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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 8974–8981
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Loss mechanisms of surface plasmon polaritons propagating on a smooth polycrystalline Cu surface

Hyun Seok Lee, Chawki Awada, Salim Boutami, Fabrice Charra, Ludovic Douillard, and Roch Espiau de Lamaestre  »View Author Affiliations


Optics Express, Vol. 20, Issue 8, pp. 8974-8981 (2012)
http://dx.doi.org/10.1364/OE.20.008974


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Abstract

We study the propagation properties of surface plasmon polaritons on a Cu surface by means of photoemission electron microscopy. Use of a CMOS process to fabricate the Cu thin film is shown to enable very high propagation distances (up to 65 μm at 750 nm wavelength), provided that the copper native oxide is removed. A critical review of the optical loss mechanisms is undertaken and shed light on the effect of single grain boundaries in increasing the propagation losses of the plasmon. A microscopic interpretation is provided, relying on groove induced electromagnetic hot spots.

© 2012 OSA

1. Introduction

The use of surface plasmon polaritons (SPP) in metal nanostructures to control light at scales lower than its natural wavelength has emerged in the past few years as a promising way of integrating optical functions in optoelectronics and biochemical sensing applications. The compatibility of SPP device fabrication with complementary metal-oxide-semiconductor (CMOS) processes would enable the development of these applications. However, the metals used in studies of propagating plasmons are generally either silver or gold [1

1. J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

], which are forbidden contaminants in a CMOS environment. Copper is also a high conductivity metal, widely used in backend CMOS processes, whose use has been surprisingly ignored in plasmon assisted devices, except in one recent example [2

2. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metaloxidesilicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010). [CrossRef] [PubMed]

]. Investigating this issue, we show here that nanoscale properties of the Cu surface microstructure, namely the topology of the grain boundaries and the oxidation of the copper surface, are crucial to the control of the SPP losses. A fabrication process of Cu films which minimizes the topological effects of grain boundaries on SPP losses is also presented. This work therefore sheds a new light on the use of copper for plasmonic applications, and is key with regard to the integration of plasmonic functions within CMOS foundries [3

3. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009). [CrossRef] [PubMed]

, 4

4. J. L. Perchec, R. E. de Lamaestre, M. Brun, N. Rochat, O. Gravrand, G. Badano, J. Hazart, and S. Nicoletti, “High rejection bandpass optical filters based on sub-wavelength metal patch arrays,” Opt. Express 19, 15720–15731 (2011). [CrossRef] [PubMed]

].

As SPP modes originate from the interaction of light with conduction electrons, they experience what is generally referred to in literature as ohmic losses [5

5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

, 6

6. P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009). [CrossRef] [PubMed]

]. These losses are usually accounted for through the use of a dielectric constant of the supporting metal. The ubiquitous model for the latter in the near infrared range of the spectrum is the Drude model [5

5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

7

7. K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010). [CrossRef] [PubMed]

]. However, experiments involving either propagating or localized plasmon modes often exhibit non negligible discrepancies between measured losses and those predicted using dielectric constants measured by ellipsometry [5

5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

7

7. K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010). [CrossRef] [PubMed]

]. This is commonly linked to the imperfections of the sample, eg its surface roughness and material quality. In smooth samples where no losses are expected by both in-plane and radiative out of plane SPP scattering [8

8. D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B 12, 4036–4046 (1975). [CrossRef]

], extra losses are usually taken into account by an additional electronic relaxation time contribution in the Drude model that would originate from the electron scattering on defects of the polycrystalline metal film: eg point defects or grain boundaries (GBs). In particular, the correlation between SPP losses and GB density was evidenced in several works [5

5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

7

7. K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010). [CrossRef] [PubMed]

, 9

9. D. Canchal-Arias and P. Dawson, “Measurement and interpretation of the mid-infrared properties of single crystal and polycrystalline gold,” Surface Science 577, 95 – 111 (2005). [CrossRef]

, 10

10. V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, “Ultrasmooth silver thin films deposited with a germanium nucleation layer,” Nano Lett. 9, 178–182 (2009). [CrossRef]

], using spatial averaging techniques. In contrast, we investigate below the SPP propagation losses at the single GB level, using high resolution imaging of a smooth surface of polycrystalline Cu by photoemission electron microscopy (PEEM). This allows the study of the above electronic effect of GBs on SPP losses.

