Spatial structures of rf ring-shaped magnetized sputtering plasmas with two facing cylindrical ZnO/Al₂O₃ targets

Figure 1 shows a front view of the ring-shaped hollow electrode with 24 cylindrical magnets consisting of 12 inner S-pole magnets and 12 outer N-pole magnets. 24 cylindrical neodymium magnets are set up symmetrically to enclose the hollow groove. Here, an iron yoke is not used to fix the magnets in this work because it is unstable to fix them and can affect the magnetic field profile around them. Instead, they are mounted in a plastic cylinder as ring-shaped products with 12 holes. The size of the magnets is 6 mm in diameter and 10 mm in length. The surface magnetic flux density is 575 mT. A 2D magnetic field simulation in a cross section of the line O–A as shown in Fig. 1 is calculated by a conventional commercial electromagnetic simulator Murata software Femtet. Figure 2 shows the simulated 2D magnetic flux lines around the magnets. It is found that the magnetic field lines close the outlet of the groove, so that electrons are expected to be confined in the hollow groove. Figure 3 shows radial profiles of the absolute magnetic flux density at various axial distances of z = 5–50 mm from the hollow electrode. Two dashed lines denote the position of the groove. Here, the absolute magnetic flux density $\left|B\right|\,$is estimated by the following equation:

$$\begin{eqnarray}&&\left|B\right|=\sqrt{{B}_{{\rm{r}}}^{2}+{B}_{{\rm{z}}}^{2}},\end{eqnarray} \tag{ 2 }$$

where B_r and B_z are the radial and axial components of the magnetic flux density as shown in Fig. 2, respectively. It is found that the magnetic flux density has a valley with a value of approximately 17 mT at z = 5 mm near the hollow electrode. It is seen that the magnetic flux density decreases with increasing the axial distance, and the absolute value is less than 5 mT at the axial positions of z ≥ 30 mm.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The Hall parameter h and Larmor radius r_L are often investigated to discuss the magnetic characteristics of electrons and ions in magnetized plasmas. ³⁶⁾ The Hall parameter h is expressed as the following equation:

$$\begin{eqnarray}&&h=\displaystyle \frac{{\omega }_{{\rm{c}}}}{{\nu }_{{\rm{c}}}},\end{eqnarray} \tag{ 3 }$$

where ${\omega }_{{\rm{c}}}$ and ${\nu }_{{\rm{c}}}$ are the angular cyclotron frequency and collision frequency of charged particles, respectively. The angular cyclotron frequency is calculated based on the electronic charge, the charged particle mass, and the magnetic flux density, while the collision frequency is estimated from the gas pressure, collision cross section, and thermal velocity. The Larmor radius r_L is given by the following equation:

$$\begin{eqnarray}&&{r}_{{\rm{L}}}=\frac{v}{{\omega }_{{\rm{c}}}},\end{eqnarray} \tag{ 4 }$$

where $v$ and ${\omega }_{{\rm{c}}}$ are the thermal velocity and the angular cyclotron frequency of charged particles, respectively.

Figures 4(a) and 4(b) show the radial profiles of the electron Hall parameter h_e and the Larmor radius r_Le at various axial distances, respectively. Here, the argon gas pressure is fixed at 0.13 Pa for calculating the Hall parameter. It is recognized that the radial profiles of the electron Hall parameter h_e and Larmor radius r_Le are proportional and inversely proportional to the radial profiles of the magnetic flux density as shown in Fig. 3, respectively. It is found that h_e is higher than 40 at all positions at a fixed Ar gas pressure of 0.13 Pa, whereas the electron Larmor radius r_Le is lower than 10 mm at all positions. In particular, r_Le is less than 1 mm at 10 mm < r < 70 mm near the hollow electrode at z ≤ 15 mm. That is, electrons are strongly confined by the magnetic field lines to produce the high-density plasma near the hollow electrode.

Zoom In Zoom Out Reset image size

Figures 5(a) and 5(b) show the radial profiles of the ion Hall parameter h_i and Larmor radius r_Li at various axial positions, respectively. It is found that the ion Hall parameter h_i is lower than 2 at all positions at a fixed Ar gas pressure of 0.13 Pa, while the ion Larmor radius r_Li is higher than 20 mm at all positions. Thus, ions are not magnetized. It is possible to measure the ion saturation current with the probe because the ions are not affected by the magnetic field. In fact, the ion Larmor radius is much larger than the probe radius of 0.5 mm.

