氮离子在射频电极的能量分布及电子碰撞率数值模拟研究
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摘要
使用PIC-MCC方法对氮气容性耦合射频辉光放电在射频电极处的离子能量分布和角度分布进行了数值模拟;计算了整个放电空间的电子碰撞激发率,电离率,离解率和离解电离率。模拟过程中考虑了电子与背景气体(氮分子N_2)的各种碰撞,以及两种离子(氮分子离子N_2+和氮原子离子N+)与背景气体(氮分子N_2)的碰撞;忽略了电子与离子之间的碰撞过程。具体工作如下所示:
1.建立了氮气射频放电等离子体过程的PIC/MCC自洽的混合模型,其中带电粒子在电场中的运动及其产生的自洽场由PIC方法描述,粒子间的碰撞过程由MCC方法描述。用Fortran语言结合模型编写了一维的PIC/MCC模拟程序,模拟了氮气射频放电的物理过程。
2.计算了氮气射频等离子体中射频电极处离子的能量分布和角度分布,及其随气压和电压幅值的变化。
3.计算了氮气射频等离子体中整个放电空间电子碰撞激发率,电离率,离解率和离解电离率的分布,同时还计算了其随放电气压和电压幅值的变化情况。
4.为了保证程序的准确性,与氮气的电子能量分布的实验结果进行了比较,结果比较吻合。
总之,氮气射频辉光放电,是一个复杂的物理过程,放电既受到多种放电条件的制约,又相互影响,相互制约。研究这些放电条件之间的内在关系,对氮化合物材料的合成以及材料表面的氮化处理有大意义。本工作为氮气射频等离子体放电过程提供了理论参考依据。
In capacitive coupling rf glow discharge of nitrogen ,energy and angle distribution of ions at electrode is numerically simulated by using the of PIC– MCC method. At the same time, we simulated the dissociation rate,ionization rate, excitation rate and dissociative ionization rate of electron at all the discharge room. Through the process of simulation, we not only considered the all kinds of collides of electron and nitrogen,but also ions and nitron. Since the value of section of all kinds of collides has big diffrence, we only considerd the elastic collisions and charge exchange collisions of ions and nitrogen. Ignoring the collisions of electronic and ion . Specific work shown below:
1 Established the PIC-MCC hybrid model of the nitrogen rf plasma discharge, in the field of charged particle movement and the self-consistent way by the PIC, the process of collision between particles by MCC method. using Fortran language, a model of combining the PIC-MCC was writed, to simulate the process of nitrogen rf discharge.
2 The calculation of nitrogen rf plasma energy and angle distribution of ions at the electrode and its distribution with discharge pressure and voltage amplitude variation.
3 Calculating the nitrogen rf plasma discharge in the space of dissociation rate, electronic, ionization rates and the distribution of dissociation rate, also simulated with the discharge pressure and the changes of the voltage amplitude.
4 In order to ensure the accuracy of the procedure, the nitrogen electronic energy distribution of experimental results were compared, and the results were good.
Anyhow, nitrogen rf glow discharge, is a complex process of discharge at various discharge conditions. Study these discharge conditions of the inner link between the material of nitrogen, and the synthesis material surface has great significance nitriding process. This work for nitrogen rf plasma discharge provides a theoretical reference.
