Studies on fluid model for numerical simulation of gas discharges in color plasma displays Studies on fluid model for numerical simulation of gas discharges in color plasma displays

Studies on fluid model for numerical simulation of gas discharges in color plasma displays

  • 期刊名字:核技术
  • 文件大小:526kb
  • 论文作者:HE Feng,LIU Chun-liang
  • 作者单位:Key Laboratory for Physical Electronics and Devices of the Ministry of Education
  • 更新时间:2020-09-15
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论文简介

oL 16 No. 2NUCLEAR SCIENCE AND TECHNIQUESapril 2005Studies on fluid model for numerical simulation of gasdischarges in color plasma displaysHE Feng, LIU Chun-Liang(Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, Xi'an 710049)Abstract The fluid models of gas discharge in alternating current plasma display panel (ac PDp) cell are discussed.From the Boltzmann equation, the hydrodynamic equations are derived, but this model consumes much computa-tional time for simulation. The drift-diffusion approximation model and the local field approximation model are obtained to simplify the numerical computation, and the approximation conditions of these two models are discussed indetail. The drift-diffusion approximation model gives more satisfactory result for PDP simulation, and the expressionof energy balance equation is given completely in this model.Key words Plasma display panel(PDP), Fluid mode, Numerical simulation, Drift-diffusion approximationCLC numbers TN136 0531 IntroductionIn this case, the electron continuity equation and theelectron energy balance equation take the similarBecause the size of the discharge cell in alternat- mathematical form. This is convenient for numericaling current plasma display panel(Ac PDP) is very computations. But in References [5],[6] and [7], thesmall (about 150 um), it is difficult to measure the expression for electron flux density does not take intodischarge parameters, such as electron density, tem- account the temperature gradient. In this report, weperature, and so on, directly. In order to understand the will review several fluid models for numerical simuladischarge characteristics in AC PDP cells, the com- tions of gas discharges in AC PDP cells and point outputer simulation has become a useful tool and has the approximation conditions for the non- LFA modelbeen developed greatly. Among the computer simula- and the LFA model. We hope that the results giventions the fluid simulation with the local field aphere can be useful to compare and interpret the simuproximation(LFA) -has been used widely. The LFAation results by different fluid modelsmodel does not take into account the electron energredistribution due to thermal conduction and convec- 2 Hydrodynamic equations for gas dis-tion and assumes the transport coefficients are thecharge plasmafunctions of the reduced field. because in AC PDPboth electric field and electron density gradient2.1 Basic assumptionschange greatly in space, and the LFa model only takesBecause the densities of electrons. ions and einto account the effect of electric field, it overesti- ited atoms in PDP cells are small as compared withmates the discharge behavior and will produce unsat- the densities of background gases, the discharge gasesisfactory modeling results. Recently, the non-LFA in PDP cells are weakly ionized gases. The Coulombmodel was developed to improve the fluid simulations collision between electron and ion is neglected. Theof gas discharges in AC PDP cells. In the non-LFA ambipolar diffusion of electron and ion is also nemodel, the electron energy balance equation is taken glected. The transport coefficients related to electroninto account and the transport coefficients are asare dependent on the electron energy. The transportsumed to be the functions of the electron mean energy. coefficients not related to electrons are assumed to be中国煤化工Received date: 2004-05-0CNMHGNo.2 HE Feng et al: Studies on fluid model for numerical simulation of gas discharges in color plasma displaysl21constantThe hydrodynamic equation for electrons can beThe dynamic equations for electrons include the derived from Eq (1) by the moment methodl8Iand theontinuity equation, the momentum transfer equation expressions can be written as followsand the energy balance equation. The dynamic equaContinuity equationtions for ions include the continuity equation and theflux density equation. The self-consistent electric fieldV(nu)=S-Sis solved from the Poissons equation. The dynamicwhere S*=kIonization rateequations for neutrals include the continuity equationand the flux density equation. The temperature of ionsgmm, is recombination rate k, is ionizationand neutrals are assumed to be constant2.2 Hydrodynamic equationsrate coefficients; and gi is recombination rate coefficientsThe hydrodynamic equation for the gas dischargeMomentum transfer equationplasma can be derived from the boltzmann equationby the moment method. 8 Without lack of generality.+(u。