环状样品等离子体源离子注入过程两维Particle-in-Cell计算机模拟
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摘要
近年来,等离子体源离子注入(PSII)在改善材料表面性能方面得到了广泛应用。该技术是把待加工的样品直接放在等离子体中,当样品上施加一个负偏压脉冲后,电子被电场迅速驱逐并远离样品表面,而离子几乎保持静止,从而在样品表面附近形成了一个离子鞘层。在鞘层中电场的作用下,离子被源源不断地加速注入到样品表面,从而达到改善材料表面性能的目的。在这一技术中,等离子体鞘层的时空演化对材料表面改性有着非常重要的影响。
本文利用两维Particle-in-Cell模型,研究了在高压脉冲作用下,环形样品各表面的等离子体源离子注入过程中离子的动力学行为。利用泊松方程、离子运动方程和电子Boltzmann分布,考察了等离子体鞘层中电势分布、鞘层边界演化、离子密度分布、离子运动状态矢量分布和离子注入剂量分布的时空演化规律。
Particle-in-Cell模型能够实现对注入离子的有效跟踪,反映离子在空间场中的运动情况,完备地描述鞘层演化规律和离子的动力学行为。随着鞘层的演化,电场会出现“聚焦”现象,导致离子在飞行过程中会彼此穿越,造成样品边缘附近离子注入剂量的极度不均匀,即在样品边缘附近出现三个注入剂量高峰。这一分析方法对实际等离子体源离子注入应用具有重要的指导作用。
Recently plasma source ion implantation (PSII) has been widely applied to modify the surface properties of materials. Plasma source ion implantation is a process in which a target is pulse biased to a high negative voltage to form an expanding plasma sheath, electronics has been rapidly expelled of the electric field and away from the target surface, while the ions remain almost stationary. Thus the ions are continuously accelerated to implant the sample surface by the change electric field of the sheath, so as to achieve to modify the surface properties. In plasma source ion implantation process, the sheath evolution has a very important influence on the surface modification of materials.
In this thesis, a two-dimensional Particle-in-Cell model is applied to solve the problem of computing ion dynamics in the ion implantation process on each surface of a ring for the high voltage pulses. The potential distribution of the plasma sheath, the evolution of the sheath’s boundary, the distribution of the ion density, the distribution of the ion motion and the distribution of the ion dose are calculated by the Poisson’s equation, the motion equations of ion and the Boltzmann distribution.
The Particle-in-Cell model can be used to track trajectories of ions in the plasma sheath and describe the sheath evolution and the ion dynamics behavior completely. With the evolution of the sheath, the ion focusing effects due to the sheath potential near the brim of the ring are observed and cause the extreme non-uniform ion implantation dose on the target surface, there are three peaks of implantation dose near the brim of the sample. This method would be very helpful to the design of practical plasma source ion implantation processes.
本文利用两维Particle-in-Cell模型,研究了在高压脉冲作用下,环形样品各表面的等离子体源离子注入过程中离子的动力学行为。利用泊松方程、离子运动方程和电子Boltzmann分布,考察了等离子体鞘层中电势分布、鞘层边界演化、离子密度分布、离子运动状态矢量分布和离子注入剂量分布的时空演化规律。
Particle-in-Cell模型能够实现对注入离子的有效跟踪,反映离子在空间场中的运动情况,完备地描述鞘层演化规律和离子的动力学行为。随着鞘层的演化,电场会出现“聚焦”现象,导致离子在飞行过程中会彼此穿越,造成样品边缘附近离子注入剂量的极度不均匀,即在样品边缘附近出现三个注入剂量高峰。这一分析方法对实际等离子体源离子注入应用具有重要的指导作用。
Recently plasma source ion implantation (PSII) has been widely applied to modify the surface properties of materials. Plasma source ion implantation is a process in which a target is pulse biased to a high negative voltage to form an expanding plasma sheath, electronics has been rapidly expelled of the electric field and away from the target surface, while the ions remain almost stationary. Thus the ions are continuously accelerated to implant the sample surface by the change electric field of the sheath, so as to achieve to modify the surface properties. In plasma source ion implantation process, the sheath evolution has a very important influence on the surface modification of materials.
