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1、ᜧắᦻDISCONTINUOUSFINITEVOLUMEMETHODFORSEMICONDUCTORDEVICESBaiBingSchoolofMathematicalSciences,ShandongNormalUniversityJinan,Shandong,250014ABSTRACTInthisarticle,themathematicalmodelofsemiconductordevicesweresearchediswidelyusedinthetheoreticaldesignofsolarcells,photo
2、electricdetector,photodiode,laserdiodeandothersemiconductor.Thenumericalsimulationtechniqueisanemergingtechnologyfordesigningsemiconductordevices.Numericalmethodsplayanimportantroleinthenumericalsimulation.Inactualproduction,peoplehopetoobtainsolutionofse,paccuratelytoguidet
3、hedesignofthesemiconductor.Ithasbeenfoundthattheelectronicpotentialisnotappearintheconcentrationequationdirectly,whileitsgradientappearintheconcentrationequation.Wecanapproximatepotentialgradientbychoosingahighprecisionmethodtoimprovetheconcentrationapproximationresults.Acco
4、rdingtotheconvection-dominatepropertiesofconcentrationequation,weintroducethecharacteristiclinetohandletheconvectionterm.Thepurposeofthisarticleistoestablishahigh-precisionschemenameddiscontinuousmixedvolumemethodandcharacteristicdiscontinuousvolumemethodforthefollowingmathe
5、maticalmodelofsemiconductordevices.(a)—A^=a(p—e+N(x)),(x,t)GQxJ,de(b)dt=V•[DeVe—/ie(x)eV^]—R(e,p),(x,t)GQxJ,dp(C)dt=V[DpVp+Hp(x)pV^]—R(e,p),(x,v)GQ.Thisschemecanapproximatethepotential,fieldintensity,electronconcentration3万方数据ᜧắᦻandholeconcentrationsimultaneously.Ou
6、rargumentshowsthatthemethodinheritstheadvantagesofdiscontinuousfiniteelementvolumemethod,whichishighorderaccuracy,parallelizability,stabilityandsimplicityofspaceconstruction.Inaddition,wecanbetterapproximateconcentrationthroughhighprecisioncomputationofthefieldintensityandav
7、oidthenumericaldispersionofthefrontatthesametime.Throughthetheoreticalanalysisoftheschemewhichwehaveproposed,wecanobtainL2-errorestimateof^,H(div)-errorestimateofit,L2-errorestimateofeandL2-errorestimateofp.Keywords:themathematicalmodelofsemiconductordevices,discontinuousfin
8、itevolumemethod,theerrorestimates,numericalsimulation.SubjectClassification