Lecture #3Band Gap and Material ClassificationMeasuring Band Gap EnergyDensity of StatesDopingDoping Silicon with DonorsDoping Silicon with AcceptorsDonor / Acceptor Levels (Band Model)Charge-Carrier ConcentrationsN-type MaterialP-type MaterialTerminologySummaryLecture #3OUTLINE• Band gap energy• Density of states• DopingRead: Chapter 2 (Section 2.3)EE130 Lecture 3, Slide 2Spring 2007Band Gap and Material Classification Ec EvEG=1.12 eV EcEG= ~9 eVSi SiO2metalEcEv•Filled bands and empty bands do not allow current flow•Insulators have large EG•Semiconductors have small EG•Metals have no band gap–conduction band is partially filledEE130 Lecture 3, Slide 3Spring 2007Measuring Band Gap Energy-EG can be determined from the minimum energy (h of photonsthat are absorbed by the semiconductor.photonphoton energy: h v EGEcEvelectron hole Band gap energies of selected semiconductorsSemiconductor Ge Si GaAsBand gap (eV) 0.67 1.12 1.42EE130 Lecture 3, Slide 4Spring 2007Density of States EEcEvEcEv 2)(32**hEEmmEgcnnc 2)(32**hEEmmEgvppvgc(E)gv(E)E EcE Evg(E)dE = number of states per cm3 in the energy range between E and E+dENear the band edges:EE130 Lecture 3, Slide 5Spring 2007Donors: P, As, Sb Acceptors: B, Al, Ga, InDopingBy substituting a Si atom with a special impurity atom (Column V or Column III element), a conduction electron or hole is created.EE130 Lecture 3, Slide 6Spring 2007Doping Silicon with DonorsExample: Add arsenic (As) atom to the Si crystalThe loosely bound 5th valence electron of the As atom “breaks free” and becomes a mobile electron for current conduction.EE130 Lecture 3, Slide 7Spring 2007Example: Add boron (B) atom to the Si crystalDoping Silicon with AcceptorsThe B atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, carrying current as a positive charge.EE130 Lecture 3, Slide 8Spring 2007Donor / Acceptor Levels (Band Model)EcEvDonor LevelAcceptor LevelEDEADonor ionization energyAcceptor ionization energy Ionization energy of selected donors and acceptors in siliconAcceptorsDopant Sb P As B Al InIonization energy, Ec-Ed or Ea-Ev (meV)39 45 54 45 67 160DonorsEE130 Lecture 3, Slide 9Spring 2007Charge-Carrier ConcentrationsND: ionized donor concentration (cm-3)NA: ionized acceptor concentration (cm-3)Charge neutrality condition: ND + p = NA + nAt thermal equilibrium, n p = ni2 (“Law of Mass Action”)Note: Carrier concentrations depend on net dopant concentration (ND - NA) !EE130 Lecture 3, Slide 10Spring 2007N-type MaterialND >> NA(ND – NA >> ni):EE130 Lecture 3, Slide 11Spring 2007P-type MaterialNA >> ND(NA – ND >> ni):EE130 Lecture 3, Slide 12Spring 2007Terminologydonor: impurity atom that increases nacceptor: impurity atom that increases pn-type material: contains more electrons than holesp-type material: contains more holes than electronsmajority carrier: the most abundant carrier minority carrier: the least abundant carrier intrinsic semiconductor: n = p = niextrinsic semiconductor: doped semiconductorEE130 Lecture 3, Slide 13Spring 2007Summary•The band gap energy is the energy required to free an electron from a covalent bond.–EG for Si at 300K = 1.12eV–Insulators have large EG; semiconductors have small EG•Dopants in Si:–Reside on lattice sites (substituting for Si)–Group-V elements contribute conduction electrons, and are called donors–Group-III elements contribute holes, and are called acceptors–Very low ionization energies (<50 meV) ionized at room temperatureDopant concentrations typically range from 1014 cm-3 to 1020
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