Thin gold layers – experimental optical properties and their correlation with classical Drude, non-local and ab-initio calculations

We present our latest findings regarding the optical properties of thin Au films and their relation with currently available models, from classical Drude, with thickness correction, to non-local estimations and abinitio calculations predictions. Thin metallic layers, in particular Au, are the main building block in plasmonic and metamaterials community [1]. However, there have been very few measurements of their optical properties, especially regarding the dependence on the film thickness [2]. Using a non-metallic adhesion layer, we showed that we can obtain ultra-smooth and thin Au layers [3] supporting surface plasmon polariton propagation characteristics very close to the theoretical ones [4]. Here, we present their experimental permittivity and compare it to several available models from literature. The experimental data was obtained on layers between 8 and 22 nm thick, using ellipsometry measurements in the range of 675 to 1750nm to limit the influence of the interband transitions and use a simple Durde model. In general, the dependence of the collision energy with thickness tt is considered to be in the form of Γ(tt) = Γ0 + AA ∗ vvff tt ⁄ [5]. For nano-spheres, the free factor AA is assumed to be unity [6]. In the case of our nano-layers the best fit is for a factor AA of 0.06, significantly smaller (Fig 1(a)). As second finding, no clear trend in the behaviour of the plasma energy, as defined by the Drude model (Fig 1(b)) was observed. The GNOR non-local model [7] shows a variation of the plasma energy within the error of the measure and a general trend of the collision energy that matches our data. The model from [8] predicts a change of the plasma energy that does not consistently match our experimental data. Ab-initio calculations on particles with diameters smaller than 3 nm show collision energies having a similar trend as the one observed experimentally [9]. We present experimental data and their comparison to different theoretical models for Au layer permittivity with no other metallic influence. Involving metallic adhesion layers would complicate the problem manifold [10]. To conclude, the size-dependent damping of Au was much smaller than expected, and there was no measurable plasmon energy change. Further analysis, especially for thicknesses below 10nm is required. Fig. 1 The fitted values of the collision (a) and plasma (b) energy from the measured ellipsometer data. The full line is the best fit with the 1/tt dependence. Dotted lines show the 95% confidence interval. The computed error bars (red lines) are too small to be visible. The fitting was made between 675 to 1750nm, to minimise the influence of the Lorentz terms. References [1] R. Malureanu and A. Lavrinenko, "Ultra-thin films for plasmonics: a technology overview," Nanotechnol. Rev. 4, 259–275 (2015). [2] D. I. Yakubovsky, A. V. Arsenin, Y. V. Stebunov, D. Y. Fedyanin, and V. S. Volkov, "Optical constants and structural properties of thin gold films," Opt. Express 25, 25574 (2017). [3] L. Leandro, R. Malureanu, N. Rozlosnik, and A. Lavrinenko, "Ultrathin, ultrasmooth gold layer on dielectrics without the use of additional metallic adhesion layers.," ACS Appl. Mater. Interfaces 7, 5797–5802 (2015). [4] J. Sukham, O. Takayama, A. V. Lavrinenko, and R. Malureanu, "High-Quality Ultrathin Gold Layers with an APTMS Adhesion for Optimal Performance of Surface Plasmon Polariton-Based Devices," ACS Appl. Mater. Interfaces 9, (2017). [5] U. Kreibig and C. v. Fragstein, "The limitation of electron mean free path in small silver particles," Zeitschrift fur Phys. 224, 307–323 (1969). [6] J. A. Gordon and R. W. Ziolkowski, "The design and simulated performance of a coated nano-particle laser.," Opt. Express 15, 2622– 2653 (2007). [7] N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, "A generalized non-local optical response theory for plasmonic nanostructures," Nat. Commun. 5, 3809 (2014). [8] I. V. Bondarev and V. M. Shalaev, "Universal features of the optical properties of ultrathin plasmonic films," Opt. Mater. Express 7, 3731 (2017). [9] Y. He and T. Zeng, "First-Principles Study and Model of Dielectric Functions of Silver Nanoparticles," J. Phys. Chem. C 114, 18023– 18030 (2010). [10] M. Todeschini, A. Bastos da Silva Fanta, F. Jensen, J. B. Wagner, and A. Han, "Influence of Ti and Cr Adhesion Layers on Ultrathin Au Films," ACS Appl. Mater. Interfaces 9, 37374–37385 (2017). (a) (b)