SemiconductorSemiconductor FundamentalsFundamentals

YuanYuan--Huei ChangHuei Chang

Lattice: periodical arrangement of atomsLattice: periodical arrangement of atoms

Body-centered Zinc-Blende

Periodical potential of a lattice and the electronPeriodical potential of a lattice and the electronwavefunctionwavefunction

http://www.mtmi.vu.lt/pfk/funkc_dariniai/quant_mech/bands.htm

•• Bloch theoremBloch theorem

U (U (rr))== U (U (r+Rr+R),), RR is any lattice vectoris any lattice vector H=H=PP22/2m+ U (/2m+ U (rr)) HH ΦΦ = E= E ΦΦ HH ΦΦ = E= E ΦΦΦΦkk ((rr))= e= e ik·rik·r uu ((rr)) uu ((rr) =) = uu ((r+Rr+R)) kk could be used to specify the electroniccould be used to specify the electronic

state and p=state and p=ћћkk, is the crystal momentum of, is the crystal momentum ofthe electron in the latticethe electron in the lattice

From energy level toFrom energy level toenergy bandenergy band

○○ ○○△△EE

○○ ○○

○○ ○○

△△EE

△△EE

Relation between width of the energyRelation between width of the energyband and the interband and the inter--atomic distanceatomic distance

△△EE

d

Band structure of solidBand structure of solid

Conductionband

Energy gap

EF : Fermi evel

insulator metal

Valenceband

What is a holeWhat is a hole

The collective motion of nThe collective motion of n--1 electrons.1 electrons.When a filled band has holes, it canWhen a filled band has holes, it can

conduct electricity.conduct electricity.conduct electricity.conduct electricity.

missing 電洞

Sum=0

Net effect

EE--k relation for an electron in a latticek relation for an electron in a lattice

For an electron in the vacuum E =For an electron in the vacuum E = ћћ22kk22/2m./2m. In a lattice E(k) is usually a very complicated functionIn a lattice E(k) is usually a very complicated function

http://zh.wikipedia.org/wiki/%E5%8D%8A%E5%AF%BC%E4%BD%93

EE-- k and vk and v--k relation for an electronk relation for an electronin a latticein a lattice

A filled band does not conduct

有效質量有效質量(effective mass)(effective mass)

In vacuum E =In vacuum E = ћћ22kk22/2m and m is independent of E./2m and m is independent of E. In a lattice E=E(k).In a lattice E=E(k). E(k)=E(k)= ћћωω(k), and v(k), and vgg=d=dωω/dk/dk vvgg=(1/=(1/ ћћ)) dE/dkdE/dk

a=d va=d v /dt=(1//dt=(1/ ћћ)) dd22E/dkdt=(1/E/dkdt=(1/ ћћ)) dd22E/dkE/dk22 (dk/dt)(dk/dt) a=d va=d vgg/dt=(1//dt=(1/ ћћ)) dd22E/dkdt=(1/E/dkdt=(1/ ћћ)) dd22E/dkE/dk22 (dk/dt)(dk/dt) p=p= ћћk, F=dp/dt=k, F=dp/dt= ћ ћ dk/dtdk/dt dk/dt= (1/dk/dt= (1/ ћћ)) FF a=(1/a=(1/ ћћ22)F)F dd22E/dkE/dk22

m*m* --11= (1/= (1/ ћћ22)) dd22E/dkE/dk22

m*m*ijij--11= (1/= (1/ ћћ22) ∂) ∂22E/E/ ∂∂kkii ∂∂kkjj

semiconductorssemiconductors

1. Intrinsic semiconductor is an insulator1. Intrinsic semiconductor is an insulator2. The conduction property of the SC is2. The conduction property of the SC is

determined by the impurity in the SC.determined by the impurity in the SC.3. Whether a semiconductor is useful depends3. Whether a semiconductor is useful depends3. Whether a semiconductor is useful depends3. Whether a semiconductor is useful depends

onona. Low defect density pure substrate coulda. Low defect density pure substrate could

be obtained.be obtained.b. Controlled doping of n and p typeb. Controlled doping of n and p type

impurities can be achievedimpurities can be achieved

Donor and acceptorDonor and acceptor

http://www.physics.udel.edu/~watson/scen103/colloq2000/doping-donor.html

Binding energy of donor and acceptorBinding energy of donor and acceptor