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The effects of structural design parameters on the performance of nano-replicated photonic crystal (PC) label-free biosensors were examined by the analysis of simulated reflection spectra of PC structures. The grating pitch, duty, scaled grating height and scaled TiO_{2} layer thickness were selected as the design factors to optimize the PC structure. The peak wavelength value (PWV), full width at half maximum of the peak, figure of merit for the bulk and surface sensitivities, and surface/bulk sensitivity ratio were also selected as the responses to optimize the PC label-free biosensor performance. A parametric study showed that the grating pitch was the dominant factor for PWV, and that it had low interaction effects with other scaled design factors. Therefore, we can isolate the effect of grating pitch using scaled design factors. For the design of PC-label free biosensor, one should consider that: (1) the PWV can be measured by the reflection peak measurement instruments, (2) the grating pitch and duty can be manufactured using conventional lithography systems, and (3) the optimum design is less sensitive to the grating height and TiO_{2} layer thickness variations in the fabrication process. In this paper, we suggested a design guide for highly sensitive PC biosensor in which one select the grating pitch and duty based on the limitations of the lithography and measurement system, and conduct a multi objective optimization of the grating height and TiO_{2} layer thickness for maximizing performance and minimizing the influence of parameter variation. Through multi-objective optimization of a PC structure with a fixed grating height of 550 nm and a duty of 50%, we obtained a surface FOM of 66.18 RIU^{−1} and an S/B ratio of 34.8%, with a grating height of 117 nm and TiO_{2} height of 210 nm.

A photonic crystal (PC) is a periodic arrangement of dielectric materials. PCs can support guided-mode resonance when the evanescent (cut-off) diffracted orders of a periodic sub-wavelength surface structure couple with the modes of an effective high-index layer. The energy is coupled with ‘leaky modes’ that escape from the structure in both the forward and backward directions because of its diffractive nature. They interfere with the directly transmitted and reflected zeroth orders: this leads to a strong reflection about a resonant wavelength whose line width and spectral location are set by the physical parameters of the device [

As with other sensors, the detection sensitivity is the critical factor in PC label-free biosensors. Some approaches proposed to improve their detection sensitivity include the following: Ganesh

Among the various structures and materials, a PC composed of a nano-replicated polymer grating (_{2} high-index layer (_{2} layer were selected as the design factors. Since the optimization process considering full design factors is time consuming and may provide meaninglessness results (the optimum structure is too hard to fabricate or the performance of the PC structure is too hard to measure), the scaled design factors were used to provide an effective and reasonable design guideline for PC biosensor. The duty (_{0} and TiO_{2} height _{1} relative to the grating pitch _{0} and _{1} of 0.1–0.5 were used in this study. The range of design parameters was selected considering the limits of inexpensive nano-pattering processes and readout instruments.

To represent the performance of PC label-free biosensors, the following responses were selected: the peak wavelength value (PWV), the full width at half maximum (FWHM) of the peak, the ‘figure of merit’ (FOM), and the surface to bulk ratio (S/B ratio). The PWV is an important design factor for PC label-free biosensors, because the target PWV range can depend on the readout instruments. In addition, some bio-molecules can be damaged by illumination at a specific wavelength of light. The FWHM of the resonance peak is also important for defining the performance of optical resonance sensors, because the sensor resolution is inversely related to the FWHM [

An RCWA (DiffractMod, RSOFT) study was performed to calculate the responses, because it could estimate the performance of PC structures quite closely [_{0} = 0.3, and _{1} = 0.2) in water solution for the light sources with different polarizations as depicted in

To calculate the surface sensitivity, the surface region was assumed to be a volume lying within 25 nm from all exposed surfaces at the top of the PC. The sample materials in the PC biosensor were assumed to have a RI range of 1.2 to 1.5 (_{surf}_{bulk}

Because the response of the PC to normally incident illumination is coupled with the second-order Bragg condition, the PWV is proportional to the grating pitch and RI such that:

In _{eff}_{surf}_{0} = 0.3, _{1} = 0.2, and _{bulk}_{surf}_{surf}_{0}_{1}_{0}_{1}_{1} values showed different results. It was noted that _{1} were dominant factors for PWV. _{eff}

_{eff}_{eff}_{0}, and _{1}. Although

_{0} = 0.3, and _{1} = 0.2) and the other structures in which one design factor was changed from the base structure. As with the results in _{0} and _{1}. This revealed that there were strong interaction effects between _{0}, and _{1}. Therefore, optimization of multiple design factors considering the interaction effects is required to maximize the performance of PC label-free biosensors.

Because we used scaled factors for the duty, grating height, and thickness of the TiO_{2} layer, the grating pitch did not show any interaction effects with the other design factors. Therefore, we were able to isolate the pitch for the optimization of PC-label free biosensors. Regarding the remaining three design factors, we could fix the duty depending on limitations in the fabrication process. Highly expensive patterning equipment cannot be used to pattern the master of PC label-free biosensors to match their disposable characteristics. Considering the critical dimension of the KrF laser projection lithographic system that is generally used to fabricate PC masters (∼130 nm), a duty of 50% is preferable for most PC label-free biosensors. Although a duty of ∼50% showed relatively large FWHM in _{0} and _{1} should be conducted. Because optimization is a way to not only find structural parameters that maximize the performance of the device but also minimize the effects of parameter variation, the optimization process of _{0} and _{1} is rational, since the dimensional accuracies and repeatability of the grating height and TiO_{2} layer thickness during fabrication are lower than those of the grating pitch and duty.

