Ion energy distribution of plasma ions of a hollow cathode discharge in Ar + N$_2$ and Ar + O$_2$ gas mixtures

Abstract

A hollow cathode discharge with a Ti cathode and a positively biased ring anode was operated in Ar + N$_2$ or Ar + O$_2$ gas mixtures. The energy distribution of plasma ions is investigated with the help of energy-resolved mass spectrometry. Singly and doubly charged Ar$^+$ and Ar$^{2+}$ ions and molecular N$_2^+$ or O$_2^+$ ions are the most abundant ionic species. The kinetic energy of all plasma ions is enhanced by a positive anode voltage.

Graphical abstract

1 Introduction

Hollow cathode (HC) discharges are frequently used in many applications, e.g., in atomic spectroscopy, laser technology, as UV generators, and for deposition of thin solid films [1,2,3,4,5,6,7,8,9,10,11]. Typical HCs are made from a cylindrical tube which is open on one or both ends. The discharge is sustained by electrons which undergo a pendulum motion inside the HC [2, 12,13,14,15]. HC discharges are often operated without a dedicated anode and instead use the walls of the vacuum chamber for this purpose [16, 17]. To stabilize the HC discharge, an extra ring anode was recently implemented [18, 19]. A biased ring anode offers the additional benefit of controlling the plasma potential outside the HC and the kinetic energy of plasma ions impinging on a substrate [20].

In this communication, we investigate a HC discharge with positively biased anode in a reactive gas environment. Ar + N$_2$ and Ar + O$_2$ gas mixtures are employed, and the energy distribution of several plasma ions is investigated.

2 Experiment

A hollow cathode (HC) made from titanium rod (purity 99.95%, length 40 mm, outer diameter 12 mm, inner diameter of 5 mm) is mounted inside a vacuum chamber (Fig. 1) [20]. The HC tube is open on one end and connected to a water-cooling jacket (holder) on the other end. Argon gas is admitted to the hollow cathode through a ceramic gas pipe connected to its back side with a gas flow controller. Typical argon flow rates during HC operation are in the range of 40–280 sccm. N$_2$ (purity 99.995%) or O$_2$ gas (purity 99.995%) is admitted directly to the vacuum chamber using a second gas flow controller at typical gas flow rates of 10 sccm. The gas pressure in the vacuum chamber was maintained at 2.1 Pa. The gas pressure inside the nozzle is much larger, however, and, for an Ar gas flow rate of 140 sccm, in the range of 50 Pa [9].

Fig. 1

Experimental set-up with hollow cathode, and orifice of EQP analyzer. Gas inlet positions for Ar and N$_2$ or O$_2$ are indicated (schematic)

A ring anode made from a DN 63 CF copper gasket (inner diameter 63 mm, outer diameter 82 mm, thickness 2 mm) is mounted at a distance of 100 mm from the cathode. The hollow cathode is powered by a DC power supply (Advanced Energy MDX–500) operated in current regulation mode with a typical discharge current of 0.5 A. The anode is powered by a regulated laboratory DC voltage supply (Manson HCS-3204) with a maximal output voltage of 60 V.

Energy-resolved mass spectrometry is performed with a commercial Hiden EQP 1000 mass/energy analyzer (Hiden Analytical Ltd., UK) [21, 22]. The instrument is mounted opposite to the hollow cathode and the anode at a distance of 120 mm from the anode (Fig. 1).

3 Results and discussion

Typical ion mass spectra are displayed in Fig. 2 for a HC discharge operated in Ar + N$_2$ and Ar + O$_2$ gas mixtures with an Ar gas flow rate of 80 sccm, a reactive gas (N$_2$, O$_2$) flow rate of 10 sccm, a gas pressure of 1.05 Pa, and a discharge current of 0.5 A. The anode voltage was set to + 60 V. The kinetic energy of detected ions was set to 45 eV which, as we shall see below, is smaller than the value where the maximum ion intensity occurs. The spectra are dominated by singly charged Ar$^+$ ($m/z=40$), doubly charged Ar$^{2+}$ ($m/z=20$), and molecular N$_2^+$ ($m/z=28$) or O$_2^+$ ($m/z=32$) ions (m and z are mass and charge number, respectively). Also present are singly charged Ti$^+$ ($m/z=48$), N$^+$ ($m/z=14$) or O$^+$ ($m/z=16$), and molecular Ar$_2^+$ ($m/z=80$) ions. In addition, we find a significant number of other molecular ions. Molecular ArN$^+$ ($m/z=54$) and ArN$_2^+$ ($m/z=68$) or ArO$^+$ ($m/z=56$) and TiO$^+$ ($m/z=64$) ions are produced with the Ar + N$_2$ or Ar + O$_2$ gas mixture, respectively.

