**1. Introduction**

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The development of nanobiosensors dedicated to early disease diagnosis has an utmost societal interest. The biosensors based on gold nanostructures are known to be efficient and tunable [30, 43]. As an illustration, the objective of the European project *Nanonatenna* (F5-2009 241818) under the "Health" research area of the seventh framework program, is the development of a high sensitive and specific nanosensor based on extraordinary optical signal enhancement dedicated to the in vitro proteins detection and disease diagnosis (cancer, cardiovascular or infectious diseases). The diagnosis process is based on the in vitro detection of the presence of small quantities of the target protein. The consortium of 12 partners works on the design of nanoantennas to reach biosensor high sensitivity. For this, gratings of gold nanoparticles are used to enhance locally the optical signal when excited by an adequate illumination.

The underlying physical phenomenon is the localized surface plasmon resonance (LSPR). The surface plasmon resonance is defined by Raether: "The electron charges on a metal boundary can perform coherent fluctuations which are called surface plasma oscillations" [39]. According to [32], "Localized surface plasmons are non-propagating excitations of the conduction electrons of metallic nanostructures coupled to the electromagnetic field. . . The curved surface of the particles exerts an effective restoring force of the driven electrons, so that a resonance can arise, leading to field amplification both inside and in the near-field zone outside the particle." The position of the LSPR can therefore be tuned by modifying the shape and size of the nanoparticles. It can be adapted to the specific excitation of molecules deposited on the nanoparticle surface, and the detection of a very few quantity is therefore expected.

©2012 Kessentini and Barchiesi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Kessentini and Barchiesi; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Kessentini and Barchiesi licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A periodic arrangement of nanoparticles is used to increase the sensitivity of the biosensor. The prolate and oblate exhibit LSPRs which are related to their asymmetry, leading to a distribution of energy in different LSPR modes [21]. Coupling between transverse and longitudinal LSPR occurs. To prevent this effect which could decrease the efficiency of the biosensor, gratings of gold cylindric nanoparticles have been extensively studied [11, 19, 21– 23, 45]. In that papers, the tuning of the LSPR has been proved by varying the diameter of nanocylinders or seldom their height.

Even if the fabrication process of nanodevices has been continuously improved and more control and precision were achieved [25, 46], the process of deposition of metal on the substrate is subject to incertitudes on the size of the nanostructures that are generally rough. Moreover, a thin intermediate layer (chromium, titanium. . . ) is used to stick gold on substrate. This adhesion layer is usually neglected in simulations, excepted in a few studies for Surface Plasmon Resonance based biosensor [3, 6, 7], and in the case of cylinder-based transducer [42]. Nevertheless in the theoretical and numerical studies, the roughness of the gold nanostructures are neglected and the nanometric adhesion layer of gold on substrate is rarely included.

This chapter is dedicated to the parametric study of a specific nanobiosensor, made of a grating of gold nanocylinders deposited on a dielectric substrate and the goal is to investigate the influence of adhesion layer and roughness on the position of the LSPR as a function of the geometrical parameters of cylinders: their diameter *D* and height *h*. The first section is devoted to the validation of the model by comparison to previous simulations with Finite Difference Time Domain [42], and to experimental results [20, 21, 23]. The analysis of the parametric study is given in section 3 and a method to deduce heuristic laws for the LSPR is also proposed, before concluding.
