P型半导体掺有受主杂质（第III族元素，如Al，Ga，In）后的半导体。其电子浓度小于空穴浓度。在价带上面形成一个具有自由电子占据的能级。称为受主能级Electron energyBatomsitesevery10Siatoms多数载流子：E.xDistance空穴into crystal少数载流子B-BBBE.电子0.05eVEVB(a)(b)(a)BorondopedSicrystal.Bhasonlythreevalenceelectrons.When itsubstitutesfora Siatomoneof its bondshas an electronmissingand thereforeahole.(b)Energybanddiagramforap-typeSidopedwith1ppmB.Thereareacceptorenergylevels justaboveE,aroundB-sites.TheseacceptorlevelsacceptelectronsfromtheVBandthereforecreateholesintheVB?1999S.0.Kasap,Optoelectronics(PrenticeHall)
掺有受主杂质（第III族元素，如Al,Ga,In）后的半导 体。其电子浓度小于空穴浓度。在价带上面形成一个 具有自由电子占据的能级，称为受主能级 B – h + (a) x B – Ev Ea B atom sites every 10 6 Si atoms Distance into crystal ~0.05 eV B – B – B – h + VB Ec Electron energy (b) (a) Boron doped Si crystal. B has only three valence electrons. When it substitutes for a Si atom one of its bonds has an electron missing and therefore a hole. (b) Energy band diagram for a p-type Si doped with 1 ppm B. There are acceptor energy levels just above Ev around B– sites. These acceptor levels accept electrons from the VB and therefore create holes in the VB. ?1999 S.O. Kasap, Optoelectronics (Prentice Hall) 多数载流子： 空穴 少数载流子： 电子 P型半导体
粒子的统计分布·态密度g（E）(a)(b)(c)(d)E g(E)x(E-E)"EE·费米-荻拉克概率函?E+x[I-(E)]数（在能量为E的能级CBForArea=-n,(E)dE=n上找到一个电子的几率）electronsn(E)1E.-E.f(E)=1+exp[E-E,)/k]E,EF·导带上的电子密度：E,P(E)"E0000n= [g(E)f(E)dEArea=pFor holesVBE0JE)n(E)orp(E)g(E)kgT(a)Energybanddiagram.(b)Densityof states (numberofstates perunitenergyperE，为体系的Fermi能级，kunitvolume).(c)Fermi-Diracprobabilityfunction (probabilityofoccupancyofastate).(d)Theproductofg(E)andf(E)istheenergydensityofelectronsintheCB为Boltzmann常数，T为绝(number of electrons per unit energy per unit volume). The area under ne(E) vs. E is对温度，Nc有效态密度：theelectronconcentrationN。= 2(2mkgT / h2j3/2?1999S.0.Kasap,Optoelectronics (PrenticeHall)
粒子的统计分布 E g(E) fE) EF n E (E) or p E (E) E E For electrons For holes [1–f(E)] nE (E) p E (E) Area = p Area =•nE (E)dE = n Ec Ev Ev Ec 0 Ec + EF VB CB (a) (b) (c) (d) g(E) (E–Ec ) 1/2 (a) Energy band diagram. (b) Density of states (number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a state). (d) The product of g(E) and f(E) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under nE (E) vs. E is the electron concentration. ?1999 S.O. Kasap, Optoelectronics (Prentice Hall) (E E ) k T f E + − f = 1 exp 1 ( ) Ef 为体系的Fermi能级，k 为Boltzmann常数，T 为绝 对温度，Nc有效态密度： •费米-荻拉克概率函 数（在能量为E的能级 上找到一个电子的几率) ( ) ( ) ( ) − = − = k T E E N n g E f E dE B c F c EC exp * 2 3 / 2 N 2(2 m k T / h ] c = e B •导带上的电子密度： •态密度g（E）
价带上空隙的密度(EF-E,)p~ N,expk,TN.是有效态密度：N, = 2(2πm,k,T / h2j3/2·Fermi能级1kTlnEEH+gN22费米能级反映导带的电子与价带的空穴密度的差别
( ) − − k T E E p N B F exp = + − u c Fi g N N E E E k T ln 2 1 2 1 •价带上空隙的密度 * 2 3/ 2 N 2(2 m k T / h ] u = h B Nu 是有效态密度： •Fermi 能级 费米能级:反映导带的电子与价带的空穴密度的差别
本征半导体的粒子分布：ElectronenergyE(electricfleld)Electron~2kgTconcentrationdistributionElectronConductionband2No.of electronstatesEFE, - Ec-EvNo.of bole statesHValencebandHoleHoleconcentration2kTdistribution(b)(a)
本征半导体的粒子分布：
N型半导体的粒子分布ElectronenergyElectron cncentrationConductian banddistnbutionNo,of electronstates~2kgTFNNo. of hale stateHolecomcentratiomValence banddistribution(a)(b)
N型半导体的粒子分布