# Highly Sensitive Plasmonic Structures Utilizing a Silicon Dioxide Overlayer

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

#### 2.1. Structure Design

#### 2.2. Transfer Matrix Method

#### 2.3. Material Parameters

#### 2.3.1. Substrate (BK7 Glass) and Silicon Dioxide (${\mathrm{SiO}}_{2}$)

#### 2.3.2. Gold Layer

#### 2.3.3. Adhesion Chromium Layers

## 3. Theoretical Analysis

## 4. Fabrication of Structures

## 5. Responses of Real Structures

## 6. Experimental Analysis

#### Experimental Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Theoretical spectral reflectance ${R}_{p}\left(\lambda \right)$ for distinct gold layer thicknesses for: ${t}_{{\mathrm{SiO}}_{2}}=150$ nm (

**a**), ${t}_{{\mathrm{SiO}}_{2}}=300$ nm (

**b**). Angle of incidence $\theta ={68}^{\circ}$. Chromium layer thicknesses ${t}_{\mathrm{Cr}}=2$ nm. The analyte is water.

**Figure 3.**Theoretical spectral reflectance ratio ${R}_{p}\left(\lambda \right)$ for distinct silicon dioxide layer thicknesses (

**a**) and for distinct adhesion chromium layer thicknesses (

**b**). Gold layer thickness ${t}_{\mathrm{Au}}=38$ nm. Angle of incidence $\theta ={68}^{\circ}$. The analyte is water.

**Figure 4.**Theoretical RI sensitivity (

**a**) and figure of merit (

**b**) as a function of the silicon dioxide thickness when water was considered as an analyte. Gold layer thickness ${t}_{\mathrm{Au}}=38$ nm. Silicon dioxide thickness ${t}_{{\mathrm{SiO}}_{2}}=150$ nm. Angle of incidence $\theta ={68}^{\circ}$.

**Figure 5.**Theoretical RI sensitivity (

**a**) and figure of merit (

**b**) as a function of the gold layer thickness when water was considered as an analyte. Silicon dioxide thickness ${t}_{{\mathrm{SiO}}_{2}}=150$ nm. Chromium layer thickness ${t}_{\mathrm{Cr}}=2$ nm. Angles of incidence $\theta ={66}^{\circ}$, ${68}^{\circ}$, and ${70}^{\circ}$.

**Figure 6.**Theoretical spectral reflectance ratio ${R}_{p}\left(\lambda \right)/{R}_{s}\left(\lambda \right)$ for the silicon dioxide layer thicknesses: ${t}_{{\mathrm{SiO}}_{2}}=147.5$ nm (

**a**), ${t}_{{\mathrm{SiO}}_{2}}=270.9$ nm (

**b**). Angle of incidence $\theta ={68}^{\circ}$.

**Figure 7.**Theoretical resonance wavelength as a function of refractive index of the analyte and second-order polynomial fit for both structures (

**a**). Theoretical RI sensitivity for both structures (

**b**). Angle of incidence $\theta ={68}^{\circ}$.

**Figure 8.**Schematic drawing of the experimental setup employing the SPR structure: white light source (WLS), input optical fiber (IOF), collimating lens (CL), polarizer (P), equilateral prism (EP), analyzer (A), microscope objective (MO), read optical fiber (ROF), and personal computer (PC).

**Figure 9.**Measured spectral reflectance ratios ${R}_{p}\left(\lambda \right)/{R}_{s}^{ref}\left(\lambda \right)$ for the silicon dioxide layer thicknesses: ${t}_{{\mathrm{SiO}}_{2}}=147.5$ nm (

**a**), ${t}_{{\mathrm{SiO}}_{2}}=270.9$ nm (

**b**). The angle of incidence $\theta \approx {70.2}^{\circ}$.

**Figure 10.**Measured resonance wavelength as a function of refractive index of the analyte and second-order polynomial fit for both structures (

