Resumen de Numerical modelling of nanoporus anodic alumina photonic structures for optical. Biosensing
It is well known from a variety of studies, that some materials shown particular physical, optical and chemical properties at the nanoscale. The nanotechnology permits to scientist enhance their properties modifying the matter structure at this level and take advantage of them for the development of new devices and applications. The fields in which the nanotechnology is critical are diverse and involve different areas, such as biology, materials science, optics, energy and medical sciences. In medical sciences the development of new devices for biomedical applications are increasing the interest of research areas as, for example, drug delivery and biosensing. Particularly important is the research in biosensing in order to obtain more sensitive and reliable devices with a view for their deployment to society in the form of cost-effective and reliable diagnostic systems. The manufacturing of such devices in some cases implies the manipulation of the light in these materials at the nanoscale, for which it implies to have a deep knowledge of the optical behaviour of the structure. In this sense, the election of the appropriate material with the ability of controlling the propagation of the light through them is decisive in the development of biosensing devices.
Nanoporous Anodic Alumina (NAA) is a self-ordered porous material produced by electrochemical anodization of aluminium with an hexagonal arrangement of cylindrical pores perpendicular to their surface. In the recent years, NAA structures have generated a considerable research interest because of their physical, chemical and optical properties. Actually, their optical properties in the visible, their great tunability of the structure, their ability to act as a holder of small objects, their stability under biological conditions and their capacity to act as a scaffold to hold other nanostructures are some of the properties that make NAA especially appropriate as a platform for the development of optical biosensors. Focusing in the optical properties of the NAA, these are strongly dependent to their geometrical parameters. This fact permits to achieve a precise control of their optical properties by tuning the structure (for instance, by nanopore engineering or changing the lattice parameter of the pore arrangement). Theoretical studies on the optical properties of these NAA structures is a fundamental field of research. The numerical modelling of the optical properties of NAA permits to understand their relationship with the structural features of the NAA, providing a conceptual framework for the analysis of their optical behaviour. Additionally, these simulations are a powerful tool for the improvement of the NAA-based devices with a design fundamented on a wider knowledge basis.
Several models exist in the literature to predict the optical behaviour of NAA-based devices, however the published research on this issue is very limited. Whilst most of these models are developed for a specific type of NAA with a restricted range of geometric and optical characteristics, there exist a paucity of published studies on NAA optical modelling in a broad range of structural features.
In this thesis, we aim at to cover this existing gap with the development of a predictive models for the optical properties of the NAA valid in a wide range of geometrical characteristics, as well as the suitability of the numerical method used.
The objectives of this Thesis are: - Development of computer implementations of numerical models for the theoretical study of the optical behaviour of NAA - Analysis of the structural and the optical properties of the NAA in order to perform the modelling considering it as a one-dimensional and a two-dimensional photonic crystal.
-Theoretical study of the optical behaviour of gold-coated NAA as a proposal of application to sensing devices based on NAA.
-Theoretical study of the optical behaviour of NAA graded-index structures as a proposal of modelling tools applied to more complex structures, and a theoretical study and assessment of an alternative proposal of sensing with NAA-based graded-index structures.
The study of the optical behaviour of photonic structures based on nanoporous anodic alumina can not be addressed using a single numerical method due to the different types of structures to be considered, restricting our investigation to those more widely used for the kind of structure considered. Reflectance properties of nanoporous anodic alumina structures as a two-dimensional photonic crystal have been investigated by a three-dimensional finite differences in the time domain method. In a similar way, the reflectance properties and sensing capabilities of gold-coated nanoporous anodic alumina structures have been analyzed applying the same numerical method. Nevertheless, reflectance properties and sensing capabilities of nanoporous anodica alumina rugate filters, as well as the possibility of an alternative method of sensing with this kind of structures, have been addressed with the transfer matrix method.
