- Email: [email protected]
Long-range surface modes supported by SiO2–Ag composite thin films
Surface Science 395 (1998) 23–29
Long-range surface modes supported by SiO –Ag composite thin 2 films T. Kume a, T. Kitagawa a, S. Hayashi a,b,*, K. Yamamoto a,b a Division of Science of Materials, The Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657, Japan b Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai, Nada, Kobe 657, Japan Received 6 July 1996; accepted for publication 2 July 1997
Abstract Using a novel attenuated total reflection (ATR) method, long-range surface modes (LRSMs) supported by SiO –Ag composite 2 films were studied systematically by varying the thicknesses of the SiO –Ag composite layer (d ) and coupling-gap layer (h). Systematic 2 changes in the ATR spectra depending on d and h were observed successfully. The observed d and h dependences were in good qualitative agreement with electromagnetic calculations based on the theory of multiple reflections. © 1998 Elsevier Science B.V. Keywords: Polaritons; Reflection spectroscopy; Sputter deposition; Surface waves
1. Introduction An electromagnetic surface mode is a wave which propagates along an interface between two media with an amplitude decaying exponentially away from the interface. A well-known example of such a surface mode is the surface plasmon polariton (SPP) mode supported by a metal–dielectric interface [1,2]. In order for the SPP mode to exist, the real part of the dielectric constant of the metal should be negative and the imaginary part should be small, which is fulfilled for noble metals such as Ag and Au in the UV–visible region. Previously, several authors have reported that in a symmetric three-layer system (dielectric/metal thin film/dielectric), the SPPs on the two identical interfaces couple each other, and * Corresponding author. Fax (+81) 78 8031064; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 0 3 9- 6 0 2 8 ( 9 7 ) 0 0 59 4 - 3
then two types of SPPs (i.e. a long-range mode (LRSPP) and a short-range mode (SRSPP)) can exist [3–5]. The propagation length of the LRSPP was found to be 10–100 times as long as those of the SRSPP and the normal SPP. In recent years, it has been reported that in a symmetric system consisting of a dielectric layer, a very thin active layer and a dielectric layer, the long-range surface mode (LRSM ) can exist even if the dielectric constant of the active layer has a positive real part and/or a large imaginary part [6–12]. Experimental verification of the LRSM by attenuated total reflection (ATR) measurements has been reported for symmetric systems containing thin layers of Cr [6 ], V [7], Pd [8], Si [9] and phthalocyanine [10]. Even in the cases of metallic island films, the existence of the LRSM has been demonstrated by Yang et al. [13] and Wu et al. [14]. In this paper we are concerned with the LRSM
24
T. Kume et al. / Surface Science 395 (1998) 23–29
supported by granular metallic thin films. As the active layers, we use SiO –Ag composite films, 2 which consist of Ag nanoparticles embedded in SiO matrices. Although the existence of the 2 LRSM on island films prepared by thermal evaporation has already been demonstrated by Yang et al. [13] and Wu et al. [14], the island films are not very well suited to a systematic study of the LRSM with varying thickness because the optical properties (or effective dielectric constants) of the island films change drastically depending on the thickness, in particular in the thickness range smaller than ~20 nm [15]. As far as we are aware, there has been no systematic experimental study of the LRSM on granular metal films varying only the thickness and not varying the properties of the film (particle size and shape). One of the purposes of this paper is to realize such an experiment using a SiO –Ag composite film as the active layer. 2 Another purpose of this paper is to propose a new ATR configuration (Fig. 1), which uses a solid film as a coupling-gap material instead of the fluid commonly used until now. The solid gap is deposited not on the prism but on the active layer. This configuration has the following advantages: (i) the solid coupling gap (amorphous SiO film deposited 2 by RF sputtering) allows us to control the gap thickness very easily without a special device to
Fig. 1. ATR geometry to excite the long-range surface modes supported by the SiO –Ag composite film. The refractive index 2 of the fluid is matched to that of the prism, and the upper SiO layer acts as a coupling gap. 2
maintain the gap, and (ii) the gap layer deposited on the active layer (not on the prism) realizes a sample which is removable from the prism, permitting us to perform various other measurements. We report results of ATR measurements performed by varying systematically the thicknesses of both the SiO –Ag active layer and the SiO gap. 2 2 We could observe sharp dips in the angle-scan ATR spectra, demonstrating that SiO –Ag com2 posite films can support the LRSM. Both the propagation length (related to the width of the ATR dip) and the excitation efficiency (related to the depth of the ATR dip) were found to depend strongly on the thicknesses of the active layer and the gap. Experimental ATR spectra could be reproduced fairly well by electromagnetic calculations based on the theory of multiple reflection in a multilayer system.
