Themodeloftransientbehaviorofsemiconductorwithheat-conductionisaninitialandboundaryproblem.Alternating-directionmultisteppreconditionediterativemethodsandtheoryanalysesaregiveninthispaper.Electricpotentialequationisapproximatedbymixedfiniteelementmethod,concentrationandheat-conductionequationsareapproximatedbyGalerkinalternating-directionmultistepmethods.ErrorestimatesofoptimalorderinL2aredemonstrated.