
REFLECTIVITY OF THE NOBLE METALS
2141
Table 1. Assignment of interband transition in the noble metals at 800°K. All energies in eV. Sample
L3(Q~)
.-.
E1(L2’)
L2(Q.)
-.
E,(L2’)
X5
-n
X4’
L2’
.~.
L1
Volume effect
(X Cu Au Ag
2.18 2.49 (3.77)
2.53 3.18
3.75 3.91
4.74
+
L)
3.26
4.42
Au is relatively broad; it is assigned to the feature L3 (Q_) .. E~(L 2) and is observed at 3.18eV. The second peak, at 3.91eV, is assocI
I
0.00
iated with X5 -. X4’. These assignments are in reasonable agreement with recent 3 studies of Au, theoretical and demonand experimental’ strate the strong similarities between the interband of Au and Cu.
Ag 8.00
0.03
~
The derivative structure of Ag is the largest observed in the noble metals. The large drop in the reflectivity is a result of a hybrid plasma resonance, ~ which arises from an interaction between conduction-band electrons and d-band electrons. If interband transitions were not involved, the resonance occurHowat the 5 plasma free-electron valuewould of 9.2eV. calculated ever, the transition associated with the onset of interband structure in both Cu and Au, L 3 (Q+)4’’5 E1(L2’), expected Ag nearweak 4eV.structure Studies’ in of Ag-richisalloys haveinyielded this region; however, efforts to observe this structure in Ag itself have not been fruitful. That this feature may have been resolved in Ag in this study is suggested by the small structure in
~
200
250
300 3.50 energy (cv)
4.00
4.50
5.00
FIG. 3. The derivative of the imaginary part of the dielectric constant, d 2/dE, of Ag at 80°K. The arrow indicates the new structure. Fig. 3, is a result of the interaction of light with surface plasmons. This effect has beenprovides attributed to surface roughness;’6 the roughness the necessary coupling of the transverse photon and the plasmon. For the case of evaporated thick Ag films, the rate of evaporation and the age of the film have been found to affect the magnitude of the surface plasmon excitation. ~
d 2/dE, shown in Fig.3. The small peak in the derivative represents a weak shoulder in 2, and occurspeak at 3.77eV huge in dE at 80°K. Its proximity to the 2/dE, caused by the plasma resonance condition, would make it impossible to find if not for the sensitivity of the wavelength modulation At room temperature this shoulder is technique. barely evident. These results tend to confirm the observation7 that the interband transition in pure Ag is composed of a transition from the upper d-band to the Fermi surface and a transition from the Fermi surface to a higher conduction band. The peak at 3.29eV in d 2/dE,
seen in
In contradiction to of previous experimental 8the results this study show a large findings, ‘ temperature dependence of the surface plasmori. The peak in 2 shifts downward in energy with a decrease from 3.48eV at 300°K 3.29eV inattemperature, 80°K. The magnitude of the peak to increases at 80°K to twice that of the room ternperature contribution. This temperature dependence suggests that surface roughness is not the only factor involved in this phenomenon. The possibility of phonon-assisted excitations should also be considered.
2142
REFLECTIVITY OF THE NOBLE METALS
Vol. 9, No. 23
REFERENCES 1.
CARDONA M., Modulation Spectroscopy, Academic Press, New York, (1969).
2.
FEINLEIB
3.
BRAUNSTEIN R. and WELDOWSKY M., to be published.
4.
RIVORY
5.
EHRENREICH H. and PHILIPP H.R., Phys. Rev. 128, 1622 (1962).
6.
COOPER B.R., EHRENREICH H. and PHILIPP H.R., Phys. Rev. 138, A494 (1965).
7.
MUELLER F.M. and PHILIPS J.C., Phys. Rev. 157, 600 (1967).
8.
FONG C.Y. and COHEN M.L., Phys. Rev. Lett. 24, 306 (1970).
9.
GARFINKEL M., TIEMANN
J., Phys. Rev. Lett.
16, 1200 (1966).
J., Optics Commun. 1, 53
J.J.
(1969).
and ENGELER W.E., Phys. Rev. 148, 695 (1966).
J.
and SHEN Y.R., Phys. Rev. Leti. 25, 1486
10.
FONG C.Y., COHEN M.L., ZUCCA R.R.L., STOKES (1970).
11.
GERHARDT U., BEAGLEHOLE D. and SANDROCK R., Phys. Rev. Lett. 19, 309 (1967).
12.
CHRISTENSEN N.E. and SERAPHIN B.O., Solid State Commun. 8, 1221 (1970).
