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Grid-shadow effect in grid-enhanced plasma source ion implantation
Surface & Coatings Technology 192 (2005) 101 – 105 www.elsevier.com/locate/surfcoat
Grid-shadow effect in grid-enhanced plasma source ion implantation J.L. Wang a,*, G.L. Zhang a, Y.N. Wang b, Y.F. Liu a, S.Z. Yang a a
b
Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China State Key Laboratory of Materials Modification, Dalian University of Technology, Dalian 116023, China Received 6 February 2004; accepted in revised form 9 April 2004 Available online 10 June 2004
Abstract A grid-shadow effect is observed in grid-enhanced plasma source ion implantation (GEPSII), in which ions produced within the plasma region are extracted through a grid electrode and are then accelerated to the inner surface of a cylindrical bore for implantation. By simulating the ion transportation behaviors from the grid electrode to the inner surface using a Monte Carlo model, we find that the grid-shadow effect results from grid blocking of the ion emission on the grid electrode and that it varies with the experimental parameters such as the gap distance between the grid electrode and the inner surface, the gas pressure, and the applied negative potential. D 2004 Elsevier B.V. All rights reserved. Keywords: Ion implantation; Grid-enhanced plasma source ion implantation; Monte Carlo simulation
1. Introduction Plasma source ion implantation (PSII) or plasma immersion ion implantation (PIII) [1] is an effective technique to enhance surface properties of materials such as metals, polymers, ceramics, and semiconductors. In PSII, a target is immersed in plasma. When a series of negative highvoltage pulses are applied to the target, ions are extracted directly from the plasma and are accelerated to the target for implantation. Since this technique was proposed by Conrad et al. in 1987 [2], it has received great attention in recent years [3– 8]. Grid-enhanced plasma source ion implantation (GEPSII) is a newly proposed method in our laboratory to enhance the inner surface properties of a cylindrical bore [9,10], which has similarities to the process described by Matossian et al. [11]. In our method (see Fig. 1(a)), plasma is produced by radio frequency (rf) discharge established between the axial central cathode and the coaxial grounded grid electrode; the plasma can diffuse through the grid electrode to the inner surface of the tubular sample named the target. When a negative voltage pulse is applied on the target, positive ions within the region between the grid electrode and the inner surface can be accelerated into the target. Experimental and theoretical studies [9,10,12 – 14] have demonstrated the * Corresponding author. Tel.: +86-10-8264-9458; fax: +86-10-8264-9531. E-mail address: [email protected] (J.L. Wang). 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.04.069
advantages of this new technique over other ion implantation techniques for inner surface modification of a cylindrical bore [5,7,15]. However, grid-like patterns are observed on the inner surface processed by GEPSII (see Fig. 1(b)), and the grid-line regions corresponding to regions with fewer ions implanted, we call it the grid-shadow effect. Obviously, the existence of grid shadow may reduce the implantation uniformity on the inner surface and experimental studies [16] have shown that the surface characteristics of the shadow and unshadow areas are different, e.g., the surface hardness of the shadow area is weaker than that of the unshadowed area. In this paper, we will investigate the gridshadow effect by Monte Carlo simulation.
2. Model Fluid models are often used to calculate the ion sheath dynamics in the PSII process and we have also adopted a fluid model to calculate the ion dose and impact energy on the target in GEPSII [12,13]. However, because fluid simulation only contains the trajectories of fluid elements rather than ions and because it cannot describe details of ion transportation, in this paper, we select the Monte Carlo model to follow the ion trajectories within the region between the grid electrode and the inner surface as illustrated in Fig. 1(a), where the radius of the grid electrode and
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(a)
to the electron temperature. Therefore, the electron density within the simulation region can be assumed zero and we need only follow the ion movement in the simulation. (2) For simplifying simulation, we may assume that the radial electric field E(r) in the sheath can be expressed approximately as that used in the cathode dark sheath of dc glow discharge [17] EðrÞ ¼ 2/p ðr ra Þðrb ra Þ2 : (3) Ions emitted from the grid electrode at the neutral temperature. 2.2. Simulation procedure
(b)
Fig. 1. (a) Cross-section diagram of the GEPSII system considered and (b) the grid-shadow effect observed on the inner surface of the processed cylindrical bore by GEPSII (the grid-line regions correspond to the shadow regions).
