Numerical simulation of plasma immersion ion implantation on the inner surface of a cylindrical dielectric target

Surface & Coatings Technology 229 (2013) 168–171

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Numerical simulation of plasma immersion ion implantation on the inner surface of a cylindrical dielectric target Yun-Hu Li, Xue-Chun Li ⁎, You-Nian Wang School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, Liaoning 116024, People's Republic of China

a r t i c l e

i n f o

Available online 16 June 2012 Keywords: Inner surface Plasma immersion ion implantation Particle-in-cell PET Charging effects

a b s t r a c t Plasma immersion ion implantation of a cylindrical dielectric substrate target is simulated by a twodimensional collisionless hybrid simulation (particle ions and Boltzmann electrons). In the model, the boundary between the dielectric substrates and plasma is handled by Gauss' law, and the potential of the internal area of the dielectric substrates is solved by Laplace's equation. Using the model, the potential and the ion density distributions in the sheath are obtained. The spatiotemporal evolution of the surface potential and the incident dose along the inner surface of the cylindrical dielectric target are also calculated. The numerical results demonstrate that the surface potential on dielectric was greatly decreased owing to the charging effects and the capacitance of the dielectric. The incident dose is nonuniform. The dose peak is near the top of the bore. At the later stage of the pulse, another dose peak was created at about 0.8D (D is the ion-matrix overlap length) from the top of the bore. In order to get better implantation uniformity, it is helpful to end the pulse before the ions in the bore were consumed. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Plasma immersion ion implantation (PIII) has been applied to electrically insulating materials to enhance the properties and performance. PIII is superior to conventional beam-line ion implantation when dealing with specimens of irregular shape [1,2]. For instance, it has been successfully applied for the inner surface modification of polyethylene terephthalate (PET) bottles, and the gas-barrier property of the PET was improved greatly [3–5]. However, PIII of the interior of cylindrical tubes, especially ones that are electrically insulating materials, is technically difficult. Owing to overlapping of the converging plasma sheaths from opposite surfaces inside a tube, for a cylindrical bore with ρb = 1 (ρb is the normalized radius of the bore), the maximum ion impact energy is only 36.8% of the maximum potential drop [6]. As for the dielectric target, the ion flux and the net implantation energy decrease further due to surface charging effects and capacitance effects of the substrate. Many theoretical and experimental investigations have been performed on the interior surface of cylindrical metal tubes by PIII [7–15]. It has been found that the use of a zero potential conductive coaxial anode can increase the impact energy of the ions on the interior surfaces [12–14]. It has also been determined that the normalized auxiliary radius should range from 0.1 to

⁎ Corresponding author. E-mail address: [email protected] (X-C. Li). 0257-8972/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2012.06.025

0.3 if impact energy is desired [14]. But a very few theoretical works have been reported about PIII into cylindrical dielectric film, especially about PET substrates [16]. It is well known that the structure and evolution of the sheath near the target determine the incident ion flux and the ion impact energy. So it is important to investigate the sheath dynamics of the dielectric targets. In this paper, two-dimensional (2-D) hybrid particle-in-cell (PIC) ions and Boltzmann distribution of electron model in cylindrical coordinate are used to describe the characteristics of sheath inside a cylindrical PET-film. The inner surface charging effects of the PET are investigated with the model. The spatiotemporal evolution of the surface potential and the dose at the surface of dielectric substrates are calculated. In Section 2, the model is described. The simulation results are presented and discussed in Section 3. Conclusions are given in Section 4.

2. Model A simplified schematic of the PIII considered in our model is illustrated in Fig. 1. The target is composed of a cylindrical metal electrode and a tubular PET-film with thickness d on its inner surface. The inner radius of the metal electrode is rin, the outer is rout, and its full length is 2 L. A grounded auxiliary electrode with radius raux is placed along the axis. The whole system was symmetric at the center and only one quarter of the region was simulated as depicted in the figure. Initially, the simulation region is uniformly filled with a neutral plasma in which both the electron density ne and ion density ni equal n0, and the potential ϕ and ion velocity are zero everywhere.

