1EE105 - Fall 2005Microelectronic Devices and CircuitsLecture 6Currents in PN JunctionMOS Capacitor2AnnouncementsHomework 3, due next weekReading: Chapter 3 (3.7-3.9)23Lecture MaterialLast lecturePN junctionDiode capacitanceThis lectureDiode currentsMOS capacitor4Diode under Thermal EquilibriumDiffusion small since few carriers have enough energy to penetrate barrierDrift current is small since minority carriers are few and far between: Only minority carriers generated within a diffusion length can contribute currentImportant Point: Minority drift current independent of barrier!Diffusion current strong (exponential) function of barrierp-type n-type DNAN-------------+++++++++++++0Ebiqφ,p diffJ,p driftJ,n diffJ,ndriftJ−−++−−ThermalGenerationRecombinationCarrier with energybelow barrier heightMinority Carrier Close to Junction35Reverse BiaszReverse Bias causes an increases barrier to diffusionzDiffusion current is reduced exponentiallyzDrift current does not change zNet result: Small reverse currentp-type n-type DNAN-------+++++++()bi RqVφ++−6Forward BiaszForward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier zDiffusion current increases exponentiallyzDrift current does not change zNet result: Large forward currentp-type n-type DNAN-------+++++++()bi RqVφ++−47Diode I-V CurveDiode IV relation is an exponential functionThis exponential is due to the Boltzmann distribution of carriers versus energyFor reverse bias the current saturations to the drift current due to minority carriers1dqVkTdSIIe⎛⎞=−⎜⎟⎝⎠dqVkTdsII1−()dd SIV I→−∞ =−8Minority Carriers at Junction EdgesMinority carrier concentration at boundaries of depletion region increase as barrier lowers … the function is=−==)()(ppnnxxpxxp(minority) hole conc. on n-side of barrier(majority) hole conc. on p-side of barrierkTEnergyBarriere/)(−=(Boltzmann’s Law)kTVqDBe/)(−−=φAnnNxxp )( =59“Law of the Junction”Minority carrier concentrations at the edges of thedepletion region are given by:kTVqAnnDBeNxxp/)()(−−==φkTVqDppDBeNxxn/)()(−−=−=φNote 1: NAand NDare the majority carrier concentrations onthe other side of the junction Note 2: we can reduce these equations further by substitutingVD= 0 V (thermal equilibrium)Note 3: assumption that pn<< NDand np<< NA10Minority Carrier Concentration The minority carrier concentration in the bulk region for forward bias is a decaying exponential due to recombination p side n side -Wp Wn xn -xp0AqVkTnpe00() 1ApxqVLkTnnnpxp pe e−⎛⎞=+ −⎜⎟⎝⎠0np0pn0AqVkTpneMinority CarrierDiffusion Length611Steady-State ConcentrationsAssume that none of the diffusing holes and electrons recombine Æ get straight lines … p side n side -Wp Wn xn -xp0AqVkTnpe0np0pn0AqVkTpneThis also happens if the minority carrier diffusion lengths are much larger than Wn,p,,np npLW>>12Diode Current Densities01ApqVpdiffnkTnn ppxxdnDJqD qnedx W=−⎛⎞=≈ −⎜⎟⎝⎠00()()AqVkTpppppdn n e nxdx x W−≈−−− p side n side -Wp Wn xn -xp 0AqVkTnpe0np0pn0AqVkTpne01AnqVpdiffnkTpp nxxnDdpJqD qpedx W=⎛⎞=− ≈− −⎜⎟⎝⎠21AqVpdiffnkTidn apDDJqn eNW NW⎛⎞⎛⎞=+−⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠20ipannN=713Fabrication of IC DiodesStart with p-type substrateCreate n-well to house diodep and n+ diffusion regions are the cathode and annodeN-well must be reverse biased from substrateParasitic resistance due to well resistancep-typep+n-wellp-typen+annodecathodep14Diode Small Signal ModelThe I-V relation of a diode can be linearized()1dd d dqV v qV qvkT kT kTDD S SIiIe Iee+⎛⎞+= −≈⎜⎟⎝⎠()1ddDD DqV vIiIkT+⎛⎞+≈ + +⎜⎟⎝⎠L2312! 3!xxxex=++ + +LdDddqvigvkT≈=815Diode Capacitance We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field. the capacitance in forward bias is given byBut another charge storage mechanism comes into play in forward biasMinority carriers injected into p and n regions “stay” in each region for a whileOn average additional charge is stored in diode01.4SjjdepCA CXε=≈16Charge StorageIncreasing forward bias increases minority charge density By charge neutrality, the source voltage must supply equal and opposite chargeA detailed analysis yields: p side n side -WpWn xn -xp()0ddqV vkTnpe+0np0pn()0ddqV vkTpne+12ddqICkTτ=Time to cross junction(or minority carrier lifetime)917Diode CircuitsRectifier (AC to DC conversion)Average value circuitPeak detector (AM demodulator)DC restorerVoltage doubler / quadrupler /…18MOS CapacitorMOS = Metal Oxide SiliconSandwich of conductors separated by an insulator “Metal” is more commonly a heavily doped polysilicon layer n+or p+layerNMOS Æ p-type substrate, PMOS Æ n-type substrateOxide (SiO2)Body (p-type substrate)Gate (n+poly)011.7sεε=03.9oxεε=Very Thin!~1nmoxtx01019P-I-N JunctionUnder thermal equilibrium, the n-type poly gate is at a higher potential than the p-type substrateNo current can flow because of the insulator but this potential difference is accompanied with an electric fieldFields terminate on charge! lnapiNkTqnφ=−550mVnφ+≈Body (p-type substrate)Gate (n+poly)20Fields and Charge at EquilibriumAt equilibrium there is an electric field from the gate to the body. The charges on the gate are positive. The negative charges in the body come from a depletion regionBody (p-type substrate)++++++++++++++++++−−−−−−−−−−−−−−−−−−−−−−−−−−0dX+−oxV+−BVoxE1121Good Place to Sleep: Flat BandIf we apply a bias, we can compensate for this built-in potentialIn this case the charge on the gate goes to zero and the depletion region disappearsIn solid-state physics lingo, the energy bands are “flat”under this condition()FB pnVφφ+=− −()0GGB FBQV V==Body (p-type substrate)+−0FBV <22AccumulationIf we further decrease the potential beyond the “flat-band” condition, we essentially have a parallel plate capacitorPlenty of holes and electrons are available to charge up the platesNegative bias attracts holes under gate()GoxGBFBQCV V=−Body (p-type substrate)−+GB FBVV<++++++++++++++++++−−−−−−−−−−−−−−−−−−BGQQ=1223DepletionSimilar to equilibrium, the potential in the gate is higher than the bodyBody charge is made up of the depletion region ionsPotential drop across the body and
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