VV(nkTwe only discuss the hydrodynamic equation for elec-whereDm is collision frequency for electron mo-trons in details as the expressions for ions and neutralsmentum transferar formsEnergy balance equationBoltzmann equation for electron can be written(k7)followaf,.af Faf 8j(1)kT+mDu2->where f(v, r, t) is electron density distribution functioninkm is electron mass; F=-eE is the electric force ap-plied to electronis the collision termwhere k is thermal conductivity U is collision fre-quency for ionization and excitation; a, is energyElectron velocity v can be divided into two partsthreshold for ionization and excitation: m is mass ofv=l+形(2)atomswhere u is electron drift velocity or electron fluid vePoissons equationlocity, and w is electron random velocity or electronheat velocity.V(E)=e∑(10)Some important physical quantities can be defined as followswhere n, and ne represent the ion and electron densityElectron densityrespectively.n(,)=x,d2(3)Finally, we rewrite hydrodynamic equations forelectron in gas discharge plasma as followswhere d'v=dv dv dv =v sin ededodv is the+Vo(n2l2)=S。-S(11)Electron drift velocityn2+n(n“V)+3V(2)ene-Umneuen(,)[5v(r,v,nd'v(4)(12)Electron heat energyn+n·V公、nb。一V·(kEEmw f(r,v, t)d v中国煤化工分∑可(13)CNMHG122NUCLEAR SCIENCE AND TECHNIQUESVoL 16where a=3kT. is the electron mean energy(22)Equations (11),(12)and(13)are nonlinear partial differential equations for variables ne, He andwhere t is the characteristic time for the change ofIf we define the following vectorelectron drift velocity in time.U=ne ue ue2 ue, E](14)In order to simplify Eq (12), one adopts the following two assumptionsEqs. (I1),(12)and(13)can be written in the fol-lowing matrix form(2)the gradient of ue is very small compared withF(U,t)(15) the gradient of nkTeIn this case. the first two terms in the left handThe nonlinear equation(15)can be computed side of Eq (12)can be neglected and one can get thenumerically by Beam-Warming methodfollowing electron flux density equationT=nu =- e-neE-3mumD(16)If defining the electron mobility and the electronUn+-UB△Un△t(24)then one can get the following einstein's relationF(U+1△Un,tD kT(26)F(,)+D△Using ue and De, Eq (23) can be written in thewe can obtain the finite difference algorithm as following formfollowsTe=-ueneE)(27)(△D)C"=△F(,)(20It should be noted that in References 5,6 andUn=Un+△Un21) [7], in Eq (27) is picked out of the differentialwere I is the identityoperator v. because the electron teThe linear algebraic equation(20)can be solved in time and space,& in Eq(27)cannot be picked outby the well-known methods. Because the dimensionof the differential operator vof Eq (20) is very large, it will take very long time toNow, we can rewrite Eqs.(11) and(13)in theSince in the gas discharge of ACfollePDP, the electron density changes greatly in time ands+V·rspace, but the electron drift velocity does not changegreatly in time and space, one usually adopts theF·VEe v●KIrift-diffusion approximation instead of momentumtransfer equation to simplify the numerical computa-n2+mDnn2-n∑4(29)tionMultiplying Eq (28)by 8, one can get3 Drift-diffusion approximation modelaa7+v·。=a(S:-S)(30)In Eq. 12)can be approximated as fol-InsertiH中国煤化工: can obtainCNMHGNo. 2HE Feng et al: Studies on fluid model for numerical simulation of gas discharges in color plasma displaysl23(厂2)+2Vthe electron drift velocity remain nearly unchangedThe reason is that the electron concentration causedm1+m∑啊+(-)1) y the electric neld is cancelled byTaking dot product between Te and We, fromInserting Ie into Eq ( 36), we can write Te as theq (27), one can getfollowing formr·l2=n2=-1F·E-V(n2E)(32)r.=-5从nE-DV(n2)-=5D(37)From Eq (32), one can obtainIf neglecting the electron thermal conduction,mom"ue=-ele'23".(ne)(33) Eq(37)can be reduced as=-5n2E-5D2Nn(3From Eq (9), the thermal conductivity can be expressed by De as followsIn References [5],[6] and [7], the expression forn(34)TE=-DunCe-Dv(na)Inserting Eqs. (33)and(34)into(3tron energy balance equation can be expressed as therding to the above discussions, the expresfollowing compact formsion for I should take either Eq (37)or Eq. 38). Theeffect of electron thermal conduction is included in.E-Emneeboth electron flux density Te and electron heat fluxn∑可+2(S-S。)