In this thesis, a two-dimensional Particle-in-Cell model is applied to solve the problem of computing ion dynamics in the ion implantation process on each surface of a ring for the high voltage pulses. The potential distribution of the plasma sheath, the evolution of the sheath’s boundary, the distribution of the ion density, the distribution of the ion motion and the distribution of the ion dose are calculated by the Poisson’s equation, the motion equations of ion and the Boltzmann distribution.
The Particle-in-Cell model can be used to track trajectories of ions in the plasma sheath and describe the sheath evolution and the ion dynamics behavior completely. With the evolution of the sheath, the ion focusing effects due to the sheath potential near the brim of the ring are observed and cause the extreme non-uniform ion implantation dose on the target surface, there are three peaks of implantation dose near the brim of the sample. This method would be very helpful to the design of practical plasma source ion implantation processes.
引文
[1]孙杏凡,等离子体及其应用,高等教育出版社,1983,1:1～23
[2]N.A.克拉尔﹑A.W.特里维尔皮斯,等离子体物理学原理,原子能出版社,1983,1:3
[3]J.R.Conrad,J.L.Radtke,R.A.Dodd,F.J.Worzala and N.C.Tran,Plasma source ion implantation technique for surface modification of materials.J.Appl.Phys.1987,62(3):4591
[4]J.R.Conrad,S.Baumanne,R.Fleming and G.P.Meeker,Plasma Source Ion Implantation Dose Uniformity of a 2x2 Array of Spherical Targets, J.Appl.Phys.,1989,65:1707
[5]J.R.Conrad,Sheath thickness and potential profiles of ion-matrix sheaths for cylindrical and spherical electrodes, J.Appl.Phy., 1987, 62(3):777
[6]M.A.Lieberman,Model of plasma immersion ion implantation, J. Appl.Phys.,1989,66(7) : 2929
[7]J.T.Scheuer,M.Shamin and J.R.Conrad,Model of plasma source ion implantation in planar, cylindrical and spherical geometries, J.Appl.Phys.,1990,67(3) :1245
[8]L.Xie,F.J.Worzala,J.R.Conrad,R.A.Dodd and K.Sridharan,Influence of Temperature Nitrogen Ion lmplantation of Incoloy Alloys 908 and 909,Materials Science and Engineering, 1991,A139:179～184
[9]S.Han,H.Kim,Y.Lee,J.Lee,S.Gkim,Plasma Source Ion Implantation of Nitrogen,Carbon and Oxygen into Ti6A14V Alloy, Surf.Coat.Tech., 1996, 82,270～276
[10]T.E.Sheridan, A model of plasma source ion implantation for inner surface modification, J.Appl.Phys.,1993,74(8) :4903
[11]M.A.Lieberman,Experimental test of models of radio-frequency plasma sheaths,J.Appl. Phys.,1989,66(7):2926
[12]J.R.Conrad,J.L.Radtke,Plasma source ion implantation technique for surface modification of material,J.Appl.,1987,62(11):4591
[13]K.C.Walter,J.T.Scheuer and P.C.Mcintyre,Increased wear resistance of electrodeposited chromium through applications of plasma source ion implantation echniques,Surf Coat Tech,1996,85(1):l～6
[14]Y.S.Yang,S.C.Lee and C.Y.A.Tsao,Self-consistent analysis of a helium plasma in a cylindrical hollow cathode, Surf. Coat. Tech., 2001,141:78
[15]J.Tendys,I.J.Donnelly,M.J.Kenny and J.T.A.Pollock,Plasma immersion ion implantation using plasmas generated by radio-frequency techniques.Appl.Phys.Lett.1988,53:2143