In the first part of this thesis, the ability of a developed numerical procedure based 3D FDTD simulations in the prediction of the optical behaviour of the NAA structures with a wide range of interpore distances has been analysed. To this end, the study has been addressed for two types of nanoporous anodic alumina structures. Reflectance measurements from real samples produced with oxalic (interpore distance smaller than wavelength) and with phosphoric (interpore distance of the order of wavelength) electrolytes were collected. Subsequently, these real samples were simulated for each corresponding type of NAA structure. Henceforward, various models of increasing geometric and chemical complexity were considered in the simulations: i) a initial model that considers the flat aluminum-alumina and alumina-air interfaces, ii) a second model that considers the interface between the aluminium substrate and the alumina layer texturized with the hemispherical concavities caused by the preparation procedures, as well as the alumina barrier layer and the top surface of the alumina layer, iii) a third improved model that considers a anionic layer in the inner pore wall layer with distinct optical properties and iv) a last fourth model which contemplates absorption in the anionic layer.
he consideration of the first model in the simulations allows to establish the limits of the effective medium approximation with the transfer matrix method approach. The assumption of flat interfaces between aluminium substrate and the alumina layer is not appropriate, supporting at the same time the finite differences in the time domain as more convenient method to apply.
Although both methods, the effective medium approximation with the transfer matrix method and the finite differences in the timne domain method, shows the similar optical behaviour for nanoporous anodic alumina with short interpore distances, both methods fail in the prediction of the reflectance fall in the visible range for nanoporous anodic alumina with long interpore distances. Therefore, the conclusion is the assumption of flat interfaces is not appropriate for the modelling of the optical behaviour of nanoporous anodic alumina with long interpore distances. The subsequent consideration of the second model in the simulations, that is the consideration of the interfaces texturization, and the corresponding analysis leads to the expected reduction of reflectance for nanoporous anodic alumina with long interpore distances in the visible range. Meanwhile the reflectance for the nanoporous anodic alumina with short interpore distances maintains a good agreement with the measured data. Thus, in order to have precise predictions of the optical behaviour of the nanoporous anodic alumina for a wide range of characteristics parameters of the structure, the consideration of the texturization of the interfaces is crucial.
However, the consideration of the third and fouth models in the simulation, that is the consideration of the dual structure of the pore walls by the addition of a layer in the inner pore wall with different optical properties (with or without absorption), is traduced into the introduction of a next-to-leading order in the predictions, even though it allows a slight adjustment with the experimental measurements.
Next, a study on the capabilities of gold-coated nanoporous anodic alumina membranes as a reflectometry-based plasmonic platforms for biosensors has been made. This study has been performed by numerical simulation of the reflectance spectrum of the gold-coated nanoporous anodic alumina membranes upon the attachment of analytes (biolayer) on the gold coating and the inner pore walls. Numerical simulations based on the three-dimensional finite differences in the time domain method have been performed on two types of nanoporous anodic alumina membranes: the first ones with short interpore distances which corresponds to nanoporous anodic alumina obtained with oxalic acid electrolytes, and second with long interpore distance which corresponds to nanoporous anodic alumina obtained with phosphoric acid electrolytes. The capability of coupling a localized surface plasmon resonance from an incident beam has been studied by comparing the reflectance spectra of the short and long interpore distance gold-coated NAA with that of a solid gold film and for a nanopatterned gold film with the same distribution of holes as in NAAM, both with the same thickness as the coating on the NAAM. The attachment of the chemical/biological analytes to be detected onto the inner surface of the pores and on the gold surface forming the biolayer has been modelled as a conformal layer with a refractive index that can be different with respect to the medium filling the pores and with a given thickness.
The results presented in this chapter shows the possibility to use the gold-coated nanoporous anodic alumina membranes as a platform for plasmonic biosensors by means of reflectometric methods, providing an alternative to experimental configurations such as Kretchsmann and Otto to obtain plasmonic excitations. The nanostructuring provided by the pore distribution of the nanoporous anodic alumina membranes permits a direct coupling of the incident light with the plasmons on the metal. That coupling depends strongly on the interpore distance nanoporous anodic alumina membranes, being much more efficient for the gold-coated nanoporous anodic alumina membranes with long interpore distances.