13.
THEYE M.L., Phys. Rev. B2, 3060 (1970).
14.
MORRIS C.E. and LYNCH D.%V., Phys. Rev.
15.
IRANI G.B., HUEN T. and WOOTEN F., Phys. Rev. 83, 2385 (1971).
16.
STERN E.A., Optical Properties and Electronic Structure of Metals and Alloys, p. ABELES F., North—Holland, Amsterdam, (1966).
17.
DOBBERSTEIN P., HAMPE A. and SAUERBREY G., Phys. Leti.
18.
JASPERSON S.N. and SCHNATTERLY S.E., Phys. Rev.
182, 719 (1969). 396 edited by
27A, 256 (1968).
188, 759 (1969).
Die Interbandübergänge aufgedampfter diinner Schichten der edlen
Metalle Kupfer, Gold und Silber sind in Reflektion beobachtet worden im Energiebereich von 2.0 bis 5.0 eV als Funktion der Ternperatur, wobei Wellenl~ngenrnodulationangewandt wurde. In Kupfer und Gold sind Ergebnisse im imaginären Teil der Dialektrizitätskonstanten erhalten worden, weiche kflrzlich veröffentlichte Bandtheorien bezüglich ihrer Lage in der Brillouinschen Zone unterstützen. In Silber sind schwache Einzelheiten nahe dem Anfang der Interbandabsorption aufgelöst worden. Das Oberflächenplasrnon in Silber ist untersucht worden und hat sich als stark temperaturabh~ngigerwiesen.
Printed in Great Britain
WAVELENGTH—MODULATED REFLECTIVITY OF THE NOBLE METALS* M. Welkowsky and R. Braunstein Department of Physics, University of California, Los Angeles, California 90024 (Received 19 September 1971 by A.A. Maradudin)
The interband transitions of evaporated films of the noble metals copper, gold, and silver have been studied in reflectivity in the energy region 2.~l— 5.0eV as a function of temperature, using wavelength modulation. In copper and gold, features have been observed in the imaginary part of the dielectric constant which support recent band theories as to their location in the Brillouin zone. In silver, new weak structure has been resolved near the onset of interband absorption. The surface plasmon in silver has been studied, and shown to possess a strong temperature dependence.
THE EXISTENCE of considerable disagreement between various band calculations and experiments, regarding the number and location of the interband transitions in the noble metals, has been of concern for some time. In an effort to illuminate the problem, we have used the sensitivity of wavelength modulation derivative spectroscopy to study the noble metals Cu, Au, and Ag, in the energy range 2.0 — 5.0 eV as a function of temperature. The logarithmic energy derivative of the reflectivity of each metal has been measured, and then transformed via a Kramers—Krönig analysis to yield the optical constants of the material. So that a direct comparison could be made to theoretical predictions, the imaginary part of the dielectric constant, E2~has been calculated; the Drude free electron distribution to E~ has been neglected at energies above the onset of interband absorption, where it is a rapidly decreasing function of energy. The sensitivity of modulation techniques is well known.’ However, not all have been successfully applied to metals.2 We have utilized a double beam, single detector wavelength modulation Work supported by U.S. Army Research Office, Durham
system, which allows photon shot-noise limited measurements with sensitivities of one part in 5 The depth of modulation is controllable iO. through an electro-mechanical device to a maximum value of AA/A 10~. Typical modulation amplitudes used are 5—8 A, r.m.s., yielding a spectral resolution of 0.003 eV. Depending on the spectral region, a tungsten—iodine lamp and a xenon arc are used as sources. The single detector is an EM! 9558QB photomultiplier. The system has been described in detail elsewhere.3 Measurements were taken on thick films evaporated on sapphire substrates at vacuums of 10~torr. Immediately after preparation, the samples were placed directly into a dewar which was held at 3 x 10~torr.The use of films in this study, as opposed to bulk samples, is supported by recent measurements4 of the d.c. resistivities of Au and Ag, which showed no significant difference between the bulk and evaporated film samples. The experimental derivative reflectivity data was transformed with a Kramers—Krönig program utilizing the method of trapezoidal integration. Above the 5 eV cutoff of our spectrometer high
*
energy data to 20 eV for use in the program was taken from the reflectivity studies of Ehrenreich 2139
2140
REFLECTIVITY OF THE NOBLE METALS
Cu
0
,_.~ r
__
&oo
Ag
Co
•~
lHi~Li
23~5:~
Vol. 9, No. 23
/
energy (eV)
0.00
FIG. 1. The logarithmic derivatives of the reflectivities of Cu, Au and Ag, at 80°K.
