جملة كلية الرتبية... العدد الثالث 3102

Transcription

1 Study the Drift Velocity of Electron in Mixtures CF 4, O 2 and Ar Duha Sady Abdul Majeed University of Baghdad / College of Education (Ibn Al-Haithamm) Department of physics Keywords: drift velocity, CF 4, O 2, Ar, Boltzmann transport equation, plasma physics تقديم البحث: 3103/9/32 قبول نشر البحث: 3103/00/02 الخالصة نقذ ق ا تحساب سرعح األ جراف نألنكرر ف غاز FCان ق 4 خه ط يع O 2 ra تان سثح انى )ان جال انك رتائ /انكثافح انعذد ح نهغاز( ي ) 0Td 01³dT ( ذى انحص ل عهى ان رائج تاسرخذاو حم يعادنح ت نرسيا كا د ان سة ان حس تح ل) O( )%01 %01 %01( 2 ra FC 4 تانرراتع. جذ ا اذفاق ج ذ ت انق ى ان حس تح انق ى ان قاسح نسرعح األ جراف ز ان رائج يف ذج نرحذ ذ سرعح األ جراف نألنكرر انر يؤثر ي ى ذسرخذو نرحذ ذ خصائص انر ص ه ح نهغاز ان رأ انضع ف. ك ا ا اضافح سثح صغ رج ي FCانى 4 انخه ط ؤدي انى حص ل ز ادج ف سرعح األ جراف رنك تسثة سرعح ا جراف انعان ح قذ اخرر ا زا انخه ط أل ر ف كث ر ي انرطث قاخ ي ا ا اسرخذاي ف ان قش عهى انثالزيا قذ اظ رخ ان رائج اعر اد سرعح األ جراف عهى ان جال انك رتائ E عهى انكثافح انعذد ح نهغاز N. Abstract We have calculated the electron drift velocity in pure CF 4 and their mixtures with Ar and O 2 (10%-80%-10%)for ratios of the electric field to the gas number density E/N from 1 Td to 1000 Td (1 Td = Vcm 2 ),This is mixture is usual used in plasma etching application.the results obtained by using a simple two term solutions for Boltzmann s equation, We found good agreement between calculated and measured values for electron drift velocity in pure CF 4 and their mixtures, These results are useful for determining the electron drift velocity which is an important swarm parameter used to characterize the conductivity of a weakly ionized gas. 207

2 Introduction Carbon tetrafluoride is commonly used for plasma etching and in semiconductor manufacturing [1], and is widely used in other technological applications such as development of gaseous circuit breakers, and for development of particle detectors [2, 3], Recent studies have demonstrated a remarkable etching property of CF 4 /mixtures, which suppresses the wire coating caused by avalanches in gasses such as Ar and O 2.Hence CF 4 gas mixtures show excellent aging performance [4]. CF 4 belongs to Freon that unfortunately significantly affects global warming of our planet, because of that it is important to continue research related to removal of this Freon from the atmosphere by applying gas discharges [3]. Because of all these arguments it is important to continue research related to the kinetics of CF 4 in ionized gases in order to improve plasma etching application. CF 4 has very fast drift velocity comparing with the other gases; therefore it was assumed that CF 4 could be used in wire chambers to make a gas more resistant to aging [5]. CF 4 in mixture with oxygen is used for plasma cleaning of CVD(chemical vapor deposition ) reactors, Also these mixtures show excellent aging performance [4], But pure CF 4 plasma are rarely used in material processing and instead are diluted with Ar and O 2 to control the production of fluorocarbons and provide selectivity in etching[ 2 ]. Oxygen plasma are widely used in material processing such as photo resist aching, Surface modification [1], adding O 2 can increase etch rate (increases F/C ratio by reacting with carbon), and adding Argon inert (heavy) gas which can be added to ion enhance the etching process (reactive ion etch) because it is inert this does not affect the chemistry of the plasma [6]. In this paper we solve a time dependent Boltzmann transport equation and compute the electron drift velocity also we can compute the mean energy, Diffusion coefficient, Rate coefficients and energy flow rates for the processes being included in the calculation and treat inelastic and super elastic processes, Photon-electron(free-free)processes, Attachment and recombination, Ionization including a distribution of secondary s and an external source of electrons such as might be due to ionization by an electron beam[2]. 208

3 Theory The Boltzmann equation also often known as the Boltzmann transport equation which is an equation for the time evolution of the distribution function [7].The general form of the Boltzmann transport equation is [8] Where ƒ (r,υ,t) is the distribution function for at time t and spatial location r with velocity υ. In the present formulation it is assumed that the electric field is independent of space and time, So ƒ(r,υ,t) ƒ(υ,t). The function ƒ (υ,t) is also expressed in terms of the two-term spherical harmonic expansion[9] (1) ƒ (υ) ƒ 0 (υ) +.ƒ 1 (υ) (2) With these assumptions and including only momentum transfer, Inelastic and super elastic processes, The Boltzmann equation can be expressed in term of electron number density as [ 10,11 ] - Where 209

