Tunable resonance transmission modes in hybrid heterostructures based on porous silicon
© Pérez et al; licensee Springer. 2012
Received: 30 April 2012
Accepted: 13 July 2012
Published: 13 July 2012
In this work, we report the experimental results and theoretical analysis of strong localization of resonance transmission modes generated by hybrid periodic/quasiperiodic heterostructures (HHs) based on porous silicon. The HHs are formed by stacking a quasiperiodic Fibonacci (FN) substructure between two distributed Bragg reflectors (DBRs). FN substructure defines the number of strong localized modes that can be tunable at any given wavelength and be unfolded when a partial periodicity condition is imposed. These structures show interesting properties for biomaterials research, biosensor applications and basic studies of adsorption of organic molecules. We also demonstrate the sensitivity of HHs to material infiltration.
Photonic crystals are attractive optical materials to control and manipulate the flow of light. A periodic dielectric system (multilayered), typically consisting of two alternated dielectric materials with periodic variation of refractive index (n), is the simplest photonic crystal (PC) . The propagation of electromagnetic radiation in PCs is forbidden in specific wavelength ranges (photonic band gaps or PBGs) because the light wave is scattered at the layers’ interfaces, so the multiple-scattered waves interfere destructively into the material . The behavior of light in a periodic scattering media can be described by Bloch states . In addition, localized modes can appear into the PBGs by breaking the periodicity of the dielectric multilayer, i.e., by introducing a defect into a PC  that allows a narrow range of light wave frequencies to propagate through the whole structure. Physically, the defect is a single layer with different optical parameters (refractive index or thickness) or a completely different multilayer substructure . Novel applications to optical devices, such as all-optical circuit, dielectric mirrors, Fabry-Perot filters, distributed feedback lasers, etc., have been proposed for the above-mentioned structures with localized modes. However, not only PCs based on periodic or periodical structures with defects are of interest but also deterministic aperiodic systems or quasicrystals because of their unexpected optical features [6–10]. The quasicrystals can be considered as a class of complex dielectric structures between ordered crystals and fully random structures. These structures show PBGs, but they are non-periodic multilayer structures. The quasicrystal structures are formed of layers with optical parameters that obey deterministic rules . The Fibonacci and Thue-Morse mathematical sequences are two examples of numbers generated by deterministic rules. In order to associate these kinds of sequences to multilayer structures, it is necessary to define the so-called generators, i.e., initial layers with specific values of their optical properties.
Important applications for quasicrystal-type structures, such as band-edge lasing , optical frequency-selective filters , efficient nonlinear filters , bistability , and switching , have been suggested. In optical sensor applications based on PCs, the sensitivity is associated with the capacity for binding analyte molecules to the surface of the layers . Porous silicon (PSi) has a great capacity of binding molecules at its surface due to its large specific superficial area (≥ 200 m2/cm3) . The biocompatibility of the PSi  makes it a promising material to be used as a biosensor. PSi is a nanostructured material  considered as a mix of silicon and air with effective optical parameters, and its optical and structural features allow the fabrication of complex PCs [21–23]. Since PSi is obtained by electrochemical etching, and the porosity is directly related to the refractive index , it is possible to control its optical parameters by controlling the thickness and porosity by means of time and applied current during the process, respectively . These features allow the fabrication of several types of one-dimensional (1D) PCs and the introduction of complex defect layers into a periodic multilayer structure. The strong confinement of electromagnetic fields within the engineered defect layers is an advantage offered by PCs because it is highly dependent on the refractive indices and thickness of each constituent layer; any change in these parameters is reflected as a change in the optical response. It is possible to achieve a spectral shift of the localized modes when a slight change of refractive index in some layers or on the whole structure is induced. Such displacements could be obtained by natural or thermal oxidation of the PSi structure or by introducing into the pores some specific substances. This advantage can be exploited particularly in biosensing applications due to its high sensitivity requirements compared to other sensors, which only use the weak evanescent field for sensing . It is possible to obtain small spectral shifts in the reflectance or transmittance measures by introducing solutions or analytes into the pores of PSi, which can be monitored with exceptional precision. Numerous works have been published based on this idea, but only the simplest PSi structures (i. e. monolayers, distributed Bragg reflectors (DBRs), and several types of filters) have been used to study different molecular species as proteins [27, 28], DNA , solvents , neurons , etc. However, the optical features of PSi complex multilayer structures have not been explored widely for their application in the biosensing area. From this perspective, our interest lies on the fabrication of a highly efficient photonic structure for biosensing purposes. To achieve this goal, in this work, the fabrication of hybrid heterostructures (HHs) based on PSi is proposed. The HHs are a complex combination of the features of periodic and quasiperiodic photonic structures. The study of hybrid heterostructures has been approached in previous works by other authors but only in the theoretical aspect, and they not consider PSi nanostructures [32, 33]. It is the first experimental study of HHs based on Fibonacci (FN) sequences.
