# Effects of Variation in Geometric Parameters and Structural Configurations on the Transmission Characteristics of Terahertz-Range Spoof Surface Plasmon Polariton Interconnects for Interchip Data Communication: A Finite Element Method Study

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Modeling and Simulation Method

#### 3.1. Two Dimensional Design of SSPP Interconnect Pair

#### 3.2. Geometric Dimensions of Simulated SSPP Waveguide

#### 3.3. Simulation by Varying the Dimension

#### 3.4. Simulated Schemes

#### 3.5. Simulation Method

## 4. Results and Discussion

#### 4.1. Electric Field Distribution of SSPP Interconnect Pair

#### 4.2. Effects of Variation in Geometric Parameters on Transmission Bandwidth

#### 4.2.1. Variation in Groove Height

#### 4.2.2. Variation in Groove Width

#### 4.2.3. Variation in Groove Density

#### 4.3. Effects of Geometric Mismatches

#### 4.4. Effects of Bending

#### 4.5. Effects of Zigzag Pattern

## 5. Performance Summary and Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Pair of adjacent SSPP interconnects in two dimension (top view). (

**b**) The dimensions of the grooves including height, width and period (top view).

**Figure 2.**Different parts of an SSPP interconnect pair: (

**a**) transmitter side having input ports (1,3) and Vivaldi waveguide transition, (

**b**) receiver side having ports (2,4) and Vivaldi waveguide transition, and (

**c**) SSPP waveguide pair.

**Figure 3.**(

**a**) The face-to-face portions from both interconnects (enclosed by the red box) considered in the study. (

**b**) Actual modified geometry of SSPP interconnect pair that is designed and simulated in COMSOL Multi-physics environment.

**Figure 4.**(

**a**) Final geometry of SSPP interconnect pair system considered in this study. (

**b**) Dispersion curve of a pair of SSPP interconnects having h = 20 $\mathsf{\mu}$m, d = 20 $\mathsf{\mu}$m, a = 3 $\mathsf{\mu}$m, m = 50.

**Figure 6.**(

**a**) Elimination of cross-talk in between two interconnects comprising the SSPP pair, and (

**b**) Periodic oscillation of electric field between two metal–dielectric interfaces on both sides of the dielectric channel.

**Figure 7.**Proposed structures: (

**a**) 45${}^{\xb0}$ bent, (

**b**) 90${}^{\xb0}$ bent and (

**c**) zigzag-patterned SSPP waveguide pairs.

**Figure 8.**(

**a**) Transmission Coefficient (S${}_{21}$) and (

**b**) Coupling Coefficient (S${}_{41}$) of SSPP interconnect pair for three different groove heights, h = 20 $\mathsf{\mu}$m, 21 $\mathsf{\mu}$m and 22 $\mathsf{\mu}$m. Other parameters are a = 3 $\mathsf{\mu}$m, d = 20 $\mathsf{\mu}$m and m = 50.

**Figure 9.**Dispersion curves of SSPP interconnect pair for three different groove heights, h = 20 $\mathsf{\mu}$m, 21 $\mathsf{\mu}$m and 22 $\mathsf{\mu}$m.

**Figure 10.**(

**a**) Transmission Coefficient (S${}_{21}$) and (

**b**) Coupling Coefficient (S${}_{41}$) of SSPP interconnect pair for three different groove widths: a = 3 $\mathsf{\mu}$m, 4 $\mathsf{\mu}$m and 5 $\mathsf{\mu}$m. Other parameters are h = 20 $\mathsf{\mu}$m, d = 20 $\mathsf{\mu}$m and m = 50.

**Figure 11.**Dispersion curves of SSPP interconnect pair for three different groove widths: a = 3 $\mathsf{\mu}$m, 4 $\mathsf{\mu}$m and 5 $\mathsf{\mu}$m.