2. Experimental An ATR configuration for observing the LRSM was set up as shown in Fig. 1. A composite film (SiO and Ag) was first deposited onto a fused 2 quartz (amorphous SiO ) substrate by an RF 2 co-sputtering technique. A SiO target and small 2 pieces of Ag (2.5 mm×15 mm×2 mm) were sputtered simultaneously. The sputtering was performed in Ar gas at 2×10−2 Torr at an RF power of 50 W with a magnetron sputtering apparatus (Anelva SPF-210H ). From our previous TEM observation of the composite film [16 ], it is known that isolated Ag spherical particles of ~4 nm in diameter are dispersed in the SiO matrix. The 2 filling factor of Ag (the volume ratio of Ag to the total volume of the film) was estimated to be 0.05 [17,18]. Secondly, a gap layer of amorphous SiO was deposited onto the SiO –Ag composite 2 2 film by sputtering only the SiO target under the 2 same conditions as outlined above. The sputtered SiO gap layer and the SiO substrate act as the 2 2 surrounding media and realize a symmetric layered system. The thicknesses of the SiO –Ag and the 2 gap SiO layers, hereafter denoted as d and h, 2 respectively, were measured by a quartz microbalance calibrated by an optical-interference thickness meter.
T. Kume et al. / Surface Science 395 (1998) 23–29
To perform ATR measurements, the sample on the substrate was contacted optically to a face of a 60° high-index prism (SF10) using index matching fluid. As the fluid we chose diiodemethane (CH I ), the refractive index (n ) of which is almost 22 f the same as that of the prism (n =1.723) for the p wavelength of the laser light (l=632.8 nm) from a He–Ne laser used as the incident light. Good index matching was confirmed experimentally by observing that there is practically no reflection of the laser beam at the prism–fluid interface when the prism is contacted with the fluid kept in a small beaker. In the present ATR geometry, we can thus regard the fluid as a part of the prism, and consequently the sputtered SiO film provides 2 a well-defined gap. To measure the reflectivity as a function of the incident angle h (ATR spectrum), the prism–sample system was mounted on a rotating table driven by a stepping motor. The intensity of the reflected light was measured by a Si photodiode and a lock-in amplifier (NF LI-570). The polarization of the incident light was set to the por s-polarization using a l/2 plate. The ATR data were obtained by dividing the reflected light intensity by a reference signal, i.e. the intensity of light reflected from a bare part of the substrate, which was obtained for an incidence angle of 60°.
3. Results and discussion In Fig. 2a and b we show the d-dependences of the ATR spectra obtained for p- and s-polarized incident light, respectively. We varied the thickness of the SiO –Ag layer (d ) from 13 to 47 nm, fixing 2 the thickness of the coupling layer (h) at 1.83 mm. The critical angle of total reflection h in this c system was 57.81°. In all the spectra in Fig. 2, there are two dips in the reflectivity, located below and above h . The broad dips located below h c c correspond to the excitation of leaky guided modes in the SiO coupling layer. The sharp dips observed 2 above h are caused by the excitation of LRSM, c which propagates along the SiO –Ag composite 2 layer. It should be noted that the dips are observed for both the p- and s-polarizations. This demonstrates that not only transverse magnetic ( TM ) LRSMs exist in our system, but also transverse
25
Fig. 2. ATR spectra obtained by varying the thickness of the composite film (d) and fixing the gap-layer thickness (h) at 1.83 mm. (a) p- and (b) s-polarized incidences.
electric ( TE ) LRSMs. According to Takabayashi et al. [11], both the TM- and TE-LRSMs exist if the real part of the dielectric constant of the active thin layer (Re(e )) is larger than that of the a surrounding medium (Re(e )), and in addition, s Re(e )−Im(e )>Re(e ) is satisfied. In the present a a s sample, the above conditions are thought to be satisfied. These results demonstrate that the shape and position of the dip corresponding to the LRSM are highly sensitive to the thickness of the composite layer d for both the p- and s-polarizations. As d decreases, the dip becomes drastically sharper and shifts toward h . It is well known that a c sharper dip implies that the electromagnetic mode propagates over a longer distance [19]. Even for the broadest ATR dip obtained here, the width is less than about 0.25°, which is smaller than the typical values of the width commonly observed for the SPP on a Ag–air interface [1]. For the thinnest thickness (d=13 nm) and p-polarization (solid line
26
T. Kume et al. / Surface Science 395 (1998) 23–29
in Fig. 2a), the full width at half minimum (FWHM ) of the dip was 0.082°, which corresponds to the propagation length of ~77 mm. In Fig. 3a and b, we show the dependence of the ATR spectrum on the thickness of the gap layer obtained for p- and s-polarized incident light, respectively. The thickness of the SiO –Ag layer 2 (d) was fixed at 34 nm while the thickness of the gap layer (h) was varied from 0.65 to 2.65 mm. For both the p- and s-polarizations, the position of the sharp dip shifts monotonously to lower angles as h decreases. On the other hand, the width of the dip first increases and then decreases with decreasing h. The dip is broadest at h=0.90 mm. The behavior of the dip position and width indicates that the propagation characteristics of the LRSM are very sensitive to the gap-layer thickness. It is known that a broader ATR dip corresponds to a larger loss, i.e. a larger damping of the surface mode. From Fig. 3, the loss of the LRSM is seen to depend strongly on the gap thickness. According