the inner surface are ra and rb, respectively, with the gap distance of d. 2.1. Model assumptions In the GEPSII experiment, the gap distance between the grid electrode and the target is equalqtoffiffiffiffiffiffiffiffiffiffiffi or less than the ion – 4e0 /p matrix overlap length D (D ¼ 1 þ en0 , where /p is the applied potential, e is the atomic unit of charge, and n0 is the plasma density) [4], so the ion sheath can quickly expand to the grid electrode and then the implantation process will become stable [12,13]. Because we are only concerned about the grid-shadow effect here, we simply consider the steady-state ion implantation period when the applied potential and the sheath thickness are fixed, and our simulation region is according to the PSII ion sheath region. The basic model assumptions used are as follows: (1) The electrons react instantaneously and the applied negative voltage at the inner surface is large compared
During an ion traveling from the grid electrode to the target, it will be accelerated by the radial electric field and will undergo collisions with the neutral particles. The ion position is expressed in a cylindrical geometry by the axial position z, the radial position r, and the azimuthal angle h on the plane perpendicular to the axial direction, respectively. The ion three-dimensional motion under the radial electric field is determined by the ion velocity along the axial direction (vz), the radial direction (vr), and the direction perpendicular to the radial direction on the plane vertical to the axis of the bore (vh). Ions start at the grid electrode (r0 = ra) with initial velocities randomly chosen from a Maxwellian distribution with the neutral gas temperature (300 K). To investigate the grid-shadow effect, initial ions at the grid electrode are uniformly placed only on positions corresponding to the grid holes in the experiment; that is, h0 is uniformly distributed approximately between 0 and 2p, except some parts corresponding to the grid lines (see Fig. 2(a)). To reduce the simulation time, only ions with the initial axial position z0 of within approximately 0 – 10 mm are considered, also extracting the parts corresponding to the grid lines. The ion three-dimensional motion under the influence of the radial electric field is determined by Newton’s Laws: vr ¼ vr0 þ
qEðr0 Þ Dt mi
ð1Þ
vh ¼ vh0 ;
ð2Þ
vz ¼ vz0 ;
ð3Þ
r ¼ r0 þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ððvr0 þ vr ÞDt=2Þ2 þðvh DtÞ2 ;
z ¼ z0 þ vz0 Dt
ð4Þ ð5Þ
where vr0, vh0, vz0 and vr, vh, vz are the velocities before and after the time step Dt; r0, z0, and r, z is the position coordinate before and after Dt; E(r0) is the radial electric
J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
103
determined by a random number. Both charge exchange and elastic collisions will change the ion energy and moving directions (for details, see Refs. [8,20]). After collision is considered, the ion velocity and position advance at the next time step will be calculated again, and this procedure is repeated until all the ions reach the target. When an ion reaches the target, to obtain a clear picture describing the grid-shadow phenomena, certain information is recorded such as the azimuthal angle h and the axial position z of the ion. In order to test the validity of our numerical model, we recalculate the ion energy and angle distributions at the inner surface of a large cylindrical bore, which has been calculated by Liu and Wang [8] in cylindrical geometry using Monte Carlo model. To investigate the grid-shadow effect, we advance ions in constant time steps Dt, follow the ion azimuthal angle h and axial position z in every time step but not in constant distance step Dr as used in Liu and Wang’s simulation. Our calculated results under their conditions agree well with what they have given.
