Section 12: Intro to DevicesSection 12: Intro to DevicesExtensive reading materials on reserve, includingRobert F. Pierret, Semiconductor Device FundamentalsEE143 – Ali JaveyBond Model of Electrons and Holes Sili l i• Silicon crystal in a two-dimensionalrepresentation.Si Si SiSi Si SiSi Si SiSi Si SiSi Si SiSi Si SiSi Si SiSi Si SiSi Si Si•When an electron breaks loose and becomes a conduction EE143 – Ali Javeyelectron, a hole is also created.Semiconductors, Insulators, and ConductorsEcTop ofconduction bandEcEvEg=1.1 eVEg= 9 eVemptyEcfilledconduction bandEv•Totally filled bands and totally empty bandsSi, SemiconductorSiO2, insulatorConductor•Totally filled bands and totally empty bands do not allow current flow. (Just as there is no motion of liquid in a totally filled or totally empty bottle.)ypy )• Metal conduction band is half-filled.• Semiconductors have lower EG’s than insulators and can be dopedEE143 – Ali JaveyIntrinsic Carriers-Bottom of conduction bandelectronEnergy gap=1.12 eV+Top of valence bandholevalence bandn (electron conc)= p (hole conc) = niEE143 – Ali JaveyDopants in SiliconSi Si Si Si Si SiSi Si Si SiAs BSi Si Si Si Si Si• As, a Group V element, introduces conduction electrons and creates N-type silicon,• B, a Group III element, introduces holes and creates P-type silicon, and is called a donor.and is called an acceptor.EE143 – Ali JaveyTypes of charges in semiconductorsHoleElectronMobile Charge Carriersthey contribute to current flow with electric field is applied.IidImmobile Chargeswith electric field is applied.Ionized DonorImmobile Chargesthey DO NOTcontribute to current flow ith l t i fi ld i li dIonizedAcceptorwith electric field is applied. However, they affect the local electric fieldEE143 – Ali JaveyFermi Function–The Probability of an Energy State Being Occupied by an ElectronState Being Occupied by an ElectronEf1)(=Efis called the Fermi energy orkTEEfeEf/)(1)(−+the Fermi level. ()kTEEkBoltzmann approximation:E2kTEf+ 3kTE()kTEEfeEf−−≈)(kTEEf>>−()kTEEfEf−−1)(kTEE<<()kTEEfeEf−−≈)(EfEf– kTEf–2kTEf+ kTEfEf+ 2kT()kTEEfeEf−≈1)(kTEEf−<<−f(E)0.5 1Ef–3kT()kTEEfeEf−−−≈1)(EE143 – Ali JaveyElectron and Hole ConcentrationskTEEcCFeNn/)( −=Ncis called the effectivedifdensity of states.kTEEvFVeNp/)( −=Nvis called the effectivedensity of states of the Remember: the closer Efmoves up to Ec, the larger n is; yf fvalence band.fpc,g;the closer Efmoves down to Ev, the larger p is.For Si, Nc= 2.8×1019cm-3and Nv= 1.04×1019cm-3.EE143 – Ali JaveyShifting the Fermi LevelEE143 – Ali JaveyQuantitative Relationshipsn: electron concentration (cm-3)p : hole concentration (cm-3)Assume completelyND: donor concentration (cm-3)NA: acceptor concentration (cm-3)Assume completely ionized to form ND+and NA-1) Charge neutrality condition: ND+ p = NA+ n2) Law of Mass Action :n•p=ni22) Law of Mass Action : np niWhat happens ppwhen one doping species dominates?EE143 – Ali JaveyGeneral Effects of Doping on n and pI. (i.e., N-type) adNNn −=iadnNN >>−Ifnnpi2=NN>>NnNnp2andIf, adNN>>dNn=diNnp=andII.