4 Here N=total number density = with the index s denoting the species and the index j denoting the state; σ s = momentum transfer cross section for species s; σ sj, ϵ sj =excitation cross section and energy loss, respectively, for the j th state of species s; ä s =N s /N. The first term in eq. (3) represents the energy gain by electron from the electric field. The second term represents the energy loss in elastic collisions with the heavy species, with a correction term to account for the thermal energy of the heavy species. The quantity R sj (ϵ ) is the rate at which electrons with energy ϵ gain an energy due to super elastic collisions with molecules in state.as it stands,eq.(3)is actually independent of electron density, and in the steady state[7,8], Independent of N in the sense that the key parameters become E / N and the fractional composition of the heavy species. When processes such as attachment and ionization, which do not conserve the number density of free electron, are included in the calculation the distribution function can reach steady state and the left-hand side of eq. (3) can still be non-zero. That is, (9) Does not imply unless = 0. Although the electron density in the Boltzmann calculations is variable, The neutral atom and molecule densities are not. Modeling of the time 210

5 evolution of these species generally involves solving a set of chemical kinetics rate equations. Using the distribution function one can computes the electron drift velocity [8], And also can compute the electron mean energy, (10) (11) Where is electron energy in (ev), N is the gas density in,e /N is in( ) is electron density in ( ) Results and discussion Figure (1) and table (1) shows the electron drift velocity ( ) as a function of E /N in CF 4 and CF 4 /Ar/O 2 (mixing ratio 10/80/10) respectively. Note that the difference between pure CF 4 and the mixture and this difference seems clear in the range of (5 E/N 100) Td.In very extents lowland where (E/N 5) Td note that the drift velocity increases with increasing E/N and there is little difference between pure and the mixture. When the (E/N) values is less than (50 Td) the drift velocity become unstable. In the high range between (250 E/N 1000) note that the drift velocity increase linearly with increasing E/N and there is no clear distinction between pure CF 4 and the mixture. Our theoretical calculation results seen good agreement with the published experimental results [1], As shown in figure (2), The addition oxygen to CF 4 increases fluorine concentration and Argon inert (heavy) gas which can be added to ion enhance the etching process (reactive ion etch).because it is inert, this does not effect the chemistry of the plasma. 211

6 Conclusion (Argon and oxygen) with small amount of CF 4, are studied here in order to find gas mixtures which allow a high enough electron drift velocity, and we calculated electron drift velocity in a wide range of E/N, it is important to know the electron drift velocity in gas because it used to characterize the conductivity of a gas weakly ionized [12]. Because of high CF 4 drift velocity we found: 1. The drift velocity dependence on the electric filed. 2. Gas mixture containing CF 4 to obtain high electron drift velocities this mixture used in plasma etching [2]. Adding a small fraction of CF 4 in Ar and O 2 mixture leads to increase the drift velocity at high E/N values, and it useful to control electron energy and production of fluorocarbons and provide selectivity in etching. As discussed above there was good agreement between the present and previous results. References 1. Z.Nikitovic, V.Stojanovic, and Z.Lj.Petrovic,"Transport coefficient for electron scattering in mixtures of CF 4, Ar, and O 2 "publ.astron, obs.belgrad, No.89, pp.75-78, (2010) 2. Z.Nikitovic,V.Stojanovic,M.Radmilovic-Radjenovic,"Transport coefficients for electron in mixtures CF 4 /Ar/O 2 and CF,CF 2 or CF 3 Radicals"University of Belgrade, vol.120.pp , (2011) 3. Z.Nikitovic, V.Stojanovic and Z.LJ.Petrovic,"on the role of radicals in kinetics of plasma etchers in Ar/CF 4 mixtures"belgrad, Serbia, vol.115, pp , no.4, (2009) 4. W.S.Anderson, J.C.Armitage, E.Dunn, J.G.Heinrich, C.Lu, K.T. Mcdonald,J.Weckel and Y.Zhu"Electron attachment,effective ionization coefficient,and electron drift velocity for CF 4 gas mixtures"north- Holland,pp ,(1992) 5. M.Danilov, Yu.Guilitsky, T.Kvaratschellia, I, Tikhomirov, M.Titov, Yu.Zaitsev,"Aging Studies for the Muon Detector of HERA-B"Protvino Russia, pp.1-18, (2003) 6. Manos, D.and Flamm,D.eds.,"plasma etching,and introduction" Inc.New York,(1989) 7. Z.Bonaventura, D.Trunec,"solution of time-dependent Boltzmann Equation for electron in non-thermal plasma"masaryk University,(2007) 8. W.L.Morgan,"Elendif: Atime-dependent Boltzmann solver for partially ionized plasmas"computer physics communication 58, North-Holland, pp , (1990) 9. T.Holstein, phys.rev.70, pp.367, (1946) 212

7 10. S.D.Rockwood, phys.rev.a8, pp.2348 (1973) 11. C.J.Elliotand A.E.Greene, J.Appl.phys.47, pp.2946 (1976) 12.Tulio C.Vivaldini,Iara B.Lima,Josemary A.C.Goncalves,Suzana Botelho and Carmen C.Bueno Tobias"Measurements of electron drift velocity in Isobutane using the pulsed Townsend Technique"cidade University,Brazil,pp ,(2011) Table (1): The variation drifts velocity as a function of E/N Pure CF 4 CF 4 /O 2 /Ar (mixture) E/N V d *10 6 E/N V d *10 6 E/N V d *10 6 E/N V d *10 6 (Td) (cm/sec) (Td) (cm/sec) (Td) (cm/sec) (Td) (cm/sec)

8 Figure 1: drift velocity as a function of E/N for CF 4 /O 2 /Ar mixture and pure CF 4 Figure 2: Drift velocity as a function of E/N for pure CF 4 and mixture [1] 214