# Pulse Reverse Plating of Copper Micro-Structures in Magnetic Gradient Fields

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Experimental

#### 2.2. Numerical

## 3. Results and Discussion

#### 3.1. Electrode Kinetics Related to the Cu Layer Distribution on the WE

#### 3.2. Structured Deposit Growth

#### 3.3. Lorentz Force Effect

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sketch of the electrochemical cell with the planar WE that is magnetically templated by three magnetized iron wires. The distribution of the magnetic gradient term $B\nabla B$ on the WE is shown on the right (zoomed top view). (

**b**) Cell current measured in experiments. Top: all 30 cycles. Bottom: the first 5 cycles.

**Figure 2.**(

**a**) Result of the topology measurement. The concave shape can be clearly seen. (

**b**) The originally measured deposit profile along the line passing the three micro-structures, the concave substrate shape obtained from fitting (see text), and the corrected deposit thickness.

**Figure 3.**Morphology of the surface at the mid of the middle cone (

**left**), the rim of the middle cone (

**middle**) and in a region between the cones (

**right**) after 30 cycles.

**Figure 4.**(

**a**) Distribution of the modification factors ${f}_{\mathrm{dep}},\phantom{\rule{0.166667em}{0ex}}{f}_{\mathrm{dis}}$ for the exchange current density ${j}_{00}$. (

**b**) Deposit layer thickness along the horizontal center line passing the three cones after 1 cycle for modified and unmodified ${j}_{00}$.

**Figure 5.**Deposit layer thickness along the horizontal center line passing the three cones in (

**a**) the experiment and (

**b**) the simulation. $d=0$ is set to be at the bottom of the cones in both cases.

**Figure 6.**(

**Left**) Vertical flow velocity at a point 0.1 mm above the top center of the middle Fe wire (indicated by the black circle in the right subfigures) as a function of time. A dashed line at ${U}_{\mathrm{y}}$ = 0 is added. (

**Right**) Distribution of the concentration variation $c-{c}_{\mathrm{bulk}}$ in the center vertical plane at 160 s (deposition) and 190 s (dissolution). Black arrows represent velocity vectors.

**Figure 7.**Lorentz force component in paper direction ${f}_{\mathrm{L},\mathrm{z}}$ in the vertical center plane passing the three Fe wires at 160 s (deposition) and 190 s (dissolution).

**Figure 8.**Velocity component in paper direction ${U}_{\mathrm{z}}$ in the vertical center plane passing the three Fe wires at 160 s (deposition) and 190 s (dissolution).

Parameter | Value | Reference |
---|---|---|

${\chi}_{{\mathrm{Cu}}^{2+}}^{\mathrm{mol}}$ (${10}^{-8}{\mathrm{m}}^{3}/\mathrm{mol}$) | 1.57 | [20] |

${\chi}_{{\mathrm{H}}_{2}\mathrm{O}}$ (${10}^{-6}$) | $-9.0$ | |

${\rho}_{0}$ ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 1014 | [21] |

${\beta}_{{\mathrm{CuSO}}_{4}}$ (${10}^{-5}{\mathrm{m}}^{3}/\mathrm{mol}$) | 16 | |

${\beta}_{{\mathrm{Na}}_{2}{\mathrm{SO}}_{4}}$ (${10}^{-5}{\mathrm{m}}^{3}/\mathrm{mol}$) | $12.4$ | |

$\nu $ (${10}^{-6}{\mathrm{m}}^{2}/\mathrm{s}$) | $1.05$ | |

${V}_{\mathrm{m},\mathrm{Cu}}$$({10}^{-6}{\mathrm{m}}^{3}/\mathrm{mol})$ | 7.11 | |

${D}_{{\mathrm{Cu}}^{2+}}$ (${10}^{-10}{\mathrm{m}}^{2}/\mathrm{s}$ ) | $5.6$ | [22] |

${D}_{{\mathrm{Na}}^{+}}$ (${10}^{-10}{\mathrm{m}}^{2}/\mathrm{s}$ ) | $13.34$ | |

${D}_{{{\mathrm{SO}}_{4}}^{2-}}$ (${10}^{-10}{\mathrm{m}}^{2}/\mathrm{s}$ ) | $10.04$ | |

${z}_{\mathrm{Cu}}^{2+}$ | 2 | |

${z}_{\mathrm{Na}}^{+}$ | 1 | |

${z}_{{{\mathrm{SO}}_{4}}^{2-}}$ | −2 | |

${j}_{00}$$(\mathrm{mA}/{\mathrm{cm}}^{2})$ | 2.5 | [19,21,23,24] |

${\varphi}_{\mathrm{eq},\mathrm{Ref}}$ (V) | $0.337$ | |

$\gamma $ | 0.75 | |

${\alpha}_{\mathrm{a}}$ | 1.5 | |

${\alpha}_{\mathrm{c}}$ | 0.5 |

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**MDPI and ACS Style**

Huang, M.; Uhlemann, M.; Eckert, K.; Mutschke, G.
Pulse Reverse Plating of Copper Micro-Structures in Magnetic Gradient Fields. *Magnetochemistry* **2022**, *8*, 66.
https://doi.org/10.3390/magnetochemistry8070066

**AMA Style**

Huang M, Uhlemann M, Eckert K, Mutschke G.
Pulse Reverse Plating of Copper Micro-Structures in Magnetic Gradient Fields. *Magnetochemistry*. 2022; 8(7):66.
https://doi.org/10.3390/magnetochemistry8070066

**Chicago/Turabian Style**

Huang, Mengyuan, Margitta Uhlemann, Kerstin Eckert, and Gerd Mutschke.
2022. "Pulse Reverse Plating of Copper Micro-Structures in Magnetic Gradient Fields" *Magnetochemistry* 8, no. 7: 66.
https://doi.org/10.3390/magnetochemistry8070066