奈米碳管之导电性与导电路径.ppt

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1、Lecture5奈米碳管之導電性與導電路徑共軛結構–C=C-C=2D-view(骨架式)-電子之共振結構Isotropicconduction-electron捲成管狀後isotropicconduction仍然維持3D-view-bond(sp2)-Wavefunction(electroncloud)-bond-wavefunction價電子雲位於二個碳原子間,導電之電子雲位於上下二處骨架式120e-e--電子可於圓形3D空間內運行-電子雲重疊,造成電子可於電子雲中自由穿

2、梭,形成導電路徑如果重疊區域少,電子需藉由hopping(或是tunneling)方能穿梭電阻小電阻大六連環俯視圖側視圖骨架+電子雲(形成3Dview)電子可視為電子波,故具備向量性質而空間中向量可分成三個分量,x,y,zxyz也就是說電子可延三個方向前進1Åz由於波函數(wavefunction)沿z軸方向只延伸約1Å距離,故電子波向量沿z軸方向受限制.但沿x,y軸方向不受限制xyxyxy無外加電場沿管軸方向外加電場時Espiralconduction2D:isotropicconductio

3、n(骨架式共軛結構)碳管之導電路徑3D:alongx(circumference)andy(tubeaxial)axesconductionwithoutexternalelectricfield3D:spiralconductionoccurswhenexternalelectricfieldisapplied電子雲于碳管表面StandingwavepatternWavefunctionimageSTMimages碳管之能帶結構石墨晶格1stBrillourinzoneCBVB6k-points

4、平面圖3D-view能量最大CBjoinswithVBatk-pointsk-pointVBCBEFAbovemeansthatifanysub-bandscrossatk-pointswouldbemetallicnatureotherwisetubeisasemiconductingproperty.Oneatomoneenergylevel(sub-band)withunpairedelectronTwoatomstwoenergylevelswithonebondingandoneanti

5、-bondingbondinganti-bondingThreeatomsthreeenergylevelswithonebonding,oneanti-bondingandoneunpairedelectronEachsub-bandhasownvelocityandwavevectorIfanyofthesevectorscrossatk-pointsorinterceptEFthenanotubewouldbeametallicnature.MetallicnatureWavevectorB

6、and-gapwherea1anda2areunitvectors,andnandmareintegers.Ananotubeconstructedinthiswayiscalledan(n,m)nanotubeChiralvector=Ch=na1+ma2d=(3)1/2aC-C(m2+mn+n2)1/2/)WhereaC-C=1.42Å:thenearestneighborcarbon-carbondistance=tan-1[(3)1/2n/(2m+n)]Example:forzigz

7、agtubewhen=0with(n,0)=(9,0),d=7.05Åforarmchairtube,(n,n)=(5,5),d=6.83Åzigzagedgearmchair30:Semiconducting:metallic(0,0)(1,0)(2,0)(3,0)(4,0)(1,1)(2,2)(3,3)(2,1)(3,1)(4,1)mn(n,m)notation(3,2)(n,0):zigzagtubes(n,n):armchairtubes(n,m):chiraltubes2n+m=3

8、q;(q:integer)為何文獻總是說碳管之電性取決於管徑(tubediameter)與螺旋性(chirality)波向量隨直徑變化而位移=15=25DeterminationbytubeChirality波向量隨管之螺旋性而變化文獻說不論直徑為何只要nanotubes是armchairedge均是metallicnature(nobandgap)因為波向量永遠座落於k-points上且此六邊形對稱不隨管直徑而變化文獻說zigzagnanotube有三分之一會是metal