1.建立了氮气射频放电等离子体过程的PIC/MCC自洽的混合模型,其中带电粒子在电场中的运动及其产生的自洽场由PIC方法描述,粒子间的碰撞过程由MCC方法描述。用Fortran语言结合模型编写了一维的PIC/MCC模拟程序,模拟了氮气射频放电的物理过程。
2.计算了氮气射频等离子体中射频电极处离子的能量分布和角度分布,及其随气压和电压幅值的变化。
3.计算了氮气射频等离子体中整个放电空间电子碰撞激发率,电离率,离解率和离解电离率的分布,同时还计算了其随放电气压和电压幅值的变化情况。
4.为了保证程序的准确性,与氮气的电子能量分布的实验结果进行了比较,结果比较吻合。
总之,氮气射频辉光放电,是一个复杂的物理过程,放电既受到多种放电条件的制约,又相互影响,相互制约。研究这些放电条件之间的内在关系,对氮化合物材料的合成以及材料表面的氮化处理有大意义。本工作为氮气射频等离子体放电过程提供了理论参考依据。
In capacitive coupling rf glow discharge of nitrogen ,energy and angle distribution of ions at electrode is numerically simulated by using the of PIC– MCC method. At the same time, we simulated the dissociation rate,ionization rate, excitation rate and dissociative ionization rate of electron at all the discharge room. Through the process of simulation, we not only considered the all kinds of collides of electron and nitrogen,but also ions and nitron. Since the value of section of all kinds of collides has big diffrence, we only considerd the elastic collisions and charge exchange collisions of ions and nitrogen. Ignoring the collisions of electronic and ion . Specific work shown below:
1 Established the PIC-MCC hybrid model of the nitrogen rf plasma discharge, in the field of charged particle movement and the self-consistent way by the PIC, the process of collision between particles by MCC method. using Fortran language, a model of combining the PIC-MCC was writed, to simulate the process of nitrogen rf discharge.
2 The calculation of nitrogen rf plasma energy and angle distribution of ions at the electrode and its distribution with discharge pressure and voltage amplitude variation.
3 Calculating the nitrogen rf plasma discharge in the space of dissociation rate, electronic, ionization rates and the distribution of dissociation rate, also simulated with the discharge pressure and the changes of the voltage amplitude.
4 In order to ensure the accuracy of the procedure, the nitrogen electronic energy distribution of experimental results were compared, and the results were good.
Anyhow, nitrogen rf glow discharge, is a complex process of discharge at various discharge conditions. Study these discharge conditions of the inner link between the material of nitrogen, and the synthesis material surface has great significance nitriding process. This work for nitrogen rf plasma discharge provides a theoretical reference.
引文
[1] Zhang L Z, Yu W, Wwan J L,et al. Electron Ttransport Behaviors in the Nitrogen Direct Current Glow Discharge. Chin.Phys,2001,10(7):639-644
[2] Zhang L Z, Yu W, Han L, et al. Generation and distribution of fast atomic species(N+,Nf) in nitrogen glow discharge[J]. Plasma Science & Technology, 2006, 8(6):670-674.
[3]张连珠, N 2+离子在氮直流辉光放电中碰撞离解的作用[J].物理学报,2003,52(4): 0920-0924.
[4]张连珠,傅凤清,王增波等,氮气空心阴极辉光放电等离子体离子的蒙特卡罗模拟研究,核聚变与等离子体物理,2006,26(2):135-139
[5]张连珠,于威,氮气直流辉光放电阴极鞘层区电子行为的蒙特卡罗模拟研究,河北大学学报(自然科学版),2001,23(3):239-243
[6] Yu W,Zhang L Z,Wang J L,Monte Carlo simulation of the fast electrons and heavy particles in the CDS of nitrogen dc glow discharge.J Phys D,2001,34:3349-3355
[7] Fu Guang-sheng, Wang Jiu-Li, Yu Wei, et al. Self-Consistent Description of Nitrogen dc Glow Discharge, Chin. Phys. Lett., 2002, 19(4); 521-523
[8] Liu Chengsen, Wang Dezhen, self-Consistent Model for Pulsed Direct-Current Nitrongen Glow Discharge, Plasma Science & Technology, 2005, 7(2):2745-2747.
[9]芦岩,王友年,碰撞对非对称射频鞘层特性的影响,物理学报,2004,53(8):2661-2665.
[10]邱华檀,王友年,马腾才,碰撞效应对射频偏压电极上离子能量分布和角度分布的影响,物理学报,2002,51(6):1666-1670.
[11]戴忠玲,王友年,马腾才,射频等离子体鞘层动力学模型,物理学报,2001,50(12):1241-1248.
[12]孟显,王友年,马腾才,电子发射对稳态等离子体鞘层影响的理论研究和数值模拟,强激光与粒子束,2000,12:358.