2. Low optical loss Cu film preparation

Fig. 1 (a) AFM top-view image of the Cu surface with 10 μm x 10 μm scan range, measured grain size is 2 ± 0.8 μm, RMS roughness is 0.65 ± 0.15 nm. A and B indicate deep and shallow grooves respectively; (b) Dielectric functions for the fabricated Cu measured by ellipsometry, together with dielectric functions of copper from Palik [11]. Silver optical constants from Johnson and Christy [12] are also plotted.

3. PEEM imaging of SPP propagation

In the context of GB investigation, PEEM microscopy offers several benefits over the well-established scanning near field optical microscopy SNOM. (i) PEEM is a non-intrusive method, i.e. make no use of a scanning tip. Near field measurements are cleared from any tip-to-sample perturbation and quantitative comparison to analytical model are readily possible. (ii) PEEM opens a convenient route to address multi-length scale investigation. Indeed available fields of view range from tenths of μm (plasmons-polaritons propagation length scale) down to tenths of nm (GB length scale) with high resolution near field mapping capabilities. (iii) PEEM exploits nonlinear photoelectric effect. The acquired signal exhibits a large signal-to-noise ratio and the background removal operation is straightforward. For interested readers, a recent panorama of the real space microscopic imaging techniques devoted to plasmonics is available [17

17. R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst 135, 1175–1181 (2010). [CrossRef] [PubMed]

].

To launch a SPP wave on the planar Cu surface, we used a 150 nm × 1.5 μm dielectric (Si3N4) ridge, which is known for having a high SPP launching efficiency for obliquely incident light [18

18. H. Liu, H. Liu, P. Lalanne, X. Yang, and J.-P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008). [CrossRef]

]. The experimental layout for the dielectric launcher is depicted in Fig. 2. The geometry of this ridge was designed using 2-dimensional boundary element method (BEM) calculations in TM polarization [19

19. S. Boutami and J. Hazart, “Calculation of a point source radiation in a flat or non-flat stratified background: an alternative to sommerfeld integrals,” Euro. Phys. J.: Appl. Phys. 52, 23305 (2010). [CrossRef]

], so as to maximize the PEEM signal which results from the beating wave pattern between the propagating SPP wave and the incident beam. The 75 μm long Si3N4 ridge structure was fabricated on the Cu surface by e-beam lithography and lift-off processes. The temperature budget of the process was limited in order to minimize any roughness increase during the process, after which the RMS roughness was measured to 0.55±0.1 nm. PEEM measurements carried out under laser light excitation at a 700 nm wavelength on this sample are displayed in Fig. 3(a). Indeed, one observes a strong photoemission yield exhibiting a decreasing oscillating signal when the distance from the ridge is increased, as the SPP wave decays. In addition to the main signal, high intensity hot spots of various sizes are present, i.e. localized regions where electromagnetic field is enhanced.

Fig. 2 Experimental configuration. Blue curves are the result of the interference of the SPP mode (blue) launched from dielectric ridge and p-polarized incident light (green).
Fig. 3 For all images, the orange arrow indicates the incident light direction. (a) PEEM image at 700 nm wavelength. Launcher position is at the top of the figure. The scale bar is 4 μm. (b) higher resolution zoom of PEEM image shown in (a). A and B indicate relatively large and small hot spots respectively, in correlation with the surface defects of type A and B observed in AFM image (Fig. 1(a)). (c) LEEM and PEEM images at the same sample location. Blue triangles highlight the positions of hot spots.The scale bar length for (b) and (c) is 2 μm.