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field that decreases the surface potential of the dielectric. On the other hand, the plasma electron will diffuse to the surface of the dielectric. Therefore, the boundary between the dielectric substrates and plasma can be handled by Gauss' law [17] ε0

∂ϕ ∂ϕ −ε 0 εr 1 ¼ σ c ∂r ∂r

ð5Þ

where ε0 is the permittivity in free space, εr is the relative dielectric constant of the PET-film, ϕ1 is the potential within the dielectric substrate and σc is the surface charge density. Following the basic assumption that ions were stayed on the dielectric surface no matter whether they were implanted or deposited, σc can be obtained by counting PIC particles landing at the dielectric surface and thermal electron diffusion from the plasma [17,18]. Furthermore, at the plasma–dielectric substrate boundary (r0 = rin − d), ϕ = ϕ1 and at the dielectric substrate–metal electrode boundary(r = rin), ϕ1 = V0(t). Within the dielectric, as no real charge exists, the potential can be solved by Laplace's equation [16] 2

∇ ϕ1 ¼ 0:

ð6Þ

For convenience of calculations, the dimensionless variables are given by

Fig. 1. Schematic diagram of PIII for a cylindrical PET-film.

r ; D n N¼ i; n0

Z¼

ρ¼

The negative voltage pulse V0(t) with a rise time tr applied to the metal electrode is assumed by V 0 ðt Þ ¼ V p ½1− expð−t=t r Þ

ð1Þ

where Vp is the peak voltage of negative voltage pulse. In the simulation, the ions are cold and ion motion is collisionless. The electrons are assumed to be in thermal equilibrium. So in the bulk plasma region, we applied Poisson's equation and Boltzmann's distribution of electron to determine the space potential ϕ 2

∇ ϕ¼−


 e eϕ ni −n0 exp ε0 kT e

ð2Þ

where k is the Boltzmann's constant, Te is the electron temperature, and e is the electron charge. The ions are accelerated only by electric field. In cylindrical coordinates, the two-dimensional equations of ion motion are determined by the following equations [19]: r

Δr ¼ V i Δt− z

Δz ¼ V i Δt− r

r

z

z

Vf ¼ Vi − Vf ¼ Vi −

q ∂ϕi 2 ðΔt Þ 2M ∂r

ð3aÞ

q ∂ϕi 2 ðΔt Þ 2M ∂z

ð3bÞ

q ∂ϕi Δt M ∂r

ð4aÞ

q ∂ϕi Δt M ∂z

ð4bÞ

where q is the ion charge, M is the ion mass, and Vir, Vfr, Viz and Vfz are the initial and final velocity of an ion for a time step Δt. In order to solve Poisson's equation, the potential at the dielectric substrate surface Vs(z, t) must be determined. During PIII with dielectric substrate, the ions implanted into the surface accumulate to produce a charge layer because of the low electrical conductivity of the dielectric. The charge, in turn, builds up an opposing electric

z ; D

z

T ¼ tωpi ; r

ψ¼−

ϕ Vp

V V ; and V ρ ¼ V max V max rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     where D ¼ 4ε0 V p =qn0 is the ion-matrix overlap length [7], ωpi ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     n0 q2 =ε0 M is the ion plasma frequency, and V max ¼ 2qV p =M is VZ ¼