Fig. 2

Mass spectrum a Ar + N$_2$ and b Ar + O$_2$ gas mixture. Anode voltage + 60 V. Ar gas flow rate 80 sccm, reactive gas (N$_2$ or O$_2$) gas flow rate 10 sccm, gas pressure 1.05 Pa, discharge current 0.50 A. Detected ion energy 45 eV

Fig. 3

Ion energy distribution of a Ar$^+$ ($\circ$) and b Ti$^{+}$ ($\triangledown$) ions for a hollow cathode discharge with different anode bias in pure Ar. Ar gas flow rate 160 sccm, gas pressure 1.7 Pa, discharge current 0.5 A

Fig. 4

Ion energy distribution of Ar$^+$ ($\circ$), Ar$^{2+}$ ($\triangle$), Ti$^{+}$ ($\triangledown$), Ti$^{2+}$ ($\blacklozenge$), and Ar$_2^+$ ($\square$) ions for a hollow cathode discharge with a positively biased anode (+ 60 V) in pure Ar. Ar gas flow rate 120 sccm, gas pressure 2.1 Pa, discharge current 0.5 A. Vertical dashed line (+ 60 eV) to guide the eye only

Fig. 5

Ion energy distribution of a Ar$^+$ ($\circ$), Ar$^{2+}$ ($\triangle$), Ti$^{+}$ ($\triangledown$), Ti$^{2+}$ ($\blacklozenge$), and N$^+$ ions and b N$_2^+$ ($\circ$), ArN$^+$ ($\blacktriangle$), TiN$^+$ ($\blacktriangledown$), ArN$_2^+$ ($\diamond$) and Ar$_2^+$ ($\square$) ions for a hollow cathode discharge with a positively biased anode (+ 60 V) in an Ar + N$_2$ gas mixture. Ar gas flow 120 sccm, N$_2$ gas flow 10 sccm, gas pressure 2.1 Pa. The inset shows the N$^+$ intensity around 60 eV. Vertical dashed line (+ 60 eV) to guide the eye only

Ion energy distributions of singly charged Ar$^+$ and Ti$^+$ ions measured in pure Ar gas with different anode bias are displayed in Fig. 3. Measured energy distributions shift to higher energies with applied positive anode voltage. The intensity maximum (peak) of the distributions occurs at a kinetic energy close to $E=e_0 V_a$, where $e_0$ is the elementary charge and $V_a$ is the applied anode voltage. Ar$^+$ ions show a pronounced low-energy tail extending down to lower kinetic energy which is largely absent for Ti$^+$ ions. The low-energy tail is caused by the $\mathrm {Ar^+ + Ar \rightarrow Ar + Ar^+}$ resonant charge transfer collision which produces a slow Ar$^+$ ion. The final kinetic energy of this ion is then determined by the plasma potential where the slow ion is produced. Ti$^+$ ions do not undergo sufficient resonant charge transfer collisions since, for the corresponding $\mathrm {Ti^+ + Ti \rightarrow Ti + Ti^+}$ reaction, the Ti density is too small.

Fig. 6

Ion energy distribution of a Ar$^+$ ($\circ$), Ar$^{2+}$ ($\triangle$), Ti$^{+}$ ($\triangledown$), and O$^+$ ($\square$) ions and b O$_2^+$ ($\circ$), ArO$^+$ ($\triangle$), TiO$^+$ ($\triangledown$), and Ar$_2^+$ ($\square$) ions for a hollow cathode discharge with a positively biased anode (+ 60 V) in an Ar + O$_2$ gas mixture. Ar gas flow 120 sccm, O$_2$ gas flow 10 sccm, gas pressure 2.1 Pa. Vertical dashed line (+ 60 eV) to guide the eye only