to previous ATR studies on the SPP using the Otto geometry [2], the increase in the width with decreasing gap thickness was explained in terms of the increase in radiative loss through the prism. In the present ATR results, however, the loss first increases and then decreases as the gap becomes thinner. This behavior of the loss has been predicted theoretically by Yang et al. [12]. They explained the loss behavior as follows. The decrease in the distance between the prism coupler and the active layer leads to an increase in the radiative loss through the prism. At the same time, the presence of the prism perturbs the field distribution of the LRSM, and tends to push the electromagnetic fields into the substrate, leading to a reduction in the radiative loss. Therefore, the total radiative loss is determined by a competition between the increase caused by the approach of the prism and the decrease caused by the change in the field distribution. The former is dominant for sufficiently thick gaps, and the latter for sufficiently thin gaps. From the present ATR spectra, a gap of 0.65 mm is small enough to perturb the field distribution of LRSM. We attempted to reproduce theoretically the ATR spectra by calculating the reflectivity of a multilayer system based on Fresnel coefficients. We considered a four-layer system consisting of a prism with a dielectric constant e , a SiO layer p 2 with e , and a SiO –Ag composite layer with e 1 2 2 and a SiO substrate with e . In the actual calcula2 3 tions, the values of the dielectric constants at the excitation wavelength l=632.8 nm were necessary. We used the values described below. The SiO –Ag composite layer is a system of Ag nano2 particles ~4 nm in diameter dispersed in a SiO 2 matrix. Its dielectric constant e was computed 2 using the Maxwell-Garnett formula [20]:
C
D
e −e in m 1+3f , e =e 2 m e (1−f )+e (2+f ) in m
Fig. 3. ATR spectra obtained by varying the coupling-gap thickness (h) and fixing the thickness of the composite film (d) at 34 nm. (a) p- and (b) s-polarized incidences.
where e is the dielectric function of SiO , e is m 2 in that of Ag particles, and f is the filling factor (volume fraction of the particles). The dielectric constant of Ag nanoparticles was obtained from the bulk value [21] by taking into account the reduction of the mean free path of free electrons
T. Kume et al. / Surface Science 395 (1998) 23–29
due to scattering at particle surfaces [22]. The filling factor f was set at 0.05, which is a value estimated previously [17,18]. The literature value for a-SiO [23] (i.e. 2.12) was used for e . The 2 m value finally obtained for the composite layer is e =2.624+i0.096. The dielectric constants of the 2 prism (SF10) and the SiO substrate were taken 2 as e =2.969 and e =2.12 [23], respectively. The p 3 dielectric constant of the gap layer (e ) was set at 1 2.14, which differs slightly from the value of e . 3 The reason why e was set to 2.14 will be discussed 1 below. For the thicknesses of the layers, experimental values were used. If we assumed e =e =2.12, the calculated ATR 1 3 dips corresponding to LRSM excitation were much sharper and located at lower angles than the experimental dips. Disagreement between the calculated and experimental spectra was found even for the dips of the leaky guided modes, which are quite sensitive to the value of e . Therefore, we adjusted 1 the value of e to match the calculated dip positions 1 of the leaky guided modes to the experimental dip positions. This process yielded e =2.14, which is 1 slightly larger than e . The calculated spectra setting 3 e =2.14 were in satisfactory agreement with the 1 experimental spectra not only for the dips of the leaky guided modes, but also for the LRSM dips. Although the difference between e and e is only 1 3 0.02, the calculated LRSM dips were very different from those for the symmetric case (e =e =2.12). 1 3 The drastic change in the LRSM characteristics depending on the dielectric constants of the surrounding media was also reported by Brown et al. [6 ]. The reason why e is larger than e can be 3 1 explained as follows. In the experiments (see Fig. 1), the substrate used was a fused quartz plate, which is stoichiometric a-SiO , while the spacer layer used 2 was sputtered SiO film, which is known to be 2 slightly oxygen-deficient (or Si-rich). The slightly Si-rich nature of the sputtered SiO film is thought 2 to result in the larger value of e . 1 In Fig. 4a and b the d dependences of the ATR spectrum calculated for p and s polarizations are shown, respectively. In Fig. 5a and b, the calculated h dependences are shown. From a comparison of the experimental and calculated ATR spectra, we find that the calculated spectra reproduce fairly well, at least qualitatively, the experimental spectra. However, from a close comparison
27
Fig. 4. Calculated ATR spectra corresponding to the experimental spectra shown in Fig. 2 (varying d and fixing h).
between the experimental and calculated results, we can see that the experimental dips are generally broader and shallower than the corresponding calculated dips. One of the reasons for the broader experimental dips is as follows. From previous ATR studies of the SPP of rough metal surfaces [1], it is known that an excited SPP is scattered by the roughness into other SPP modes or radiates electromagnetic energy into the air side. Because of the increase in the decay channels, the propagation length of the SPP is reduced, and consequently the ATR dip is broadened. Similar phenomena are expected to occur for the present LRSM. The LRSM propagating in the present composite film is thought to be scattered and to emit light due to inhomogeneities arising from the inclusion of Ag nanoparticles in a-SiO . Actually, we could observe the light 2 emitted from the samples with the naked eye. This scattering process of the LRSM may lead to the broadening of the ATR dips. In the calculation, however, the scattering process is not taken into
28
T. Kume et al. / Surface Science 395 (1998) 23–29
Fig. 5. Calculated ATR spectra corresponding to the experimental spectra shown in Fig. 3 (varying h and fixing d ).
