1EE105 - Fall 2005Microelectronic Devices and CircuitsLecture 3Integrated Passives2AnnouncementsHomework 1, due today, September 6, at 5pm (drop box in Cory)Homework 2, due next Tuesday, September 13 at 5pmAll Lab sessions are still on (we will cut one for Lab 2)3Lecture MaterialLast lectureCarrier concentration and dopingCarrier velocity and mobilityIC resistorsDrift currents This lectureDiffusion currentsReview of electrostaticsIC capacitors4oxidationopticalmaskprocessstepphotoresist coatingphotoresistremoval (ashing)spin, rinse, dryacid etchphotoresiststepper exposuredevelopmentTypical operations in a single photolithographic cycle (from [Fullman]).IC Fabrication: Photo-Lithographic Process5CMOS Process at a GlanceDefine active areasEtch and fill trenchesImplant well regionsDeposit and patternpolysilicon layerImplant source and drainregions and substrate contactsCreate contact and via windowsDeposit and pattern metal layers6IC Fabrication: Si SubstratePure Si crystal is starting material (wafer)The Si wafer is extremely pure (~1 part in a billion impurities) Why so pure? Si density is about 5 10^22 atoms/cm^3Desire intentional doping from 10^14 – 10^18Want unintentional dopants to be about 1-2 orders of magnitude less dense ~ 10^12 Si wafers are polished to about 700 µm thick (mirror finish)The Si forms the substrate for the IC27IC Fabrication: OxideSi has a native oxide: SiO2SiO2(Quartz) is extremely stable and very convenient for fabricationIt’s an insulatorSiO2windows are etched using photolithographyThese openings allow ion implantation into selected regionsSiO2can block ion implantation in other areas8IC Fabrication: Patterning of SiO2Si-substrateSi-substrateSi-substrate(a) Silicon base material(b) After oxidation and depositionof negative photoresist(c) Stepper exposurePhotoresistSiO2UV-lightPatternedoptical maskExposed resistSiO2Si-substrateSi-substrateSi-substrateSiO2SiO2(d) After development and etching of resist,chemical or plasma etch of SiO2(e) After etching(f) Final result after removal of resistHardened resistHardened resistChemical or plasmaetch9IC Fabrication: Ion ImplantationSi substrate (p-type)Grow oxide (thermally)Add photoresistExpose (visible or UV source)Etch (chemical such as HF)Ion implantation (inject dopants)Diffuse (increase temperature and allow dopants to diffuse)P-type Si SubstrateoxideN-type diffusion region10“Diffusion” ResistorUsing ion implantation/diffusion, the thickness and dopant concentration of resistor is set by processE.g. 100Ω/□ (unsilicided), 10Ω/□ (silicided)Shape of the resistor is set by design (layout)Metal contacts are connected to ends of the resistorResistor is capacitively isolation from substrate Reverse-biased PN Junction!P-type Si SubstrateN-type Diffusion RegionOxide11Poly Film ResistorTo lower the capacitive parasitics, we should build the resistor further away from substrateWe can deposit a thin film of “poly” Si (heavily doped) material on top of the oxideE.g. 10-100Ω/□ (unsilicided), 1Ω/□ (silicided)Bad absolute tollerance, very good relative tolerancePolysilicon Film (N+ or P+ type)OxideP-type Si Substrate12Using Sheet Resistance (Rs)Ion-implanted (or “diffused”) IC resistor313DiffusionDiffusion occurs when there exists a concentration gradientIn the figure below, imagine that we fill the left chamber with a gas at temperate TIf we suddenly remove the divider, what happens?The gas will fill the entire volume of the new chamber. How does this occur?14Diffusion (cont)The net motion of gas molecules to the right chamber was due to the concentration gradientIf each particle moves on average left or right then eventually half will be in the right chamberIf the molecules were charged (or electrons), then there would be a net current flowThe diffusion current flows from high concentration to low concentration:15Diffusion EquationsAssume that the mean free path is λFind flux of carriers crossing x=0 plane)(λn)0(n)(λ−n0λ−λthvn )(21λthvn )(21λ−())()(21λλnnvFth−−=⎟⎟⎠⎞⎜⎜⎝⎛⎥⎦⎤⎢⎣⎡+−⎥⎦⎤⎢⎣⎡−=dxdnndxdnnvFthλλ)0()0(21dxdnvFthλ−=dxdnqvqFJthλ=−=16Einstein RelationThe thermal velocity is given by kTkTvmthn212*21=cthvτλ=Mean Free TimedxdnqkTqdxdnqvJnth⎟⎟⎠⎞⎜⎜⎝⎛==µλnnqkTDµ⎟⎟⎠⎞⎜⎜⎝⎛=**2ncnccththmqqkTmkTvvτττλ===17Total Current and Boundary ConditionsWhen both drift and diffusion are present, the total current is given by the sum:In resistors, the carrier concentration is approximately uniform and the second term is nearly zeroFor currents flowing uniformly through an interface (no charge accumulation), the field is discontinousdxdnqDnEqJJJnndiffdrift+=+=µ21JJ =2211EEσσ=1221σσ=EE)(11σJ)(22σJ18Electrostatics Review (1)Electric field go from positive charge to negative charge (by convention)In words, if the electric field changes magnitude, there has to be charge involved!Result: In a charge-free region, the electric field must be constant!+++++++++++++++++++++−−−−−−−−−−−−−−−ερ=⋅∇ E419Electrostatics Review (2)Gauss’ Law equivalently says that if there is a netelectric field leaving a region, there has to be positive charge in that region:+++++++++++++++++++++−−−−−−−−−−−−−−−Electric Fields are Leaving This Box!∫=⋅εQdSE∫∫==⋅∇VVQdVdVEεερ/εQdSEdVESV∫∫=⋅=⋅∇Recall:20Electrostatics in 1DEverything simplifies in 1-DConsider a uniform charge distributionερ==⋅∇dxdEEdxdEερ=')'()()(00dxxxExExx∫+=ερ)(xρxxdxxxExερερ00')'()( ==∫Zero fieldboundarycondition1x0ρ1x)(xE10xερ21Electrostatic PotentialThe electric field (force) is related to the potential (energy):Negative sign says that field lines go from high potential points to lower potential points (negative slope)Note: An electron should “float” to a high potential point:dxdEφ−=dxdeqEFeφ−==1φ2φdxdeFeφ−=e22More PotentialIntegrating this basic relation, we have that the potential is the integral of the field:In 1D, this is a simple integral:Going the other way, we have Poisson’s equation in 1D:∫⋅−=−CldExxr)()(0φφ)(xφ)(0xφEldr∫−=−xxdxxExx0')'()()(0φφερφ)()(22xdxxd−=23Boundary ConditionsPotential must be a continuous function. If not, the fields (forces) would be infinite Electric fields need not be continuous. We have already seen that the electric fields diverge on charges. In fact, across
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