Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7Lecture 7: IC Resistors and CapacitorsProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadLecture OutlineReview of Carrier DriftVelocity Saturation IC Process Flow Resistor LayoutDiffusion Review of ElectrostaticsMIM CapacitorsCapacitor LayoutDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadThermal EquilibriumRapid, random motion of holes and electrons at “thermal velocity” vth= 107cm/s with collisions every τc = 10-13s.Apply an electric field E and charge carriers accelerate … for τc secondszero E fieldvthpositive E vthaτ c (hole case)xkTvmthn212*21=cthvτλ=cm1010/cm106137 −−=×= ssλDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadDrift Velocity and MobilityEvpdrµ=EmqmqEmFavpccpcpecdr===⋅=ττττFor electrons: EmqmqEmFavpccpcpecdr−=−==⋅=ττττFor holes: Evndrµ−=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. Niknejad“default” values: Mobility vs. Doping in Silicon at 300 oK1000=nµ400=pµDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadSpeed Limit: Velocity Saturations/m10310×=cThermal VelocityThe field strength to cause velocity saturation may seem very largebut it’s only a few volts in a modern transistor!mmµµV110cmcmV10cmV10444==Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadDrift Current Density (Holes)The hole drift current density is: Jpdr = q p µp EHole case: drift velocity is in same direction as Ehole driftcurrent densityxEvdp JpdrDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadDrift Current Density (Electrons)electron driftcurrent densityxEvdn Jndr Electron case: drift velocity is in opposite direction as EThe electron drift current density is:Jndr= (-q) n vdnunits: Ccm-2s-1 = Acm-2EqnEnqJnndrnµµ=−−= )(()EqnqpJJJnpdrdrpnµµ+=+=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadResistivityBulk silicon: uniform doping concentration, away from surfaces n-type example: in equilibrium,no= NdWhen we apply an electric field, n = NdENqnEqJdnnnµµ==ResistivityConductivity)(, adneffdnnNNqNq −==µµσeffdnnnNq,11µσρ==cm−ΩDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadIC 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^3– Desire intentional doping from 10^14 – 10^18– Want 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 ICDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadIC Fabrication: OxideSi has a native oxide: SiO2SiO2(Quartz) is extremely stable and very convenient for fabricationIt’s an insulators so it can be used for house interconnectionIt can also be used for selective dopingSiO2windows are etched using photolithographyThese openings allow ion implantation into selected regionsSiO2can block ion implantation in other areasDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadIC 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 regionDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. Niknejad“Diffusion” ResistorUsing ion implantation/diffusion, the thickness and dopant concentration of resistor is set by processShape of the resistor is set by design (layout)Metal contacts are connected to ends of the resistorResistor is capacitively isolation from substrate – Reverse Bias PN Junction!P-type Si SubstrateN-type Diffusion RegionOxideDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadPoly 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 oxideThe poly will have a certain resistance (say 10 Ohms/sq)Polysilicon Film (N+ or P+ type)OxideP-type Si SubstrateDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadOhm’s LawCurrent I in terms of JnVoltage V in terms of electric field– Result for RIRV =JtWJAI ==LVE /=EWtJtWJAIσ===VLWtJtWJAIσ===tWLRσ1=tWLRρ=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadSheet Resistance (Rs)IC resistors have a specified thickness – not under the control of the circuit designerEliminate t by absorbing it into a new parameter: the sheet resistance (Rs)===WLRWLtWtLRsqρρ“Number of Squares”Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadUsing Sheet Resistance (Rs)Ion-implanted (or “diffused”) IC resistorDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadIdealizationsWhy does current density Jn“turn”?What is the thickness of the resistor?What is the effect of the contact regions?Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 7 Prof. A. NiknejadDiffusionDiffusion 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?Department of EECS University of California,
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