**a**). RI sensitivity measured for both structures (

**b**). The angle of incidence $\theta \approx {70.2}^{\circ}$.

**Figure 11.**Measured spectral reflectance ratios ${R}_{p}\left(\lambda \right)/{R}_{s}^{ref}\left(\lambda \right)$ (

**a**). RI sensitivity measured for a smaller angle of incidence (blue) and theoretical RI sensitivity for angle of incidence $\theta =65.{6}^{\circ}$ (red) (

**b**). The silicon dioxide layer thickness ${t}_{{\mathrm{SiO}}_{2}}=147.5$ nm.

**Figure 12.**Comparison of RI sensitivity measured for a smaller angle of incidence (blue) and theoretical RI sensitivity (red) (

**a**). Normalized optical field intensity distribution in the analyte (water) for different silicon dioxide layer thicknesses ${t}_{{\mathrm{SiO}}_{2}}$ and angles of incidence $\theta $ (

**b**).

Drude Term Parameter | Value | Oscillator 1 Parameter | Value | Oscillator 2 Parameter | Value |
---|---|---|---|---|---|

${\u03f5}_{\infty}$ | 1 | ${A}_{1}$ | 3.612 | ${A}_{2}$ | 1.423 |

${\lambda}_{p}$ (nm) | 133.85 | ${\lambda}_{1}$ (nm) | 309.11 | ${\lambda}_{2}$ (nm) | 424.06 |

${\gamma}_{p}$ (nm) | 27851 | ${\gamma}_{1}$ (nm) | 2591.3 | ${\gamma}_{2}$ (nm) | 1515.2 |

Drude Term Parameter | Value | CP Term 1 Parameter | Value | CP Term 2 Parameter | Value |
---|---|---|---|---|---|

${\u03f5}_{\infty}$ | 1.129 | ${A}_{1}$ | 33.086 | ${A}_{2}$ | 1.659 |

${\lambda}_{p}$ (nm) | 213.67 | ${\lambda}_{1}$ (nm) | 1082.3 | ${\lambda}_{2}$ (nm) | 496.5 |

${\gamma}_{p}$ (nm) | 4849.8 | ${\gamma}_{1}$ (nm) | 1153.2 | ${\gamma}_{2}$ (nm) | 2559.7 |

${\mathrm{\Phi}}_{1}$ (nm) | −0.25722 | ${\mathrm{\Phi}}_{2}$ (nm) | 0.83533 |

${\mathit{t}}_{{\mathbf{SiO}}_{2}}$ | ${\mathit{t}}_{{\mathbf{Cr}}_{1}}$ | ${\mathit{t}}_{\mathbf{Au}}$ | ${\mathit{t}}_{{\mathbf{Cr}}_{2}}$ | ${\mathit{t}}_{\mathbf{BK}7}$ |
---|---|---|---|---|

147.5 nm | 3.66 nm | 38.95 nm | 2 nm | 1 mm |

270.9 nm | 3.11 nm | 37.93 nm | 2 nm | 1 mm |

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**MDPI and ACS Style**

Chylek, J.; Maniakova, P.; Hlubina, P.; Sobota, J.; Pudis, D.
Highly Sensitive Plasmonic Structures Utilizing a Silicon Dioxide Overlayer. *Nanomaterials* **2022**, *12*, 3090.
https://doi.org/10.3390/nano12183090

**AMA Style**

Chylek J, Maniakova P, Hlubina P, Sobota J, Pudis D.
Highly Sensitive Plasmonic Structures Utilizing a Silicon Dioxide Overlayer. *Nanomaterials*. 2022; 12(18):3090.
https://doi.org/10.3390/nano12183090

**Chicago/Turabian Style**

Chylek, Jakub, Petra Maniakova, Petr Hlubina, Jaroslav Sobota, and Dusan Pudis.
2022. "Highly Sensitive Plasmonic Structures Utilizing a Silicon Dioxide Overlayer" *Nanomaterials* 12, no. 18: 3090.
https://doi.org/10.3390/nano12183090