3. Results and discussions Fig. 2. (a) The initial ion azimuthal angle distribution at the grid electrode and (b) the ion azimuthal angle distribution at the inner surface for ra = 3.9 cm, rb = 5 cm, p = 0.1 Pa, and /p = 10 kV. For clarity, h only in the range of approximately 0 – 10j are considered.
field at position r0; and q and mi are the ion charge and mass, respectively. The ion position advance for cylindrical coordinates follows Boris’ method [18]. Note that the existence of vh will cause a coordinate rotation in one time step on the plane vertical to the axial direction. If the rotation angle is Dh (sin Dh = vhDt/r), then the ion new azimuthal angle is h ¼ h0 þ Dh
ð6Þ
and accordingly, the ion new velocity in the new coordinate is 2 4
vr vh
3
2
5 ¼4 2
cosDh
sinDh
sinDh cosDh
32 54
vr vh
3 5 :
ð7Þ
1
The probability of ion collision during the time step Dt is calculated by: P = 1 exp[ nrt(e)Ds], where n is the gas density, rt(e) is the total collision cross-section varying with the ion energy e, and Ds is the ion travel distance during Dt (Dt must be small enough so that the energy [and hence rt(e)] can be regarded constant over Ds). The cross-section for charge exchange and elastic collisions considered here is obtained from Phelps [19]. This calculated probability is compared with a random number to determine whether a collision will occur, and the type of collision is also
To be consistent with our GEPSII experiment, we select N2+ as the simulated plasma ions, and all the other parameters such as the gas pressure ( p), the negative potential (/p), and the gap distance between the grid electrode and the target (d) are based on the experimental data. The size of the grid hole is 0.9 0.9 mm and the diameter of the grid line is 0.1 mm. Fig. 2(a) gives the initial ion azimuthal angle distribution f(h0) on the grid electrode in our simulation. Because the ion initial distribution on the grid electrode should be properly described by the two-dimensional distribution f (h0,z0), f(h0) is given by f ðh0 Þ ¼
Z
L
f ðh0 ; z0 Þdz;
ð8Þ
0
where L is the length of the grid electrode. f(h0) is normalized such that the integral over the whole azimuthal angle (approximately 0 – 2p) is 1. For clarity, only distribution of h0 in the range of approximately 0– 10j are presented. The uniform ion distribution regions are at angles corresponding to the grid holes and the regions without ions are at angles corresponding to the grid lines. When all the initial ions reach the inner surface, the ion azimuthal angle distribution on the inner surface f(h) can be obtained (see Fig. 2(b)). It can be seen that angles with the least ion distributions in Fig. 2(b) are rightly the angles with zero ion distributions in Fig. 2(a) and the less ion implanted regions are the corresponding shadow regions, which demonstrates that the shadow regions source from grid-line blocking of ion emission on the grid electrode. In addition, distributions in the shadow regions are also not uniform, with the minimum values at the center of the shadow regions.
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The initial ion axial distribution on the grid f(z) and the final ion axial distribution on the target f(z) are not given because they are similar to the profiles of f(h0)and f(h). During an ion traveling from the grid electrode to the target, it can be accelerated by the radial electric field and scattered due to collisions with the neutral particles. Without collisions, ions will move in line with the electric field along the radial direction and there will be no ions on the target corresponding to the grid lines which will be the worst case of the grid-shadow effect. When suffering collisions, ions will deviate from their original moving direction, which will be helpful to mitigate the grid-shadow effect on the target. In our experiment, the negative potential is on the order of 10 kV, the gas pressure is about 1.0 Pa, and the radius of the grid electrode is 2.4 or 3.9 cm, with the gap distance of 2.6 or 1.1 cm. Under such conditions, the effect of electric field acceleration greatly exceeds the effect of collision scattering. The ion movement cannot deviate much from the radial direction and so the grid-shadow effect cannot be avoided. Since increasing the negative potential can improve the electric field acceleration, and raising the gas pressure and the ion travel distance can lead to more ion collisions before implantation, we can predict that lower negative potential
(/p), higher gas pressure ( p), and longer gap distance (d) can weaken the grid-shadow effect. Our flowing calculations will try to verify the above predictions. For simplicity, we give a parameter Rs to represent the grid-shadow effect which is expressed as: Rs ¼
ns =ss ; nu =su
where ns is the total number of ions within the total shadow areas ss of the target, and nu is the total number of ions within the total unshadow areas su of the target. We define the shadow area as areas with the ion number per unit area less than the half ion number per unit area initially put in the grid holes. Obviously, higher Rs case represents weaker grid-shadow effect case. Fig. 3 gives the rate of the grid-shadow effect Rs versus the applied negative potential for different gas pressures and gap distances. It can be seen that for all the cases, Rs decreases with the applied negative potential (the electric field); for fixed negative potential and gas pressure, ions will suffer less collision scattering in the case of smaller gap distance, so Rs is lower for smaller gap distance (see Fig. 3(a)); for fixed negative potential and gap distance, lower gas pressure also means less collision scattering of ion, so Rs is lower for lower gas pressure (see Fig. 3(b)). The variations of Rs with the applied negative potential, the gas pressure, and the gap distance agree well with our recent experimental results [16].
