固体电子态

2.4Penny-Kronig—EkE(k)—E(k)()—()—2.41.—()kEa2πE(k)2.41.()()yxkkEE,=k—22.41.()()zyxkkkEE,,=k—3Cu————142.42.“”2.42.“”a—a2/k2a/n2a()Bragg—/a2.43.zzBragga12.43.Bragg(1)()2(2)k(3)(4)BB2.43.a2()21,gg()21,aaπ211=⋅ag021=⋅ag2.43.a22.43.()321,,ggg()321,,aaaV321π2aag×⋅=HNP100*110*111*2.43.——866——100*X111*L110*Kbcc2.43.——2.44.z——“”z2.44.zz————2.44.2.44.()2.45.()()zyxkkkEE,,=k—3100*X111*L110*K2.45—3100*X111*L110*K——Cu2.45—3——Al“”Ek2.45—3AlGaAs2.45—3SiGaAs2.45—3GaAs2.46z3z2/a2/L2x(L/a)=2Na2z:a222222π22NaLLa=×=×π2-182.46zz2.46z()()21232022π21EEmEN−≈h()()21232022π21EEmEN−≈h2.46zz()2.47zns2.47znsnpnsnp2.47z——npz——(1)3d,(2)3d4s2.47z——z0K2.48:(1)2(2)2.51zT0K−∝≡TkEpngB2expT0K()()EEfENnCEd⋅⋅=∫∞()1expd2π2121C2322C+−⋅−⋅=∫∞kTEEEEEmFEeh2.51T0K−∝≡TkEpngB2exp()()EEfENnCEd⋅⋅=∫∞()1expd2π2121C2322C+−⋅−⋅=∫∞kTEEEEEmFEeh()xxekTEEkTmnxFedexp2π2121C2302322−∞⋅−−⋅⋅≈∫h2πd021=⋅⋅∫∞−xxex(E-EF)kTx=(E-Ec)/kT−−=kTEENnFCCexp232302320π241TmmkmNeC⋅⋅=h−−=kTEENpFVVexp−==≡kTENNnppngV2expC2.51zT0K−⋅==≡TkENNnppngVBC2expT0K2.42-1——()():gEhchE~phphphλν==z——z—LED2.42-1——2.42-1