0.00 I
5 and Cooper, Ehrenreich and and Philipp, Philipp.6 For energies above 20eV, the extrapolation procedure chosen is amodification of the Drude formula for reflectivities above the bound plasma energy.
~nF~
____________________
2
ener:y ~V)
~
80°Kby a Kramers—Kronig analysis of the derivative data.
L R(E)
R
(Em\ m
\E
/
(1)
where is theexperimental reflectivity at energy , the highestRm energy data point.E,7~ The exponent p is varied so as to give a best fit to known optical constants at low energy.5’6 The logarithmic derivatives of the reflectivities of the noble metals at 80°K are presented in Fig. 1. The large negative structures of the derivatives, which correspond to a large drop in the reflectivity, can be correlated with the sharp rises in 2, shown in Fig. 2, and are characteristic of the onset of interband absorption in the metals. In Cu, this absorption occurs at 2.18eV. This large negative peak in the derivative of the reflectivity does not show any significant ternperature dependence. It is attributed to d-band — Fermi surface transitions: A ~ -n A 1(E,) and L3(Q~)—~ E1(L2’). The band nomenclature 7 The rapid riseisin due to Mueller and Phillips. 2 is due to the flatness of the L3 d-band, which permits a large number of interband transitions to the Fermi surface, within a narrow energy range. The first peak in ~2 is seen at 2.53eV and corresponds to the transition L3(Q_) .-~ E~ (L2’). The second peak, 3.75eV is associated 1. The thirdatpeak, at 4.74eV, is with X5 —nto X4 assigned the conduction-band transition
2’ .-~ L1. In addition to these major structures, the Kramers—Krönig inversion of the derivative spectrum has revealed a very weak feature at 3.26eV in ~ This small with to 7’8 peak and isagrees attributed theoretical predictions volume effects near X and L. There has been some diagreement among the various band calculations over the assignment of 3.75eV and 4.74eV transitions in Cu? The failure of previous experiments5’9 to resolve the second of the three major peaks seen here in 2 added to the controversy. Recent wavelength modulation data ‘° on bulk Cu at 7°Kshows structure similar to that reported here, but no attempt was made to use the reflectivity derivative results to obtain an 2 spectrum as was done in the present work. The results of the present study, supported with the symmetry analysis of piezo-optical data,’’ conclusively differentiates between the X and L transitions.
The large negative peak in the derivative of the with reflectivity Au occurstoatL 2.49eV at 80°K. As Cu, it isof attributed
3 (Q~).-n E1 (L2’).
Unlike Cu, this Au peak shifts with temperature; at 300°K ii is located at 2.44 eV. Furthermore, a comparison of the major structures of Cu and Au in Fig. 1 indicates that the onset of interband transitions in Au is not as abrupt as in Cu. This may be which correlated with the toelectron—phonon interaction, is expected be stronger in Au than in Cu.6 The first peak in the 2 spectrum of
Vol. 9, No. 23
REFLECTIVITY OF THE NOBLE METALS
2141
Table 1. Assignment of interband transition in the noble metals at 800°K. All energies in eV. Sample
L3(Q~)
.-.
E1(L2’)
L2(Q.)
-.
E,(L2’)
X5
-n
X4’
L2’
.~.
L1
Volume effect
(X Cu Au Ag
2.18 2.49 (3.77)
2.53 3.18
3.75 3.91
4.74
+
L)
3.26
4.42
Au is relatively broad; it is assigned to the feature L3 (Q_) .. E~(L 2) and is observed at 3.18eV. The second peak, at 3.91eV, is assocI
I
0.00
iated with X5 -. X4’. These assignments are in reasonable agreement with recent 3 studies of Au, theoretical and demonand experimental’ strate the strong similarities between the interband of Au and Cu.
