Overview of Silicon Semiconductor Device PhysicsSiliconEnergy BandsEnergy BandsBand DiagramsIntrinsic SemiconductorIntrinsic SiliconSemiconductor PropertiesDopingPeriodic TableDonors n-Type MaterialDonors n-Type MaterialAcceptors Make p-Type MaterialAcceptors Make p-Type MaterialThe Fermi FunctionBoltzmann DistributionBand Diagrams (Revisited)Effect of Doping on Fermi LevelEffect of Doping on Fermi LevelEquilibrium Carrier ConcentrationsEquilibrium Carrier ConcentrationsCharge Neutrality RelationshipCalculating Carrier ConcentrationsCommon Special Cases in SiliconIntrinsic Semiconductor (NA=0, ND=0)Heavily One-Sided DopingSymmetric DopingDetermination of Ef in Doped SemiconductorThermal Motion of Charged ParticlesDriftDriftResistivityDiffusionTotal Current DensitiesEinstein RelationChanges in Carrier NumbersChanges in Carrier NumbersMinority Carrier PropertiesEquations of StateEquations of State1Overview of Silicon Semiconductor Device PhysicsDr. David W. GrahamWest Virginia UniversityLane Department of Computer Science and Electrical Engineering© 2009 David W. Graham2SiliconNucleusValence BandEnergy Bands(Shells)Si has 14 ElectronsSilicon is the primary semiconductor used in VLSI systemsAt T=0K, the highest energy band occupied by an electron is called the valence band.Silicon has 4 outer shell / valence electrons3Energy Bands• Electrons try to occupy the lowest energy band possible• Not every energy level is a legal state for an electron to occupy• These legal states tend to arrange themselves in bandsAllowed Energy StatesDisallowed Energy StatesIncreasing Electron Energy}}Energy Bands4Energy BandsValence BandConduction BandEnergy BandgapEgECEVLast filled energy band at T=0KFirst unfilled energy band at T=0K5Band DiagramsEgECEVBand Diagram RepresentationEnergy plotted as a function of positionECÆ Conduction bandÆ Lowest energy state for a free electronEVÆ Valence bandÆ Highest energy state for filled outer shellsEGÆ Band gapÆ Difference in energy levels between ECand EVÆ No electrons (e-) in the bandgap (only above ECor below EV)Æ EG= 1.12eV in SiliconIncreasing electron energyIncreasing voltage6Intrinsic SemiconductorSilicon has 4 outer shell / valence electronsForms into a lattice structure to share electrons7Intrinsic SiliconECEVThe valence band is full, and no electrons are free to move aboutHowever, at temperatures above T=0K, thermal energy shakes an electron free8Semiconductor PropertiesFor T > 0KElectron shaken free and can cause current to flowe–h+• Generation – Creation of an electron (e-) and hole (h+) pair• h+ is simply a missing electron, which leaves an excess positive charge (due to an extra proton)• Recombination –if an e- and an h+ come in contact, they annihilate each other• Electrons and holes are called “carriers” because they are charged particles – when they move, they carry current• Therefore, semiconductors can conduct electricity for T > 0K … but not much current (at room temperature (300K), pure silicon has only 1 free electron per 3 trillion atoms)9Doping• Doping – Adding impurities to the silicon crystal lattice to increase the number of carriers• Add a small number of atoms to increase either the number of electrons or holes10Periodic TableColumn 4 Elements have 4 electrons in the Valence ShellColumn 3 Elements have 3 electrons in the Valence ShellColumn 5 Elements have 5 electrons in the Valence Shell11Donors n-Type MaterialDonors• Add atoms with 5 valence-band electrons• ex. Phosphorous (P)• “Donates” an extra e- that can freely travel around• Leaves behind a positively charged nucleus (cannot move)• Overall, the crystal is still electrically neutral• Called “n-type” material (added negative carriers)• ND = the concentration of donor atoms [atoms/cm3 or cm-3]~1015-1020cm-3• e- is free to move about the crystal (Mobility μn ≈1350cm2/V)+12Donors n-Type MaterialDonors• Add atoms with 5 valence-band electrons• ex. Phosphorous (P)• “Donates” an extra e- that can freely travel around• Leaves behind a positively charged nucleus (cannot move)• Overall, the crystal is still electrically neutral• Called “n-type” material (added negative carriers)• ND = the concentration of donor atoms [atoms/cm3 or cm-3]~1015-1020cm-3• e- is free to move about the crystal (Mobility μn ≈1350cm2/V)+++++++++++++++++–––––––––––––––––++n-Type Material+–+Shorthand NotationPositively charged ion; immobileNegatively charged e-; mobile;Called “majority carrier”Positively charged h+; mobile; Called “minority carrier”13Acceptors Make p-Type Material––h+Acceptors• Add atoms with only 3 valence- band electrons• ex. Boron (B)• “Accepts” e– and provides extra h+ to freely travel around• Leaves behind a negatively charged nucleus (cannot move)• Overall, the crystal is still electrically neutral• Called “p-type” silicon (added positive carriers)• NA = the concentration of acceptor atoms [atoms/cm3 or cm-3]• Movement of the hole requires breaking of a bond! (This is hard, so mobility is low, μp ≈ 500cm2/V)14Acceptors Make p-Type MaterialAcceptors• Add atoms with only 3 valence- band electrons• ex. Boron (B)• “Accepts” e– and provides extra h+ to freely travel around• Leaves behind a negatively charged nucleus (cannot move)• Overall, the crystal is still electrically neutral• Called “p-type” silicon (added positive carriers)• NA = the concentration of acceptor atoms [atoms/cm3 or cm-3]• Movement of the hole requires breaking of a bond! (This is hard, so mobility is low, μp ≈ 500cm2/V)–––––––––––––––––+++++++++++++++++––p-Type MaterialShorthand NotationNegatively charged ion; immobilePositively charged h+; mobile;Called “majority carrier”Negatively charged e-; mobile;Called “minority carrier”–+–15The Fermi Functionf(E)10.5EEfThe Fermi Function• Probability distribution function (PDF)• The probability that an available state at an energy E will be occupied by an e-E Æ Energy level of interestEfÆ Fermi levelÆ Halfway pointÆ Where f(E) = 0.5k Æ Boltzmann constant= 1.38×10-23 J/K= 8.617×10-5 eV/KT Æ Absolute temperature (in Kelvins)()()kTEEfeEf−+=1116Boltzmann Distributionf(E)10.5EEf~Ef-4kT ~Ef+4kT()()kTEEfeEf−−≈kTEEf>>−IfThenBoltzmann Distribution• Describes exponential decrease in the density of particles in thermal