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Observation of surface plasmon splitting on Ag(111) by electroreflectance spectroscopy
Volume 70A, number 5, 6
PHYSICS LETTERS
2 April 1979
OBSERVATION OF SURFACE PLASMON SPLITTING ON Ag(1 11) BY ELECTROREFLECTANCE SPECTROSCOPY R. KOTZ and H.J. LEWERENZ Fritz-Haber-Institut der Max-Planck- Gesellschaft, D- 1000 Berlin 33, Germany
and E. KRETSCHM ANN Schaferstr. 18, D-2000 Hamburg 6, Germany Received 18 January 1979
The spectral dependence of electroreflectance near the surface plasma frequency of Ag(111) has been measured for various degrees of surface roughness. The experiments clearly show a splitting of the surface plasma resonance on increasing the roughness of the sample. The results agree well with a recent theory which predicts a splitting of the surface plasmon dispersion relation on a statistically rough surface.
In a recent publication, a splitting of the surface plasma resonance on a statistically slightly rough surface has been proposed [1]. Although there has been experimental evidence for the observation of this splitting [2,3], a detailed investigation has not yet been performed. Since for that purpose it is necessary to produce a well-defined surface roughness of the sample and to apply a modulation technique, metallic electroreflectance (ER) [41in an electrochemical cell appears to be particularly suited. A typical experiment consisted of immersing a 1500 A thick Ag(1 11) film, evaporated in high vacuum on mica [5], in an electrochemical cell. The surface of the originally smooth sample was then roughened by anodic dissolution and subsequent redeposition of several atomic layers of the silver surface by using cyclic voltammetry. This technique permits a simple and accurate determination of the amount of dissolved and redeposited monolayers, which in turn can be regarded as a relative measure of the surface roughness. ER spectra were recorded for the smooth surface and then after each roughening process by applying a potential step of 0.5 V to the electrode. The measurements were performed with light at normal incidence since this suppresses contributions
452
the radiative volume plasma mode in silver [6], which is displaced to higher energies by about only 0.3 eV compared to the surface plasma resonance w~. Details of the experimental technique have recently been described [71. Typical ER spectra are displayed in fig. 1 for a smooth, a slightly rough and a rough surface. Compared to the smooth surface, the slightly rough sample shows a distinct structure originating from the surface plasmon excitation. By further increasing the roughness, a pronounced splitting of the ER minimum at 3.5 eV is observed. The separation in energy of the two minima is about 0.15 eV and the minimum occuring at hw = 3.6 eV appears to be less prominent than the lower energetic one. For comparison of our results with recent theoretical work concerning the dispersion relation of surface plasmons on a rough surface, we first calculate the response function IK/nRj2, where flR(W, K) = 0 defines the dispersion relation of surface plasmons of frequency w and wavevector K. In a reflection experiment, the response function IK/nRI2 is proportional to the additional absorption due to the excitation of surface plasmons and it has recently been shown [11that the response function for from
Volume bA, number 5, 6
PHYSICS LETTERS
2 April 1979
WAVELENGTH/nm 400
350
I
I
Re CA
9
300
o
I
~
15
~
01Ag ‘CcL __________________________________
-4.0
-3.0
-2.0
-tO
J’
~ 100__ 0 z Cd, ~ w 3.0
~.
3.2
~
H
0.0
~1.O
::~
0.002 0 PARAMETER)
PHOTON ENERGY 1eV4.0 36 38
31.
Fig. 2. Spectral dependence of the silver response function2 calculated using theafter optical ref. constants [1] for different after ref. roughness [81. Alsoparameters indicated is a the real part of the dielectric function e.
-2
_________________________ I I I I 3.0 3.4 3.8 4.2 _
PHOTON ENERGY/eV
Fig. 1. Spectral dependence of the ER signal for a smooth (...), a slightly rough and a rough Ag(111) surface; dashed curve: slightly roughened by electrochemically dissolving and redepositing 30 monolayers silver; full curve: 120 monolayers; angle of incidence of the light P~00.
and the rough surface can be regarded as the derivative of the response function. It is therefore possible to compare, by variation of a2, which curve exhibits the best agreement with the experiment. For a2 = 0.01,
high K-vector surface plasmons can be approximated by
i.e. (4)h12/XR 1/20, very good accordance between theory and experiment is obtained as evidenced in fig. 3. Here, the curve labelled experimental is the
1K!2 I_I
difference of the ER signal from the smooth and the
I
2
+H
~(~g
20)— a
JflRI
(SAg — H 2~—2, (SAg + ~H 2O)
(1)
2o)
for the case of silver in contact with water. The sur2. face roughness is characterized byroughness the parameter a Within the simple model that the consists of only one main wavelength XR with a rms height variation (4)112, the parameter a can be written as [1] a
=
( )
2ir — 20
—
2 1/2 (4)1/2
=
2.2 (4>1/2
(2)
R
more roughened sample (full line in fig. 1). As is obvious from fig. 3 all relevant experimental features are well reproduced by the theoretical approach. A finer tuning of the parameter a2 may result in a slightly improved correspondence between the two curves but this seems to us not to be jsutified because of the inherent limitations of the theoretical model. First, it is 80 ~60 40
I I ~2 =0.01
~
0.03
-
-0.02 •0
of the surface roughness structure. andFig. may2 be shows regarded K/nRI2 as ainmeasure the limit ofof thehigh average K-values angle for a smooth and four differently rough surfaces. The theoretical curves were obtained using the frequency dependent optical constants given by Irani et al. [8]. Although the maximum of the response function for a2 = 0 dominates in fig. 2, no structure originating from surface plasmon excitation is expected to show up in the experiment, since the excitation probability is proportional to a2. The difference in the ER signal from the smooth
~
20 0 -20 40 -60
001
~ I~~~~EORY
,~-
-
-0.01 -
-
-0.02
-
80 . - -0.03 3.0 3.2 3.4 3.6 3.8 4.0 PHOTON ENERGY/eV Fig. 3. Comparison of the differentiated response function. for a2 = 0.01 with the difference of the ER signal for the smooth and stronger roughened surface in fig. 1; p
=
00.