Figure 4 compares ion energy distributions of singly charged Ar$^+$, Ti$^+$, and Ar$_2^+$ and doubly charged Ar$^{2+}$ and Ti$^{2+}$ ions plotted versus reduced energy $\tilde{E} = E/z$, where E is the kinetic energy divided by the charge number z. Similar results have been published before [20]. Singly and doubly charged argon ions show a pronounced low-energy tail which presumably is caused by resonant charge changing collisions, e.g., Ar$^{z+}$ + Ar $\rightarrow$ Ar + Ar$^{z+}$. In comparison, the low-energy tail is less pronounced for Ar$^{2+}$ compared to Ar$^+$ ions. The difference is explained by the smaller resonant charge transfer cross section of Ar$^{2+}$ compared to Ar$^+$ ions [22,23,24]. The low-energy tail is much less pronounced for Ti$^+$, Ti$^{2+}$, and Ar$_2^+$ ions. The small intensity of Ti$^{2+}$ ions is not understood yet.

3.1 Ar + N$_2$

Ion energy distributions of singly charged Ar$^+$, Ti$^+$, and N$^+$ and doubly charged Ar$^{2+}$ and Ti$^{2+}$ ions of a HC discharge in Ar + N$_2$ are compared in Fig. 5a. Ar$^+$ ions constitute the dominant mono-atomic ion species, followed by N$^+$, Ti$^+$, and Ar$^{2+}$ ions. Ti$^{2+}$ ions are the least abundant of the investigated species. We want to emphasize that no mass-dependent calibration was applied when comparing different ions. A mass-dependent sensitivity of a similar instrument was investigated by Welzel and Ellmer, and no mass dependence was observed in the mass range $m/z > 20$ [25].

Ar$^+$ and Ar$^{2+}$ ions again display a pronounced and monotonously declining low-energy tail. N$^+$ ions show a complicated low-energy tail structure with two broad humps near 15 eV and 33 eV which may result from in-flight dissociation of N-containing molecules. In addition, N$^+$ ions show a pronounced high-energy tail extending to larger energies beyond 70 eV. As shown by the inset, the main N$^+$ peak around 60 eV splits into 3 sub-peaks with energies of 59.5 eV, 60.8 eV, and 61.6 eV whose origin is not known.

Figure 5b displays ion energy distributions of N$_2^+$, ArN$^+$, ArN$_2^+$, TiN$^+$, and Ar$_2^+$ molecular ions. The N$_2^+$ ion intensity is comparable to Ar$^+$. Ar$_2^+$, ArN$^+$, and ArN$_2^+$ ions are of a comparable intensity. Also observed are TiN$^+$ ions, albeit with small intensity. The extracted TiN$^+$/Ti$^+$ ratio is small and amounts to about $7 \times 10^{-4}$. The broad structure at $\approx 48$ eV observed for ArN$^+$ ions is presumably due to in-flight dissociation of ArN$_2^+$ ions whereby the kinetic energy is shared between the product ArN$^+$ ion and N atom according to the mass ratio.

3.2 Ar + O$_2$

Ion energy distributions of singly charged Ar$^+$, Ti$^+$, and O$^+$ and doubly charged Ar$^{2+}$ ions of a HC discharge in Ar + O$_2$ are compared in Fig. 6. Ar$^+$ ions are the most abundant atomic species followed by O$^+$ and Ar$^{2+}$ ions. Ti$^+$ are the least abundant of the investigated atomic ion species. Molecular ions are compared in Fig. 6b. Molecular O$_2^+$ is the dominant ion species with a 1.5$\times$ larger intensity compared to Ar$^+$, followed by TiO$^+$, and Ar$^{2+}$ ions. The extracted TiO$^+$/Ti$^+$ ratio is rather large and about 17. Also observed are ArO$^+$ ions which have the smallest intensity of the investigated molecular species. Ti$^{2+}$ ions were not investigated due to a too small intensity. The energetic position of the ions is about 58.5 eV and, hence 1.5 eV lower than for the Ar or Ar + N$_2$ gas mixtures. We attribute this small albeit significant difference to the existence of negative ions in the plasma which reduces the plasma potential.