account. Another source of the discrepancies between experiments and calculations seems to be the differences in the values of the dielectric constants used in the calculations as compared to their real values. In particular, the dielectric constant of the SiO –Ag composite layer (e ) estimated by the 2 2 Maxwell-Garnett formula may contain an error which arises from deviations of the parameters used (the filling factor of Ag and the dielectric constants of Ag particles and SiO ) from the real 2 values. Even if the error of e is very small, 2 discrepancies between calculated and experimental spectra are observable because the LRSM is highly sensitive to the dielectric constant of the active layer. Further theoretical studies are necessary to achieve a quantitative agreement between the experimental and calculated ATR spectra.
4. Conclusion By successively depositing SiO –Ag and SiO 2 2 layers on a fused quartz substrate, we prepared a
symmetric system (SiO /SiO –Ag/SiO ) and inves2 2 2 tigated the LRSM supported by the SiO –Ag com2 posite film using a novel ATR method. The ATR spectra were measured by systematically varying the thicknesses of the composite layer d and coupling-gap layer h. For both p- and s-polarized incident light, sharp ATR dips were clearly observed. The present ATR results clearly demonstrate the changes in the LRSM propagation characteristics depending on d and h. A thinner composite film gave a longer propagation length, and at d=13 nm the estimated propagation length was 77 mm. From the h dependence of the LRSM, at h=0.93 mm the LRSM was found to be considerably modulated by the presence of the prism. The experimental d and h dependences of the LRSM could be reproduced fairly well by a theoretical calculation based on the theory of multiple reflections, although further theoretical studies are necessary to achieve quantitative agreement between experimental and theoretical ATR spectra. The success in the excitation of LRSMs supported by the SiO –Ag composite layer demon2 strated in this paper may suggest the possibility of new kind of surface-enhanced optical experiments. For example, second-harmonic generation by Ag nanoparticles enhanced by excitation of the LRSMs seems to be a promising experiment.
Acknowledgements This work was partially supported by a Grantin-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
References [1] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer, Berlin, 1988. [2] A. Otto, Z. Phys. 216 (1968) 398. [3] D. Salid, Phys. Rev. Lett. 26 (1981) 1927. [4] Y. Kuwamura, M. Fukui, O. Yada, J. Phys. Soc. Jpn. 52 (1983) 2350. [5] H. Dohi, Y. Kuwamura, M. Fukui, O. Yada, J. Phys. Soc. Jpn. 53 (1984) 2828. [6 ] G.P. Bryan-Brown, F. Yang, G.W. Bradberry, J.R. Sambles, J. Opt. Soc. Am. B 8 (1991) 765.
T. Kume et al. / Surface Science 395 (1998) 23–29 [7] F. Yang, J.R. Sambles, G.W. Bradberry, Phys. Rev. Lett. 64 (1990) 559. [8] F. Yang, J.R. Sambles, G.W. Bradberry, Phys. Rev. B 44 (1991) 5855. [9] M. Takabayashi, M. Haraguchi, M. Fukui, J. Opt. Soc. Am. B 12 (1995) 2406. [10] R.J. Crook, F. Yang, J.R. Sambles, J. Mod. Opt. 40 (1993) 243. [11] M. Takabayashi, H. Shiba, M. Hamaguchi, M. Fukui, J. Phys. Soc. Jpn. 62 (1993) 2719. [12] F. Yang, J.R. Sambles, G.W. Bradberry, J. Mod. Opt. 38 (1991) 707. [13] F. Yang, G.W. Bradberry, J.R. Sambles, Phys. Rev. Lett. 66 (1991) 2030. [14] Z.C. Wu, E.T. Arakawa, T. Inagaki, T. Thundat, L.J. Schowalter, Phys. Rev. B 49 (1994) 7782.
29
[15] M. Fukui, K. Oda, Appl. Surf. Sci. 33/34 (1988) 882. [16 ] M. Fujii, T. Nagareda, S. Hayashi, K. Yamamoto, Phys. Rev. B 44 (1991) 6243. [17] T. Kume, N. Nakagawa, S. Hayashi, K. Yamanoto, Superlatt. Microstruct. 15 (1994) 459. [18] T. Kume, N. Nakagawa, S. Hayashi, K. Yamanoto, Solid State Commun. 93 (1995) 171. [19] R. Bruns, H. Raether, Z. Phys. 237 (1970) 98. [20] J.C. Maxwell-Garnett, Philos. Trans. R. Soc. London A 203 (1904) 358; 205 (1906) 237. [21] D.W. Lynch, W.R. Hunter, in: E.D. Palik ( Ed.), Handbook of Optical Constants of Solids, Academic Press, Orlando, FL, 1985, p. 350. [22] U. Kreibig, C.V. Fragstein, Z. Phys. 224 (1969) 307. [23] H.R. Philipp, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, Orlando, FL, 1985, p. 749.