[16]D.Z.Wang,T.C.Ma,A monte carlo simulation model for plasma source ion implantation,J.Appl.Phys.,1993,73(9):4171
[17]D.Z.Wang,T.C.Ma,Energy and angle distributions of ions striking a sphereical target in plasma source ion implantation, J.Appl.Phys.,1994,75(3):1338
[18]D.Z.Wang,T.C.Ma and X.L.Deng,Model of collisional sheath evolution in plasma sourceion implantation,J.Appl.Phys.,1994,75(3):1335
[19]宋远红,宫野,王德真,等离子体源离子注入鞘层随时空演化的数值模拟,计算物理,1995,15:8
[20]X.Lu,S.S.K.Iyer,C.M.Hu,N.W.Cheung,J.Min,Z.N.Fan and P.K.Chu, separation of plasma implantation of oxygen to form silicon on insulator,Appl.Phys.Lett.,1997.71:2767
[21]S.S.K.Iyer,X,Lu,J.B.Liu,J.Min,Z.Fan,P.K.Chu, C.M.Hu and N. W. Cheung, separation of plasma implantation of oxygen(simox) operational phase space. IEEE.Trans. Plasma Sci., 1997,25:1128
[22]P.K.Chu,S.Qin,C.Chan,N.W.Cheung and P.K.Ko,Instrumental and process considerations for the fabrication of silicon-on-insulator,IEEE.Trans.Plasma Sci.,1998,26(2):79
[23]X.Lu,S.S.K.Iyer,M.D.Stratmhan,P.K.Chu and B.Doyle, Hydrogen Induced Silicon Surface Layer Cleavage.Appl. Phys. Lett.,1997,71:1804
[24]D.T.K.Kwok,Z.M.Zeng,P.K.Chu and T.E.Sheridan,Hybrid simulation of sheath and ion dynamics of plasma implantation into ring shaped targets,J.Phys.D:AppI.Phys.,2001,34:1091
[25]Tat-Kun Kwok,Xu-Chu Zeng,Qing-Chuan Chen,Paul K.Chu and T.E.Sheridan,Inner Surface Plasma Immersion Ion Implantation Using an Auxiliary Electrode,IEEE.Trans. Plasma.Sci.,1999,27:225
[26]X.B.Tian,P.K.Chu,Target temperature simulation during fast pulsing plasma immersion ion implantation,J.Phys D:Appl.Phys.,2001,34:1639
[27]刘成森,王德真.空心圆管端点附近等离子体源离子注入过程中鞘层的时空演化,物理学报,2003,52(1),110～113
[28]Q.Y.Tong,K.Gutiahr,S.Hopfe,U.gosele and T.H.Lee,Layer splitting process in hydrogen- implanted Si,Ge,SiC,and diamond substrates.Appl.Phys.Lett.1997,70:1390
[29]M.A.Lieberman,A.J.Lichtenberg,Principles of plasma Diseharges and Materials Processing, New York:John Wiley & Sons,1994,137
[30]L.Tan,R.A.Dodd and W.C.Crone,Corrosion and wear-corrosion behavior of NiTi modified by plasma source ion implantation,Biomater,2003, 24(22):3938
[31]P.K.Chu and X.Zeng.Hydrogen Induced Surface Blistering of Sample Chuck Materials in Hydrogen Plasma Immersion Ion Implantation.J.Vac.sci.Technol.2001.19:2301
[32]X.Lu,S.S.K.Iyer,J.Lee,B.Dooyle,Z.N.Fan,P.K.Chu,C.M.Hu and N.W. Cheung,Plasma Immersion Ion Implantation for SOI Synthesis:SIMOX and Ion-Cut.J.Electron.Mater.1998. 27:1059
[33]M.Bruel,Silicon-on-insulator material technology.Electron.Lett.1995,31:1201
[34]W.Wang,J.H.Booske and C.Baum,Modification of bearing steel surface by nitrogen plasma source ion implantation for corrosion protection, Surf Coat Tech,1999,111(1):97
[35]L.B.Freund,A lower bound on implant density to induce wafer splitting informing compliant substrate structures.Appl.Phys.Lett.1997.70:3519
[36]R.A.Stewart,M.A.Lieberman,Model of plasma immersion ion implantation for voltagepulses finite rise and fall times, J. Appl.Phys.,1991,70(7):3481
[37]V.Vahedi,M.A.Lieberman and M.V.Alves,A one-dimensional collisional model for plasma-immersion ion implantation, J. Appl. Phys., 1991,69(4):2008