the ion velocity corresponding to the peak voltage Vp. The surface potential (Vs) of the PET-film is zero at the beginning of the simulation. At t = 0, the negative voltage pulse V0(t) is applied to the metal electrode. We can obtain the potential ψ1 within the dielectric target by solving Laplace's equation with the finite difference method. Then the surface potential of the PET-film is determined, i.e. Vs(z, t) = ψ1(z, r0, t). The space potential ψ can be calculated by solving Poisson's equation. Using the solved space potential ψ, the position and velocity of each ion at time t are defined from Eqs. (3a)–(4b). After the ions update their position and velocity, they will be weighted to the four corners of the mesh containing the ion. Therefore, we get the normalized ion density N within the simulation region and ready for the next time step of iteration. The boundary conditions are ψ = 0.0 at the top and right-hand, ∂ψ/∂ρ = 0.0 at the left-hand, and ∂ψ/∂Z = 0.0 at the bottom. When the ion hits the cylindrical metal electrode, it will be removed. Whereas at the dielectric, it was assumed to stay on the dielectric surface and the dose will automatically be accumulated surrounding the bombardment area [18]. If the ion across the boundary ρ = 0 or Z = 0, it is assumed that another particle from the other side with reverse ion velocity V ρ or V Z will cross the boundary refilling the lost particle [17]. 3. Results and discussions Nitrogen is used as the working gas (most of ions are N2+) and the simulation parameters are chosen as follows: raux =5 mm, rin =49 mm, rout =52 mm, d=1 mm, L=150 mm, n0 =6.8×109 cm− 3, Vp =–30 kV, kTe =1.5 eV, trωpi =1.0, and εr =3.3. We choose a grid spacing h=Δr=Δz=0.5 mm and a time step of Δt=10− 10 s. The simulation region is chosen to be 10 cm in the radial direction and 20 cm in height. The

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Fig. 2. Temporal evolution of the normalized potential contours.

model was solved on a 200×400 grid and 100 super-particle (ions) were initially placed in each cell. Each super-particle is assigned a certain weight, according to its coordinates [20]. The simulation was terminated at tωpi =20, by which time the sheath has nearly reached the right boundary. The temporal evolution of the potential contour lines is shown in Fig. 2 for tωpi = 1, 5, 10, and 20. When the target is biased with a high negative voltage, an electric field builds up around the target. Ions in the bore are accelerated and implanted into the PET-film. The potential contour lines' strength depends on the shape of the target and on the space charge distribution. As there are fewer ions inside the bore with time, the potential contour lines inside the bore −1 , the dynamic sheath spread more quickly. At about t = 4.5ωpi touches the ground electrode and then expands upwards. In a deeper

region of the bore, the parallel potential lines implying that there is only a radial electric field in this region, sheath expansion here is somewhat one dimensional. Due to the charge accumulation and ion focusing effects, the potential contour lines near the top of the inner surface were greatly distorted. Normalized ion density in the whole simulation region is displayed in Fig. 3 at tωpi = 1, 5, 10, and 20. With the evolution of the sheath, ion density inside the bore was gradually reduced. At −1 , the inside of the bore is observed to be empty and only t = 10ωpi a small region about 0.8D from the top of the bore continues to get implanted. Many of these implanted ions originate from outside of the bore and have the axial and radius velocity. As a result, the dose nonuniformity is more severe near the top of the inner surface of the dielectric (see Fig. 5).

Fig. 3. Temporal evolution of the normalized ion density.

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gets a stable value. At the later stage of the pulse, as the ions present initially inside the bore have been exhausted, the deeper region of the bore is not implanted. With the expansion of sheath, ions initially outside the bore enter it, and another dose peak appears at about 0.8D from the top of the bore (see Fig. 5). This is due to the incident ions from the outside of the bore as aforementioned. Therefore, In order to get better implantation uniformity, it is helpful to end the pulse before the ions inside the bore were consumed. 4. Conclusion

Fig. 4. Evolution of the surface potential of the bore.

The potential along the inner surface of the bore for tωpi = 1, 5, 10, and 20 is depicted in Fig. 4. As the deposited ions cannot be neutralized during the voltage pulse, the charge effects lead to the reduction of the surface potential once the negative pulse voltage is applied to the metal electrode. Considering the bent of electric field lines and the inertia of ions, the charge accumulated on the surface of the bore is not uniform, the surface potential is a function of surface position. The charge effects are greater near the top of the bore. A low peak of surface potential is near, but not at the top of the bore, and its position is moving inward with time. The influence of the PETfilm thickness on the surface potential is also shown in Fig. 4, and we can see that the charge effects are enhanced with the increase of the thickness of the PET-film. Nonuniform surface potential distribution will have an influence on the ion trajectory and results in nonuniform dose on the target surface. Evolution of the incident dose (it is obtained by counting PIC particles landing at the dielectric surface) along the inner surface of the bore is shown in Fig. 5. The dose in the deeper region of the bore is low, but has a better uniformity. The dose peak can be seen near the top of the bore, and it is correspondent to the surface poten−1 , the dose in the deeper region tial and ion density. At about t = 10ωpi

Fig. 5. Evolution of the incident dose along the inner surface of the bore.