Long-range surface modes supported by SiO –Ag composite thin 2 films T. Kume a, T. Kitagawa a, S. Hayashi a,b,*, K. Yamamoto a,b a Division of Science of Materials, The Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657, Japan b Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai, Nada, Kobe 657, Japan Received 6 July 1996; accepted for publication 2 July 1997
Abstract Using a novel attenuated total reflection (ATR) method, long-range surface modes (LRSMs) supported by SiO –Ag composite 2 films were studied systematically by varying the thicknesses of the SiO –Ag composite layer (d ) and coupling-gap layer (h). Systematic 2 changes in the ATR spectra depending on d and h were observed successfully. The observed d and h dependences were in good qualitative agreement with electromagnetic calculations based on the theory of multiple reflections. © 1998 Elsevier Science B.V. Keywords: Polaritons; Reflection spectroscopy; Sputter deposition; Surface waves
1. Introduction An electromagnetic surface mode is a wave which propagates along an interface between two media with an amplitude decaying exponentially away from the interface. A well-known example of such a surface mode is the surface plasmon polariton (SPP) mode supported by a metal–dielectric interface [1,2]. In order for the SPP mode to exist, the real part of the dielectric constant of the metal should be negative and the imaginary part should be small, which is fulfilled for noble metals such as Ag and Au in the UV–visible region. Previously, several authors have reported that in a symmetric three-layer system (dielectric/metal thin film/dielectric), the SPPs on the two identical interfaces couple each other, and * Corresponding author. Fax (+81) 78 8031064; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 0 3 9- 6 0 2 8 ( 9 7 ) 0 0 59 4 - 3
then two types of SPPs (i.e. a long-range mode (LRSPP) and a short-range mode (SRSPP)) can exist [3–5]. The propagation length of the LRSPP was found to be 10–100 times as long as those of the SRSPP and the normal SPP. In recent years, it has been reported that in a symmetric system consisting of a dielectric layer, a very thin active layer and a dielectric layer, the long-range surface mode (LRSM ) can exist even if the dielectric constant of the active layer has a positive real part and/or a large imaginary part [6–12]. Experimental verification of the LRSM by attenuated total reflection (ATR) measurements has been reported for symmetric systems containing thin layers of Cr [6 ], V [7], Pd [8], Si [9] and phthalocyanine [10]. Even in the cases of metallic island films, the existence of the LRSM has been demonstrated by Yang et al. [13] and Wu et al. [14]. In this paper we are concerned with the LRSM
24
T. Kume et al. / Surface Science 395 (1998) 23–29
supported by granular metallic thin films. As the active layers, we use SiO –Ag composite films, 2 which consist of Ag nanoparticles embedded in SiO matrices. Although the existence of the 2 LRSM on island films prepared by thermal evaporation has already been demonstrated by Yang et al. [13] and Wu et al. [14], the island films are not very well suited to a systematic study of the LRSM with varying thickness because the optical properties (or effective dielectric constants) of the island films change drastically depending on the thickness, in particular in the thickness range smaller than ~20 nm [15]. As far as we are aware, there has been no systematic experimental study of the LRSM on granular metal films varying only the thickness and not varying the properties of the film (particle size and shape). One of the purposes of this paper is to realize such an experiment using a SiO –Ag composite film as the active layer. 2 Another purpose of this paper is to propose a new ATR configuration (Fig. 1), which uses a solid film as a coupling-gap material instead of the fluid commonly used until now. The solid gap is deposited not on the prism but on the active layer. This configuration has the following advantages: (i) the solid coupling gap (amorphous SiO film deposited 2 by RF sputtering) allows us to control the gap thickness very easily without a special device to
Fig. 1. ATR geometry to excite the long-range surface modes supported by the SiO –Ag composite film. The refractive index 2 of the fluid is matched to that of the prism, and the upper SiO layer acts as a coupling gap. 2
maintain the gap, and (ii) the gap layer deposited on the active layer (not on the prism) realizes a sample which is removable from the prism, permitting us to perform various other measurements. We report results of ATR measurements performed by varying systematically the thicknesses of both the SiO –Ag active layer and the SiO gap. 2 2 We could observe sharp dips in the angle-scan ATR spectra, demonstrating that SiO –Ag com2 posite films can support the LRSM. Both the propagation length (related to the width of the ATR dip) and the excitation efficiency (related to the depth of the ATR dip) were found to depend strongly on the thicknesses of the active layer and the gap. Experimental ATR spectra could be reproduced fairly well by electromagnetic calculations based on the theory of multiple reflection in a multilayer system.
