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1、PHYSICALREVIEWB,VOLUME65,115318Absolutesurfaceenergiesofgroup-IVsemiconductors:DependenceonorientationandreconstructionA.A.Stekolnikov,J.FurthmuÈller,andF.BechstedtInstitutfuÈrFestkoÈrpertheorieundTheoretischeOptik,Friedrich-Schiller-UniversitaÈt,07743Jena,Germany~Received13July2001;r
2、evisedmanuscriptreceived23October2001;published28February2002!Weuseaplane-wave-pseudopotentialcodetostudythesurfaceenergeticsfortheelementalsemiconductorsGe,Si,anddiamondfrom®rstprinciples.Variousreconstructiongeometriesincluding131,231,c(432),c(238),and737ofthelow-indexsurfaces~100!,
3、~110!,and~111!areoptimizedwithrespecttotheatomiccoordinates.Theresultingtotalenergiesarerelatedtotheaccompanyingbandstructures.Chemicaltrendsarederived.Thedifferentreconstructionbehaviorisdiscussedintermsofatomicsizesandorbitalenergies.DOI:10.1103/PhysRevB.65.115318PACSnumber~s!:68.35
4、.Bs,68.35.Md,73.20.At,61.50.AhI.INTRODUCTIONdimer-basedreconstructions.18,19Atroomtemperature,SiandGeexhibita231reconstructiongovernedbyasymmet-20Theabsolutevalueofthesurfacefreeenergyofacrystal-ricdimers~AD's!.Astaggeredarrangementofthesedimerslinesolidisoneofthemostimportantfundamen
5、talquantities19explainsthec(432)low-temperaturephaseofSi~100!.whichcharacterizesalargenumberofbasicandappliedphe-Symmetricdimers~SD's!dominatethe231reconstructionnomena.Amongthemarecrystalgrowth,surfacefaceting,21oftheC~100!surface.Thetopographyofaclean~110!growthofthinlayers,andthesh
6、apeofsmallcrystallites.Onesurfaceissomewhatdifferentfromthatofa~111!surfaceofthefascinatingproblemsconcernstheequilibriumshapewithstepstructures.Rather,itisrepresentedbylong-rangeofnanocrystallitesfabricatedfromgroup-IVmaterialsger-22,23reconstructions,e.g.,1632.Ontheotherhand,astudym
7、anium~Ge!,silicon~Si!,andperhapsalsodiamond~C!.withinthe131translationalsymmetryshouldgivethebasicTheformationofself-assembledislandsorquantumdots,structuralandelectronicfeaturesofsuchsurfaces.ThetwoduringtheepitaxialgrowthofGeonSi~100!~Refs.1and2!atomsinacorrespondingunitcellareallow
8、edtor