[38]D.Z.Wang,T.C.Ma,Model of collisional sheath evolution in plasma source ion implantation,J.Appl.Phys.,1993,74(4):2986
[39]王德人,《非线性方程组解法与最优化方法》,人民教育出版社,1979
[40]切尼,金凯德,《数值数学和计算》,复旦大学出版社,1991
[41] M.P.Hong,G.A.Emmert,Two-dimensional fluid modeling of time-dependent plasma sheath,J.Vac.Sci.Technol B.,1994,12(2):889
[42]T.E.Sheridan,Pulsed sheath dynamics in a small cylindrical bore, Phys Plasmas,1994, 1(10):485
[43]T.E.Sheridan,Pulsed-sheath ion dynamics in a trench,J. Appl.Phys.,1995,28:1095
[44]D.Z.Wang,T.C.Ma and Y.Gong,A Monte Carlo simulation model for plasma source ion implantation,J.Appl.Phys.,1993,73(9):4171
[45]C.S.Liu,D.Z.Wang,Monte Carlo simulation of ions inside a cylindrical bore for plasma source ion implantation, J.Appl.Phys.,2002,91(1):32
[46]D.T.K.Kwok,R.K.Y.Fu,Two dimensional particle-in-cell plasma immersion ion implantation simulation of gear/windmill geometry in cylindrical coordinates along the plane,Surf Clat Tech, 2002, 156:97～100
[47]T.E.Sheridan,Ion focusing by an expanding,two-dimensional plasma sheath,Appl.Phys. Lett.,1996,68(14):1918
[48]B.Rauschenbach,S.Mandl,Plasma sheath expansion around trenches in plasma immersion ion implantation,Nucl.Instr.and Meth.in Phys.Res.B2003,206:803
[49]R.Faej,B.D.Volder,Application of particle-in-cell simulation to plasma source ion implantation,J.Vae.Sci.Technol B.,1994,12(2):884～888
[50]D.T.K.Kwok,X.C.Zeng,Direct current plasma implantation using a grounded conducting grid,J.Appl.Phys.,2000,87(9):4095
[51]D.T.K.Kwok,Z.M.Zeng,Hybrid simulation of sheath and ion dynamics of plasma implantation into ring-shaped targets,J. Appl. Phys.,2001,34:1099
[52]T.E.Sheridan,Particle-in-cell simulation of the pulsed sheath in a trench, IEEE Trans Plasma Sci,1996,24(1):58
[53]Lieberman M.A.Model of Plasma Immersion Ion Implantation.J.Appl.Phys. 1989,66: 2926～2932
[54]Z.Y.Xia and C.Chan,Modeling and experiment on plasma source ion implantation. J.Appl. Phys.,1993,73(8):3651
[55]T.E.Sheridan,T.K.Kwok and P.K.Chu,Kinetic model for plasma-based ion implantation of a short cylindrical tube with auxiliary electrode,Appl.Phys.Lett.,1998,72:1826
[2]N.A.克拉尔﹑A.W.特里维尔皮斯,等离子体物理学原理,原子能出版社,1983,1:3
[3]J.R.Conrad,J.L.Radtke,R.A.Dodd,F.J.Worzala and N.C.Tran,Plasma source ion implantation technique for surface modification of materials.J.Appl.Phys.1987,62(3):4591
[4]J.R.Conrad,S.Baumanne,R.Fleming and G.P.Meeker,Plasma Source Ion Implantation Dose Uniformity of a 2x2 Array of Spherical Targets, J.Appl.Phys.,1989,65:1707
[5]J.R.Conrad,Sheath thickness and potential profiles of ion-matrix sheaths for cylindrical and spherical electrodes, J.Appl.Phy., 1987, 62(3):777
[6]M.A.Lieberman,Model of plasma immersion ion implantation, J. Appl.Phys.,1989,66(7) : 2929
[7]J.T.Scheuer,M.Shamin and J.R.Conrad,Model of plasma source ion implantation in planar, cylindrical and spherical geometries, J.Appl.Phys.,1990,67(3) :1245
[8]L.Xie,F.J.Worzala,J.R.Conrad,R.A.Dodd and K.Sridharan,Influence of Temperature Nitrogen Ion lmplantation of Incoloy Alloys 908 and 909,Materials Science and Engineering, 1991,A139:179～184
