# The Effect of Magnetic Field Strength and Geometry on the Deposition Rate and Ionized Flux Fraction in the HiPIMS Discharge

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Deposition Rate

#### 3.2. Ionized Flux Fraction

## 4. Discussion

#### 4.1. Discharge Physics

#### 4.2. Deposition Rate and Ionized Flux Fraction

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A schematic of the magnetron sputtering chamber. The magnetron assembly and the probe holder with the m-QCM are mounted on movable bellows that can be controlled with millimeter precision. The red arrows indicate linear motion.

**Figure 2.**The measured magnetic field (flux density $\mathbf{B}$) and field line directions for the various magnetic field configurations. Normalized arrows indicate the magnetic field direction, the color scale indicates the magnitude of the magnetic field $\left|\mathbf{B}\right|=\sqrt{{B}_{r}^{2}+{B}_{z}^{2}}$. The value of ${B}_{r}$ above the race track at $z=11$ mm is given in the inset for each case.

**Figure 3.**The HiPIMS discharge current and voltage waveforms recorded for various magnetic field configurations: (

**a**) the discharge voltage in fixed voltage mode; (

**b**) the discharge current in fixed voltage mode; and (

**c**) discharge current in fixed peak current mode. The Ar pressure was set to 1 Pa. The pulse width was 100 $\mathsf{\mu}$s at an average power of 300 W.

**Figure 4.**The Ti deposition rate from both dcMS and HiPIMS discharges operated in fixed voltage mode and fixed peak current mode using various magnetic field configurations, measured at 70 mm axial distance over center of cathode. The magnet configurations on the x-axis are ordered from high $\left|\mathbf{B}\right|$ at the left to low $\left|\mathbf{B}\right|$ on the right. The recorded $|{B}_{r,\mathrm{rt}}|$ value above the race track was used as a measure of $\left|\mathbf{B}\right|$.

**Figure 5.**The RSD of Ti deposition rates from both dcMS and HiPIMS discharges operated in fixed voltage mode and fixed peak current mode using various magnetic field configurations. The rates measured at 70 mm axial distance over center, race track and edge of cathode. The magnet configurations on the x-axis are ordered with increasing ${z}_{\mathrm{null}}$ from left to right.

**Figure 6.**The Ti ionized flux fraction in a HiPIMS discharge using various magnet configurations measured at 70 mm axial distance over the center of the cathode. The discharge is operated in the HiPIMS fixed voltage and fixed peak current modes. The magnet configurations on the x-axis are ordered from high $\left|\mathbf{B}\right|$ at the left to low $\left|\mathbf{B}\right|$ on the right. The recorded $|{B}_{r,\mathrm{rt}}|$ value above the race track was used as a measure of $\left|\mathbf{B}\right|$.

**Figure 7.**The Ti ionized flux faction in a HiPIMS discharge using various magnet configurations measured at 30 mm axial distance over the center of the cathode. The discharge was operated in the HiPIMS fixed voltage and fixed peak current modes. The magnet configurations on the x-axis are ordered from high $\left|\mathbf{B}\right|$ at the left to low $\left|\mathbf{B}\right|$ on the right. The recorded $|{B}_{r,\mathrm{rt}}|$ value above the race track was used as a measure of $\left|\mathbf{B}\right|$.

**Figure 8.**The peak discharge current (left y-axis) when operating in fixed voltage mode (${V}_{\mathrm{D}}=625$ V) and the discharge voltage (right $y\u2013$axis) when operating in fixed peak discharge current mode (${I}_{\mathrm{D},\mathrm{max}}=40$ A) as a function of the magnetic field strength over the race track (${B}_{r,\mathrm{rt}}$ in Table 1). o all magnets moved together (C0E0, C5E5, and C10E10) and fixed voltage operation, + magnets mixed (C0E5, C5E0, C10E0 and C0E10) and fixed voltage operation, ◇ all magnets moved together (C0E0, C5E5, and C10E10) and fixed peak current operation, and △ magnets mixed (C0E5, C5E0, C10E0 and C0E10) and fixed peak current operation.

**Figure 9.**Experimentally determined combinations of ${F}_{\mathrm{DR}}$ and ${F}_{\mathrm{flux}}$ at $z=70$ mm, for all three radial positions, and for all magnetic field configurations. The configurations C0E0, C5E5, and C10E10 are denoted by o corresponding to variable $\left|\mathbf{B}\right|$ when all the magnets were moved together. The configurations C0E5, C5E0, C10E0 and C0E10 where the two magnets were moved relative to each other are denoted by x. The discharges were operated at constant voltage and constant average power. Lines of constant ${\alpha}_{\mathrm{t}}$ (solid blue lines) and constant ${\beta}_{\mathrm{t}}$ (dashed green lines), calculated using Equations (3) and (4), respectively, give approximate estimate of these parameters for the studied discharges.

**Figure 10.**(

**a**) The ionization probability ${\alpha}_{\mathrm{t}}$ and (

**b**) the back attraction probability ${\beta}_{\mathrm{t}}$ for the ions of the sputtered species versus the magnetic field strength above the race track $(r=25$ mm). o both magnets moved together (C0E0, C5E5, and C10E10) over race track in fixed voltage operation, x both magnets moved together (C0E0, C5E5, and C10E10) over center in fixed voltage operation, + magnets mixed (C0E5, C5E0, C10E0 and C0E10) over race track in fixed voltage operation, △ magnets mixed (C0E5, C5E0, C10E0 and C0E10) over center in fixed voltage operation, ◇ both magnets moved together (C0E0, C5E5, and C10E10) over center in fixed peak current operation, and □ magnets mixed (C0E5, C5E0, C10E0 and C0E10) over center in fixed peak current operation.