4. Conclusions We have investigated the grid-shadow effect observed in the GEPSII experiment for inner surface modification of a cylindrical bore by Monte Carlo simulation. Typical calculated results such as the ion azimuthal angle distribution on the inner surface of the bore can clearly show the gridshadow effect. By varying the external parameters in the calculation, it is found that larger gap distance, higher gas pressure, and lower negative potential can reduce the gridshadow effect, which is consistent with the corresponding experimental results. However, it should be pointed out that, such selection of parameters for mitigating the grid-shadow effect are undesirable for improving the ion impact energy [13] and will accordingly reduce the surface hardness of the processed sample [16]. Now we are revising our experimental devices to reduce the grid-shadow effect, e.g., changing the grid electrode into lines parallel to the axial direction and making the cylindrical bore rotating.
Acknowledgements Fig. 3. Rate of the grid-shadow effect Rs versus the applied negative potential for (a) different grid electrode radius at p = 0.1 Pa and (b) for different gas pressures at ra = 3.9 cm.
This work is supported by the National High Technology Research and Development Program of China (863
J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
Program) under Grant No. 2002A331020, the National Natural Science Foundation of China under Grant Nos. 50071068 and 10275088, and the Science and Technology program of Beijing Municipal Science and Technology Commission under Grant No. H020420160130. The authors would like to thank Dr. Bin Liu in the University of Iowa for his helpful discussions on this paper.
References [1] A. Anders, Handbook of Plasma Immersion Ion Implantation and Deposition, Wiley, New York, 2000. [2] J.R. Conrad, J.L. Radtke, R.A. Dodd, F.J. Worzala, N.C. Tran, J. Appl. Phys. 62 (1987) 4591. [3] M.A. Lieberman, J. Appl. Phys. 66 (1989) 2926. [4] G.A. Emmert, M.A. Henry, J. Appl. Phys. 71 (1992) 113. [5] T.E. Sheridan, J. Appl. Phys. 74 (1993) 4903. [6] K.C. Walter, J.T. Scheuer, P.C. Mcintyre, N. Yu, M. Nastasi, Surf. Coat. Technol. 85 (1996) 1. [7] X.C. Zeng, T.K. Kwok, A.G. Liu, P.K. Chu, B.Y. Tang, J. Appl. Phys. 83 (1998) 44.