[13] Bogaerts Annemie,Gijbels Renaat, The role of fast argon ions and atoms in the ionization of argon in a direct current glow discharge: a mathematical simulation,Applied Physics,1995,78:6427-6431
[14] Bogaerts Annemie, Gijbels Renaat, Goedheer Wim.Hybrid modeling of a capacitively coupled radio frequency glow discharge in argon: combined Monte Carlo and fluid model,Japanese journal of applied physics,1999,38: 4404-4415.
[15] Yan M., Bogaerts Annemie, Gijbels Renaat, Goedheer W.J, Spatial behavior of energy relaxation of electrons in capacitively coupled discharges: comparison between Ar and SiH4 , Journal of applied physics,2000,87(8):3628-3636.
[16] Yan M,Bogaerts Annemie, Goedheer W.J, Gijbels Renaat,Electron energy distribution function in capacitively coupled RF discharges: differences between electropositive Ar and electronegative sih4 discharges ,Plasma sources science and technology ,2000,9:583-591.
[17] Ivanov Vladimir, Proshina Olga, Rakhimova Tatyana, Rakhimov Alexander, Herrebout Dieter, Bogaerts Annemie, Comparison of a one-dimensional particle-in-cell-Monte Carlo model and a one-dimensional fluid model for a CH4H2 capacitively coupled radio frequency discharge, Journal of applied physics,2002,91(10):6296-6302.
[18] GeorgieVa Violeta, Bogaerts Annemie, Gijbels Renaat,Numerical investigation of ion energy distribution functions in single and dual frequency capacitively coupled plasma reactors,Physical review E,2004,69.
[19] Georgieva Violeta, Bogaerts Annemie,Numerical simulation of dual frequency etching reactors:influence of the external process parameters on the plasma characteristics,Journal of applied Physics,2005,98(2):1-13.
[20] Charles C, Boswell R W and Porteous R K,Measurement and modeling of ion energy distribution,functions in a low pressure argon plasma diffusing from a 13.56 MHz helicon source, Vacuum Science and Technology A,1992,10:168.
[21] Gottscho R A, Ion transport anisotropy in low pressure,high-density plasmas, Vacuum Science and Technology B,1884,11.
[22] Holber W M and Forster J, Ion energetics in electron cyclotron resonance discharges, Vacuum Science and Technology A,1990,8:3720.
[23] Hopwood J, Ion bombardment energy distributions in a radio frequency induction plasma, Appl. Phys. Lett.1993,62:940.
[24] Benoit-Cattin P and Bernard L C, Anomalies of the energy of positive ions extracted from high-frequency ion sources, Journal of Applied Physics, 1968, 39 :5723.
[25] Farouki R T, Hamaguchi S and Dalvie M, Analysis of a kinematic model for ion transport in rf plasma sheaths, Physical Review A,1992,45:5913.
[26] Kushner M J, Distribution of ion energies incident on electrodes in capacitively coupled rf discharges, Journal of Applied Physics, 1985, 58: 4024.
[27] Thompson B E, Sawin H H and Fischer D , Monte-Carlo simulation of ion transport through rf glow-discharge sheaths , Journal of Applied Physics ,1988 ,63: 2241.
[28] Barnes M S, Forster J C and Keller J H, Ion kinetics in low-pressure, electropoositive, RF glow discharge sheaths,IEEE Transactions on Plasma Sciences, 1991,19: 240.
[29] May P W, Field D and Klemperer D F , Modeling radio-frequency discharges: effects of collisions upon ion and neutral particle energy distributions, Journal of Applied Physics , 1992 71: 3721.
[30] Vender D and Boswell R W ,Numerical modeling of low-pressure RF plasmas, IEEE Transactions on Plasma Sciences,1990, 18 :725.
[31] Surendra M and Graves D B, Particle simulation of radio-frequency glow discharges, IEEE Transactions on Plasma Sciences, 1991,19: 144.
[32] Zhong-Ling Dai and You-Nian Wang, Multiple ion dynamics model for thecollisionless rf sheaths and the ion energy distributions at rf-biased electrodes in fluorocarbon plasmas,Physical Review E,2002,66:1
[33] R. J. M. M. Snijkers, M. J. M. van Sambeek, G. M. W. Kroesen, and F. J. de Hoog, Mass-resolved ion energy measurements at the grounded electrode of an argon rf plasma, Appl Phys Lett,1993,63(3):308-316.