453
Volume 70A, number 5, 6
PHYSICS LETTERS
very likely that with our roughening technique a vanety of roughness wavevectors is produced. As a consequence the superposition of the associated response functions may lead to a smearing out of the experimental structure. In addition, there is some uncertainty concerning the optical constants in that spatial region into which the surface plasmon field penetrates for the K-values under consideration (K 10w/c). Nevertheless, the close similarity of the experimental and theoretical results seems to indicate that these restrictions are of minor importance. The authors would like to thank Prof. H. Genischer for his very encouraging support. Two of the authors (R.K. and H.J.L.) thank the Deutsche Forschungsgemeinschaft for financial support.
454
2 April 1979
References [1] E. Kretschmann, T.L. Ferrell and J.C. Ashley, to be published. D.M. Koib and R. Kdtz, Surf. Sd. 64 (1977) 96. [3] M.S. Chung, E.T. Arakawa and T.A. Callcott, to be published.
121
[4] J.D.E. McIntyre, in: Advances in electrochemistry and electrochemical engineering, Vol. 9, ed. R.H. Muller (Wiley—Interscience, New York, 1973) p. 61. [5] H. Laucht, J.K. Sass, H.J. Lewerenz and K.L. Kliewer, Surf. Sci. 62 (1977) 106. [6] J.K. Sass, H. Laucht and K.L. Kliewer, Phys. Rev. Lett. 35 (1975) 1461. [7] D.M. Koib and R. Kötz, Surf. Sci. 64 (1977) 698. [8] G.B. Irani, T. Huen and F. Wooten, J. Opt. Soc. Am. 61 (1971) 128.
PHYSICS LETTERS
2 April 1979
OBSERVATION OF SURFACE PLASMON SPLITTING ON Ag(1 11) BY ELECTROREFLECTANCE SPECTROSCOPY R. KOTZ and H.J. LEWERENZ Fritz-Haber-Institut der Max-Planck- Gesellschaft, D- 1000 Berlin 33, Germany
and E. KRETSCHM ANN Schaferstr. 18, D-2000 Hamburg 6, Germany Received 18 January 1979
The spectral dependence of electroreflectance near the surface plasma frequency of Ag(111) has been measured for various degrees of surface roughness. The experiments clearly show a splitting of the surface plasma resonance on increasing the roughness of the sample. The results agree well with a recent theory which predicts a splitting of the surface plasmon dispersion relation on a statistically rough surface.
In a recent publication, a splitting of the surface plasma resonance on a statistically slightly rough surface has been proposed [1]. Although there has been experimental evidence for the observation of this splitting [2,3], a detailed investigation has not yet been performed. Since for that purpose it is necessary to produce a well-defined surface roughness of the sample and to apply a modulation technique, metallic electroreflectance (ER) [41in an electrochemical cell appears to be particularly suited. A typical experiment consisted of immersing a 1500 A thick Ag(1 11) film, evaporated in high vacuum on mica [5], in an electrochemical cell. The surface of the originally smooth sample was then roughened by anodic dissolution and subsequent redeposition of several atomic layers of the silver surface by using cyclic voltammetry. This technique permits a simple and accurate determination of the amount of dissolved and redeposited monolayers, which in turn can be regarded as a relative measure of the surface roughness. ER spectra were recorded for the smooth surface and then after each roughening process by applying a potential step of 0.5 V to the electrode. The measurements were performed with light at normal incidence since this suppresses contributions
452
the radiative volume plasma mode in silver [6], which is displaced to higher energies by about only 0.3 eV compared to the surface plasma resonance w~. Details of the experimental technique have recently been described [71. Typical ER spectra are displayed in fig. 1 for a smooth, a slightly rough and a rough surface. Compared to the smooth surface, the slightly rough sample shows a distinct structure originating from the surface plasmon excitation. By further increasing the roughness, a pronounced splitting of the ER minimum at 3.5 eV is observed. The separation in energy of the two minima is about 0.15 eV and the minimum occuring at hw = 3.6 eV appears to be less prominent than the lower energetic one. For comparison of our results with recent theoretical work concerning the dispersion relation of surface plasmons on a rough surface, we first calculate the response function IK/nRj2, where flR(W, K) = 0 defines the dispersion relation of surface plasmons of frequency w and wavevector K. In a reflection experiment, the response function IK/nRI2 is proportional to the additional absorption due to the excitation of surface plasmons and it has recently been shown [11that the response function for from
Volume bA, number 5, 6
PHYSICS LETTERS
2 April 1979
WAVELENGTH/nm 400
350
I
I
Re CA
9
300
o
I
~
15
~
01Ag ‘CcL __________________________________
-4.0
-3.0
-2.0
-tO
J’
~ 100__ 0 z Cd, ~ w 3.0
~.
