EECS130 Integrated Circuit DevicesAnnouncementsSlide Number 3Slide Number 4Doping Profile of “Idealized Junctions”Qualitative ElectrostaticsSlide Number 7Equilibrium ConditionsSlide Number 9Built-in Potential as a function of Na and NdSlide Number 11The Depletion ApproximationField in the Depletion Layer Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Reverse-Biased PN JunctionSlide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30EECS130 Integrated Circuit DevicesProfessor Ali Javey9/18/2007PN JunctionsLecture 1Reading: Chapter 5Announcements• For THIS WEEK ONLY, Prof. Javey's office hours will be held on Tuesday, Sept 18 3:30-4:30 pm and Wednesday, Sept 19 5-6 pm.• Exam 1 (Oct 4) will cover Semiconductor Fundamentals, Fabrication, and PN junctions.• HW2 is due…… right now.• HW3 is now posted on the web. • You can check your grades on bspace.• Check out the group discussion board.PN JunctionsA PN junction is present in every semiconductor device.N-typeP-typeDonorsVIReverse bias Forward biasN PVIdiodesymbol–+N-regionP-region(a)(b)(c)(d)DepletionlayerNeutralP-regionNeutralN-regionEfEnergy Band Diagram and Depletion Layer of a PN JunctionA depletion layer exists at the PN junction. n ≈ 0 and p ≈ 0 in the depletion layer.EcEfEvEcEvEfEcEvEfEvEcDoping Profile of “Idealized Junctions”pnpnQualitative ElectrostaticsBand diagramBuilt in-potentialFrom ε=-dV/dxWhen the junction is formed, electrons from the n-side and holes from the p-side will diffuse leaving behind charged dopant atoms. Remember that the dopant atoms cannot move! Electrons will leave behind positively charged donor atoms and holes will leave behind negatively charged acceptor atoms.The net result is the build up of an electric field from the positively charged atoms to the negatively charged atoms, i.e., from the n- side to p-side. When steady state condition is reached after the formation of junction (how long this takes?) the net electric field (or the built in potential) will prevent further diffusion of electrons and holes. In other words, there will be drift and diffusion currents such that net electron and hole currents will be zero.Formation of pn junctionsEquilibrium ConditionsUnder equilibrium conditions, the net electron current and hole current will be zero.NA = 1017 cm−3ND = 1016 cm−3hole diffusion currenthole drift currentnet current = 0E-fieldP-typeN-type2lniadbinNNqkTV =Built-in PotentialdckTAqcdNNqkTAeNNn ln=⇒==−22lniackTBqcainNNqkTBeNNnn =⇒==−⎟⎟⎠⎞⎜⎜⎝⎛−=−=dciacbiNNnNNqkTABV lnln2N-regionP-region(b)EfEcEvqVbiqBqABuilt-in Potential as a function of Na and NdPoisson’s Equationεs : semiconductor permittivity (~12εo for Si)ρ: charge density (C/cm3)What can Poisson’s equation tell us?)The Depletion ApproximationWe assume that the free carrier concentration inside the depletion region is zero.We assume that the charge density outside the depletion region is zero and q(Nd -Na ) inside the depletion.On the P-side of the depletion layer, ρ= –qNaOn the N-side, ρ= qNdNP Depletion Layer Neutral Region –xn 0 xpx xp–xnqNd–qNax E–xn xp ρ 0Neutral Region saqNdxdε−=)()(1xxqNCxqNxpsasa−=+−=εε)()(nsdxxqNx+=εField in the Depletion LayerField in the Depletion Layer The electric field is continuous at x = 0.Na xp = Nd xnA one-sided junction is called a N+P junction or P+N junctionNP Depletion Layer Neutral Region –xn 0 xpNeutral RegionPotential in the Depletion LayerD1 =0Depletion WidthDepletion WidthEXAMPLE: A P+N junction has Na =1020 cm-3 and Nd =1017cm-3. What is a) its built in potential, b)Wdep , c)xn , and d) xp ?Solution:a) b)c)d)V 1cm10cm1010lnV026.0ln620617202≈×==−−iadbinNNqkTφμm 12.010106.111085.812222/1171914=⎟⎟⎠⎞⎜⎜⎝⎛××××××=≈−−dbisdepqNWφεμm 12.0=≈depnWx0Å 2.1μm102.14≈=×==−adnpNNxxReverse-Biased PN JunctiondensitydopantlighterNNNad 1111≈+=• Does the depletion layerwiden or shrink withincreasing reverse bias?+–VN P(a)(b) V = 0(c) reverse-biasedqVAqNbarrier potentialqNVVWsAbisdep⋅=+=εε2|)|(2EcEfEvEfEvqVbiEcEcEfnEvqVbi + qVAEcEfpEvReverse-Biased PN JunctionForward Biased PN JunctionNote: simply replace Vbi with Vbi -VACapacitance-Voltage Characteristics• Is Cdep a good thing?• What are three ways to reduce Cdep ?NP NdNaConductor Insulator Conductor WdepdepsdepWACε=Capacitance-Voltage Characteristics22222)(21AqNVAWCSbisdepdepεφε+==Vr 1/Cdep2Increasing reverse biasSlope = 2/qNεsA2 – φbiCapacitance dataJunction BreakdownA Zener diode is designed to operate in the breakdown mode.VIVB, breakdownForward CurrentSmall leakageCurrentvoltagePeak Electric Field2/1|)|(2)0(⎥⎦⎤⎢⎣⎡+==rbispVqNφεN+PNaNeutral Region0xpxxp(a)(b)increasingreverse biasincreasing reverse biaspTunneling BreakdownDominant breakdown cause when both sides of a junction are very heavily doped.bicritsBqNVφε−=22V/cm106≈=critp(a)(b)Empty StatesFilled StatesVI(c)Breakdown-EvEcEvEcEfAvalanche Breakdown impact ionizationqNVcritsB22ε=avalanche breakdownEcEfnEcEvEfporiginalelectronelectron-holepair generationdaBN1N1N1V
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