2. Experimental An ATR configuration for observing the LRSM was set up as shown in Fig. 1. A composite film (SiO and Ag) was first deposited onto a fused 2 quartz (amorphous SiO ) substrate by an RF 2 co-sputtering technique. A SiO target and small 2 pieces of Ag (2.5 mm×15 mm×2 mm) were sputtered simultaneously. The sputtering was performed in Ar gas at 2×10−2 Torr at an RF power of 50 W with a magnetron sputtering apparatus (Anelva SPF-210H ). From our previous TEM observation of the composite film [16 ], it is known that isolated Ag spherical particles of ~4 nm in diameter are dispersed in the SiO matrix. The 2 filling factor of Ag (the volume ratio of Ag to the total volume of the film) was estimated to be 0.05 [17,18]. Secondly, a gap layer of amorphous SiO was deposited onto the SiO –Ag composite 2 2 film by sputtering only the SiO target under the 2 same conditions as outlined above. The sputtered SiO gap layer and the SiO substrate act as the 2 2 surrounding media and realize a symmetric layered system. The thicknesses of the SiO –Ag and the 2 gap SiO layers, hereafter denoted as d and h, 2 respectively, were measured by a quartz microbalance calibrated by an optical-interference thickness meter.
T. Kume et al. / Surface Science 395 (1998) 23–29
To perform ATR measurements, the sample on the substrate was contacted optically to a face of a 60° high-index prism (SF10) using index matching fluid. As the fluid we chose diiodemethane (CH I ), the refractive index (n ) of which is almost 22 f the same as that of the prism (n =1.723) for the p wavelength of the laser light (l=632.8 nm) from a He–Ne laser used as the incident light. Good index matching was confirmed experimentally by observing that there is practically no reflection of the laser beam at the prism–fluid interface when the prism is contacted with the fluid kept in a small beaker. In the present ATR geometry, we can thus regard the fluid as a part of the prism, and consequently the sputtered SiO film provides 2 a well-defined gap. To measure the reflectivity as a function of the incident angle h (ATR spectrum), the prism–sample system was mounted on a rotating table driven by a stepping motor. The intensity of the reflected light was measured by a Si photodiode and a lock-in amplifier (NF LI-570). The polarization of the incident light was set to the por s-polarization using a l/2 plate. The ATR data were obtained by dividing the reflected light intensity by a reference signal, i.e. the intensity of light reflected from a bare part of the substrate, which was obtained for an incidence angle of 60°.
3. Results and discussion In Fig. 2a and b we show the d-dependences of the ATR spectra obtained for p- and s-polarized incident light, respectively. We varied the thickness of the SiO –Ag layer (d ) from 13 to 47 nm, fixing 2 the thickness of the coupling layer (h) at 1.83 mm. The critical angle of total reflection h in this c system was 57.81°. In all the spectra in Fig. 2, there are two dips in the reflectivity, located below and above h . The broad dips located below h c c correspond to the excitation of leaky guided modes in the SiO coupling layer. The sharp dips observed 2 above h are caused by the excitation of LRSM, c which propagates along the SiO –Ag composite 2 layer. It should be noted that the dips are observed for both the p- and s-polarizations. This demonstrates that not only transverse magnetic ( TM ) LRSMs exist in our system, but also transverse
25
Fig. 2. ATR spectra obtained by varying the thickness of the composite film (d) and fixing the gap-layer thickness (h) at 1.83 mm. (a) p- and (b) s-polarized incidences.
electric ( TE ) LRSMs. According to Takabayashi et al. [11], both the TM- and TE-LRSMs exist if the real part of the dielectric constant of the active thin layer (Re(e )) is larger than that of the a surrounding medium (Re(e )), and in addition, s Re(e )−Im(e )>Re(e ) is satisfied. In the present a a s sample, the above conditions are thought to be satisfied. These results demonstrate that the shape and position of the dip corresponding to the LRSM are highly sensitive to the thickness of the composite layer d for both the p- and s-polarizations. As d decreases, the dip becomes drastically sharper and shifts toward h . It is well known that a c sharper dip implies that the electromagnetic mode propagates over a longer distance [19]. Even for the broadest ATR dip obtained here, the width is less than about 0.25°, which is smaller than the typical values of the width commonly observed for the SPP on a Ag–air interface [1]. For the thinnest thickness (d=13 nm) and p-polarization (solid line
26
T. Kume et al. / Surface Science 395 (1998) 23–29
in Fig. 2a), the full width at half minimum (FWHM ) of the dip was 0.082°, which corresponds to the propagation length of ~77 mm. In Fig. 3a and b, we show the dependence of the ATR spectrum on the thickness of the gap layer obtained for p- and s-polarized incident light, respectively. The thickness of the SiO –Ag layer 2 (d) was fixed at 34 nm while the thickness of the gap layer (h) was varied from 0.65 to 2.65 mm. For both the p- and s-polarizations, the position of the sharp dip shifts monotonously to lower angles as h decreases. On the other hand, the width of the dip first increases and then decreases with decreasing h. The dip is broadest at h=0.90 mm. The behavior of the dip position and width indicates that the propagation characteristics of the LRSM are very sensitive to the gap-layer thickness. It is known that a broader ATR dip corresponds to a larger loss, i.e. a larger damping of the surface mode. From Fig. 3, the loss of the LRSM is seen to depend strongly on the gap thickness. According