4. Grain boundaries related losses

5. Native oxide losses

As we use an interferometric PEEM configuration, accurate comparison between experimental and theoretical calculation of the SPP modes complex wavevector can also be achieved. Here also lies a material issue, as the existence of a very thin native copper oxide, is shown to have a significant impact on the SPP propagation losses. Parallel wavevector mismatch between the SPP kSPP and the plane wave k// = k0 sin(θ), θ being the incidence angle, is responsible for the beating fringe period observed in PEEM λbeat = 2π/(kSPPk//). From the optical constant measured by ellipsometry, one predicts λbeat =11 μm at a 700 nm wavelength. However we measure λbeat =10 ± 0.3 μm (Fig. 4(a)). In general, a bilayer of thin native oxides Cu2O (1.3 nm) and CuO (2 nm) grows on surface by exposition of Cu films to air [24

24. P. Keil, R. Frahm, and D. Ltzenkirchen-Hecht, “Native oxidation of sputter deposited polycrystalline copper thin films during short and long exposure times: Comparative investigation by specular and non-specular grazing incidence x-ray absorption spectroscopy,” Corrosion Science 52, 1305–1316 (2010). [CrossRef]

]. These layers modify the complex SPP wavevector kSPPeff, which we calculated using a finite-differential time-domain (FDTD Lumerical) mode analysis. From a tabulated optical index of copper oxides [25], we found (kSPPeff)=1.12.7×104m1, allowing a fit of the fringe period from the experimental PEEM data (Fig. 4(a)). The fit was performed by adjusting the amplitudes of the SPP wave and the incident field, and their respective phase difference. We used optical constants and thicknesses of copper oxide, as well as the optical constants of Cu measured by ellipsometry as fixed inputs of the model. CuO and Cu2O being both semiconductors whose gap lies in the near infrared range, they are optically absorbing, and therefore substantially impact the amount of optical losses experienced by the SPP (Fig. 4(b)). In Fig. 4(b), the SPP propagation length is calculated by using the formula L=λ4π1+εmεm in the pristine Cu surface case (red curve), where εm is the dielectric constant of Cu measured by ellipsometry in section 2; or the formula L=(2(kSPPeff))1 in the case a native oxide is present (blue curve). The SPP propagation length is shown to decrease by about 50% in the latter case. Despite its very low thickness, the oxide layers experience a much higher electric field than the metal surface, leading to a significant optical loss.

Fig. 4 (a) fit of the PEEM data using the complex optical index calculated by an FDTD mode analysis. Fit is achieved by considering the interference of the incident plane wave and a SPP mode whose propagation constant is calculated by FDTD, for distances from the Si3N4 ridge above 10μm. (b) Comparison between the SPP propagation length expected from the ellipsometric data with that obtained by taking into account the native oxide layer, and calculated by FDTD.

6. Conclusion

We have provided microscopic evidence that GB induced losses of SPP modes originate from surface topology. GBs lead to absorbing electromagnetic hot spots through grain grooving effects which occur during deposition [5

5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

], annealing [6

6. P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009). [CrossRef] [PubMed]

], or polishing/aging (this work). These field enhancements increase the local optical absorption. Using a CMOS process to fabricate the Cu thin film we were able to significantly limit the amount of excess losses from these electromagnetic hot spots. Cu is also shown to enable very high SPP propagation lengths (up to 65 μm at 750 nm wavelength), provided that surface oxidation is avoided.

Acknowledgments

This work has been supported by CEA internal Programme Transverse Nanoscience, the French National Agency (ANR) through LETI Carnot Funding, and by ANR Program in Nanosciences and Nanotechnologies (PEEMPlasmon project ANR-08-NANO-034). We acknowledge the PTA for access to clean room facilities and process technologies team for Cu film preparation, S. Maitrejean for discussions, and D. Fowler for his careful reading of the manuscript.

References and links

1.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60, 9061–9068 (1999). [CrossRef]

2.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metaloxidesilicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010). [CrossRef] [PubMed]

3.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009). [CrossRef] [PubMed]

4.

J. L. Perchec, R. E. de Lamaestre, M. Brun, N. Rochat, O. Gravrand, G. Badano, J. Hazart, and S. Nicoletti, “High rejection bandpass optical filters based on sub-wavelength metal patch arrays,” Opt. Express 19, 15720–15731 (2011). [CrossRef] [PubMed]

5.

M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett. 93, 113110 (2008). [CrossRef]

6.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009). [CrossRef] [PubMed]

7.

