2.1. The apparatus

This magnetron sputtering deposition method is shown schematically in Fig.1. The coating system mainly includes a pipe-to-be-coated of Φ86 mm×540 mm, molecular pump system, gas control system, discharge power supply, cathode wires, a sample holder and a solenoid. The cathode is of two types: twisted Ti, Zr and V wires in a total diameter of 2.5 mm, and a Φ1 mm Pd wire. Details of the deposition system can be found in Ref. [5]. Film thickness was measured by a Sirion 200 Schottky field SEM (scanning electron microscope).

Fig. 1:Full-screen View

Schematic diagram of the sputtering coating system.

2.2. Methods

The deposition rate calculation and transport of sputtered particles from the target towards the walls have been discussed for decades [6-8]. The models based on continuum equations are developed to simulate the evolution of surfaces in three dimensions, and useful information is provided on morphology of step coverage for various amounts of surface diffusion and angular distributions [9]. Other models mainly rely on a kinetic Monte Carlo method. For example, the “Effective Thermalizing Collision” (ETC) approximation has successfully explained the Keller-Simmons (K-S) formula, using an empirical equation in classical magnetron sputtering deposition with a single gas [10]. However, the models are complicated, less portable and time-consuming. According to a comparison between experiment and simulation results, we found that the deposition rate of single component Pd metal film can be estimated by the sputtering depth for cylindrical pipe coating.

2.2.1. Depth sputtered off the Pd target and deposition rate of the Pd film

The depth sputtered from the Pd target, D, can be expressed as [11]:

$D=\frac{JY{r}^{3}t}{e_0}$ (1)

where J is the beam current density, Y is the sputtering yield, t is the time of sputtering, r³ is the volume of an atom of the target and e₀ is the electron charge. Certainties in Y lead to certainties in the thickness scale, D. There are a number of predictive relations to calculate Y, based on Sigmund’s theory [12]. In this article, we used Eq. (2) developed by Matsunami et al. [13] and Eq. (3), which was improved later from Eq. (2) by Yamamura and Tawara [14].

$Y\text{=}\frac{\text{0}\text{.042}Q{\alpha }^{\text{*}}}{U_{\text{0}}}\frac{S_{\text{n}}(E)}{1+0.35U_0{s}_{\text{e}}(\epsilon )}{(1-{(\frac{E_{\text{th}}}{E})}^{1/2})}^s$ (2) $Y\text{=}\frac{\text{0}\text{.042}Q{\alpha }^{\text{*}}}{U_{\text{0}}}\frac{S_{\text{n}}(E)}{1+\frac{W{\epsilon }^{-0.2}}{1+{(M_1/7)}^3}{s}_{\text{e}}(\epsilon )}{(1-{(\frac{E_{\text{th}}}{E})}^{1/2})}^s$ (3)

where, S_n(E) is the nuclear stopping power per atom, U₀ is the surface binding energy per atom, Q = 0.47–4.6 in Eq. (2) and Q =0.54–2.62 in Eq. (3), W is obtained from a look-up table provided for 34 elements, M₂ is the target atom’s mass, M₁ is the incident ion mass, s is a constant, and s_e(ε) is the inelastic electronic stopping power. In Eq. (2),

${\alpha }^{\text{*}}=0.08+0.164{(M_2/M_1)}^{0.4}+0.0145{(M_2/M_1)}^{1.29}$ (4)

and

$E_{\text{th}}=\left[1.9+3.8(M_1/M_2)+0.134{(M_2/M_1)}^{1.24}\right]U_0$ (5)

In Eq. (3),

(6)

and

$\begin{array}{l}{E}_{\text{th}}=\left[1+5.7(M_1/M_2)\right](U_0\text{/γ), }{M}_2>M_1\text{,}\\ =6.7(U_0\text{/γ)}，M_2<M_1\end{array}$ (7)

where

$\text{γ=}\frac{\text{4}{M}_1{M}_2}{{(M_1\text{+}{M}_2)}^{\text{2}}}$ (8)

and, when E is in eV,

$\epsilon \text{=}\frac{\text{0}\text{.03255}}{Z_1{Z}_2{(Z_1{}^{2/3}+Z_2{}^{2/3})}^{1/2}}\frac{M_2}{M_1\text{+}{M}_2}E$ (9)

According to Ref. [15-17], errors of the SEM measurements are about 5%. We compared the argon ion deposition yield of Pd film obtained by Eqs. (2) and (3) with the experimental data in energy range 350–700 eV. The deposition rate C is the film thickness (T) over the deposition time (t). Adopting Wolfram Mathematica software, deposition rate of Pd film for a cylindrical pipe was calculated by the two models. Under experimental conditions given in Table 1, seven Pd film samples were deposited on silicon substrates, and the film thicknesses were measured by SEM. In the film coating process, the discharge voltage fluctuated slightly. So, in the simulation, the discharge voltage was chosen at the relatively stable discharge voltage of the film coating process. The simulated and measured Pd film deposition rates are given in Fig.2(a).