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[8] C.S. Liu, D.Z. Wang, J. Appl. Phys. 91 (2002) 32. [9] B. Liu, G.L. Zhang, D.J. Cheng, C.Z. Liu, R. He, S.Z. Yang, J. Vac. Sci. Technol., A, Vac. Surf. Films 19 (2001) 2958. [10] B. Liu, C.Z. Liu, D.J. Cheng, G.L. Zhang, R. He, S.Z. Yang, Nucl. Instrum. Methods Phys. Res., B Beam Interact. Mater. Atoms 184 (2001) 644. [11] J.N. Matossian, R.W. Schumacher, D.M. Pepper, Material Plasma Processing Surface Potential Control, US Patent 5374456, 1994. [12] J.L. Wang, G.L. Zhang, S.H. Fan, W.B. Yang, S.Z. Yang, Chin. Phys. Lett. 19 (2002) 1473. [13] J.L. Wang, G.L. Zhang, S.H. Fan, W.B. Yang, S.Z. Yang, J. Phys., D, Appl. Phys. 36 (2003) 1192. [14] G.L. Zhang, J.L. Wang, W.B. Yang, S.H. Fan, C.Z. Liu, S.Z. Yang, Acta Phys. Sin. 52 (2003) 2213 (in Chinese). [15] M. Sun, S.Z. Yang, X.C. Chen, J. Vac. Sci. Technol., A, Vac. Surf. Films 14 (1996) 3071. [16] G.L. Zhang, J.L. Wang, Y.F. Liu, W.B. Yang, S.H. Fan, C.Z. Liu, S.Z. Yang, Chin. Phys. Lett. 21 (2004) 1114. [17] H.L. Wei, Z.L. Liu, Acta Phys. Sin. 43 (1994) 950 (in Chinese). [18] C.K. Birdsall, A.B. Langdon, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, 1985, p. 338. [19] A.V. Phelps, J. Phys. Chem. Ref. Data 20 (1991) 557. [20] W. Yu, L.Z. Zhang, J.L. Wang, L. Han, G.S. Fu, J. Phys., D, Appl. Phys. 34 (2001) 3349.
Grid-shadow effect in grid-enhanced plasma source ion implantation J.L. Wang a,*, G.L. Zhang a, Y.N. Wang b, Y.F. Liu a, S.Z. Yang a a
b
Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China State Key Laboratory of Materials Modification, Dalian University of Technology, Dalian 116023, China Received 6 February 2004; accepted in revised form 9 April 2004 Available online 10 June 2004
Abstract A grid-shadow effect is observed in grid-enhanced plasma source ion implantation (GEPSII), in which ions produced within the plasma region are extracted through a grid electrode and are then accelerated to the inner surface of a cylindrical bore for implantation. By simulating the ion transportation behaviors from the grid electrode to the inner surface using a Monte Carlo model, we find that the grid-shadow effect results from grid blocking of the ion emission on the grid electrode and that it varies with the experimental parameters such as the gap distance between the grid electrode and the inner surface, the gas pressure, and the applied negative potential. D 2004 Elsevier B.V. All rights reserved. Keywords: Ion implantation; Grid-enhanced plasma source ion implantation; Monte Carlo simulation
1. Introduction Plasma source ion implantation (PSII) or plasma immersion ion implantation (PIII) [1] is an effective technique to enhance surface properties of materials such as metals, polymers, ceramics, and semiconductors. In PSII, a target is immersed in plasma. When a series of negative highvoltage pulses are applied to the target, ions are extracted directly from the plasma and are accelerated to the target for implantation. Since this technique was proposed by Conrad et al. in 1987 [2], it has received great attention in recent years [3– 8]. Grid-enhanced plasma source ion implantation (GEPSII) is a newly proposed method in our laboratory to enhance the inner surface properties of a cylindrical bore [9,10], which has similarities to the process described by Matossian et al. [11]. In our method (see Fig. 1(a)), plasma is produced by radio frequency (rf) discharge established between the axial central cathode and the coaxial grounded grid electrode; the plasma can diffuse through the grid electrode to the inner surface of the tubular sample named the target. When a negative voltage pulse is applied on the target, positive ions within the region between the grid electrode and the inner surface can be accelerated into the target. Experimental and theoretical studies [9,10,12 – 14] have demonstrated the * Corresponding author. Tel.: +86-10-8264-9458; fax: +86-10-8264-9531. E-mail address: [email protected] (J.L. Wang). 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.04.069
advantages of this new technique over other ion implantation techniques for inner surface modification of a cylindrical bore [5,7,15]. However, grid-like patterns are observed on the inner surface processed by GEPSII (see Fig. 1(b)), and the grid-line regions corresponding to regions with fewer ions implanted, we call it the grid-shadow effect. Obviously, the existence of grid shadow may reduce the implantation uniformity on the inner surface and experimental studies [16] have shown that the surface characteristics of the shadow and unshadow areas are different, e.g., the surface hardness of the shadow area is weaker than that of the unshadowed area. In this paper, we will investigate the gridshadow effect by Monte Carlo simulation.