**Figure 12.**(

**a**) Transmission Coefficient (S${}_{21}$) and (

**b**) Coupling Coefficient (S${}_{41}$) for a pair of SSPP interconnects for three different groove densities: d = 40 $\mathsf{\mu}$m, 20 $\mathsf{\mu}$m and 10 $\mathsf{\mu}$m, andm = 25, 50 and 100. Other parameters are a = 3 $\mathsf{\mu}$m, h = 20 $\mathsf{\mu}$m and L = 1000 $\mathsf{\mu}$m.

**Figure 14.**Magnetic field distributions when number of grooves are (

**a**) m = 25, (

**b**) m = 50 and (

**c**) m = 100 at 1.237 THz frequency. lc represents the coupling length in (

**b**,

**c**).

**Figure 15.**(

**a**) Transmission coefficient (${S}_{21}$) and (

**b**) coupling coefficient (${S}_{41}$) of mismatched pair of SSPP interconnects for three different mismatches in groove height.

**Figure 16.**(

**a**) Transmission coefficient (${S}_{21}$) and (

**b**) coupling coefficient (${S}_{41}$) of mismatched pair of SSPP interconnects for three different mismatches in groove width.

**Figure 17.**(

**a**) Transmission coefficient (S${}_{21}$) and (

**b**) coupling coefficient (S${}_{41}$) of straight, 45${}^{\xb0}$ bent and 90${}^{\xb0}$ bent pairs of SSPP interconnects.

**Figure 18.**(

**a**) Transmission coefficient (S${}_{21}$) and (

**b**) coupling coefficient (S${}_{41}$) of zigzag patterned and straight SSPP interconnect pairs.

Geometric Parameters | Fundamental Values | Varied Parameter Values | Constant Parameter Values |
---|---|---|---|

Groove height (h) | 20 $\mathsf{\mu}$m | h = 20 $\mathsf{\mu}$m, 21 $\mathsf{\mu}$m, 22 $\mathsf{\mu}$m | a = 3 $\mathsf{\mu}$m; d = 20 $\mathsf{\mu}$m; m = 50 |

Groove width (a) | 3 $\mathsf{\mu}$m | a = 3 $\mathsf{\mu}$m, 4 $\mathsf{\mu}$m, 5 $\mathsf{\mu}$m | h = 20 $\mathsf{\mu}$m; d = 20 $\mathsf{\mu}$m; m = 50 |

Groove period (d) and Number of grooves (m) | d = 20 $\mathsf{\mu}$m and m = 50 | d = 40 $\mathsf{\mu}$m, 20 $\mathsf{\mu}$m, 10 $\mathsf{\mu}$m; m = 25, 50, 100 | a = 3 $\mathsf{\mu}$m; h = 20 $\mathsf{\mu}$m |

Design | Dimensions | Internal Passbands (−3 dB Band) (THz) | −3 dB BW of Intl. Passbands (GHz) | Number of Available Passbands in the SSPP Channel | Reflection Coefficient (within −3 dB Band) | Freq. of Maximum Transmission (THz) | Transmission Coefficient at Centre Frequency (Approx.) | Average Transmission Coefficient (dB) (within −3 dB Band) | Upper Cutoff Freq. of the SSPP Channel (THz) |
---|---|---|---|---|---|---|---|---|---|

2.846–2.867 | 21 | −18 dB | 2.8515 | −0.5 dB | −1.16 | ||||

h = 20 $\mathsf{\mu}$m | 2.896–2.924 | 28 | −22.49 dB | 2.907 | −0.2 dB | −1.07 | |||

Design | d = 20 $\mathsf{\mu}$m | 2.956–2.988 | 32 | 6 | −20.98 dB | 2.972 | −0.23 dB | −0.86 | |

