Analysis of Electron Transport Coefficients in SiH4 Gas Using Boltzmann Equation in the Presence of Applied Electric Field

Main Article Content

Mohammad M. Othman
Sherzad Aziz Taha
Idrees H


Swarm parameters EEDF Effective ionization coefficient. Plasmas Boltzmann equation


Monosilane (SiH4) plasma has numerous applications in plasma processing, transport coefficients   are better to understanding and modeling of these gas discharge processes. The electron swarms in a monosilane gas under influence of uniform electric field can be calculated using two term approximation of Boltzmann equation for the range 1 ≤ E/N ≤ 1000 Td (1 Td= 1x10-17 V.cm2). The effective ionization coefficient's (α-η)/N and electron swarm parameters are calculated and compared with experimental and theoretical values  of drift velocity, characteristic energy, mean electron energy and ionization coefficient. The critical field strength (E/N) calculated from the effective ionization curves. A set of electron molecule collisions has been assembled for monsilane gas which gave a good fit between the calculated and experimental values over the range of  E/N investigated. The calculated distribution functions (EEDF) are found to be non-Maxwellian, having energy variations which reflect the important electron / molecule energy exchange processes. In addition, the percentages of energy lost by different types of elastic and inelastic collisions are given as a function of  electric field strength E/N.