2. Model Fluid models are often used to calculate the ion sheath dynamics in the PSII process and we have also adopted a fluid model to calculate the ion dose and impact energy on the target in GEPSII [12,13]. However, because fluid simulation only contains the trajectories of fluid elements rather than ions and because it cannot describe details of ion transportation, in this paper, we select the Monte Carlo model to follow the ion trajectories within the region between the grid electrode and the inner surface as illustrated in Fig. 1(a), where the radius of the grid electrode and
102
J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
(a)
to the electron temperature. Therefore, the electron density within the simulation region can be assumed zero and we need only follow the ion movement in the simulation. (2) For simplifying simulation, we may assume that the radial electric field E(r) in the sheath can be expressed approximately as that used in the cathode dark sheath of dc glow discharge [17] EðrÞ ¼ 2/p ðr ra Þðrb ra Þ2 : (3) Ions emitted from the grid electrode at the neutral temperature. 2.2. Simulation procedure
(b)
Fig. 1. (a) Cross-section diagram of the GEPSII system considered and (b) the grid-shadow effect observed on the inner surface of the processed cylindrical bore by GEPSII (the grid-line regions correspond to the shadow regions).
the inner surface are ra and rb, respectively, with the gap distance of d. 2.1. Model assumptions In the GEPSII experiment, the gap distance between the grid electrode and the target is equalqtoffiffiffiffiffiffiffiffiffiffiffi or less than the ion – 4e0 /p matrix overlap length D (D ¼ 1 þ en0 , where /p is the applied potential, e is the atomic unit of charge, and n0 is the plasma density) [4], so the ion sheath can quickly expand to the grid electrode and then the implantation process will become stable [12,13]. Because we are only concerned about the grid-shadow effect here, we simply consider the steady-state ion implantation period when the applied potential and the sheath thickness are fixed, and our simulation region is according to the PSII ion sheath region. The basic model assumptions used are as follows: (1) The electrons react instantaneously and the applied negative voltage at the inner surface is large compared
During an ion traveling from the grid electrode to the target, it will be accelerated by the radial electric field and will undergo collisions with the neutral particles. The ion position is expressed in a cylindrical geometry by the axial position z, the radial position r, and the azimuthal angle h on the plane perpendicular to the axial direction, respectively. The ion three-dimensional motion under the radial electric field is determined by the ion velocity along the axial direction (vz), the radial direction (vr), and the direction perpendicular to the radial direction on the plane vertical to the axis of the bore (vh). Ions start at the grid electrode (r0 = ra) with initial velocities randomly chosen from a Maxwellian distribution with the neutral gas temperature (300 K). To investigate the grid-shadow effect, initial ions at the grid electrode are uniformly placed only on positions corresponding to the grid holes in the experiment; that is, h0 is uniformly distributed approximately between 0 and 2p, except some parts corresponding to the grid lines (see Fig. 2(a)). To reduce the simulation time, only ions with the initial axial position z0 of within approximately 0 – 10 mm are considered, also extracting the parts corresponding to the grid lines. The ion three-dimensional motion under the influence of the radial electric field is determined by Newton’s Laws: vr ¼ vr0 þ
qEðr0 Þ Dt mi
ð1Þ
vh ¼ vh0 ;
ð2Þ
vz ¼ vz0 ;
ð3Þ
r ¼ r0 þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ððvr0 þ vr ÞDt=2Þ2 þðvh DtÞ2 ;
z ¼ z0 þ vz0 Dt
ð4Þ ð5Þ
where vr0, vh0, vz0 and vr, vh, vz are the velocities before and after the time step Dt; r0, z0, and r, z is the position coordinate before and after Dt; E(r0) is the radial electric
J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
103
determined by a random number. Both charge exchange and elastic collisions will change the ion energy and moving directions (for details, see Refs. [8,20]). After collision is considered, the ion velocity and position advance at the next time step will be calculated again, and this procedure is repeated until all the ions reach the target. When an ion reaches the target, to obtain a clear picture describing the grid-shadow phenomena, certain information is recorded such as the azimuthal angle h and the axial position z of the ion. In order to test the validity of our numerical model, we recalculate the ion energy and angle distributions at the inner surface of a large cylindrical bore, which has been calculated by Liu and Wang [8] in cylindrical geometry using Monte Carlo model. To investigate the grid-shadow effect, we advance ions in constant time steps Dt, follow the ion azimuthal angle h and axial position z in every time step but not in constant distance step Dr as used in Liu and Wang’s simulation. Our calculated results under their conditions agree well with what they have given.