In summary, PIII on the inner surface of a cylindrical dielectric target is simulated by the two-dimensional PIC method. Our results show that the surface potential on dielectric was greatly decreased owing to the charging effects and the capacitance of the dielectric. The surface potential and the incident dose along the surface of the cylindrical dielectric target are nonuniform. The dose peak is near the top of the bore. At the later stage of the pulse, another dose peak was created at about 0.8D from the top of the bore. In order to get better implantation uniformity, it is helpful to end the pulse before the ions in the bore were consumed. Acknowledgment This work was supported by the National Basic Research Program of China (No. 2010CB832901). References [1] J.R. Conrad, J.L. Radtke, R.A. Dodol, F.J. Worzala, N.C. Tran, J. Appl. Phys. 62 (1987) 4591. [2] S. Han, Y. Lee, H. Kim, G. Kim, J. Lee, J. Yoon, G. Kim, Surf. Coat. Technol. 93 (1997) 261. [3] N. Sakudo, H. Endo, R. Yoneda, Y. Ohmura, N. Ikenaga, Surf. Coat. Technol. 196 (2005) 394. [4] N. Sakudo, D. Mizutani, Y. Ohmura, H. Endo, R. Yoneda, N. Ikenaga, et al., Nucl. Instrum. Meth. Phys. Res. B 206 (2003) 687. [5] S. Okuji, M. Sekiya, M. Nakabayashi, H. Endo, N. Sakudo, K. Nagai, Nucl. Instrum. Meth. Phys. Res. B 242 (2006) 353. [6] T.E. Sheridan, Phys. Plasmas 1 (1994) 3485. [7] T.E. Sheridan, J. Appl. Phys. 74 (1993) 4903. [8] X.C. Zeng, B.Y. Tang, P.K. Chu, Appl. Phys. Lett. 69 (1996) 3815. [9] X.C. Zeng, T.K. Kwok, A.G. Liu, P.K. Chu, B.Y. Tang, T.E. Sheridan, Appl. Phys. Lett. 71 (1997) 1035. [10] T.E. Sheridan, J. Appl. Phys. 80 (1996) 66. [11] A.G. Liu, X.F. Wang, B.Y. Tang, P.K. Chu, J. Appl. Phys. 84 (1998) 1859. [12] T.E. Sheridan, T.K. Kwok, P.K. Chu, Appl. Phys. Lett. 72 (1998) 1826. [13] D.T.K. Kwok, X.C. Zeng, Q.C. Chen, P.K. Chu, T.E. Sheridan, IEEE Trans. Plasma Sci. 27 (1999) 225. [14] X.C. Zeng, T.K. Kwok, A.G. Liu, P.K. Chu, B.Y. Tang, Appl. Phys. Lett. 83 (1998) 44. [15] X.B. Tian, C.Z. Gong, Y.X. Huang, H.F. Jiang, S.Q. Yang, R.K.Y. Fu, P.K. Chu, Surf. Coat. Technol. 203 (2009) 2727. [16] N. Sakudo, T. Shinohara, S. Amaya, H. Endo, S. Okuji, N. Ikenaga, Nucl. Instrum. Meth. Phys. Res. B 242 (2006) 349. [17] D.T.K. Kwok, IEEE Trans. Plasma Sci. 34 (2006) 1059. [18] G.A. Emmert, J. Vac. Sci. Technol., B 12 (1994) 880. [19] D.T.K. Kwok, Z.M. Zeng, P.K. Chu, T.E. Sheridan, J. Phys. D: Appl. Phys. 34 (2001) 1091. [20] C. Soria-Hoyo, F. Pontiga, A. Castellanos, J. Phys. D: Appl. Phys. 41 (2008) 205.