Furthermore, this gold-coated nanoporous anodic alumina membrane permits the definition of a sensitivity function. Numerical simulations demonstrate that the attachment of a biolayer on the gold coating and on the inner pore walls produces a shift on the resonant wavelength of the plasmon resonance. The shift shows a linear dependence with the refractive index of the biolayer, what permits to define the sensitivity as the shift of the resonant wavelength per refractive index unit. This sensitivity increases with the thickness of the biolayer. Additionally, the sensitivity function defined can be optimized for a specific gold thin film layer and a specific analyte to detect. The sensitivity decreases as the thickness of the gold thin film on the nanoporous anodic alumina increases. A study of the electric field distribution produced by the different gold thicknesses can explain that result: a lower thickness in the gold thin film results in a larger fraction of the electric field in the space region where the biolayer deposits, resulting in a greater interaction volume. However, such increase in sensitivity has the disadvantage of a decrease in the resonance Q-factor, which can reduce the resolution in the measurement of the shift under experimental conditions. This suggests that an optimal thickness of the gold coating has to be determined for each specific experimental conditions.
Finally, in the las part of the thesis, the optical response of nanoporous anodic alumina-based rugate filters has been modelled with a numerical procedure based on the transfer matrix method with an effective medium approximation. To this end, reflectance measurements from real samples produced using eight different sinusoidal anodization profiles to generate eight different types of nanoporous anodic alumina rugate filters were performed. Subsequently, these real samples were simulated for each corresponding type of nanoporous anodic alumina rugate filters. Henceforward, a model in which the pore morphology shows a sinusoidal variation of the pore diameter in depth and a modulation period along the pore length is considered. The porosity of the NAA-RF is modified in depth by that pore geometry, and in turn the effective refractive index is also in depth modulated. An effective medium approximation permits the creation of a multilayered system with constant refractive index for each layer. Reflectance spectra calculations are performed using the transfer matrix method and analyzed by adjusting the geometrical parameters in order to obtain the best fit between the experimental and the calculated reflectance.
The results presented in this chapter shows the possibility to relate the fabrication parameters (the offset current, the amplitude current and the period) with the geometric characteristics (the interpore distance, the average pore diameter, the pore modulation amplitude and the modulation period) of nanoporous anodic alumina rugate filters. The numerical model developed is able to determine crucial geometrical parameters such as average pore diameter and the pore modulation amplitude. The pore geometry of the nanoporous anodic alumina rugate filters induces a modification in depth of the porosity which in turn produces a modulation of the effective refractive index with the pore length. As a result of this effective refractive index oscillatory behaviour the nanoporous anodic alumina rugate filters reflectance spectra show photonic stop bands. The central wavelength of these photonic stop bands increases as the applied offset current increases. By adjusting the geometrical parameters, the numerical model developed is able to reproduce the experimental central wavelengths of these photonic stop bands. The simulations indicate an increasing trend of the pore diameter with increasing the offset current, demonstrating a relationship between these two parameters.
On the other hand, experimental results indicates that the effect of the amplitude current in the reflectance spectra of the nanoporous anodic alumina rugate filters results in that the central wavelength of each photonic stop band is not affected by a variation of the amplitude current. In contrast, a variation on the intensity of the central wavelength of the reflectance spectra is observed which increases as the amplitude current increases. The numerical model developed is able to reproduce the experimental behaviour and the heights of the central wavelengths of the photonic stop band, by adjustingpore modulation amplitude and obtain a best fit with the experimental and calculated reflectance. The simulations suggest the existence of a relationship between the amplitude current as a fabrication parameter with the pore modulation amplitude as a geometrical parameter. However, further analysis will be necessary in order to relate in detail these two parameters. Furthermore, the nanoporous anodic alumina rugate filters permit the definition of a sensitivity function. Numerical simulations demonstrate that changes in the refractive index of the medium that fills the pores produces a shift on the central wavelength position of the photonic stop band. The shift shows a linear dependence with the refractive index of the pore filling medium, which permits to define the sensitivity as the shift of the central wavelength position of the photonic stop band per refractive index unit. This sensitivity increases with the refractive index of the medium. The effect of the pore diameter and the pore modulation amplitude on the sensitivity of nanoporous anodic alumina rugate filters have been demonstrated, revealing an increasing trend of the sensitivity with the average pore diameter. On the other hand, in contrast, it has been demonstrated that the pore modulation amplitude does not influence the sensitivity of the NAA-RF. Finally, an alternative method of sensing with NAA-RFs is proposed and evaluated. The optical characteristics of this NAA-RF based system are assessed by analysing directly the area closed under the final resulting spectrum. This process permits to establish a sensing parameter as the area closed by each signal spectrum by refractive index unit, showing a increasing trend in the signal response as the refractive index that fills the pores increases.