3. Results and discussions Fig. 2. (a) The initial ion azimuthal angle distribution at the grid electrode and (b) the ion azimuthal angle distribution at the inner surface for ra = 3.9 cm, rb = 5 cm, p = 0.1 Pa, and /p = 10 kV. For clarity, h only in the range of approximately 0 – 10j are considered.
field at position r0; and q and mi are the ion charge and mass, respectively. The ion position advance for cylindrical coordinates follows Boris’ method [18]. Note that the existence of vh will cause a coordinate rotation in one time step on the plane vertical to the axial direction. If the rotation angle is Dh (sin Dh = vhDt/r), then the ion new azimuthal angle is h ¼ h0 þ Dh
ð6Þ
and accordingly, the ion new velocity in the new coordinate is 2 4
vr vh
3
2
5 ¼4 2
cosDh
sinDh
sinDh cosDh
32 54
vr vh
3 5 :
ð7Þ
1
The probability of ion collision during the time step Dt is calculated by: P = 1 exp[ nrt(e)Ds], where n is the gas density, rt(e) is the total collision cross-section varying with the ion energy e, and Ds is the ion travel distance during Dt (Dt must be small enough so that the energy [and hence rt(e)] can be regarded constant over Ds). The cross-section for charge exchange and elastic collisions considered here is obtained from Phelps [19]. This calculated probability is compared with a random number to determine whether a collision will occur, and the type of collision is also
To be consistent with our GEPSII experiment, we select N2+ as the simulated plasma ions, and all the other parameters such as the gas pressure ( p), the negative potential (/p), and the gap distance between the grid electrode and the target (d) are based on the experimental data. The size of the grid hole is 0.9 0.9 mm and the diameter of the grid line is 0.1 mm. Fig. 2(a) gives the initial ion azimuthal angle distribution f(h0) on the grid electrode in our simulation. Because the ion initial distribution on the grid electrode should be properly described by the two-dimensional distribution f (h0,z0), f(h0) is given by f ðh0 Þ ¼
Z
L
f ðh0 ; z0 Þdz;
ð8Þ
0
where L is the length of the grid electrode. f(h0) is normalized such that the integral over the whole azimuthal angle (approximately 0 – 2p) is 1. For clarity, only distribution of h0 in the range of approximately 0– 10j are presented. The uniform ion distribution regions are at angles corresponding to the grid holes and the regions without ions are at angles corresponding to the grid lines. When all the initial ions reach the inner surface, the ion azimuthal angle distribution on the inner surface f(h) can be obtained (see Fig. 2(b)). It can be seen that angles with the least ion distributions in Fig. 2(b) are rightly the angles with zero ion distributions in Fig. 2(a) and the less ion implanted regions are the corresponding shadow regions, which demonstrates that the shadow regions source from grid-line blocking of ion emission on the grid electrode. In addition, distributions in the shadow regions are also not uniform, with the minimum values at the center of the shadow regions.