[9]S.Han,H.Kim,Y.Lee,J.Lee,S.Gkim,Plasma Source Ion Implantation of Nitrogen,Carbon and Oxygen into Ti6A14V Alloy, Surf.Coat.Tech., 1996, 82,270～276
[10]T.E.Sheridan, A model of plasma source ion implantation for inner surface modification, J.Appl.Phys.,1993,74(8) :4903
[11]M.A.Lieberman,Experimental test of models of radio-frequency plasma sheaths,J.Appl. Phys.,1989,66(7):2926
[12]J.R.Conrad,J.L.Radtke,Plasma source ion implantation technique for surface modification of material,J.Appl.,1987,62(11):4591
[13]K.C.Walter,J.T.Scheuer and P.C.Mcintyre,Increased wear resistance of electrodeposited chromium through applications of plasma source ion implantation echniques,Surf Coat Tech,1996,85(1):l～6
[14]Y.S.Yang,S.C.Lee and C.Y.A.Tsao,Self-consistent analysis of a helium plasma in a cylindrical hollow cathode, Surf. Coat. Tech., 2001,141:78
[15]J.Tendys,I.J.Donnelly,M.J.Kenny and J.T.A.Pollock,Plasma immersion ion implantation using plasmas generated by radio-frequency techniques.Appl.Phys.Lett.1988,53:2143
[16]D.Z.Wang,T.C.Ma,A monte carlo simulation model for plasma source ion implantation,J.Appl.Phys.,1993,73(9):4171
[17]D.Z.Wang,T.C.Ma,Energy and angle distributions of ions striking a sphereical target in plasma source ion implantation, J.Appl.Phys.,1994,75(3):1338
[18]D.Z.Wang,T.C.Ma and X.L.Deng,Model of collisional sheath evolution in plasma sourceion implantation,J.Appl.Phys.,1994,75(3):1335
[19]宋远红,宫野,王德真,等离子体源离子注入鞘层随时空演化的数值模拟,计算物理,1995,15:8
[20]X.Lu,S.S.K.Iyer,C.M.Hu,N.W.Cheung,J.Min,Z.N.Fan and P.K.Chu, separation of plasma implantation of oxygen to form silicon on insulator,Appl.Phys.Lett.,1997.71:2767
[21]S.S.K.Iyer,X,Lu,J.B.Liu,J.Min,Z.Fan,P.K.Chu, C.M.Hu and N. W. Cheung, separation of plasma implantation of oxygen(simox) operational phase space. IEEE.Trans. Plasma Sci., 1997,25:1128
[22]P.K.Chu,S.Qin,C.Chan,N.W.Cheung and P.K.Ko,Instrumental and process considerations for the fabrication of silicon-on-insulator,IEEE.Trans.Plasma Sci.,1998,26(2):79
[23]X.Lu,S.S.K.Iyer,M.D.Stratmhan,P.K.Chu and B.Doyle, Hydrogen Induced Silicon Surface Layer Cleavage.Appl. Phys. Lett.,1997,71:1804
[24]D.T.K.Kwok,Z.M.Zeng,P.K.Chu and T.E.Sheridan,Hybrid simulation of sheath and ion dynamics of plasma implantation into ring shaped targets,J.Phys.D:AppI.Phys.,2001,34:1091
[25]Tat-Kun Kwok,Xu-Chu Zeng,Qing-Chuan Chen,Paul K.Chu and T.E.Sheridan,Inner Surface Plasma Immersion Ion Implantation Using an Auxiliary Electrode,IEEE.Trans. Plasma.Sci.,1999,27:225
[26]X.B.Tian,P.K.Chu,Target temperature simulation during fast pulsing plasma immersion ion implantation,J.Phys D:Appl.Phys.,2001,34:1639
[27]刘成森,王德真.空心圆管端点附近等离子体源离子注入过程中鞘层的时空演化,物理学报,2003,52(1),110～113
[28]Q.Y.Tong,K.Gutiahr,S.Hopfe,U.gosele and T.H.Lee,Layer splitting process in hydrogen- implanted Si,Ge,SiC,and diamond substrates.Appl.Phys.Lett.1997,70:1390
[29]M.A.Lieberman,A.J.Lichtenberg,Principles of plasma Diseharges and Materials Processing, New York:John Wiley & Sons,1994,137
[30]L.Tan,R.A.Dodd and W.C.Crone,Corrosion and wear-corrosion behavior of NiTi modified by plasma source ion implantation,Biomater,2003, 24(22):3938
