# Efficient Fabrication Process of Ordered Metal Nanodot Arrays for Infrared Plasmonic Sensor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fabrication Process for Metal Nanodot Array

## 3. Experimental Results and Agglomeration Mechanism by Thermal Dewetting

#### 3.1. Agglomeration of a Single Nanodot

_{c}. When the agglomeration is completed, θ

_{c}is determined by the balance of the surface energy of the substrate γ

_{S}, the surface energy of the nanodot γ

_{M}, and the interface energy between the metal film and the substrate γ

_{I}. This is expressed by Young’s equation [42]:

_{1}is calculated as follows:

_{M}is the area of the dot surface, and S

_{I}is the area of the interface between the dot and the substrate. They are calculated by the following equations:

_{1}and G

_{2}

^{single}. As for the calculation, the grid size P was 1000 nm, and the contact angle θ

_{c}was 90°. The surface energy of Au and SiO

_{2}referred to in the literature was adopted as ${\gamma}_{M}$ and ${\gamma}_{I}$, respectively. It was shown that the free energy after dewetting G

_{2}

^{single}was smaller than that before dewetting G

_{1}and nanodots are formed when the thickness of the metal film was small enough. In addition, this equation indicates possibility that agglomeration does not occur when the metal film is too thick.

#### 3.2. Agglomeration Mechanism of Multiple Nanodots

_{1}and D

_{2}are formed in a square grid, as shown in Figure 7.

_{1}and V

_{2}are the volumes of these dots. By expressing the ratio of D

_{1}and D

_{2}by k, i.e., ${D}_{2}=k{D}_{1}$. the diameters of these dots are calculated by the following equation:

_{M}and S

_{I}are calculated by the following equations:

_{M}of Equation (11). When the film becomes thicker, the increase in free energy against the increase in the dot number becomes larger and, therefore, a thick film is easier to agglomerate to a large dot.

## 4. Optical Properties of Au Nanodot Arrays

## 5. Conclusion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Number of Points | Average of Minimum Distance | Standard Deviation |
---|---|---|

2 | 0.52106 | 0.24783 |

3 | 0.30556 | 0.16004 |

4 | 0.21179 | 0.10976 |

5 | 0.16233 | 0.08362 |

6 | 0.13189 | 0.06816 |

7 | 0.11103 | 0.05737 |

8 | 0.09583 | 0.04959 |

9 | 0.08436 | 0.04367 |

10 | 0.07538 | 0.03904 |

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**Figure 2.**Nano plastic-forming device and knife edge tool made of single crystal diamond. (

**a**) whole image of the device; (

**b**) optical microscope image of the tool; (

**c**) illustration for nanogroove fabrication method.

**Figure 3.**Field-emission scanning electron microscope (FE-SEM) micrographs of gold nanodot array generated by annealing; (

**a**) t = 10 nm, P = 250 nm, T = 700 °C; (

**b**) t = 10 nm, P = 500 nm, T = 700 °C; (

**c**) t = 10 nm, P = 1000 nm, T = 700 °C; (

**d**) t = 17 nm, P = 1000 nm, T = 700 °C; (

**e**) t = 40 nm, P = 1000 nm, T = 1000 °C; (

**f**) t = 40 nm, P = 1200 nm, T = 1000 °C.

**Figure 6.**Variation of free energies G

_{1}and G

_{2}

^{single}as calculated by Equation (4) and (8).

**Figure 8.**Comparison between theoretical value of critical film thickness ratio and experimental value of dot formation.

**Figure 12.**Effects of refractive index on absorbance spectra of nanodot array of 460 nm in diameter.

Thickness of Gold Film t, nm | Grid Size P, nm | Annealing Temperature T, °C | Annealing Time, min |
---|---|---|---|

5 | 50, 75, 100, 175, 250 | 700 | 10 |

10 | 250, 500, 1000 | 700 | 10 |

30 | 800, 900 | 1000 | 10 |

40 | 1000, 1200 | 1000 | 10 |

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Yoshino, M.; Kubota, Y.; Nakagawa, Y.; Terano, M.
Efficient Fabrication Process of Ordered Metal Nanodot Arrays for Infrared Plasmonic Sensor. *Micromachines* **2019**, *10*, 385.
https://doi.org/10.3390/mi10060385

**AMA Style**

Yoshino M, Kubota Y, Nakagawa Y, Terano M.
Efficient Fabrication Process of Ordered Metal Nanodot Arrays for Infrared Plasmonic Sensor. *Micromachines*. 2019; 10(6):385.
https://doi.org/10.3390/mi10060385

**Chicago/Turabian Style**

Yoshino, Masahiko, Yusuke Kubota, Yuki Nakagawa, and Motoki Terano.
2019. "Efficient Fabrication Process of Ordered Metal Nanodot Arrays for Infrared Plasmonic Sensor" *Micromachines* 10, no. 6: 385.
https://doi.org/10.3390/mi10060385