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J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
The initial ion axial distribution on the grid f(z) and the final ion axial distribution on the target f(z) are not given because they are similar to the profiles of f(h0)and f(h). During an ion traveling from the grid electrode to the target, it can be accelerated by the radial electric field and scattered due to collisions with the neutral particles. Without collisions, ions will move in line with the electric field along the radial direction and there will be no ions on the target corresponding to the grid lines which will be the worst case of the grid-shadow effect. When suffering collisions, ions will deviate from their original moving direction, which will be helpful to mitigate the grid-shadow effect on the target. In our experiment, the negative potential is on the order of 10 kV, the gas pressure is about 1.0 Pa, and the radius of the grid electrode is 2.4 or 3.9 cm, with the gap distance of 2.6 or 1.1 cm. Under such conditions, the effect of electric field acceleration greatly exceeds the effect of collision scattering. The ion movement cannot deviate much from the radial direction and so the grid-shadow effect cannot be avoided. Since increasing the negative potential can improve the electric field acceleration, and raising the gas pressure and the ion travel distance can lead to more ion collisions before implantation, we can predict that lower negative potential
(/p), higher gas pressure ( p), and longer gap distance (d) can weaken the grid-shadow effect. Our flowing calculations will try to verify the above predictions. For simplicity, we give a parameter Rs to represent the grid-shadow effect which is expressed as: Rs ¼
ns =ss ; nu =su
where ns is the total number of ions within the total shadow areas ss of the target, and nu is the total number of ions within the total unshadow areas su of the target. We define the shadow area as areas with the ion number per unit area less than the half ion number per unit area initially put in the grid holes. Obviously, higher Rs case represents weaker grid-shadow effect case. Fig. 3 gives the rate of the grid-shadow effect Rs versus the applied negative potential for different gas pressures and gap distances. It can be seen that for all the cases, Rs decreases with the applied negative potential (the electric field); for fixed negative potential and gas pressure, ions will suffer less collision scattering in the case of smaller gap distance, so Rs is lower for smaller gap distance (see Fig. 3(a)); for fixed negative potential and gap distance, lower gas pressure also means less collision scattering of ion, so Rs is lower for lower gas pressure (see Fig. 3(b)). The variations of Rs with the applied negative potential, the gas pressure, and the gap distance agree well with our recent experimental results [16].
4. Conclusions We have investigated the grid-shadow effect observed in the GEPSII experiment for inner surface modification of a cylindrical bore by Monte Carlo simulation. Typical calculated results such as the ion azimuthal angle distribution on the inner surface of the bore can clearly show the gridshadow effect. By varying the external parameters in the calculation, it is found that larger gap distance, higher gas pressure, and lower negative potential can reduce the gridshadow effect, which is consistent with the corresponding experimental results. However, it should be pointed out that, such selection of parameters for mitigating the grid-shadow effect are undesirable for improving the ion impact energy [13] and will accordingly reduce the surface hardness of the processed sample [16]. Now we are revising our experimental devices to reduce the grid-shadow effect, e.g., changing the grid electrode into lines parallel to the axial direction and making the cylindrical bore rotating.
Acknowledgements Fig. 3. Rate of the grid-shadow effect Rs versus the applied negative potential for (a) different grid electrode radius at p = 0.1 Pa and (b) for different gas pressures at ra = 3.9 cm.
This work is supported by the National High Technology Research and Development Program of China (863
J.L. Wang et al. / Surface & Coatings Technology 192 (2005) 101–105
Program) under Grant No. 2002A331020, the National Natural Science Foundation of China under Grant Nos. 50071068 and 10275088, and the Science and Technology program of Beijing Municipal Science and Technology Commission under Grant No. H020420160130. The authors would like to thank Dr. Bin Liu in the University of Iowa for his helpful discussions on this paper.
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