# Electrical Permittivity and Conductivity of a Graphene Nanoplatelet Contact in the Microwave Range

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation and Structural Characterization of the Sample Circuits

#### 2.2. Electromagnetic Model

#### 2.3. Electromagnetic Characterization

## 3. Results and Discussion

#### 3.1. Structural Characterization of the Nanomaterial and of the Circuit

#### 3.2. Electromagnetic Simulations and Sensitivity Analysis

_{11}is: always decreasing with the frequency; decreasing with ${\epsilon}^{\prime}$ at high frequencies but mostly insensitive to it at low frequencies (Figure 7a); decreasing with the conductivity $\sigma $ by a factor almost independent on frequency (Figure 7b); decreasing with the length l by a factor almost independent on frequency up to values of about 2x the gap length, being insensitive to further length increase (Figure 7c); decreasing with the height h by a factor almost independent on frequency (Figure 7d).

_{12}is always increasing with the frequency; increasing with ${\epsilon}^{\prime}$ (Figure 7a); increasing with the conductivity $\sigma $ at low frequencies but mostly insensitive to it at high frequencies (Figure 7b); increasing with the length l by a factor almost independent on frequency up to values of about 2× the gap length, being insensitive to further length increase (Figure 7c); increasing with the height h by a factor almost independent on frequency (Figure 7d).

#### 3.3. Electromagnetic Characterization and Results Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Microstrip geometrical model implemented in CST Microwave Studio, with the waveports highlighted in red. The inset describes the gap with the extra material box.

**Figure 4.**Setup for the microwave range characterization. (

**a**) overall system; (

**b**) details of the microstrip inserted into the text-fixture.

**Figure 5.**SEM images of: (

**a**) GNP powder at a magnification 1000×; (

**b**) GNP contact created after the self-assembly process (sample 2, with estimation of the extra length).

**Figure 7.**Computed scattering parameters S

_{11}and S

_{12}in the microwave range when varying: (

**a**) the dielectric constant and (

**b**) the conductivity of the GNP contact; (

**c**) the length and (

**d**) the height of the box of extra-material deposited on the gap.

**Figure 8.**Experimental characterization of the test-vehicles in the microwave range: (

**a**) measured S-parameters for Sample #1, for three different runs; (

**b**) measured vs simulated S-parameters for Sample #2.

**Table 1.**Values of the geometrical parameters for the microstrip in Figure 2.

A (mm) | B (mm) | W (mm) | H (mm) | L (mm) |
---|---|---|---|---|

50 | 20 | 1.0 | 0.5 | 0.1 |

Element | C | O | Fe | Na | Mg | Al | Si | S | Ca | Cr |

Content (%) | 87.10 | 10.90 | 0.13 | 0.16 | 0.13 | 0.24 | 0.59 | 0.38 | 0.21 | 0.11 |

Dimension | Sample 1 | Sample 2 |
---|---|---|

h (µm) | 10–20 | 48–55 |

l (mm) | 0.10–0.44 | 0.10–0.50 |

Parameter | Sample 1 | Sample 2 |
---|---|---|

σ(_{DC}) (S/m) | 2.4 | 2.5 |

σ (S/m) | 4 | 10 |

${\epsilon}^{\prime}$ | 23 | 40 |

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**MDPI and ACS Style**

Bellucci, S.; Maffucci, A.; Maksimenko, S.; Micciulla, F.; Migliore, M.D.; Paddubskaya, A.; Pinchera, D.; Schettino, F.
Electrical Permittivity and Conductivity of a Graphene Nanoplatelet Contact in the Microwave Range. *Materials* **2018**, *11*, 2519.
https://doi.org/10.3390/ma11122519

**AMA Style**

Bellucci S, Maffucci A, Maksimenko S, Micciulla F, Migliore MD, Paddubskaya A, Pinchera D, Schettino F.
Electrical Permittivity and Conductivity of a Graphene Nanoplatelet Contact in the Microwave Range. *Materials*. 2018; 11(12):2519.
https://doi.org/10.3390/ma11122519

**Chicago/Turabian Style**

Bellucci, Stefano, Antonio Maffucci, Sergey Maksimenko, Federico Micciulla, Marco D. Migliore, Alesia Paddubskaya, Daniele Pinchera, and Fulvio Schettino.
2018. "Electrical Permittivity and Conductivity of a Graphene Nanoplatelet Contact in the Microwave Range" *Materials* 11, no. 12: 2519.
https://doi.org/10.3390/ma11122519