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10, 916–922 (2010). [CrossRef] [PubMed]

8.

D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B 12, 4036–4046 (1975). [CrossRef]

9.

D. Canchal-Arias and P. Dawson, “Measurement and interpretation of the mid-infrared properties of single crystal and polycrystalline gold,” Surface Science 577, 95 – 111 (2005). [CrossRef]

10.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, “Ultrasmooth silver thin films deposited with a germanium nucleation layer,” Nano Lett. 9, 178–182 (2009). [CrossRef]

11.

E. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1985).

12.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

13.

V. Jousseaume, M. Assous, A. Zenasni, S. Maitrejean, B. Remiat, P. Leduc, H. Trouve, C. Le Cornec, M. Fayolle, A. Roule, F. Ciaramella, D. Bouchu, T. David, A. Roman, D. Scevola, T. Morel, D. Rebiscoul, G. Prokopowicz, M. Jackman, C. Guedj, D. Louis, M. Gallagher, and G. Passemard, “Cu/ulk (k=2.0) integration for 45 nm node and below using an improved hybrid material with conventional beol processing and a late porogen removal,” in “Interconnect Technology Conference, 2005. Proceedings of the IEEE 2005 International,” (2005), pp. 60–62.

14.

N. Ashcroft and N. Mermin, Solid State Physics (Orlando, 1976).

15.

L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P.-M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett. 8, 935–940 (2008). [CrossRef] [PubMed]

16.

L. Douillard and F. Charra, “High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies,” J. of Phys. D 44, 464002 (2011). [CrossRef]

17.

R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst 135, 1175–1181 (2010). [CrossRef] [PubMed]

18.

H. Liu, H. Liu, P. Lalanne, X. Yang, and J.-P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008). [CrossRef]

19.

S. Boutami and J. Hazart, “Calculation of a point source radiation in a flat or non-flat stratified background: an alternative to sommerfeld integrals,” Euro. Phys. J.: Appl. Phys. 52, 23305 (2010). [CrossRef]

20.

J. A. Sánchez-Gil, “Localized surface-plasmon polaritons in disordered nanostructured metal surfaces: Shape versus anderson-localized resonances,” Phys. Rev. B 68, 113410 (2003). [CrossRef]

21.

P. Dawson and M. G. Boyle, “Light emission from scanning tunnelling microscope on polycrystalline au films -what is happening at the single-grain level?” J. Opt. A, Pure Appl. Opt. 8, S219 (2006). [CrossRef]

22.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100, 066408 (2008). [CrossRef] [PubMed]

23.

S. J. Orfanidis, Electromagnetic waves and antennas (Piscataway, NJ, 2004).

24.

P. Keil, R. Frahm, and D. Ltzenkirchen-Hecht, “Native oxidation of sputter deposited polycrystalline copper thin films during short and long exposure times: Comparative investigation by specular and non-specular grazing incidence x-ray absorption spectroscopy,” Corrosion Science 52, 1305–1316 (2010). [CrossRef]

25.

http://refractiveindex.info.

OCIS Codes
(030.5770) Coherence and statistical optics : Roughness
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(160.3900) Materials : Metals
(190.4180) Nonlinear optics : Multiphoton processes
(240.6680) Optics at surfaces : Surface plasmons
(240.6675) Optics at surfaces : Surface photoemission and photoelectron spectroscopy

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 13, 2011
Revised Manuscript: January 23, 2012
Manuscript Accepted: February 2, 2012
Published: April 3, 2012

Citation
Hyun Seok Lee, Chawki Awada, Salim Boutami, Fabrice Charra, Ludovic Douillard, and Roch Espiau de Lamaestre, "Loss mechanisms of surface plasmon polaritons propagating on a smooth polycrystalline Cu surface," Opt. Express 20, 8974-8981 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8974