de2. References [5],[6] and [7count the electron heat flux density e, but ignore theeffect of the electron thermal conduction in the elec-T=eT8-EDnve(36)tron flux density Te. So Eq (39)is not a reasonablewhere Te is the electron energy flux densityThe first term in the right hand side of Eq (35)For ions, due to the assumption of the constantrepresents the energy loss due to the joule heating; thesecond term represents the energy loss due to the elastion and the ion flux density can be given as followsth atoms: the third term.T=S-Senergy loss due to the inelastic collision with atoms;and the fourth term represents the energy gain due toT=un E-DVn(41)the new electron generation. The effect of the seconBecause the generation and combination of elecdary electron emission can be included in the bound. trons and ions are in pare, the source term for ionsary conditionthe same as for electronsIn References [5], [6 and [7], only the first termThe self-consistent electric field can be solvedand the third term in the right hand side of Eq (35)are the following Poissons equationtaken into accountV·(aE)=e∑n-n)(42)The expressions of Eqs. (28)and (35) have similar mathematical forms. This makes it convenient toFor neutrals, due to the assumption of the conadopt the same numerical algorithmstant temperature, the expressions for the continuityThe reasonable interpretation of the electron enequation and the neutral flux density can be given asergy balance equation (35) shows that thefollowsdrift-diffusion approximation is a good approximationV.=S-S(43)This model reflects a fact that the strong spatial variation of both electric field and electron density make中国煤化工CNMHG124NUCLEAR SCIENCE AND TECHNIQUESVoL 16where S, is the gain rate of excited atoms; and SJ≈J=-e=enE+eDVn。(52The above equation shows that both electric fieldis the loss rate of excited atomsand electron density gradient contribute electric cur-rent density. The LFA model enhances the effect of4 Local field approximation modelelectric field and will yield more electric current andIn the local field approximation model, it is a lower firing voltage than thesumed that the electron temperature is constant andIn some literatures, the electron density gradientthe transport coefficients are functions of the reducedterm in Eq (52)is ignored in the expression for electron current density: this will enhance the effect offield E/N, where N is density of the background gaseselectric field further. The reason is that the effect ofBecause the electron temperature gradient vanishes, itelectric field will facilitate the concentration of elecis not needed to solve the electron energy balancetrons and the effect of electron density gradient canequationcels the electron concentrationFrom Eqs.(27)and(28), we can obtain the elec-tron continuity equation and the electron flux densitIt is anticipated that there maybe exist the regionequation as follows:in which the electric field changes greatly, the lfamodel will produce the strong spatial variation for些+V(45) someeters, but these parameters turn out tochange slowly in realityT=-unE-DVnThe Lfa model has been successfully applied toSimilarly, the ion continuity equation and the ionsimulating several glow discharges. We guess thatflux density equation can be written as followsthese glow discharges, such as plasma processingVL=Se-S(47) equipment, one desires the uniform distribution ofplasma, the electron density gradient is not so largeT=u nE-DVnthat in AC PDP, so the lfa model can produce theThe self-consistent electric field can be solved by reasonable simulation resultsthe following Poisson's equation5 ConclusionsV·(EE)=(49)The full hydrodynamic equations can describeThe neutral continuity equation and the neutralthe gas discharge in the cells of AC PDP, but itflux density equation can be expressed as followsequations. The drift-diffusion approximation is a good(50) model to simulate the gas discharge in the cells of AC(51) PDP and it can yield the reasonable simulation resultsSome errors in the literatures for the drift-diffusionIn usual simulations, the relationships between ueapproximation have been corrected. The LFA modeld e/N and between L; and e/N are obtained fromeasy to implement the computer simulation for ACnumerical computation of the zero-dimensionalpdP but it enhances the effect of electric field andBoltzmann equation with dC electric field. The otherwill yield more electric current density and lower firtransport coefficients related to electrons are also ob-tained by similar methodsmodel should be interpreted carefully. We think thatSince there exist strong spatial variations of theelectric field and the electron and ion density in thethe validity of the Lfa model for application to ACPDP should be verified further by experimental resultscells of ac pdp the lfa model overestimates theand other more exact numerical simulationseffect from the electric field and seems unrealisticIf neglecting the electric current from ions, weReferencescan write the electric current density as follows2792No.2 HE Feng et al: Studies on fluid model for numerical simulation of gas discharges in color plasma displaysl252 Meunier J, Belengure Ph, Beouf J P J Appl Phys, 1995,3460-346978(2):731-745esenW. van slooten u et al. j3 Veerasingam R, Campbell R B, McGrath R T. IEEE TransAppl Phys,2000,88(5):2252-2262Plasma Sci.,1995,23(4):688-6977 Veronis G Inan U S. J Appl Phys, 2002, 91(12)4 Campbell R B, Veerasingam R, McGrath R T. IEEE TransPlasma sci,1995,23(4):698-7088 Glant B E. Fundamentals of plasma physics, New York:5 Rauf S, Kushner M J. J Appl Phys, 1999, 85(7)Academic press. 198中国煤化工CNMHG

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