[34] J. Liu, G. L. Huppert, and H. H. Sawin, Ion bombardment in rf plasmas, Journal of Applied Physics,1990,68(8):3916-3934.
[35] A. Manenschijn, G. C. A. M. Janssen, E. van der Drift, and S. Radelaar, Measurement of ion impact energy and ion flux at the rf electrode of a parallel plate reactive ion etcher , Journal of Applied Physics,1991,69(3): 1253– 1262.
[36] J. K. Olthoff, R. J. Van Brunt, S. B. Radovanov, J. A. Use of an ion energy analyser-mass spectrometer to measure ion kinetic-energy distributions from RF discharges in argon-helium gas mixtures , Measurement and Technology,1994,141(2):105– 110.
[37] Snijkers, R. J. M. M. van Sambeek, M. J. M. Kroesen, G. M. W.; de Hoog, F. J, Mass-resolved ion energy measurements at the grounded electrode of an argon rf plasma, Applied Physics Letters,1993,63(3): 308-310.
[38] D Barton, D J Heason, R D Short and J W Bradley,The measurement and control of the ion energy distribution function at a surface in an RF plasma, Meas. Sci. Technol,2000,11: 1726–1731.
[39] W J Goedheer, Lecture notes on radio-frequency discharges, dc potentials, ion and electron energy distributions, Plasma Sources Sci,2000,9: 507–516.
[40] Vendor, D.Boswell, R. W, Numerical modeling of low-pressure RF plasmas, IEEE Transactions on Plasma Science, 1990,18(4):725-732.
[41] E Kawamura, V Vahedi,M A Lieberman and C K Birdsall,Ion energy distributions in rf sheaths ; review,analysis and simulation,Plasma sources Sci.Technol,1999,8: 45-60.
[42] Wild C and Koidl P , Structured ion energy distribution in radio frequencyglow-discharge systems, Appl. Phys. Lett. 1989,54:505
[43] I.V. Schweigert, Different Modes of a Capacitively Coupled Radio-Frequency Discharge in Methane, Physical Review Letters,2004,92
[44] A L Alexandrov and I V Schweigert,Two-dimensional PIC–MCC simulations of a capacitively coupled radio frequency discharge in methane, PLASMA SOURCES SCIENCE AND TECHNOLOGY.2005,14:209-213
[45] S.M. Levitskii, Zh. Tekh. Fiz,Sov. Phys. Tech. Phys.,1957,2: 887 .
[46] C. K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, 1985.
[47] V Vahedit, C K Birdsall, M A Liebermant, G DiPesoS and T D Rognlien ,Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II: comparisons with laboratory measurements of electron energy dktribution functions, Plasma Sources Sci, Technol, 1993,2: 273-278.
[48] C K Birdsall,Particle-in-cell Charged-Particle Simulations,Plus Monte Carlo Collisions With Nertral Atoms,PIC-MCC,IEEE transactions on plasma science,1991,19(2).
[49] J van Dijk, G M W Kroesen and A Bogaerts, Plasma modelling and numerical Simulation, JOURNAL OF PHYSICS D: APPLIED PHYSICS,2009,42.
[50] H C Kim1, F Iza, S S Yang, M Radmilovic-Radjenovic and J K Lee, Particle and fluid simulations of low-temperature plasma discharges:benchmarks and kinetic effect, JOURNAL OF PHYSICS D: APPLIED PHYSICS,38 2005,38: 283–301.
[51] T.M. Minea , J. Bretagne, G. Gousset, L. Magne, D. Pagnon, M. Touzeau, PIC-MCC simulation of a rf planar magnetron discharge and comparison with experiment, Surface and Coatings Technology, 1999.
[52]李小泽,王建国,童长江,张海,充填不同气体相对论返波管特性的PIC-MCC模拟,物理学报,2008,57(7):4613-4623.
[53]郑飞腾,杨中海,金晓林,空心阴极类火花放电初始电离过程的PIC-MCC模拟,物理学报, 2008,57(2):990-998.