Ag 8.00
0.03
~
The derivative structure of Ag is the largest observed in the noble metals. The large drop in the reflectivity is a result of a hybrid plasma resonance, ~ which arises from an interaction between conduction-band electrons and d-band electrons. If interband transitions were not involved, the resonance occurHowat the 5 plasma free-electron valuewould of 9.2eV. calculated ever, the transition associated with the onset of interband structure in both Cu and Au, L 3 (Q+)4’’5 E1(L2’), expected Ag nearweak 4eV.structure Studies’ in of Ag-richisalloys haveinyielded this region; however, efforts to observe this structure in Ag itself have not been fruitful. That this feature may have been resolved in Ag in this study is suggested by the small structure in
~
200
250
300 3.50 energy (cv)
4.00
4.50
5.00
FIG. 3. The derivative of the imaginary part of the dielectric constant, d 2/dE, of Ag at 80°K. The arrow indicates the new structure. Fig. 3, is a result of the interaction of light with surface plasmons. This effect has beenprovides attributed to surface roughness;’6 the roughness the necessary coupling of the transverse photon and the plasmon. For the case of evaporated thick Ag films, the rate of evaporation and the age of the film have been found to affect the magnitude of the surface plasmon excitation. ~
d 2/dE, shown in Fig.3. The small peak in the derivative represents a weak shoulder in 2, and occurspeak at 3.77eV huge in dE at 80°K. Its proximity to the 2/dE, caused by the plasma resonance condition, would make it impossible to find if not for the sensitivity of the wavelength modulation At room temperature this shoulder is technique. barely evident. These results tend to confirm the observation7 that the interband transition in pure Ag is composed of a transition from the upper d-band to the Fermi surface and a transition from the Fermi surface to a higher conduction band. The peak at 3.29eV in d 2/dE,
seen in
In contradiction to of previous experimental 8the results this study show a large findings, ‘ temperature dependence of the surface plasmori. The peak in 2 shifts downward in energy with a decrease from 3.48eV at 300°K 3.29eV inattemperature, 80°K. The magnitude of the peak to increases at 80°K to twice that of the room ternperature contribution. This temperature dependence suggests that surface roughness is not the only factor involved in this phenomenon. The possibility of phonon-assisted excitations should also be considered.
2142
REFLECTIVITY OF THE NOBLE METALS
Vol. 9, No. 23
REFERENCES 1.
CARDONA M., Modulation Spectroscopy, Academic Press, New York, (1969).
2.
FEINLEIB
3.
BRAUNSTEIN R. and WELDOWSKY M., to be published.
4.
RIVORY
5.
EHRENREICH H. and PHILIPP H.R., Phys. Rev. 128, 1622 (1962).
6.
COOPER B.R., EHRENREICH H. and PHILIPP H.R., Phys. Rev. 138, A494 (1965).
7.
MUELLER F.M. and PHILIPS J.C., Phys. Rev. 157, 600 (1967).
8.
FONG C.Y. and COHEN M.L., Phys. Rev. Lett. 24, 306 (1970).
9.
GARFINKEL M., TIEMANN
J., Phys. Rev. Lett.
16, 1200 (1966).
J., Optics Commun. 1, 53
J.J.
(1969).
and ENGELER W.E., Phys. Rev. 148, 695 (1966).
J.
and SHEN Y.R., Phys. Rev. Leti. 25, 1486
10.
FONG C.Y., COHEN M.L., ZUCCA R.R.L., STOKES (1970).
11.
GERHARDT U., BEAGLEHOLE D. and SANDROCK R., Phys. Rev. Lett. 19, 309 (1967).
12.
CHRISTENSEN N.E. and SERAPHIN B.O., Solid State Commun. 8, 1221 (1970).
13.
THEYE M.L., Phys. Rev. B2, 3060 (1970).
14.
MORRIS C.E. and LYNCH D.%V., Phys. Rev.
15.
IRANI G.B., HUEN T. and WOOTEN F., Phys. Rev. 83, 2385 (1971).
16.
STERN E.A., Optical Properties and Electronic Structure of Metals and Alloys, p. ABELES F., North—Holland, Amsterdam, (1966).
17.
DOBBERSTEIN P., HAMPE A. and SAUERBREY G., Phys. Leti.
18.
JASPERSON S.N. and SCHNATTERLY S.E., Phys. Rev.
182, 719 (1969). 396 edited by
27A, 256 (1968).
188, 759 (1969).
Die Interbandübergänge aufgedampfter diinner Schichten der edlen
Metalle Kupfer, Gold und Silber sind in Reflektion beobachtet worden im Energiebereich von 2.0 bis 5.0 eV als Funktion der Ternperatur, wobei Wellenl~ngenrnodulationangewandt wurde. In Kupfer und Gold sind Ergebnisse im imaginären Teil der Dialektrizitätskonstanten erhalten worden, weiche kflrzlich veröffentlichte Bandtheorien bezüglich ihrer Lage in der Brillouinschen Zone unterstützen. In Silber sind schwache Einzelheiten nahe dem Anfang der Interbandabsorption aufgelöst worden. Das Oberflächenplasrnon in Silber ist untersucht worden und hat sich als stark temperaturabh~ngigerwiesen.