Forthetransientbehaviorofasemiconductordevice,themodifiedmethodofcharacteristicswithalternating-directionfiniteelementproceduresfornonrectangularregionisputforward.Sometechniques,suchascalculusofvariations,isoparametrictransformation，patchapproximation,operator-splitting,characteristicmethod,symmetricalreflection,energymethod,negativenormestimateandapriorestimatesandtechniques,areemployed.Inthenonrectangularregioncase,optimalorderestimatesinL^2normarederivedfortheerrorintheapproximationsolution.Thusthewell-knowntheoreticalproblemhasbeenthoroughlyandcompletelysolved.