Table 1Full-screen View

Parameters to prepare the seven Pd film samples on silicon substrates.

Samples	Discharge current (A)	Stable discharge voltage (V)	Working pressure (Pa)	Gas flow (sccm)
#1	0.02	385	2	2.0
#2	0.02	420	2	2.0
#3	0.02	440	2	3.0
#4	0.03	500	2	2.0
#5	0.03	690	2	2.0
#6	0.04	526	2	2.0
#7	0.04	548	5	2.0

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Fig. 2Full-screen View

Comparison the measured Pd film deposition rates with those calculated using Eqs. (2) and (3).

In most cases, the error ranges −7% ~ 6% for the experimental results and the values calculated using Eq.(3), and 2% ~ 11% for the experimental results and the values calculated using Eq.(3), though the largest error is 16% for both models.

M. P. Seah et al. considered effects of amorphization, damage and implanted ions occurring in the early stage of sputtering and used Q = 0.018/r³, where r is the average interatomic spacing. With this improvement, the Pd film deposition rates calculated using Eq.(2) deviate by −2.5% ~ 20% from the experimental, as shown in Fig. 2(b); while they are just −7.7% ~ 10% for the results calculated by Eq.(3). Particularly, for Samples 1, 5, 6 and 7, the errors are 0%, −1.6%, 0.8% and 1.6%, respectively; while for Samples 2, 3 and 4, the errors are −7.7%,−7.7% and 10%, respectively.

Therefore, in most cases, the deposition rate (C) is basically the same as the depth sputtered (D), which can be used to estimate the Pd film thickness.

3.1 The influence of working pressure on deposition rates

At discharge current of 0.2 A, magnetic field strength of 120 Gauss and gas flow rate of 2 sccm, the deposition rates of TiZrV films on silicon substrates was studied under working pressure of 1–20 Pa. The results are shown in Table 3. At 2 Pa, the deposition rate of TiZrV was the highest (266 nm/h), and the discharge voltage was the highest, too.

At discharge current of 0.04 A, magnetic field strength of 175 Gauss and gas flow of 2.0 sccm, the deposition rates of Pd films on TiZrV film substrates was measured at working pressure of 2−20 Pa (Table 4). Again, at 2 Pa, the deposition rate of Pd film (244 nm/h) and the discharge voltage were the highest.

3.2 The influence of gas flow on deposition rates

At discharge current of 0.25 A, working pressure of 2 Pa, and magnetic field strength of 123 Gauss, the deposition rates of TiZrV films on silicon substrate was studied at gas flow rate of 1, 3 and 4 sccm (Table 5). The highest deposition rate of TiZrV films was 278 nm/h at 1 sccm. The influence of gas flow on the deposition rates is closely related to the discharge voltage. High discharge voltage contributes to the improvement of the deposition rates of TiZrV films. This was found the same for Pd films, as shown in Table 6. At 2 sccm, the deposition rate of Pd films was the highest (240 nm/h).

3.3. The influence of magnetic field strength on deposition rates

At discharge current of 0.2 A, working pressure of 2 Pa, and gas flow of 2 sccm, the deposition rates of TiZrV films on silicon substrate was studied under magnetic field strengths of 82–177 Gauss (Table 7). At 82 Gauss, the highest deposition rate of TiZrV film was 500 nm/h. High discharge voltage increased the deposition rate of TiZrV film. This was found the same for Pd films (Table 8). The highest deposition rate of Pd films was 240 nm/h at 175 Gauss.

3.4. The influence of discharge current on deposition rates

At working pressure of 2 Pa, magnetic field strength of 175 Gauss and gas flow rate of 2 sccm, the deposition rates of TiZrV films on silicon substrate was studied under discharge currents of 0.10, 0.25 and 0.50 A (Table 9). At 0.5 A, the deposition rate of TiZrV thin film was the highest (316 nm/h).

According to the magnetron sputtering model proposed by John A.Thornton [15], the averaged ion current J_{i_mean} can be related to the discharge current (I_dc) by:

where R is the average radius of high density plasma torus with a bright glow close to the cathode, and w is the width of high density plasma torus. Ions current increases with the discharge current. According to Eq.(15), film deposition rate R_sput increases with ion current. Table 9 shows positive relationship between the deposition rate and discharge current but it is not linear. Because when the discharge current increases, R and w will change slightly. In short, theoretical analysis is consistent with the experimental results.

where γ_sput~1, n is the atomic density of target material.

It was found the same results hold for the influence of discharge current on the deposition rates of Pd films. When the discharge current was 0.03 A, the deposition rate of Pd film was the highest, about 217 nm/h.