搜索
2.2(1895,LA.Lorentz,PDrude)1.—()()2.—()3.—4.—0K“”5.—6.—2.2(1930s,A.Sommerfeld1.z—zz())()()(2)(22iiiirrrriiiiiiiiVmHψεψψ=+∇−=∧hz—()()constVNii≡⋅⋅⋅⋅⋅⋅rrrr,,,,,212.2()()zyxEzyxm,,,,2202ψψ=∇−h2.L(0x,y,zL)(1)(2)(3)2.2()()()()zhygxfzyx⋅⋅=,,ψ)(dddddd222222202fghEzhfgyghfxfghm⋅=++−hEzhhyggxffm=++−22222202dd1dd1dd12h02dd21022=+fEmxfh02dd22022=+gEmygh02dd23022=+hEmzhhEEEE=++3212.20)(2d)(d21022=+xfEmxxfh()xikxeAxf1=21022hEmkx=()()zyxzyLx,,,,ψψ=+()()xfLxf=+1=LikxeLnkx1π2=n10,1,2,3,4,5,……()()rk•=++=iAzkykxkiAzyxzyxexp)](exp[,,ψ2.221022hEmkx=Lnkixiπ2=ni0,1,2,3,4,5,……()()rk•=++=iexp)](iexp[,,AzkykxkAzyxzyxψ1ddd32)(*==∫∫∫LAzyxvψψ()()[]rk⋅=++=i231exp1,,321eVzkykxkiLzyxzyxnnnψ()()2322212022222022π42321nnnLmkkkmEzyxnnn++=++=hh2.2(1)z——z————()2.21cm10nm“”(0K)2120222022π421nLmkmExn⋅==hh020222102022max810π4102π4mLLmE×=××=hheV3.9J1049.1101.98101005.1π1831206822max=×=×××××≈−−−En10K“”aZvaLZZaLn442VV1≈−=a=0.2nmZv=22.2LnEnLmEnn1222π411202211∝=⋅≈h∆eV105.7J102.110101.9101005.1π725231106822max−−−−−×=×=×××××≈E∆eV75.0J102.11010101.9101005.1π19931106822max=×=××××××≈−−−−E∆1cm10nm()[]1202221212022122π412π4111nLmnnLmEEEnnn⋅≈−−⋅=−=−hh∆62.2——()——1eV13“”2.2zz2.23.(1)——zz——Lnkixiπ2=3,2,1,0±±±=in()3,2,1=i…(2)n1n2n3ms()2.2(1)k4.(k)(2)“”2/L(3)————2.2(1)5.(2)“”2/L(2/L)3kk~(k+dk)()2π2dπ432×⋅Lkk(3)0222mkEh=2022hEmk=EEmk2d2d20⋅=h()VEEmVEEEm⋅⋅⋅=⋅⋅⋅d2π212d2π2π8212320223203hh21232022π21)(EmEN=h2.26.FermiDirac(2)——GibbsPauliF-D(1)(3)FermiEzUzSWSklnW1exp1)(F+−=kTEEEf2.26.FermiDirac(4)()≤=0F0F01EEEEEf()()()−≈==−≈1/05.01/1FFFkTEEEEkTEEEfT0KT0K7.(1)()()()EfENEZ⋅=1exp1)(F+−=kTEEEf2.27.(2)0K波矢空间中的图像2.27.(3)T0K——2.2110eV8.(1)(2)0Kz0K()()()EEfENEEZNeVdd00⋅⋅==∫∫∞∞()EEmEENNFFEEeVd22π1d000232020∫∫==h()023220F2π3mNEeVh⋅=zT0K−≈20F20FF12π1EkTEE2.2.1.z0K()EEmEEENEFFEEd22π1d000232320200t∫∫==hzT0K+≈20F20125π1EkTEE()()()EEfENEEEZEEdd00t∫∫∞∞⋅=⋅=0F250F23202532π3153ENEmeV⋅⋅=⋅⋅=h0F06.0EE=0K2.2.1.105106m/s—0K0K2102=mEVFF0K2.2.2.+≈20F20125π1EkTEEz[]TEZNCVAeV∂∂=VTTZNEkCVAFeV⋅=⋅⋅=γ0222πkTkTE23213=⋅=RZCVeV23=z经典自由电子理论4.730.701.351.380.350.500.911.1CoCuAlNa2.2.2.zaVCeVaVVCCC+=3Rz