Abstract 52 | PDF Downloads 43


Akdim, M.R. and W.J. Goedheer, W. J. (2003). Modeling of Dust in a Silane/Hydrogen Plasma, J. Appl. Phys., 94(1), 104-109.
Al-Amin, S. A. J. and Lucas, J. (1988). Electron swarm in mixtures of metal vapor and argon gas, J. Phys. D: Apll. Phys., 21(8), 1261-1270.
Boogaard, A., Ozturk, M., Gusev, E., Kovalgin, Alexeij Y., Brunets, I. Iwai, H., Antonius A.I., Aarnink, Koester, S., Robertus A.M. Wolters, Kwong, D.,J., Holleman, J., Roozeboom, F., Timans, P. and Jurriaan Schmitz. (2007). On the verification of EEDFs in plasmas with silane using optical emission spectroscopy, ECS Transactions., 6(1), 259-270.
Chatham, H., Hils, D., Robertson, R. and Gallagher, A. (1984). Total and Partial Electron Collisional Ionization Cross Sections for CH4, C2H6, SiH4 and Si2H6, J. Chem. Phys., 81(4), 1770-1777.
Cottrell, T. L. and Walker, I. C. (1965). Drift Velocities of Slow Electrons in Polyatomic Gases, Transactions of the Faraday Society, 61, 1585-1593.
Engelhardt, A. G. and Phelps A. V. (1963). Elastic and Inelastic Collision Cross Sections in Hydrogen and Deuterium from Transyort Coefficients, Phys. Rev., 131(5), 2115-2128.
Frost, L. S. and Phelps, A. V. (1962). Rotational Excitation and Momentum Transfer Cross Sections for Electrons in H2 and N2 from Transport Coefficients, Phys. Rev., 127(5), 1621-1633.
Frost, L. S. and Phelps, A. V. (1964). Momentum transfer cross section for slow electrons in He, Ar, Kr and Xe from transport coefficient, Phys. Rev., 136(6), A1538-A1545.
Garscadden, A., Duke, G. L. and Bailey, W. F. (1983). Electron Kinetics of Silane Discharges, Appl. Phys. Lett., 43(11), 1012-1014.
Haq, S. U. (2005). Electron collision cross-sections in monosilane (SiH4) molecule: an investigation and analysis, Annual Report Conference on Electrical Insulation and Dielectric Phenomena, pp.39-42.
Hayashi, M. (1987). Electron collision cross sections for molecules determined from beam and swarm data, in Swarm Studies and Inelastic Electron-Molecule Collisions, L. C. Pitchford, B. V. McKoy, A. Chutjian, and S. Trajmar, Eds. Berlin, Springer-Verlag.
Kawaguchi, S, Takahashi, K., Satoh, K. and Itoh, H. (2017). Electron collision cross section sets of TMS and TEOS vapours, Plasma Sources Science and Technology, 26(5), 101384(13pp).
Kitamori, K., Tagashira, H. and Sakai, Y. (1980). Development of electron avalanches in argon-an exact Boltzmann equation analysis, J. Phys. D: Appl. Phys., 13(4), 535-550.
Kovalgin, A. Y., Boogaard, A. and Wolters, R. A. (2009) Impact of Small Deviations in EEDF on Silane-based Plasma Chemistry, ECS transactions, 25(8), 429-436.
Kurachi, M. and Nakamura, Y. (1989). Electron collision cross sections for the monosilane molecule, J. Phys. D: Appl. Phys., 22(1), 107-112.
Kurachi, M. and Nakamura, Y. (1991). Electron Swarm Parameters in SiH4-Rare Gas Mixtures and Collision Cross Sections For Monosilane Molecules, IEEE Transaction on Plasma science, 19(2), 262-269.
Kurachi, M. and Nakamura, Y. (1988). Electron swarm parameters in SiH4-Ar mixtures, J. Phys. D: Appl. Phys., 21(4), 602-606.
Lisovskiy,V., Booth J- P., Landry K., Douai, D., Cassagne, V. and Yegorenkov, V. (2007). Electron Drift Velocity in Silane in Strong Electric Fields Determined from rf Breakdown Curves, J. Phys. D: Appl. Phys., 40(11), 408–3410.
Liu Xiaojiao,Yin Junchuan,Zhang Jiawei,Li Ming,Yang Peizhi,Hu Zhihua, (2016). Boron Doped a-SiOx:H Prepared by H2 Diluted SiH4+CO2 Plasma, Int. J. Electrochem. Sci., 11(12), 10827-10836.
Lyka, B. Amanatides, E. and Mataras, D. (2006). Simulation of the Electrical Properties of SiH4/H2 RF Discharge, Jap. J. Appl. Phys., 45(10B), 8172-8176.
Mathieson, K. J., Millican, P. G., Walker, I. C. and Curtis, M. G. (1987). Low-energy-electron Collision Cross-sections in Silane, Journal of the Chemical Society Faraday Transactions 2, 83(6), 1041-1048.
Matsui, T., Maejima, K., Bidiville, A., Sai, H., Koida, T., Suezaki, T., Matsumoto, M., Saito, K. Yoshida, I. and Kondo, M. (2016). High-efficiency thin-film silicon solar cells realized by integrating stable a-Si:H absorbers into improved device design, Japanese Journal of Applied Physics, 54(8S1), 08KB10(4pp).
Millicant, P. G. and Walker, I. C. (1987). Electron swarm characteristic energies (Dr/μ) in methane, perdeuteromethane, silane, perdeuterosilane, phosphine and hydrogen sulphide at low E/N. J. Phys. D: Appl. Phys., 20(2), 193-196.
Morgan, W. L. and Penetrante, B. M. (1990). ELENDIF: A time-dependent Boltzmann solver for partially ionized plasmas, Computer Physics Communications, 58(1-2), 127-152.
