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1、SupportingInformationfor“ZincOxideQuantumRods”(JA031696+)†MingYin,YiGu,IgorL.Kuskovsky,TamarAndelman,YimeiZhu,G.F.Neumark,andStephenO’Brien*CalculationsofZincOxideQuantumRodsrelatedtotheFreeExcitonicPLTransitionEnergy:Withinamodelofcylindricalwellwithinfi
2、nitebarriers,thefreeexcitonicPLtransitionenergy2222hxνn1hxνn1Eg+2+2−Eb(1D)(1)2rme2rmhisgivenby:thwhereEg(=3.36eVatT=300K[1])isthebulkZnObandgapenergy,xνnisthen-zerooftheBesselfunction,Jν(x);me(=0.28m0[1])andmh(=0.59m0[1])aretheeffectivemassesofelectronsan
3、dholes,respectively;ristheradiusofnanorods,andEb(1D)isthebindingenergyof1-Dexciton.InthenanorodswithradiussmallerthantheexcitonBohrradius(aex),whichisthecasehere(aex~2nm,r~1.1nmfromTEM),itcanbeshown[2]thatEb(1D)≈8Eb(3D),whereEb(3D)isthebulkexcitonbindinge
4、nergy.Thus,usingtheEq.(1),weobtain,forthegroundstateenergy(3.55eVfromthefirstabsorptionpeak),r≈1.3nm,whichisingoodagreementwiththevalueestimatedfromTEM(1.1nm).Thecalculatedvalueisslightlyhighersinceactuallythereisapenetrationoftheelectronwavefunctionintot
5、hesurroundingmedia(ligands)andthereforetheinfinite-barriermodelgivestheeffectiveradiusthatincludesthepenetrationlength.Thus,the“real”radiusofnanorodscanbeestimatedasrreal=r−lp,withlpgivenby2hlp=(2)2me(∆E−∆Ee)where∆EistheelectronaffinityofZnO(4.29eV[3])and
6、∆Eeistheelectronconfinementenergy(thesecondterminEq.(1)).Wethenobtainlp≈0.2nm,givingrreal≈1.1nm,theexactsamevalueasthatestimatedfromTEM.Furthermore,usingEq.(1)andr=1.3nm,weestimatealsotheenergyofthefirstexcitedexcitonleveltobearound4.60eV,whichisinexcelle
7、ntagreementwiththeexperimentalresults(seetheinsettoFig.3).[1]B.K.Meyer,H.Alves,D.M.Hofmann,W.Kriegseis,D.Forster,F.Bertram,J.Christen,A.Hoffmann,M.Straßburg,M.Dworzak,U.Haboeck,andA.V.Rodina,PhysicaStatusSolidi(b)241,231(2004).[2]M.W.Lee,H.C.Hsueh,H.-M.Li
8、n,andC.-C.Chen,Phys.Rev.B67,161309(2003).[3]K.B.SundaramandA.Khan,J.Vac.Sci.Technol.A15,428(1997)X-rayPowderDiffraction:AnalysisoftheZincOxideNanorodsbytheRietveldMethod2000018000160001400012000100008000tensityIn600