[54] Hyun Chul KIM, Oleg MANUILENKO and Jae Koo LEE, Particle-In-CellMonte-Carlo Simulation of Capacitive RF Discharges: Comparison with Experimental Data, Japanese Journal of Applied Physics, 2005,44(4): 1957–1958.
[55]邵褔球,等离子体粒子模拟,北京,科学出版社,2002.
[56] C.K.Birdsall and A.B.Langdon, Plasma Physics Via Computer Simulation, New York:McGraw-Hill,1985.
[57] V.Vahedi,G.Dipeso,C.K.Birdsall,et al,Capacitive RF discharge modelde by particle-in-cell Monte Carlo simulation I:Analysis of mumerical techniques,Plasma. Souc. Technol,1993,2:261-272.
[58]俆学基,诸定昌,气体放电物理,上海:复旦大学出版社,1996,105.
[59] H C Kim, F Iza, S S Yang, M Radmilovic-Radjenovic and J K Lee, Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects,Journal of Physics D:Applide Physics,2005,38:283-301.
[60]蒲以康,等离子体放电原理与材料处理,北京:科学出版社,2007.
[2] Zhang L Z, Yu W, Han L, et al. Generation and distribution of fast atomic species(N+,Nf) in nitrogen glow discharge[J]. Plasma Science & Technology, 2006, 8(6):670-674.
[3]张连珠, N 2+离子在氮直流辉光放电中碰撞离解的作用[J].物理学报,2003,52(4): 0920-0924.
[4]张连珠,傅凤清,王增波等,氮气空心阴极辉光放电等离子体离子的蒙特卡罗模拟研究,核聚变与等离子体物理,2006,26(2):135-139
[5]张连珠,于威,氮气直流辉光放电阴极鞘层区电子行为的蒙特卡罗模拟研究,河北大学学报(自然科学版),2001,23(3):239-243
[6] Yu W,Zhang L Z,Wang J L,Monte Carlo simulation of the fast electrons and heavy particles in the CDS of nitrogen dc glow discharge.J Phys D,2001,34:3349-3355
[7] Fu Guang-sheng, Wang Jiu-Li, Yu Wei, et al. Self-Consistent Description of Nitrogen dc Glow Discharge, Chin. Phys. Lett., 2002, 19(4); 521-523
[8] Liu Chengsen, Wang Dezhen, self-Consistent Model for Pulsed Direct-Current Nitrongen Glow Discharge, Plasma Science & Technology, 2005, 7(2):2745-2747.
[9]芦岩,王友年,碰撞对非对称射频鞘层特性的影响,物理学报,2004,53(8):2661-2665.
[10]邱华檀,王友年,马腾才,碰撞效应对射频偏压电极上离子能量分布和角度分布的影响,物理学报,2002,51(6):1666-1670.
[11]戴忠玲,王友年,马腾才,射频等离子体鞘层动力学模型,物理学报,2001,50(12):1241-1248.
[12]孟显,王友年,马腾才,电子发射对稳态等离子体鞘层影响的理论研究和数值模拟,强激光与粒子束,2000,12:358.
[13] Bogaerts Annemie,Gijbels Renaat, The role of fast argon ions and atoms in the ionization of argon in a direct current glow discharge: a mathematical simulation,Applied Physics,1995,78:6427-6431
[14] Bogaerts Annemie, Gijbels Renaat, Goedheer Wim.Hybrid modeling of a capacitively coupled radio frequency glow discharge in argon: combined Monte Carlo and fluid model,Japanese journal of applied physics,1999,38: 4404-4415.
[15] Yan M., Bogaerts Annemie, Gijbels Renaat, Goedheer W.J, Spatial behavior of energy relaxation of electrons in capacitively coupled discharges: comparison between Ar and SiH4 , Journal of applied physics,2000,87(8):3628-3636.
[16] Yan M,Bogaerts Annemie, Goedheer W.J, Gijbels Renaat,Electron energy distribution function in capacitively coupled RF discharges: differences between electropositive Ar and electronegative sih4 discharges ,Plasma sources science and technology ,2000,9:583-591.
[17] Ivanov Vladimir, Proshina Olga, Rakhimova Tatyana, Rakhimov Alexander, Herrebout Dieter, Bogaerts Annemie, Comparison of a one-dimensional particle-in-cell-Monte Carlo model and a one-dimensional fluid model for a CH4H2 capacitively coupled radio frequency discharge, Journal of applied physics,2002,91(10):6296-6302.