3.2
~
H
0.0
~1.O
::~
0.002 0 PARAMETER)
PHOTON ENERGY 1eV4.0 36 38
31.
Fig. 2. Spectral dependence of the silver response function2 calculated using theafter optical ref. constants [1] for different after ref. roughness [81. Alsoparameters indicated is a the real part of the dielectric function e.
-2
_________________________ I I I I 3.0 3.4 3.8 4.2 _
PHOTON ENERGY/eV
Fig. 1. Spectral dependence of the ER signal for a smooth (...), a slightly rough and a rough Ag(111) surface; dashed curve: slightly roughened by electrochemically dissolving and redepositing 30 monolayers silver; full curve: 120 monolayers; angle of incidence of the light P~00.
and the rough surface can be regarded as the derivative of the response function. It is therefore possible to compare, by variation of a2, which curve exhibits the best agreement with the experiment. For a2 = 0.01,
high K-vector surface plasmons can be approximated by
i.e. (4)h12/XR 1/20, very good accordance between theory and experiment is obtained as evidenced in fig. 3. Here, the curve labelled experimental is the
1K!2 I_I
difference of the ER signal from the smooth and the
I
2
+H
~(~g
20)— a
JflRI
(SAg — H 2~—2, (SAg + ~H 2O)
(1)
2o)
for the case of silver in contact with water. The sur2. face roughness is characterized byroughness the parameter a Within the simple model that the consists of only one main wavelength XR with a rms height variation (4)112, the parameter a can be written as [1] a
=
( )
2ir — 20
—
2 1/2 (4)1/2
=
2.2 (4>1/2
(2)
R
more roughened sample (full line in fig. 1). As is obvious from fig. 3 all relevant experimental features are well reproduced by the theoretical approach. A finer tuning of the parameter a2 may result in a slightly improved correspondence between the two curves but this seems to us not to be jsutified because of the inherent limitations of the theoretical model. First, it is 80 ~60 40
I I ~2 =0.01
~
0.03
-
-0.02 •0
of the surface roughness structure. andFig. may2 be shows regarded K/nRI2 as ainmeasure the limit ofof thehigh average K-values angle for a smooth and four differently rough surfaces. The theoretical curves were obtained using the frequency dependent optical constants given by Irani et al. [8]. Although the maximum of the response function for a2 = 0 dominates in fig. 2, no structure originating from surface plasmon excitation is expected to show up in the experiment, since the excitation probability is proportional to a2. The difference in the ER signal from the smooth
~
20 0 -20 40 -60
001
~ I~~~~EORY
,~-
-
-0.01 -
-
-0.02
-
80 . - -0.03 3.0 3.2 3.4 3.6 3.8 4.0 PHOTON ENERGY/eV Fig. 3. Comparison of the differentiated response function. for a2 = 0.01 with the difference of the ER signal for the smooth and stronger roughened surface in fig. 1; p
=
00.
453
Volume 70A, number 5, 6
PHYSICS LETTERS
very likely that with our roughening technique a vanety of roughness wavevectors is produced. As a consequence the superposition of the associated response functions may lead to a smearing out of the experimental structure. In addition, there is some uncertainty concerning the optical constants in that spatial region into which the surface plasmon field penetrates for the K-values under consideration (K 10w/c). Nevertheless, the close similarity of the experimental and theoretical results seems to indicate that these restrictions are of minor importance. The authors would like to thank Prof. H. Genischer for his very encouraging support. Two of the authors (R.K. and H.J.L.) thank the Deutsche Forschungsgemeinschaft for financial support.
454
2 April 1979
References [1] E. Kretschmann, T.L. Ferrell and J.C. Ashley, to be published. D.M. Koib and R. Kdtz, Surf. Sd. 64 (1977) 96. [3] M.S. Chung, E.T. Arakawa and T.A. Callcott, to be published.
121
[4] J.D.E. McIntyre, in: Advances in electrochemistry and electrochemical engineering, Vol. 9, ed. R.H. Muller (Wiley—Interscience, New York, 1973) p. 61. [5] H. Laucht, J.K. Sass, H.J. Lewerenz and K.L. Kliewer, Surf. Sci. 62 (1977) 106. [6] J.K. Sass, H. Laucht and K.L. Kliewer, Phys. Rev. Lett. 35 (1975) 1461. [7] D.M. Koib and R. Kötz, Surf. Sci. 64 (1977) 698. [8] G.B. Irani, T. Huen and F. Wooten, J. Opt. Soc. Am. 61 (1971) 128.