四面体法测态密度

Wuhan,Hubei,430074,P.R.China120046Wuhan,Hubei,430074,P.R.China2fccs,,,TheCalculationofDoswithTetrahedronMethodAbstract:TaketheenergybandofSorbitaloffcccrystalasanexample,wemeasureitbyTight-BindingTheoryandthencalculateitsdensityofstate(Dos)withTetrahedronMethod.Withthismethod,firstlythefirstBrillouinZoneisdividedintosometinytetrahedrons,andeachtetrahedron'scontributingtoDosiscalculated,thenthetotalDoscanbeknown.Finally,weusedifferentnumberoftetrahedronstogetdifferentDoslinesandanalyzethecongruityofthemwithothercalculationmethods.Keywords:Tight-BindingTheory;Dosfunction;TetrahedronMethod;Densityofstate;Dosline.1Wuhan,Hubei,430074,P.R.China3,,,,,,,E→E+∆E,∆Z,N(E)=limZE∆∆(TightBinding)linearcombinationofatomicorbitals,LCAOTightBindingSlater—KosterOLCAO12k+KWuhan,Hubei,430074,P.R.China4(APM)APMLAPMMuffin—tin(LMTO)Muffin—tinMuffin—tinZ1973Hohenberg—Kohn,1979DiracKohn—Shams'iikRatiiJeεε=−−∑iJJ,'iikRatinnJeεε=−−∑is,,,12(1/2,0,-1/2),(1/2,0,1/2),(-1/2,0,-1/2),(-1/2,0,1/2),(0,-1/2,-1/2),(0,1/2,-1/2),(0,-1/2,1/2)(0,-1/2,1/2)(-1/2,-1/2,0)(1/2,-1/2,0),(-1/2,1/2,0),(1/2,1/2,0)'14(coscoscoscoscoscos)222222yyxxzzkkakakakakakaJεε=−++k,E(k)=,EE+∆EZk,∆3(2)Vπ,,∆Z=3)(2Vπ(E-E+∆E)Wuhan,Hubei,430074,P.R.China5dSdk∆Z=3(2)VπdSdk∫dkdSdkkE∇=E∆kE∇∆Z=3(2)kVEπ⎛⎞∇⎜⎟⎝⎠∫∆EN(E)=3(2)kVdSEπ∇∫E(k),,N(E)=34kVdSEπ∇∫2.3,1E2E3E4E1E≥2E≥3E≥4E(3)KE(K)44()()()EkEkbkk=+•−rb341[()()]iiibEkEk==−∑irWuhan,Hubei,430074,P.R.China6''231kkrv×=,''312kkrv×=,''123kkrv×='4jjkkk=−1'''123(vkkk=•×)()iEρ32(()(2)idSEEbρπ⎡⎤Ω=⎢⎥⎣⎦)Ω()dSE2430320121341()0EEEfEEEffdSEEEEfEEEE≤≤⎧⎪≤≤−⎪⎨≤≤⎪⎪≤≥⎩[]240342414()()2()()(vbEEf)EEEEEE•−=−−−3[]231342313()()2()()(vbEEf)EEEEEE•−=−−−4[]213141312()()2()()(vbEEf)EEEEEE•−=−−−5πWuhan,Hubei,430074,P.R.China7(1,1,1),,0()4**[cos()cos()cos()cos()cos()cos()]222222yyxxzzkakakakakakaEkEAT=+++,1E≥2E≥3E≥4E,E,12345()dSE32(()(2)idSEEbρπ⎡⎤Ω=⎢⎥⎣⎦)EE,E(),EE41fccsabWuhan,Hubei,430074,P.R.China82fccs93750(1)E-8.02.0EE=2.0E2.00E=2.0(2)N(E)=3(2)kVdSEπ∇∫kE∇(k)0=0kkE∇(3)Wuhan,Hubei,430074,P.R.China934841625750Wuhan,Hubei,430074,P.R.China106307276000820250Wuhan,Hubei,430074,P.R.China119937507.(1),,(2)(3)Wuhan,Hubei,430074,P.R.China12:[1]2002[2]1998[3]1993[4].1988[5]1998667[6]19974(4)1819[7]öWuhan,Hubei,430074,P.R.China13öö