[18] GeorgieVa Violeta, Bogaerts Annemie, Gijbels Renaat,Numerical investigation of ion energy distribution functions in single and dual frequency capacitively coupled plasma reactors,Physical review E,2004,69.
[19] Georgieva Violeta, Bogaerts Annemie,Numerical simulation of dual frequency etching reactors:influence of the external process parameters on the plasma characteristics,Journal of applied Physics,2005,98(2):1-13.
[20] Charles C, Boswell R W and Porteous R K,Measurement and modeling of ion energy distribution,functions in a low pressure argon plasma diffusing from a 13.56 MHz helicon source, Vacuum Science and Technology A,1992,10:168.
[21] Gottscho R A, Ion transport anisotropy in low pressure,high-density plasmas, Vacuum Science and Technology B,1884,11.
[22] Holber W M and Forster J, Ion energetics in electron cyclotron resonance discharges, Vacuum Science and Technology A,1990,8:3720.
[23] Hopwood J, Ion bombardment energy distributions in a radio frequency induction plasma, Appl. Phys. Lett.1993,62:940.
[24] Benoit-Cattin P and Bernard L C, Anomalies of the energy of positive ions extracted from high-frequency ion sources, Journal of Applied Physics, 1968, 39 :5723.
[25] Farouki R T, Hamaguchi S and Dalvie M, Analysis of a kinematic model for ion transport in rf plasma sheaths, Physical Review A,1992,45:5913.
[26] Kushner M J, Distribution of ion energies incident on electrodes in capacitively coupled rf discharges, Journal of Applied Physics, 1985, 58: 4024.
[27] Thompson B E, Sawin H H and Fischer D , Monte-Carlo simulation of ion transport through rf glow-discharge sheaths , Journal of Applied Physics ,1988 ,63: 2241.
[28] Barnes M S, Forster J C and Keller J H, Ion kinetics in low-pressure, electropoositive, RF glow discharge sheaths,IEEE Transactions on Plasma Sciences, 1991,19: 240.
[29] May P W, Field D and Klemperer D F , Modeling radio-frequency discharges: effects of collisions upon ion and neutral particle energy distributions, Journal of Applied Physics , 1992 71: 3721.
[30] Vender D and Boswell R W ,Numerical modeling of low-pressure RF plasmas, IEEE Transactions on Plasma Sciences,1990, 18 :725.
[31] Surendra M and Graves D B, Particle simulation of radio-frequency glow discharges, IEEE Transactions on Plasma Sciences, 1991,19: 144.
[32] Zhong-Ling Dai and You-Nian Wang, Multiple ion dynamics model for thecollisionless rf sheaths and the ion energy distributions at rf-biased electrodes in fluorocarbon plasmas,Physical Review E,2002,66:1
[33] R. J. M. M. Snijkers, M. J. M. van Sambeek, G. M. W. Kroesen, and F. J. de Hoog, Mass-resolved ion energy measurements at the grounded electrode of an argon rf plasma, Appl Phys Lett,1993,63(3):308-316.
[34] J. Liu, G. L. Huppert, and H. H. Sawin, Ion bombardment in rf plasmas, Journal of Applied Physics,1990,68(8):3916-3934.
[35] A. Manenschijn, G. C. A. M. Janssen, E. van der Drift, and S. Radelaar, Measurement of ion impact energy and ion flux at the rf electrode of a parallel plate reactive ion etcher , Journal of Applied Physics,1991,69(3): 1253– 1262.
[36] J. K. Olthoff, R. J. Van Brunt, S. B. Radovanov, J. A. Use of an ion energy analyser-mass spectrometer to measure ion kinetic-energy distributions from RF discharges in argon-helium gas mixtures , Measurement and Technology,1994,141(2):105– 110.
[37] Snijkers, R. J. M. M. van Sambeek, M. J. M. Kroesen, G. M. W.; de Hoog, F. J, Mass-resolved ion energy measurements at the grounded electrode of an argon rf plasma, Applied Physics Letters,1993,63(3): 308-310.