[31]P.K.Chu and X.Zeng.Hydrogen Induced Surface Blistering of Sample Chuck Materials in Hydrogen Plasma Immersion Ion Implantation.J.Vac.sci.Technol.2001.19:2301
[32]X.Lu,S.S.K.Iyer,J.Lee,B.Dooyle,Z.N.Fan,P.K.Chu,C.M.Hu and N.W. Cheung,Plasma Immersion Ion Implantation for SOI Synthesis:SIMOX and Ion-Cut.J.Electron.Mater.1998. 27:1059
[33]M.Bruel,Silicon-on-insulator material technology.Electron.Lett.1995,31:1201
[34]W.Wang,J.H.Booske and C.Baum,Modification of bearing steel surface by nitrogen plasma source ion implantation for corrosion protection, Surf Coat Tech,1999,111(1):97
[35]L.B.Freund,A lower bound on implant density to induce wafer splitting informing compliant substrate structures.Appl.Phys.Lett.1997.70:3519
[36]R.A.Stewart,M.A.Lieberman,Model of plasma immersion ion implantation for voltagepulses finite rise and fall times, J. Appl.Phys.,1991,70(7):3481
[37]V.Vahedi,M.A.Lieberman and M.V.Alves,A one-dimensional collisional model for plasma-immersion ion implantation, J. Appl. Phys., 1991,69(4):2008
[38]D.Z.Wang,T.C.Ma,Model of collisional sheath evolution in plasma source ion implantation,J.Appl.Phys.,1993,74(4):2986
[39]王德人,《非线性方程组解法与最优化方法》,人民教育出版社,1979
[40]切尼,金凯德,《数值数学和计算》,复旦大学出版社,1991
[41] M.P.Hong,G.A.Emmert,Two-dimensional fluid modeling of time-dependent plasma sheath,J.Vac.Sci.Technol B.,1994,12(2):889
[42]T.E.Sheridan,Pulsed sheath dynamics in a small cylindrical bore, Phys Plasmas,1994, 1(10):485
[43]T.E.Sheridan,Pulsed-sheath ion dynamics in a trench,J. Appl.Phys.,1995,28:1095
[44]D.Z.Wang,T.C.Ma and Y.Gong,A Monte Carlo simulation model for plasma source ion implantation,J.Appl.Phys.,1993,73(9):4171
[45]C.S.Liu,D.Z.Wang,Monte Carlo simulation of ions inside a cylindrical bore for plasma source ion implantation, J.Appl.Phys.,2002,91(1):32
[46]D.T.K.Kwok,R.K.Y.Fu,Two dimensional particle-in-cell plasma immersion ion implantation simulation of gear/windmill geometry in cylindrical coordinates along the plane,Surf Clat Tech, 2002, 156:97～100
[47]T.E.Sheridan,Ion focusing by an expanding,two-dimensional plasma sheath,Appl.Phys. Lett.,1996,68(14):1918
[48]B.Rauschenbach,S.Mandl,Plasma sheath expansion around trenches in plasma immersion ion implantation,Nucl.Instr.and Meth.in Phys.Res.B2003,206:803
[49]R.Faej,B.D.Volder,Application of particle-in-cell simulation to plasma source ion implantation,J.Vae.Sci.Technol B.,1994,12(2):884～888
[50]D.T.K.Kwok,X.C.Zeng,Direct current plasma implantation using a grounded conducting grid,J.Appl.Phys.,2000,87(9):4095
[51]D.T.K.Kwok,Z.M.Zeng,Hybrid simulation of sheath and ion dynamics of plasma implantation into ring-shaped targets,J. Appl. Phys.,2001,34:1099
[52]T.E.Sheridan,Particle-in-cell simulation of the pulsed sheath in a trench, IEEE Trans Plasma Sci,1996,24(1):58
[53]Lieberman M.A.Model of Plasma Immersion Ion Implantation.J.Appl.Phys. 1989,66: 2926～2932
[54]Z.Y.Xia and C.Chan,Modeling and experiment on plasma source ion implantation. J.Appl. Phys.,1993,73(8):3651
[55]T.E.Sheridan,T.K.Kwok and P.K.Chu,Kinetic model for plasma-based ion implantation of a short cylindrical tube with auxiliary electrode,Appl.Phys.Lett.,1998,72:1826