(i.e., P-type) idanNN >>−daNNp −=pnni2=If, daNN>>aNp=aiNnn2=andEE143 – Ali Javey,daapaiCarrier Drift• When an electric field is applied to a semiconductor, mobile carriers will be accelerated by the electrostatic force. This force superimposes on the random thermal motion of carriers:1231234electron45electronE45electronE=0E.g. Electrons drift in the direction opposite to the E-fieldÆ Current flowsEAverage drift velocity = | v | = μEC i biliEE143 – Ali JaveyCarrier mobilityCarrier Mobility• Mobile carriers are always in random thermal motion. If no electric field is applied, the average current in any direction is zero. •Mobility is reduced bySi•Mobility is reduced by1) collisions with the vibrating atoms“phonon scattering”--phonon scattering2) deflection by ionized impurity atoms “Coulombic scattering”As+-B--EE143 – Ali JaveyTotal Mobility14001600111+=10001200Electrons -1 s-1)impurityphononimpurityphononμμμτττ111+=600800ility (cm2 V-impurityphononμμμ200400HolesMobi1E14 1E15 1E16 1E17 1E18 1E19 1E200Total Impurity Concenration (atoms cm-3)Na+Nd(cm-3)EE143 – Ali JaveyTotal Impurity Concenration (atoms cm)Na Nd(cm)Conductivity and ResistivityJ=qpv=qpμEJp,drift qpv qpμpEJn drift= –qnv = qnμnEn,drift qqμnJ=J+J=σE=(qnμ+qpμ)EJdrift = Jn,drift + Jp,drift = σE=(qnμn+qpμp)Econductivity of a semiconductor isσ=qnμ+qpμ∴conductivity of a semiconductor is σ= qnμn+ qpμpResistivity, ρ= 1/ σ∴EE143 – Ali JaveyRelationship between Resistivity and Dopant DensitypypyP-typeTY cm-3N-typePtypeDOPANT DENSIDρ=1/σRESISTIVITY (Ω⋅cm)EE143 – Ali Javeyρ 1/σVIVIVISheet ResistanceWLRWtLRs==ρ+_tWIMaterial with resistivity ρ+_tWIMaterial with resistivity ρ+_tWIMaterial with resistivity ρRsis the resistance when W = L(in ohms/square)LLLtRsρ≡if ρ is independent of depth x • Rsvalue for a given conductive layer (e.g. doped Si, metals) in IC or MEMS technology is used)gy– for design and layout of resistors– for estimating values of parasitic resistance in a device or EE143 – Ali JaveycircuitDiffusion CurrentParticles diffuse from higher concentration to lower concentration locations.EE143 – Ali JaveyDiffusion CurrentdxdnqDJndiffusionn=,dxdpqDJpdiffusionp−=,D is called the diffusion constant. Signs explained:npx xEE143 – Ali JaveyGeneration/Recombination ProcessesRecombination continues until excess carriers = 0.EE143 – Ali JaveyTime constant of decay is called recombination lifetimeContinuity Equations• Combining all the carrier actions:otherstnGthermalRtndifftndrifttntn∂∂−∂∂∂∂∂∂∂∂+++=• Now, by the definition of current, we know:othersGthermalRdiffdriftJJJJNNyN∇∂∂∂∂∂11)(• Since a change in carrier concentration must occur from a net currentNqzJyJxJqdifftndrifttnJNzNyNx⋅∇=++=+∂∂∂∂∂∂∂∂∂∂11)(• Therefore, we can compactly write the continuity equation as:nnNnJ∂∂∂∂∂∂++⋅∇=1thtpGth lRtpPqtpothertGthermalRtNqtJJ∂∂∂∂∂∂∂−∂∂++⋅∇−=++∇1EE143 – Ali JaveyothertGthermalRtqt∂−∂∂PN Junctions Donors N-typeP-typeIVI–+VNPIA PN junction is present in almost every semiconductor device.Reverse bias Forward biasdiodesymbolEE143 – Ali Javeyjp yEnergy Band Diagram and Depletion LayerN-regionP-region(a)Ef(b)EcEfEvEc(c)n 0 and p 0in the
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