In addition to the main peak at 58.5 eV, the energy distributions of O$^+$, Ti$^+$, and ArO$^+$ display pronounced low-energy peaks at 42 eV, 37 eV, and 51 eV, respectively. It appears likely that these peak originate from in-flight dissociation of larger molecular ions similar to the peak observed for ArN$^+$ ions (see above). For example, the peak at 37 eV observed for Ti$^+$ ions could arise from dissociation of TiO$_2^+$ ions, i.e., TiO$_2^+$ $\rightarrow$ Ti$^+$ + O$_2$. The pronounced high-energy tail above 60 eV observed for O$^+$ ions could originate from dissociate ionization of O$_2$ molecules via a repulsive intermediate state, i.e., $e^-$ + O$_2$ $\rightarrow$ O$_2^{+*}$ + 2 $e^-$ followed by O$_2^{+*}$ $\rightarrow$ O$^+$ + O.

Fig. 7

Energy-integrated Ti$^+$/Ar$^+$, Ar$^{2+}$/Ar$^+$, and Ar$_2^+$/Ar$^+$ ratio for a HC discharge in Ar, Ar + N$_2$, and Ar + O$_2$ gas mixtures. Anode voltage + 60 V. Discharge current 0.50 A. Ar gas flow 120 sccm, Ar gas pressure 2.1 Pa. N$_2$ or O$_2$ gas flow 10 sccm

3.3 Ion Ratios

Measured Ti$^+$/Ar$^+$, Ar$^{2+}$/Ar$^+$, and Ar$_2^+$/Ar$^+$ ion ratios derived from the energy integrated ion energy distributions are displayed in Fig. 7. Positively charged ions are produced in some distance from the negatively biased cathode. The main process for Ar$^+$, Ti$^+$, and Ar$^{2+}$ ion formation is ionization by electron impact [26]. The dominant loss mechanism is via diffusion and the subsequent recombination on surrounding surfaces. Under equilibrium conditions, the corresponding reaction rates are equal and the ion density $n_+$ is obtained from

$$\begin{aligned} k_+ n_e n_a = \frac{D_+}{\Lambda ^2} n_+, \end{aligned}$$

(1)

where the left and the right sides of the eqnarray correspond to the formation rate and to the loss by diffusion. $k_+$ and k$_{2+}$ are rate coefficients for single ionization and double ionization, respectively, $n_e$ and $n_a$ are electron and atom density, respectively, D is the diffusion constant, L is the length of the plasma column, and $\Lambda = L/\pi$. Assuming equal diffusion constants for Ar$^+$ and Ar$^{2+}$ ions, we obtain

$$\begin{aligned} \frac{n_{2+}}{n_+} = \frac{k_{2+}}{k_+}. \end{aligned}$$

(2)

The observed Ar$^{2+}$/Ar$^+$ ion ratio is about 10% for Ar, in fair agreement with more recent observations [26], but considerably smaller (about 2%) for Ar + N$_2$ and Ar + O$_2$ gas mixtures. The ratio is quite large considering the plasma conditions which are characterized by a small electron temperature of 0.8 eV only [20] which is typical for DC and pulsed HC discharges [15, 27].

Semi-empirical cross sections for single and multiple ionization of argon atoms by electron impact are available from Deutsch et al. [28,29,30,31]. A simple estimate shows that formation of doubly ionized Ar$^{2+}$ ions with such low-electron electrons is rather unlikely. Secondary electrons are produced inside the plasma region but also via ion bombardment at the cathode’s surface. The subsequently acceleration of the latter electrons in the cathode sheath yields energetic electrons which attain rather large kinetic energies corresponding to the cathode fall potential, i.e., electron energies of several 100 eV. Ionization by energetic electrons, hence, can produce both singly and doubly charged ions. Calculated Ar$^{2+}$/Ar$^+$ ratios based on the available semi-empirical cross sections of Deutsch et al. [28,29,30] yield 5% and 9% at electron energies of 100 eV and 300 eV, respectively, which are in reasonable agreement with the observed ratio. The small Ar$^{2+}$/Ar$^+$ ratio in Ar + N$_2$ or Ar + O$_2$ is presumably caused by additional Ar$^{2+}$ loss processes, for example, charge changing or rearrangement reactions with N$_2$ or O$_2$ molecules, e.g., [32]

$$\begin{aligned} \mathrm {Ar^{2+} + O_2 \rightarrow ArO^+ + O^+}. \end{aligned}$$

(3)