[38] D Barton, D J Heason, R D Short and J W Bradley,The measurement and control of the ion energy distribution function at a surface in an RF plasma, Meas. Sci. Technol,2000,11: 1726–1731.
[39] W J Goedheer, Lecture notes on radio-frequency discharges, dc potentials, ion and electron energy distributions, Plasma Sources Sci,2000,9: 507–516.
[40] Vendor, D.Boswell, R. W, Numerical modeling of low-pressure RF plasmas, IEEE Transactions on Plasma Science, 1990,18(4):725-732.
[41] E Kawamura, V Vahedi,M A Lieberman and C K Birdsall,Ion energy distributions in rf sheaths ; review,analysis and simulation,Plasma sources Sci.Technol,1999,8: 45-60.
[42] Wild C and Koidl P , Structured ion energy distribution in radio frequencyglow-discharge systems, Appl. Phys. Lett. 1989,54:505
[43] I.V. Schweigert, Different Modes of a Capacitively Coupled Radio-Frequency Discharge in Methane, Physical Review Letters,2004,92
[44] A L Alexandrov and I V Schweigert,Two-dimensional PIC–MCC simulations of a capacitively coupled radio frequency discharge in methane, PLASMA SOURCES SCIENCE AND TECHNOLOGY.2005,14:209-213
[45] S.M. Levitskii, Zh. Tekh. Fiz,Sov. Phys. Tech. Phys.,1957,2: 887 .
[46] C. K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, 1985.
[47] V Vahedit, C K Birdsall, M A Liebermant, G DiPesoS and T D Rognlien ,Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II: comparisons with laboratory measurements of electron energy dktribution functions, Plasma Sources Sci, Technol, 1993,2: 273-278.
[48] C K Birdsall,Particle-in-cell Charged-Particle Simulations,Plus Monte Carlo Collisions With Nertral Atoms,PIC-MCC,IEEE transactions on plasma science,1991,19(2).
[49] J van Dijk, G M W Kroesen and A Bogaerts, Plasma modelling and numerical Simulation, JOURNAL OF PHYSICS D: APPLIED PHYSICS,2009,42.
[50] H C Kim1, F Iza, S S Yang, M Radmilovic-Radjenovic and J K Lee, Particle and fluid simulations of low-temperature plasma discharges:benchmarks and kinetic effect, JOURNAL OF PHYSICS D: APPLIED PHYSICS,38 2005,38: 283–301.
[51] T.M. Minea , J. Bretagne, G. Gousset, L. Magne, D. Pagnon, M. Touzeau, PIC-MCC simulation of a rf planar magnetron discharge and comparison with experiment, Surface and Coatings Technology, 1999.
[52]李小泽,王建国,童长江,张海,充填不同气体相对论返波管特性的PIC-MCC模拟,物理学报,2008,57(7):4613-4623.
[53]郑飞腾,杨中海,金晓林,空心阴极类火花放电初始电离过程的PIC-MCC模拟,物理学报, 2008,57(2):990-998.
[54] Hyun Chul KIM, Oleg MANUILENKO and Jae Koo LEE, Particle-In-CellMonte-Carlo Simulation of Capacitive RF Discharges: Comparison with Experimental Data, Japanese Journal of Applied Physics, 2005,44(4): 1957–1958.
[55]邵褔球,等离子体粒子模拟,北京,科学出版社,2002.
[56] C.K.Birdsall and A.B.Langdon, Plasma Physics Via Computer Simulation, New York:McGraw-Hill,1985.
[57] V.Vahedi,G.Dipeso,C.K.Birdsall,et al,Capacitive RF discharge modelde by particle-in-cell Monte Carlo simulation I:Analysis of mumerical techniques,Plasma. Souc. Technol,1993,2:261-272.
[58]俆学基,诸定昌,气体放电物理,上海:复旦大学出版社,1996,105.
[59] H C Kim, F Iza, S S Yang, M Radmilovic-Radjenovic and J K Lee, Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects,Journal of Physics D:Applide Physics,2005,38:283-301.
[60]蒲以康,等离子体放电原理与材料处理,北京:科学出版社,2007.