**Figure 11.**(

**a**) The ionization probability of the sputtered species; and (

**b**) the ionized flux fraction above the race track versus the peak discharge current. o both magnets moved together (C0E0, C5E5, and C10E10) over the race track in fixed voltage operation, x both magnets moved together (C0E0, C5E5, and C10E10) over center in fixed voltage operation, + magnets mixed (C0E5, C5E0, C10E0 and C0E10) over race track in fixed voltage operation, △ magnets mixed (C0E5, C5E0, C10E0 and C0E10) over center in fixed voltage operation, ◇ both magnets moved together (C0E0, C5E5, and C10E10) over center in fixed peak current operation, and □ magnets mixed (C0E5, C5E0, C10E0 and C0E10) over center in fixed peak current operation.

**Table 1.**Discharge operating parameters for the investigated dcMS and HiPIMS discharges in fixed voltage and in fixed peak current modes. The average discharge power was kept at 300 W for all the discharges. For HiPIMS discharges, the pulse length was 100 $\mathsf{\mu}$s while the pulse frequency was varied to maintain a constant averaged power. The absolute magnetic field strength and the degree of balancing was varied by displacing the center magnet (C) and the outer ring magnet at the target edge (E). Each configuration is referred to using the displaced distance (in mm) of each magnet from the target backing plate. In this notation, C0E0 refers to a magnetron configuration where the center and outer magnets touch the backing plate.

Magnet | dcMS | HiPIMS | HiPIMS | HiPIMS | |||||||||
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Fixed Voltage | Fixed Peak Current | Fixed Peak Current | |||||||||||

${\mathit{B}}_{\mathit{r},\mathbf{rt}}$ | ${\mathbf{z}}_{\mathbf{null}}$ | ${\mathit{V}}_{\mathbf{D}}$ | ${\mathit{I}}_{\mathbf{D}}$ | ${\mathit{V}}_{\mathbf{D}}$ | ${\mathit{I}}_{\mathbf{D}\mathbf{,}\mathbf{peak}}$ | ${\mathit{f}}_{\mathbf{pulse}}$ | ${\mathit{V}}_{\mathbf{D}}$ | ${\mathit{I}}_{\mathbf{D},\mathbf{peak}}$ | ${\mathit{f}}_{\mathbf{pulse}}$ | ${\mathit{V}}_{\mathbf{D}}$ | ${\mathit{I}}_{\mathbf{D}\mathbf{,}\mathbf{peak}}$ | ${\mathit{f}}_{\mathbf{pulse}}$ | |

[Gauss] | [mm] | [V] | [A] | [V] | [A] | [Hz] | [V] | [A] | [Hz] | [V] | [A] | [Hz] | |

C0E0 | 238 | 66 | 339 | 0.885 | 625 | 80 | 54 | 510 | 40 | 143 | 555 | 80 | 60 |

C0E5 | 217 | 70 | 308 | 0.974 | 625 | 54 | 76 | 565 | 40 | 123 | 580 | 80 | 56 |

C0E10 | 213 | 74 | 311 | 0.964 | 625 | 35 | 115 | 650 | 40 | 111 | |||

C5E0 | 181 | 53 | 317 | 0.946 | 625 | 53 | 80 | 557 | 40 | 129 | 582 | 80 | 58 |

C5E5 | 161 | 59 | 334 | 0.926 | 625 | 36 | 97 | 655 | 40 | 97 | 649 | 80 | 295 |

C10E0 | 137 | 43 | 312 | 0.961 | 625 | 31 | 134 | 660 | 40 | 99 | 636 | 80 | 295 |

C10E10 | 111 | 52 | 330 | 0.909 | 625 | 12 | 450 |

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**MDPI and ACS Style**

Hajihoseini, H.; Čada, M.; Hubička, Z.; Ünaldi, S.; Raadu, M.A.; Brenning, N.; Gudmundsson, J.T.; Lundin, D.
The Effect of Magnetic Field Strength and Geometry on the Deposition Rate and Ionized Flux Fraction in the HiPIMS Discharge. *Plasma* **2019**, *2*, 201-221.
https://doi.org/10.3390/plasma2020015

**AMA Style**

Hajihoseini H, Čada M, Hubička Z, Ünaldi S, Raadu MA, Brenning N, Gudmundsson JT, Lundin D.
The Effect of Magnetic Field Strength and Geometry on the Deposition Rate and Ionized Flux Fraction in the HiPIMS Discharge. *Plasma*. 2019; 2(2):201-221.
https://doi.org/10.3390/plasma2020015

**Chicago/Turabian Style**

Hajihoseini, Hamidreza, Martin Čada, Zdenek Hubička, Selen Ünaldi, Michael A. Raadu, Nils Brenning, Jon Tomas Gudmundsson, and Daniel Lundin.
2019. "The Effect of Magnetic Field Strength and Geometry on the Deposition Rate and Ionized Flux Fraction in the HiPIMS Discharge" *Plasma* 2, no. 2: 201-221.
https://doi.org/10.3390/plasma2020015