Zoom In Zoom Out Reset image size

Figure 6 shows the radial profile of the ion flux at various axial distances of z = 5–50 mm from the rf powered electrode at an argon pressure of 0.13 Pa. Here, the radius of the rf electrode is 78 mm and the position of the groove is between r = 38 and 48 mm. The magnitude of the ion flux is of the order of 10²⁰ m⁻² s⁻¹. It is seen that the radial profile of the ion flux has a peak of 2.3 × 10²⁰ m⁻² s⁻¹ (the ion density is n_i ≈ 1.5 × 10¹¹ m⁻³ under the assumption of an electron temperature of 4 eV based on our previous work ³⁰⁾) at r = 45.5 mm and z = 5 mm and then the peak decreases from 2.3 to 1.7 × 10²⁰ m⁻² s⁻¹ gradually with increasing the axial distance z from 10 to 20 mm. The radial profile of the ion flux approaches a uniform profile with increasing axial distance z from 20 to 50 mm. This phenomenon is ascribed by a diffusion effect of ions.

Zoom In Zoom Out Reset image size

Figure 7 shows the radial profile of the ion flux at a gas pressure of 0.67 Pa. The ion flux has a peak of 3.1 × 10²⁰ m⁻² s⁻¹ (n_i ≈ 2.0 × 10¹¹ m⁻³) at r = 45.5 mm in the ring-shaped groove. The peak value for p = 0.67 Pa is approximately 1.3 times higher than that for p = 0.13 Pa. The peak decreases from 2.8 to 2.0 × 10²⁰ m⁻² s⁻¹ gradually with increasing the axial distance z from 10 to 20 mm and the radial profile of the ion flux becomes uniform.

Zoom In Zoom Out Reset image size

Figure 8 shows the radial profile of the ion flux at an argon pressure of 0.93 Pa. The peak value is 3.2 × 10²⁰ m⁻² s⁻¹ (n_i ≈ 2.0 × 10¹² m⁻³) at r = 45.5 mm. The magnitude of the ion flux is of the order of 10²¹ m⁻² s⁻¹ and becomes ten times higher than that observed at the gas pressure of 0.13 Pa. It seems that the spatial structure of the ion flux at a gas pressure of 0.93 Pa is similar to that observed for the gas pressures of 0.13 and 0.67 Pa.

Zoom In Zoom Out Reset image size

Table I shows ion flux measured in three different sputtering systems, i.e. a DC magnetron, ³⁷⁾ a high-power impulse magnetron sputtering (HiPIMS), ³⁸⁾ and in the plasma source used in this work. These previous works on the DC magnetrons and the HiPIMS ^37,38) have not reported the spatial profile of the ion flux, but the maximum value of its radial profile. Comparing the ion flux in these sputtering systems is difficult because of the different experimental conditions. The ion flux in our work is the highest value among these systems, although the input power in the other system is 5–10 times higher than the one used in this work. Thus, our sputtering system produces high-density plasma more efficiently.

In this section, the transport of the ions generated in the rf ring-shaped magnetized sputtering plasmas with two facing cylindrical AZO targets has only been described, although a discussion including the transport of sputtered species and radicals is also important for preparing thin films. However, the ion flux profile is strongly related to the spatial distributions of the sputtered species and radicals generated in the plasma and determines the spatial structure of the deposited film.

The radial profile of the ion flux was found to change with increasing the axial position at various gas pressures. A finite deviation of the ion flux profile is present at all spatial positions and all gas pressures as shown in Figs. 6–8. In order to discuss the axial variation of this deviation of the ion flux profile from a perfectly uniform profile quantitatively, this deviation needs to be defined based on the radial profile of the ion flux. The deviation D of the radial profile of the ion flux is defined by the following equation:

$$\begin{eqnarray}&&D=\frac{{{\rm{\Gamma }}}_{{\rm{i}}\,\max }-{{\rm{\Gamma }}}_{{\rm{i}}\,\min }}{{{\rm{\Gamma }}}_{{\rm{i}}\,\max }+{{\rm{\Gamma }}}_{{\rm{i}}\,\min }},\end{eqnarray} \tag{ 5 }$$

where Γ_imax and Γ_imin denote the maximum and minimum values of the radial profile of the ion flux, respectively. The parameter D = 0 means that the radial profile of the ion flux is completely uniform. Since the ion flux influences the quality of the deposited films, D determines the radial profile of the film thickness and its characteristics, such as resistivity and transparency of the deposited AZO films which play a very important role for the performance of electronic devices.

The axial profile of the deviation D at various gas pressures is shown in Fig. 9. Here, D is normalized by the value at z = 5 mm. It is seen that the axial profile of the deviation D has two decay characteristics consisting of a 1st decay from z = 5 to 20 mm and a 2nd decay from z = 30 to 50 mm. It is found for an argon gas pressure of p = 0.13 Pa that the deviation D decreases from 1 to 0.41 with increasing axial position z from 5 to 20 mm and then has a peak of 0.49, and again decreases from 0.49 to 0.36 with increasing z from 30 to 50 mm. The data for p = 0.67 and 0.93 Pa show the same profile as the data for p = 0.13 Pa. The characteristic decay length λ for the 1st and 2nd decay lines is obtained from the following equation:

$$\begin{eqnarray}&&D=\exp \left(-\displaystyle \frac{z}{\lambda }\right).\end{eqnarray} \tag{ 6 }$$

Therefore, the exponential characteristics are based on the diffusion mechanism, i.e. the ions diffuse due to the presence of a density gradience to minimize the deviation of the radial profile of the ion flux. The physical meaning of the decay lengths is related to the diffusion lengths of the ions.