The observed Ti$^+$/Ar$^+$ ratio is about 2% for Ar and Ar + N$_2$ and one order of magnitude smaller (about $2 \times 10^{-3}$) for the Ar + O$_2$ gas mixture. Ti$^+$ ions are produced by a two-step process, i.e., via sputtering of neutral Ti atoms inside the HC and the subsequent ionization by electron impact in the plasma region between cathode and anode. Cross sections and rate coefficients for electron impact ionization of Ti compared to ionization of Ar are much larger at low energies which is due to the lower ionization energy of Ti (6.83 eV [33]) compared to Ar (15.76 eV). Ionization by low-energy electrons, hence, cannot explain the small Ti$^+$/Ar$^+$ ratio. At larger electron energies of several 100 eV, the rate coefficients for ionization of Ar and Ti by electron impact are much larger and about equal [34]. Assuming ionization by high-energy electrons as the dominant ionization mechanism and about equal diffusion coefficients for Ar$^+$ and Ti$^+$, we have

$$\begin{aligned} \frac{n_+^{\mathrm {Ti}}}{n_+^{\mathrm {Ar}}} \approx \frac{n_a^{\mathrm {Ti}}}{n_a^{\mathrm {Ar}}}. \end{aligned}$$

(4)

The observed small Ti$^+$/Ar$^+$ ratio presumably reflects the much smaller atom density of sputtered Ti atoms compared to Ar atoms. The even smaller Ti$^+$/Ar$^+$ ratio observed for the Ar + O$_2$ gas mixture is readily explained by the additional formation of TiO$^+$ ions resulting in a strong reduction of the Ti$^+$ intensity.

Formation of Ar$_2^+$ ions is more complicated. Most likely are gas phase processes, in particular, (i) three-body reactions of Ar$^+$ ions with two neutral argon atoms, Ar$^+$ + Ar + Ar $\rightarrow$ Ar$_2^+$ + Ar, (ii) associative ionization of two metastable Ar$_m$ atoms, Ar$_m$ + Ar$_m\,\rightarrow \,\mathrm{Ar}_2^+$ + $e^-$, and (iii) associative ionization of highly excited Ar$^{**}$ with neutral Ar atoms, Ar$^{**}$ + Ar $\rightarrow$ Ar$_2^+$ + $e^-$ [21, 26]. The here observed ratios are $3.5 \times 10^{-3}$ for Ar and Ar + N$_2$ gas mixtures and $6.7 \times 10^{-3}$ for Ar + O$_2$. Larger ratios were observed by Bogaerts and Gijbels for a dc glow discharge at a gas pressure of 75 Pa where due to the much larger gas pressure (density) the 3-body reaction process is more likely [26].

4 Conclusions

Ion energy distribution measurements have been taken for a hollow cathode discharge in reactive Ar + N$_2$ and Ar + O$_2$ gas mixtures. The discharge is operated with a positively biased anode which enhances the plasma potential and, hence, the kinetic energy of plasma ions. For an anode bias voltage of + 60 V, the measured ion energy distributions peak at $E=60$ eV for Ar and Ar + N$_2$ gas mixtures and at 58.5 eV for Ar + O$_2$. The difference is attributed to the presence of negative ions in the Ar + O$_2$ discharge. Ar$^+$ and Ar$^{2+}$ ions additionally display a pronounced low-energy tail which we attribute to resonant charge exchange processes. N$^+$ and O$^+$ ions show more complicated energy distributions including a pronounced high-energy tail which may reflect the formation via intermediate N$_2^{+ *}$ or O$_2^{+ *}$ repulsive states. Formation of molecular Ar$_2^+$ and of TiN$^+$, ArN$^+$, and ArN$_2^+$ ions or TiO$^+$ and ArO$^+$ ions with the Ar + N$_2$ or Ar + O$_2$ gas mixtures are observed. There is a huge difference between the TiN$^+$/Ti$^+$ and TiO$^+$/Ti$^+$ ratios. The extracted TiN$^+$/Ti$^+$ and TiO$^+$/Ti$^+$ ratios are about $7 \times 10^{-4}$ and 17, respectively, and thus rather different. It may reflect the different reaction enthalpies during the collisions of, e.g., Ti$^+$ ions with N$_2$ or O$_2$ molecules. The Ar$^{2+}$/Ar$^+$ ion ratio is larger than expected for a discharge with an electron temperature of typically 0.8 eV. It is concluded that high energy electrons which orginate from the negatively biased cathode are responsible for the comparatively large Ar$^{2+}$/Ar$^+$ ratio of several percent.