to previous ATR studies on the SPP using the Otto geometry [2], the increase in the width with decreasing gap thickness was explained in terms of the increase in radiative loss through the prism. In the present ATR results, however, the loss first increases and then decreases as the gap becomes thinner. This behavior of the loss has been predicted theoretically by Yang et al. [12]. They explained the loss behavior as follows. The decrease in the distance between the prism coupler and the active layer leads to an increase in the radiative loss through the prism. At the same time, the presence of the prism perturbs the field distribution of the LRSM, and tends to push the electromagnetic fields into the substrate, leading to a reduction in the radiative loss. Therefore, the total radiative loss is determined by a competition between the increase caused by the approach of the prism and the decrease caused by the change in the field distribution. The former is dominant for sufficiently thick gaps, and the latter for sufficiently thin gaps. From the present ATR spectra, a gap of 0.65 mm is small enough to perturb the field distribution of LRSM. We attempted to reproduce theoretically the ATR spectra by calculating the reflectivity of a multilayer system based on Fresnel coefficients. We considered a four-layer system consisting of a prism with a dielectric constant e , a SiO layer p 2 with e , and a SiO –Ag composite layer with e 1 2 2 and a SiO substrate with e . In the actual calcula2 3 tions, the values of the dielectric constants at the excitation wavelength l=632.8 nm were necessary. We used the values described below. The SiO –Ag composite layer is a system of Ag nano2 particles ~4 nm in diameter dispersed in a SiO 2 matrix. Its dielectric constant e was computed 2 using the Maxwell-Garnett formula [20]:
C
D
e −e in m 1+3f , e =e 2 m e (1−f )+e (2+f ) in m
Fig. 3. ATR spectra obtained by varying the coupling-gap thickness (h) and fixing the thickness of the composite film (d) at 34 nm. (a) p- and (b) s-polarized incidences.
where e is the dielectric function of SiO , e is m 2 in that of Ag particles, and f is the filling factor (volume fraction of the particles). The dielectric constant of Ag nanoparticles was obtained from the bulk value [21] by taking into account the reduction of the mean free path of free electrons
T. Kume et al. / Surface Science 395 (1998) 23–29
due to scattering at particle surfaces [22]. The filling factor f was set at 0.05, which is a value estimated previously [17,18]. The literature value for a-SiO [23] (i.e. 2.12) was used for e . The 2 m value finally obtained for the composite layer is e =2.624+i0.096. The dielectric constants of the 2 prism (SF10) and the SiO substrate were taken 2 as e =2.969 and e =2.12 [23], respectively. The p 3 dielectric constant of the gap layer (e ) was set at 1 2.14, which differs slightly from the value of e . 3 The reason why e was set to 2.14 will be discussed 1 below. For the thicknesses of the layers, experimental values were used. If we assumed e =e =2.12, the calculated ATR 1 3 dips corresponding to LRSM excitation were much sharper and located at lower angles than the experimental dips. Disagreement between the calculated and experimental spectra was found even for the dips of the leaky guided modes, which are quite sensitive to the value of e . Therefore, we adjusted 1 the value of e to match the calculated dip positions 1 of the leaky guided modes to the experimental dip positions. This process yielded e =2.14, which is 1 slightly larger than e . The calculated spectra setting 3 e =2.14 were in satisfactory agreement with the 1 experimental spectra not only for the dips of the leaky guided modes, but also for the LRSM dips. Although the difference between e and e is only 1 3 0.02, the calculated LRSM dips were very different from those for the symmetric case (e =e =2.12). 1 3 The drastic change in the LRSM characteristics depending on the dielectric constants of the surrounding media was also reported by Brown et al. [6 ]. The reason why e is larger than e can be 3 1 explained as follows. In the experiments (see Fig. 1), the substrate used was a fused quartz plate, which is stoichiometric a-SiO , while the spacer layer used 2 was sputtered SiO film, which is known to be 2 slightly oxygen-deficient (or Si-rich). The slightly Si-rich nature of the sputtered SiO film is thought 2 to result in the larger value of e . 1 In Fig. 4a and b the d dependences of the ATR spectrum calculated for p and s polarizations are shown, respectively. In Fig. 5a and b, the calculated h dependences are shown. From a comparison of the experimental and calculated ATR spectra, we find that the calculated spectra reproduce fairly well, at least qualitatively, the experimental spectra. However, from a close comparison
27
Fig. 4. Calculated ATR spectra corresponding to the experimental spectra shown in Fig. 2 (varying d and fixing h).
between the experimental and calculated results, we can see that the experimental dips are generally broader and shallower than the corresponding calculated dips. One of the reasons for the broader experimental dips is as follows. From previous ATR studies of the SPP of rough metal surfaces [1], it is known that an excited SPP is scattered by the roughness into other SPP modes or radiates electromagnetic energy into the air side. Because of the increase in the decay channels, the propagation length of the SPP is reduced, and consequently the ATR dip is broadened. Similar phenomena are expected to occur for the present LRSM. The LRSM propagating in the present composite film is thought to be scattered and to emit light due to inhomogeneities arising from the inclusion of Ag nanoparticles in a-SiO . Actually, we could observe the light 2 emitted from the samples with the naked eye. This scattering process of the LRSM may lead to the broadening of the ATR dips. In the calculation, however, the scattering process is not taken into
28
T. Kume et al. / Surface Science 395 (1998) 23–29
Fig. 5. Calculated ATR spectra corresponding to the experimental spectra shown in Fig. 3 (varying h and fixing d ).
