models.plasma.drift_diffusion_tutorial

《models.plasma.drift_diffusion_tutorial》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、SolvedwithCOMSOLMultiphysics4.1.©COPYRIGHT2010COMSOLAB.DriftDiffusionTutorialIntroductionThefoundationoftheCOMSOLMultiphysicsPlasmaModuleistheDriftDiffusioninterfacewhichdescribesthetransportofelectronsinanelectricfield.TheDriftDiffusioninterfacesolvesapairofreaction/convection/diff

2、usionequations,onefortheelectrondensityandtheotherfortheelectronenergydensity.Themeanelectronenergyiscomputedbydividingtheelectronenergydensitybytheelectronnumberdensity.ModelDefinitionThistutorialexamplecomputestheelectronnumberdensityandmeanelectronenergyinadrifttube.Electronsarer

3、eleasedduetothermionicemissionontheleftboundarywithanassumedmeanelectronenergy.Theelectronsarethenacceleratedtowardstherightboundaryduetoanimposedexternalelectricfieldwhichisorientedintheoppositedirectionfromtheelectrondriftvelocity:Figure1:Inthedrifttubetheelectronsentertheleftboun

4、daryandareacceleratedbytheelectricfieldtowardthewall.MODELEQUATIONSAsimplemodelissetuptotesttheDriftDiffusionphysicsinterface.Theequationssolvedare,fortheelectronnumberdensity:∂()∇Γn+⋅=R(1)∂teeewhereΓ=–()µ•En–D•∇n(2)eeeeeDRIFTDIFFUSIONTUTORIAL

5、1SolvedwithCOMSOLMultiphysics4.1.©COPYR

6、IGHT2010COMSOLAB.3and,nedenotestheelectrondensity(1/m),Reistheelectronrateexpression32(1/(m·s)),µeistheelectronmobilitywhichiseitherascalarortensor(m/(V·s)),Eistheelectricfield(V/m),andDeistheelectrondiffusivity,whichiseitherascalaroratensor.ThefirsttermontherightsideofEquation2repr

7、esentsmigrationofelectronsduetoanelectricfield.ThesecondstermontherightsideofEquation2representsdiffusionofelectronsfromregionsofhighelectrondensitytolowelectrondensity.AnequationfortheelectronenergydensityissolvedinconjunctionwithEquation1.Theequationis:∂()∇Γn+⋅+E⋅Γ=R(3)∂tεεeεwhere

8、Γ=–()µ•En–D•∇n.(4)εεεεε3Here,nεistheelectronenergydensity(V/m),Rεistheenergyloss/gaindueto32inelasticcollisions(V/(m·s)),µεistheelectronenergymobility(m/(V·s)),Eisthe2electricfield(V/m),andDεistheelectronenergydiffusivity(m/s).Thesubscriptεreferstoelectronenergy.Thethirdtermonthelef

9、tsideofEquation3rep