1 | a = 3 $\mathsf{\mu}$m | 3.022–3.056 | 34 | −16.96 dB | 3.039 | −0.3 dB | −1.27 | 3.25 | |

m = 50 | 3.091–3.12 | 29 | −11.05 dB | 3.105 | −0.02 dB | −1.41 | |||

3.16–3.18 | 20 | −7.35 dB | 3.17 | −0.036 dB | −2.19 | ||||

h = 20 $\mathsf{\mu}$m | 2.828–2.862 | 34 | −25.43 dB | 2.845 | −0.05 dB | −1.08 | |||

Design | d = 20 $\mathsf{\mu}$m | 2.9–2.935 | 35 | −16.7 dB | 2.917 | −0.04 dB | −0.98 | ||

2 | a = 4 $\mathsf{\mu}$m | 2.975–3.0115 | 36.5 | 4 | −12.06 dB | 2.998 | −0.4 dB | −1.47 | 3.165 |

m = 50 | 3.053–3.083 | 30 | −7.82 dB | 3.073 | −0.2 dB | −2.03 | |||

h = 20 $\mathsf{\mu}$m | |||||||||

Design | d = 20 $\mathsf{\mu}$m | 2.88–2.92 | 40 | −19.43 dB | 2.895 | −0.2 dB | −7.28 | ||

3 | a = 5 $\mathsf{\mu}$m | 2 | 3.09 | ||||||

m = 50 | 2.96–3.00 | 40 | −11.91 dB | 2.98 | −0.25 dB | −4 | |||

h = 21 $\mathsf{\mu}$m | 2.855–2.883 | 28 | −22.54 dB | 2.87 | −0.1 dB | −1.14 | |||

Design | d = 20 $\mathsf{\mu}$m | 2.91–2.94 | 30 | −16.39 dB | 2.927 | −0.05 dB | −1.30 | ||

4 | a = 3 $\mathsf{\mu}$m | 2.97–3.00 | 30 | 4 | −11.97 dB | 2.99 | −0.3 dB | −1.64 | 3.12 |

m = 50 | 3.03–3.05 | 20 | −8.29 dB | 3.047 | −0.15 dB | −2.24 | |||

h = 22 $\mathsf{\mu}$m | 2.81–2.836 | 26 | −16.38 dB | 2.824 | −0.1 dB | −1.10 | |||

Design | d = 20 $\mathsf{\mu}$m | 2.863–2.888 | 25 | 3 | −11.43 dB | 2.872 | −0.46 dB | −1.50 | |

5 | a = 3 $\mathsf{\mu}$m | 2.918–2.92 | 18 | −7.54 dB | 2.925 | −0.6 dB | −1.94 | 2.98 | |

m = 50 | |||||||||

h = 20 $\mathsf{\mu}$m | 2.887–2.936 | 49 | −13.76 dB | 2.913 | −0.05 dB | −1.27 | |||

Design | d = 10 $\mathsf{\mu}$m | 2.99–3.04 | 50 | 3 | −10.41 dB | 3.011 | −0.35 dB | −1.77 | |

6 | a = 3 $\mathsf{\mu}$m | 3.11–3.14 | 30 | −6.08 dB | 3.14 | −0.1 dB | −2.74 | 3.365 | |

m = 100 | |||||||||

h${}_{1}$ = 20 $\mathsf{\mu}$m | |||||||||

h${}_{2}$ = 22 $\mathsf{\mu}$m | |||||||||

Design | d = 20 $\mathsf{\mu}$m | 2.82–3.22 | 400 | 1 | −12.01 dB | 2.94 | −0.3 dB | −1.43 | 3.23 |

7 | a = 3 $\mathsf{\mu}$m | ||||||||

m = 50 |

**Table 3.**Performance comparison of proposed SSPP based interconnect with state of the art SSPP interconnect.

Reference | Simulated Frequency Range | Reflection Coefficient (dB) | Transmission Coefficient(dB) | Bandwidth (−3 dB) | Type of SSPP Waveguide |
---|---|---|---|---|---|