Nagpal, R. and Garscadden, A. (1994). A new Collision Cross Section Set for Silane, Gaseous Dielectrics VII, pp.39-45.
Nakamura, Y. (2013). Electron Swarm Parameters and Electron Collision Cross Sections, Fusion Science and Technology, 63(3), 378 -384.
Nakamura, V. and Lucas, J. (1978). Electron drift velocity and momentum cross-section in mercury, sodium and thallium vapors. II. Theoretical, J. phys. D: Appl. Phys., 11(3), 337-345.
Nighan, W. L. (1970). Electron Energy Distributions and Collision Rates in Electrically Excited N2, CO, and CO2, Phys. Rev., 2A(5), 1989–2000.
Nolet, G. (1975). Kinetics of Decomposition of Silane (Diluted in Argon) in a Low Pressure Glow Discharge J. Elecrrochem. Soc., 122 (8), 1030-1034.
Ohmori, Y., Shimozuma, M. and Tagashirai, H. (1986). Boltzmann equation analysis of electron swarm behaviour in monosilane, J. Phys. D: Appl. Phys., 19(6), 1029-1040.
Othman, M. M. (2011). Electron transport coefficients in SiH4-Kr mixtures in D.C. field, Proceedings of the 4th International Science Conference of Salahaddin University- Erbil, Kurdistan, Iraq, October 18-20, vol. 3, 833-842.
Peck, J.A. (2014). Modeling and Experimental Process Optimization for a SiH4+H2 Surface wave Plasma Discharge for Silicon Photo voltages. Master Thesis , University of IIIinois at Urbana-Champaign.
Pfau, S. and Winkler, R. (1990). Electron Collision Rates and Transport Coefficients of a Weakly Ionized dc Plasma in Ar/SiH4 mixtures, Contrib. Plasma Phys., 30(5), 587-597.
Pham Xuan Hien, Byung-Hoon Jeon and Do Anh Tuan, (2013). Electron Collision Cross Sections for the BF3 Molecule and Electron Transport Coefficients in BF3–Ar and BF3–SiH4 Mixtures, Journal of the Physical Society of Japan, 82(3), 034301(pp.8).
Pollock, W. J. (1968). Momentum transfer and vibrational cross-sections in non-polar gases, Transactions of the Faraday Society, 64, 2919-2926.
Shimada, T., Nakamura, Y., Lj Petrović, Z. and Makabe, T. (2003),. Electron Transport Coefficients in SiH4 and Si2H6 in dc and rf Fields, J. Phys. D: Appl. Phys., 36(16), 1936–1946.
Shimozuma, M. and Tagashira, H. (1986). Measurement of the Ionization and Attachment Coefficients in Monosilane and Disilane, J. Phys. D: Appl. Phys,, 19(9), L179-L182.
Shimozuma, M., Kaneko, Y., Taneda , A., Hasegawa, H. and H. Tagashira, H. (1983). Papers of Tech. Grp. Eleclrical Discharges, (Tokyo: IEE Japan), no. ED- 83-86.
Smith, K. and Thomson, R. M. (1978). Computer Modeling of Gas Lasers, New York, Plenum Press.
Sto, N., Kawashima, Y. and Tagashira, H. (1989). Electron Swarm Parameters in SiH4/H2, Ann. Rep. Fac. Educ., 49(1), 69-78.
Sueoka, O., Mori, S., and Hamada, A. (1994). Total cross section measurements for positrons and electrons colliding with molecules.I. SiH4 and CF4, J. Phys. B: At. Mol. Opt. Phys., 27(20), 1453-1465.
Tachibana, K., Tadokoro, H., Harima, H. and Urano, Y. (1982). Diffusion of Si atoms and thin film deposition in a silane-argon plasma, J. Phys. D: Appl. Phys., 15(1), 177-184.
Tochitani, G., Shimozuma, M. and Tagashira, H. (1993). Deposition of Silicon Oxide Films from TEOS by Low Frequency Plasma Chemical Vapor Deposition, J. Vac. Sci. Technol., 11A(2), 400-405.
Vasenkov, A. V. (1999). Monte Carlo Simulation of Electron Beam Plasma in a Silane-Argon Mixtures, J. Phys. D: Appl. Phys., 32(3), 240-L245.
Verma, P. Kaur, J. and Antonya, B. (2017). Electron-silane scattering cross section for plasma assisted processes, Physics of Plasma, 24(3), 033501(pp. 9).
Wen-Zhu J. Xi-Feng W. Yuan-Hong S. and You-Nian W. (2017). Fluid simulation of RF capacitively coupled SiH4/N2/O2 and SiH4 dusty plasmas, 1 st Asia-Pacific Conference on Plasma Physics, Chengdu, China, 18-23.
Xi-Feng, W. Wen-Zhu, J. Yuan-Hong S. Ying-Ying, Z. Zhong-Ling, D. and You-Nian, W. (2017). Hybrid Simulation of Electron energy Distributions and Plasma Characteristics in Pulsed RF CCP Sustained in Ar and SiH4/Ar discharges, Physics of Plasmas, 24(11), 113503(11pp.).
Xingwen Li, Hu Zhao and Shenli Jia. (2012). Dielectric breakdown properties of SF6–N2 mixtures in the temperaturerange 300–3000K, J. Phys. D: Appl. Phys., 45(44), 445202(7pp).
Yamaguchi, Y., Sumiyama, A., Hattori, R. I., Morokuma, Y. and Makabe, T. (1989). A Model of Amorphous Silicon Deposition in DC Glow Discharge in Silane, J. Phys. D: Appl. Phys., 22( 4), 505-511.
Yasunori, T. (2004). Prediction of dielectric properties of N2/O2 mixtures in the temperature range of 300–3500K, J. Phys. D: Appl. Phys., 37(6), 851–859.
Yoshida, K., Sato, R., Yokota, T., Kishimoto, Y. and Date, H. (2011). Electron Transport Properties in HSi(OC2H5)3 Vapor, Japanese Journal of Applied Physics, 50(12R), 120210(6pp.