account. Another source of the discrepancies between experiments and calculations seems to be the differences in the values of the dielectric constants used in the calculations as compared to their real values. In particular, the dielectric constant of the SiO –Ag composite layer (e ) estimated by the 2 2 Maxwell-Garnett formula may contain an error which arises from deviations of the parameters used (the filling factor of Ag and the dielectric constants of Ag particles and SiO ) from the real 2 values. Even if the error of e is very small, 2 discrepancies between calculated and experimental spectra are observable because the LRSM is highly sensitive to the dielectric constant of the active layer. Further theoretical studies are necessary to achieve a quantitative agreement between the experimental and calculated ATR spectra.
4. Conclusion By successively depositing SiO –Ag and SiO 2 2 layers on a fused quartz substrate, we prepared a
symmetric system (SiO /SiO –Ag/SiO ) and inves2 2 2 tigated the LRSM supported by the SiO –Ag com2 posite film using a novel ATR method. The ATR spectra were measured by systematically varying the thicknesses of the composite layer d and coupling-gap layer h. For both p- and s-polarized incident light, sharp ATR dips were clearly observed. The present ATR results clearly demonstrate the changes in the LRSM propagation characteristics depending on d and h. A thinner composite film gave a longer propagation length, and at d=13 nm the estimated propagation length was 77 mm. From the h dependence of the LRSM, at h=0.93 mm the LRSM was found to be considerably modulated by the presence of the prism. The experimental d and h dependences of the LRSM could be reproduced fairly well by a theoretical calculation based on the theory of multiple reflections, although further theoretical studies are necessary to achieve quantitative agreement between experimental and theoretical ATR spectra. The success in the excitation of LRSMs supported by the SiO –Ag composite layer demon2 strated in this paper may suggest the possibility of new kind of surface-enhanced optical experiments. For example, second-harmonic generation by Ag nanoparticles enhanced by excitation of the LRSMs seems to be a promising experiment.
Acknowledgements This work was partially supported by a Grantin-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
References [1] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer, Berlin, 1988. [2] A. Otto, Z. Phys. 216 (1968) 398. [3] D. Salid, Phys. Rev. Lett. 26 (1981) 1927. [4] Y. Kuwamura, M. Fukui, O. Yada, J. Phys. Soc. Jpn. 52 (1983) 2350. [5] H. Dohi, Y. Kuwamura, M. Fukui, O. Yada, J. Phys. Soc. Jpn. 53 (1984) 2828. [6 ] G.P. Bryan-Brown, F. Yang, G.W. Bradberry, J.R. Sambles, J. Opt. Soc. Am. B 8 (1991) 765.
T. Kume et al. / Surface Science 395 (1998) 23–29 [7] F. Yang, J.R. Sambles, G.W. Bradberry, Phys. Rev. Lett. 64 (1990) 559. [8] F. Yang, J.R. Sambles, G.W. Bradberry, Phys. Rev. B 44 (1991) 5855. [9] M. Takabayashi, M. Haraguchi, M. Fukui, J. Opt. Soc. Am. B 12 (1995) 2406. [10] R.J. Crook, F. Yang, J.R. Sambles, J. Mod. Opt. 40 (1993) 243. [11] M. Takabayashi, H. Shiba, M. Hamaguchi, M. Fukui, J. Phys. Soc. Jpn. 62 (1993) 2719. [12] F. Yang, J.R. Sambles, G.W. Bradberry, J. Mod. Opt. 38 (1991) 707. [13] F. Yang, G.W. Bradberry, J.R. Sambles, Phys. Rev. Lett. 66 (1991) 2030. [14] Z.C. Wu, E.T. Arakawa, T. Inagaki, T. Thundat, L.J. Schowalter, Phys. Rev. B 49 (1994) 7782.
29
[15] M. Fukui, K. Oda, Appl. Surf. Sci. 33/34 (1988) 882. [16 ] M. Fujii, T. Nagareda, S. Hayashi, K. Yamamoto, Phys. Rev. B 44 (1991) 6243. [17] T. Kume, N. Nakagawa, S. Hayashi, K. Yamanoto, Superlatt. Microstruct. 15 (1994) 459. [18] T. Kume, N. Nakagawa, S. Hayashi, K. Yamanoto, Solid State Commun. 93 (1995) 171. [19] R. Bruns, H. Raether, Z. Phys. 237 (1970) 98. [20] J.C. Maxwell-Garnett, Philos. Trans. R. Soc. London A 203 (1904) 358; 205 (1906) 237. [21] D.W. Lynch, W.R. Hunter, in: E.D. Palik ( Ed.), Handbook of Optical Constants of Solids, Academic Press, Orlando, FL, 1985, p. 350. [22] U. Kreibig, C.V. Fragstein, Z. Phys. 224 (1969) 307. [23] H.R. Philipp, in: E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, Orlando, FL, 1985, p. 749.