In this study, as an example, design optimization was undertaken for PC label-free biosensors with a pitch of 550 nm and duty of 50%, to minimize the detection limits of surface biosensors. For this purpose, the surface FOM (_{1}) and S/B ratio (_{2}) were selected as the objective functions. Because spectral peaks with very narrow bandwidth require an expensive spectrum analyzing system, the FWHM (_{3}) was also considered as the objective function. To optimize the two design factors and three responses, a factorial design of experiments was first performed for _{0} and _{1}. The data were then fitted using an ^{th} order polynomial regression function based on the least-squares method:
_{ij}_{k}^{th} estimate response. To obtain the estimate responses with a coefficient of determination ^{2}_{1}) and a third-order function was used for both the S/B ratio (_{2}) and FWHM (_{3}). _{1}) and S/B ratio (_{2}). These parameters could be transformed to _{1} and _{2} as:
_{i}_{i}_{i}_{i}_{3}) was transformed to _{3} as:
_{3}_{3}_{1} and _{2} are more important than _{3} for highly sensitive PC biosensors, the weighting factors _{1}, _{2}, _{3}, and _{4} were set to be 0.5, 0.5, 0.2, and 0.2, respectively. After estimate responses were transformed into individual desirability functions _{i}_{i}

The overall desirability function _{0}, _{1}) values were (0.2135, 0.3816). These scaled values were transformed into real values of the structural dimensions, such as a grating height of 117 nm and TiO_{2} layer thickness of 210 nm. Under these conditions, the estimated surface FOM (_{1}) was 62.73 RIU^{−1}, the S/B ratio (_{2}) was 34.80%, and the FWHM (_{3}) was 0.78 nm. From the RCWA simulation of PC label-free biosensors with optimal structures, the calculated surface FOM was 66.18 RIU^{−1}, the S/B ratio was 34.72%, and the FWHM was 0.62 nm. We noted that the estimated values were similar to the calculated values. This clearly revealed that our design approach was reasonable. Compared to the base model (_{0} = 0.3, _{1} = 0.2), the surface FOM was improved from 34.90 to 66.18 RIU^{−1} (∼ 90% enhancement), while the S/B ratio was maintained (34.2 and 34.8% for the base and optimal models) in the optimal design.

We performed a parametric study of the effects of structural design factors on the performance of PC label-free biosensors. The bulk and surface FOM, S/B ratio, and FWHM were proposed to define the performance of PC biosensors. To minimize the interaction effects and isolate the effect of grating height, the scaled design factors to the grating pitch were used in the parametric study. From the parametric study, the duty, scaled grating height, and scaled TiO_{2} thickness were found to have only slight interactions with the grating pitch but considerable interactions with each other in terms of the PC biosensor performance. Because the grating pitch and duty are difficult to control because of limitations in lithography systems (unlike the grating height and TiO_{2} thickness), we proposed a design rule for highly sensitive PC biosensors in which a grating height and duty are first selected by considering the lithography system capability and target PWV value, and then a multi-objective optimization process for the grating height and TiO_{2} thickness is considered. Because of the relatively lower dimensional accuracy and repeatability of the grating height and TiO_{2} layer thickness during fabrication compared to the grating pitch and duty, the proposed optimization method is useful for minimizing the performance variations caused by changes in the former variables. In this study, a surface FOM of 66.18 RIU^{−1} and S/B ratio of 34.8% was achieved for an optimal surface biosensor structure with a pitch of 550 nm, a duty of 0.5, a grating height of 117 nm, and TiO_{2} layer thickness of 210 nm. The optimized structural values of the scaled grating height and TiO_{2} layer thickness could not be applied to PC structures with different grating pitches and duty, because the FWHM was affected by the grating pitch and the duty showed strong interaction effects with _{0} and _{1}. However, we believe that the results of this work will be valuable for understanding the influence of the design parameters on PC biosensor performance, and for designing highly sensitive and robust PC biosensors. Furthermore, the results are invaluable for the optimization of other PC applications, including (but not limited to) optical filters, PC SERS biosensors, and enhanced-fluorescence biosensors.

This research was supported by the Chung-Ang University Research Scholarship Grants in 2011.

Schematic diagram of a PC structure composed of a replicated grating and a TiO_{2} layer. The method for detecting the resonance reflection peak is also shown.

Comparison of the reflection peak spectra of the PC structure (_{0}_{1}

(_{0}_{1}_{0}_{1}_{0}_{1}

Effects of the duty on the (_{0} = 0.3, and _{1} = 0.2).

Response surfaces of the (_{0} and _{1} (