Zoom In Zoom Out Reset image size

It is seen that their decay lengths almost decrease with increasing the gas pressure as shown in Fig. 9. Table II shows the characteristic decay length λ estimated from the axial profile of deviation D. It is found that the 1st decay length is short with a length of 13.9–17.5 mm, and the 2nd decay length is long with a length of 52.6–66.7 mm.

The deviation of the radial profiles of the ion flux as shown in Figs. 6–8 is strongly related to the radial gradient of the ion flux. That is, the deviation should decrease with increasing the radial gradient of the ion flux so that the radial profile of the ion flux approaches a uniform profile.

As shown in Table II, for the 1st decay line, the decay length decreases from 17.5 to 13.9 mm with increasing gas pressure from 0.13 to 0.93 Pa, while for the 2nd decay line, it decreases from 66.7 to 52.6 mm. For the 1st decay line as shown in Fig. 9, the axial position of the radial gradient of the ion flux is selected at z = 5 mm, whereas for 2nd decay line, it is chosen at z = 30 mm. The radial gradients of the ion flux for the peak are estimated from the data as shown in Figs. 6–8. For the 1st decay property, Table III shows the radial gradients of the ion flux at r = 45.5 mm towards the center and the edge for z = 5 mm at various gas pressures of 0.13, 0.67, and 0.93 Pa in Figs. 6–8. For Ar gas pressure of 0.13 Pa, the radial gradients towards the center and the edge are 7.2 × 10²¹ and 7.8 × 10²¹ m⁻³ s⁻¹, respectively. When the gas pressure increases from 0.67 to 0.93 Pa, the radial gradient towards the center increases from 1.1 × 10²¹ to 1.1 × 10²³ m⁻³ s⁻¹, whereas the radial gradient towards the edge increases from 1.2 × 10²² to 1.2 × 10²³ m⁻³ s⁻¹. Thus, the 1st decay length decreases with increasing the gas pressure.

Table III. Radial gradients of the ion flux at r = 45.5 mm towards the center and the edge for z = 5 mm at various gas pressures of 0.13, 0.67 and 0.93 Pa in Figs. 6–8 for 1st decay line.

Ar gas pressure p (Pa)	${\left|\tfrac{d{{\rm{\Gamma }}}_{{\rm{i}}}}{dr}\right|}_{{\rm{center}}}$ (m−3s−1)	${\left|\tfrac{d{{\rm{\Gamma }}}_{{\rm{i}}}}{dr}\right|}_{{\rm{edge}}}$ (m−3s−1)
0.13	7.2 × 1021	7.8 × 1021
0.67	1.1 × 1022	1.2 × 1022
0.93	1.1 × 1023	1.2 × 1023

As shown in Fig. 9, the axial profile of the deviation of the ion flux also indicates the 2nd decay characteristic at various gas pressures. This results from the peaks of the ion flux at r = 14.7 mm and 20.3 mm as shown in Figs. 6–8. Table IV shows radial gradients of the ion flux at r = 14.7 mm for Ar gas pressure of 0.13 Pa and r = 20.3 mm for Ar gas pressures of 0.67 and 0.93 Pa towards the center and the edge for z = 30 mm in Figs. 6–8 for the 2nd decay property. It is seen that the radial gradients towards the center and the edge are 7.2 × 10²⁰ and 6.6 × 10²⁰ m⁻³ s⁻¹, respectively for the gas pressure of 0.13 Pa, whereas for the gas pressure of 0.67 Pa, are 5.4 × 10²⁰ and 1.6 × 10²¹ m⁻³ s⁻¹, respectively. On the other hand, for the gas pressure of 0.93 Pa, the radial gradients towards the center and the edge are 7.3 × 10²¹ and 1.5 × 10²² m⁻³ s⁻¹, respectively. The radial gradients for 2nd decay line are lower than those for the 1st decay line so that the decay length for 2nd decay line is longer than the one for the 1st decay line.

Table IV. Radial gradients of the ion flux at r = 14.7 mm for an Ar gas pressure of 0.13 Pa and r = 20.3 mm for an Ar gas pressure of 0.67 and 0.93 Pa towards the center and the edge for z = 30 mm in Figs. 6–8 for 2nd decay property.

Ar gas pressure p (Pa)	${\left|\tfrac{d{{\rm{\Gamma }}}_{{\rm{i}}}}{dr}\right|}_{{\rm{center}}}$ (m−3 s−1)	${\left|\tfrac{d{{\rm{\Gamma }}}_{{\rm{i}}}}{dr}\right|}_{{\rm{edge}}}$ (m−3 s−1)
0.13	7.2 × 1020	6.6 × 1020
0.67	5.4 × 1020	1.6 × 1021
0.93	7.3 × 1021	1.5 × 1022