Ref. [11] | 0–400 GHz | ∼−2.5 dB | ∼ 20 GHz | SPP T-line | |

Ref. [18] | 2–14 GHz | <−10 dB | ∼−1 dB | ∼13 GHz | Oval-Ring SSPP unit |

Ref. [22] | 0–0.6 THz | <−12 dB | ∼−2 dB | ∼300 GHz | Ultra Compact SSPP TL |

Ref. [23] | 0.2–1.4 THz | - | >−4 dB | ∼250 GHz | Coplanar Strip (CPS) SSPP |

Ref. [30] | 0–10 GHz | <−15 dB | >−1 dB and <−0.1 dB | - | Unilateral Subwavelength Periodic Corrugations (USPCs) |

Ref. [30] | 0–10 GHz | <−15 dB | >−0.9 dB and <−0.1 dB | - | Bilateral Subwavelength Periodic Corrugations (BSPCs) |

Ref. [31] | 0–0.9 THz | <−10 dB | >−4.3 dB and <−3 dB | No −3 dB band is found | H-shaped structure with Y-splitter |

Ref.[32] | 6–11 GHz | <−10 dB | ∼−1.5 dB | ∼4 GHz | Frequency Selective SSPP structure |

Ref. [33] | 46.1–73.7 GHz | <−10 dB | ∼−1.08 dB | 27.6 GHz | SIW BPF based on SSPP |

Ref. [34] | 0–14 GHz | <−10 dB | ∼−0.37 dB (minimum) | 5.9 GHz | SSPP waveguide with fishbone slot unit cell |

Ref. [35] | 0.3–0.5 THz | - | ∼−0.6 dB | ∼100 GHz | SSPP waveguide with V grooves |

Ref. [36] | 0.4–1.6 THz | <−10 dB | ∼−1.0 dB | ∼ 90 GHz | Plasmonic waveguides based on spiral-shaped units |

Ref. [37] | 0.3–0.8 THz | - | <−1.5dB | ∼100 GHz | Curved terahertz surface plasmonic waveguide |

Ref. [38] | 0.18–0.32 THz | <−20 dB | >−2dB | ∼60 GHz | Surface-integrated plasmonic waveguide (SIPW) |

Ref. [39] | 0.04–0.12 THz | <−10 dB | ∼−1.5dB | 40 GHz | Millimetre-wave E-plane waveguide |

This work | 2–4 THz | <−12 dB | ∼−1.43 dB | 400 GHz | SSPP interconnect pair with 2 $\mathsf{\mu}$m mismatch in groove height |

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**MDPI and ACS Style**

Daiyan, K.M.; Abi, S.B.; Rashid, A.B.M.H.-U.; Shawkat, M.S.A.
Effects of Variation in Geometric Parameters and Structural Configurations on the Transmission Characteristics of Terahertz-Range Spoof Surface Plasmon Polariton Interconnects for Interchip Data Communication: A Finite Element Method Study. *Electronics* **2023**, *12*, 3719.
https://doi.org/10.3390/electronics12173719

**AMA Style**

Daiyan KM, Abi SB, Rashid ABMH-U, Shawkat MSA.
Effects of Variation in Geometric Parameters and Structural Configurations on the Transmission Characteristics of Terahertz-Range Spoof Surface Plasmon Polariton Interconnects for Interchip Data Communication: A Finite Element Method Study. *Electronics*. 2023; 12(17):3719.
https://doi.org/10.3390/electronics12173719

**Chicago/Turabian Style**

Daiyan, K. M., Shaiokh Bin Abi, A. B. M. Harun-Ur Rashid, and MST Shamim Ara Shawkat.
2023. "Effects of Variation in Geometric Parameters and Structural Configurations on the Transmission Characteristics of Terahertz-Range Spoof Surface Plasmon Polariton Interconnects for Interchip Data Communication: A Finite Element Method Study" *Electronics* 12, no. 17: 3719.
https://doi.org/10.3390/electronics12173719