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References

  1. J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B60, 9061–9068 (1999). [CrossRef]
  2. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metaloxidesilicon nanophotonics,” Nano Lett.10, 2922–2926 (2010). [CrossRef] [PubMed]
  3. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett.9, 897–902 (2009). [CrossRef] [PubMed]
  4. J. L. Perchec, R. E. de Lamaestre, M. Brun, N. Rochat, O. Gravrand, G. Badano, J. Hazart, and S. Nicoletti, “High rejection bandpass optical filters based on sub-wavelength metal patch arrays,” Opt. Express19, 15720–15731 (2011). [CrossRef] [PubMed]
  5. M. Kuttge, E. J. R. Vesseur, J. Verhoeven, H. J. Lezec, H. A. Atwater, and A. Polman, “Loss mechanisms of surface plasmon polaritons on gold probed by cathodoluminescence imaging spectroscopy.” Appl. Phys. Lett.93, 113110 (2008). [CrossRef]
  6. P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science325, 594–597 (2009). [CrossRef] [PubMed]
  7. K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett.10, 916–922 (2010). [CrossRef] [PubMed]
  8. D. L. Mills, “Attenuation of surface polaritons by surface roughness,” Phys. Rev. B12, 4036–4046 (1975). [CrossRef]
  9. D. Canchal-Arias and P. Dawson, “Measurement and interpretation of the mid-infrared properties of single crystal and polycrystalline gold,” Surface Science577, 95 – 111 (2005). [CrossRef]
  10. V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, “Ultrasmooth silver thin films deposited with a germanium nucleation layer,” Nano Lett.9, 178–182 (2009). [CrossRef]
  11. E. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1985).
  12. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370–4379 (1972). [CrossRef]
  13. V. Jousseaume, M. Assous, A. Zenasni, S. Maitrejean, B. Remiat, P. Leduc, H. Trouve, C. Le Cornec, M. Fayolle, A. Roule, F. Ciaramella, D. Bouchu, T. David, A. Roman, D. Scevola, T. Morel, D. Rebiscoul, G. Prokopowicz, M. Jackman, C. Guedj, D. Louis, M. Gallagher, and G. Passemard, “Cu/ulk (k=2.0) integration for 45 nm node and below using an improved hybrid material with conventional beol processing and a late porogen removal,” in “Interconnect Technology Conference, 2005. Proceedings of the IEEE 2005 International,” (2005), pp. 60–62.
  14. N. Ashcroft and N. Mermin, Solid State Physics (Orlando, 1976).
  15. L. Douillard, F. Charra, Z. Korczak, R. Bachelot, S. Kostcheev, G. Lerondel, P.-M. Adam, and P. Royer, “Short range plasmon resonators probed by photoemission electron microscopy,” Nano Lett.8, 935–940 (2008). [CrossRef] [PubMed]
  16. L. Douillard and F. Charra, “High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies,” J. of Phys. D44, 464002 (2011). [CrossRef]
  17. R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst135, 1175–1181 (2010). [CrossRef] [PubMed]
  18. H. Liu, H. Liu, P. Lalanne, X. Yang, and J.-P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron.14, 1522–1529 (2008). [CrossRef]
  19. S. Boutami and J. Hazart, “Calculation of a point source radiation in a flat or non-flat stratified background: an alternative to sommerfeld integrals,” Euro. Phys. J.: Appl. Phys.52, 23305 (2010). [CrossRef]
  20. J. A. Sánchez-Gil, “Localized surface-plasmon polaritons in disordered nanostructured metal surfaces: Shape versus anderson-localized resonances,” Phys. Rev. B68, 113410 (2003). [CrossRef]
  21. P. Dawson and M. G. Boyle, “Light emission from scanning tunnelling microscope on polycrystalline au films -what is happening at the single-grain level?” J. Opt. A, Pure Appl. Opt.8, S219 (2006). [CrossRef]
  22. J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100, 066408 (2008). [CrossRef] [PubMed]
  23. S. J. Orfanidis, Electromagnetic waves and antennas (Piscataway, NJ, 2004).
  24. P. Keil, R. Frahm, and D. Ltzenkirchen-Hecht, “Native oxidation of sputter deposited polycrystalline copper thin films during short and long exposure times: Comparative investigation by specular and non-specular grazing incidence x-ray absorption spectroscopy,” Corrosion Science52, 1305–1316 (2010). [CrossRef]
  25. http://refractiveindex.info .

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