固体物理基础能带理论Ⅰ

1、准连续能级Band - 1Band - 2Band - 3Band gapBand gap1221ba,221A,221S21s2p2s分裂2分裂N原子原子分子晶体k)()(nRrVrV)()(rErH)()()(222rErrVm)()(ruerrk i)()(ruRrun)()(reRrnRk innRk ie)()(nRrVrV)()(nRrHrH)()()(rErrH)()()(nnnRrERrRrH)()()(nnRrERrrH)()(rRrnRn12nRmnmnRRRRnRRKn)()(reRrnRk innnRRiexp)()()()(332211NrNrNrr1nRk ie11

2、2233()2nk RkNNNhuu ),(332211333222111NlNlNlbNlbNlbNlk2, 12,2iiiNNN33)2(Vkk)()(laxVxVLxVLxxxV0, 0,)(V)()(2000222xExVdtdm整数:,2lNalklVmkEk2220ikxkeLx1)(0左矢00)(kxk右矢00)*(kxk0000)(*)(kkkkNakkdxxx)()(xVVxVHkxVkEk)()1 (002)2()(kkkkEEkxVkE000)1 ()(kkkkkEEkxVkkxVkkxVkHkk)()(LxkkidxxVeLkxVk0)()(1)(annaxkkiNnd

3、xxVeNa)1()(10)(1naxakkiNnnakkiakkiNnnakkidVeaeNdVeeNakxVk0)(10)(0)(10)()(11)(1)(lGlbalkk211110210)(NnnilNnnakkieNeNakkiNakkiNnnakkieeNeN)()(10)(111112)()22()(lliNaNalNaliNakkieeealkk2nGnbkk naaniVdVeakxVk02)(1)(0)1 (VEknnkankkmVE2222)2(221k1k2k1V1V2V)1 (2)1 (anankkankanan00kkba220000421nkkkkVEEEEE12

4、1222nnnnnnnnnnVTTVTVVTTVTVEnV2kmakk2Ek)()(222miimimatxxxxxxVmNmimimiHim, 2 , 1, 2 , 1,)(mixx i1i1imixxmi,m1m1m )()(222xExxVm mmatxxVxV)(xmixx mkmmmikmkmiakxxax, mnnimidxxxxxnimi*,Neamxikkm xexxxecexxxecxxkikxmmnixxikikxmmniikxnknnmnm)( mmimikmmimmatkmnnikxxVaxxVxxVmaxxakmn222EH )()(222xkxxVmkk matmx

5、xVxVVmmkkimiVniaaEmn,mmiknknmiVaniakm,)(nixxni,*mmxxikimiVnieEnm, mmimatnixxikidxxxxxVxVxxeEnm* ssikximnmxxikimiatnmixxikixJexxJedVVxxeEsnmnm* dVxxdVVxxxxJimnmiiatnminm0*mxx 0 ,0iVsixJms01sx xVxVVatm0)(xi 0 ,0iVsixJms 221100ssikxssikxissikxixJexJeJxJeEsss)(sixx 1,inm dVJi201 nm dVaJii*1 kaJJeeJJkEii

6、kaikaicos21010bNlNlakl2 hiihbkikihGkkhbkGkk, kaJJkiicos210一个原子能级i对应一个能带，不同的原子能级对应不同的能带。当原子形成固体后，形成了一系列能带能量较低的能级对应的能带较窄能量较高的能级对应的能带较宽 kaJJkiicos210 k1 k3 k4 k2 hiiGkkaakaaaak22光波格波,qcqvsdkdEdkdv1 1vkkn tddtddtddnknkvkkkvFk tten,),(rBkvrEkFktdd tten,),(rBkvrE下面讨论电子的质量。从基本关系式出发： Fkkvk,1 kkkFdtdv221mFdtdv与 类比zyxzyzxzzyyxyzxyxx