Fibonacci order, substructure, and sequence
FN sequence and number
of defects Generators:
F0= C, F1= CD
F0= 0, F1= 1
The reflectivity measurements of 1D photonic crystals based on PSi structures were carried out in an Agilent spectrophotometer (Cary 5000 UV-VIS-NIR, Agilent Technologies, Santa Clara, CA, USA), with the specular reflectance accessory (VASRA). All the spectra were measured at an angle of incidence of 20°. Reflectivity measurements were carried out with a p-polarized beam. The experimental results were compared with those given by the theory.
where for p-polarization and q jμ =(k jz ) for s-polarization; ϕ j = k jz d j k j = (ω/ c) n j k jz is the component of the wave vector along the growth direction of the system in the j− th layer given by ; and is the complex refractive index. The reflectivity of the system is given in terms of the matrix elements of the total transfer matrix according to . We have implemented a realistic transfer matrix approach by considering the wavelength dependence of the refractive index as well as the optical absorption. Absorption is a very important parameter, especially when considering the visible region of the electromagnetic spectrum.
Results and discussion
The effective refractive index in PSi is the result of a homogeneous mixture of air and silicon, so any material infiltration into the pores displaces off part of the air. Consequently, a red- or blueshift could be expected in the optical reflectance spectra due to a partial change of the optical parameters. The same effect is expected in monolayers and multilayers or even in more complex PSi structures. So, red- or blueshift can be monitored in order to estimate the sensitivity of the structures. To achieve this in multilayered structures, it is preferable to have strong localized modes in order to follow more easily the spectral displacements. The HHs developed in this work have the strong localized modes needed, but they are observed in very complex structures. However, we want to demonstrate that these complex structures make them more sensitive to material infiltration, in particular, when biological molecules are placed into the pores of HHs based on PSi. In order to know the feasibility of the HHs to be used as biosensors, 3-aminopropyltriethoxysilane (APTES) molecule was attached to the internal surface of the structure . To do this, it is necessary to follow a specific process described here: (1) HHs based on PSi were thermally stabilized at 900°C under oxygen flow; (2) APTES silanization was done in a 5% solution with toluene during 1.5 h; (3) the samples were rinsed with toluene and dried under nitrogen flow, and finally, (4) samples were baked in an oven at 110°C for 15 min. The procedure to silane’s modification is well described elsewhere .
Theoretical simulation is also presented in Figure 7 (dashed line). In this case, unlike the first simulations and as a result of changes in the effective refractive index produced by thermal oxidation and APTES infiltration, we introduced a constant Δ n i in order to reproduce the best possible experimental reflectance, where i corresponds to layers A, B, C and D. The values of Δ n i were adjusted, taking into account that the silicon dioxide grows at the expense of silicon (reducing the effective refractive index) and APTES displaces the air from the pores (increasing the effective refractive index). We found that the values of Δ n i induced by the APTES attachment on the oxidized layers is ≤0.09 for each layer. Figure 7 shows a good agreement between the experimental and calculated spectra. The simulation of the optical spectra, based on experimental data of the HHs structures with the molecule infiltration, could give us a quantitative analysis method for material infiltration even at a very low concentration.
In conclusion, we have been able to demonstrate the fabrication of hybrid heterostructures consisting of dielectric multilayers of distributed Bragg reflectors and Fibonacci type. Even considering the complexity of the HHs and the multiple factors involved in PSi formation, we obtain a very high quality and reproducibility in PSi multilayers in our experimental setup. The possibility to localize resonant modes and tuning them has been proven. Unfolding of resonant modes can be generated by repeating periodically the hybrid structure. The theoretical model is in good agreement with the experimental data, so it could be used to estimate changes in optical responses of chemically modified structures. Such hybrid heterostructures can be very promising in the field of optoelectronics, optical communications , and biosensors .
This work has been partially supported by CONACyT under project No. 101486 and by PROMEP “Red Temática”. SEM images: Instituto Potosino de Investigación Científica y Tecnológica A. C. (IPICYT).
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