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Electromigration Electromigration 충북대학교 전자정보대학 김영석 2011. 9 Ref: J. Lienig 1 Metal: Parasitic Resistance/Capacitance Sheet Resistance of Metal ≈ 0.1Ω / square Typical Parasitic Capacitances of Metals Typical parasitics in both long- and short-channel CMOS processes, Baker 전자정보대학 김영석 2 Metal: Signal Delay Ex: Resistance and Delay of metal1 1mm long and 200nm wide ldrawn =1mm / 50nm = 20,000, wdrawn = 200nm / 50nm = 4 0.1Ω 1000μm R = ⋅ = 500Ω square 0.2μm C = area ⋅C plate + perimeter ⋅C fringe = (1000μm⋅0.2μm)⋅23aF / μm2 + (2000μm + 0.4μm)⋅79aF / μm =162 fF td = 0.35RC = 0.35⋅500Ω⋅162 fF = 28ps 전자정보대학 김영석 3 Metal: Current Limitations Electromigration: Too much current => Electrons Migrate J al =1mA/ μm E1Ex 1 λ = 0.05μm, wdrawn = 3, Imax = ? sol) Imax = J al ⋅W = (1mA/ μm)⋅(0.15μm) =150μA Ex 2 λ = 0.05μm, wdrawn = 3, l =1cm, Vdrop = ? sol) Imax =150μA 10,000μm V = R ⋅ I = 0.1Ω / square⋅ ⋅150μA =1V drop max 0.15μm 전자정보대학 김영석 4 Electromigration Theory 전자정보대학 김영석 5 Electromigration: Definition Electromigration is the forced movement of metal ions due to an electric field 금속에 전류가 흐를 때 일어나는 금속 이온의 이동 현상 전자정보대학 김영석 6 Electromigration: History Discovered by Gerardin in 1861 Black’s equation to predict the Metal Failure in 1969 A E MTTF(Mean Time to Failure) = exp( a ) J n kT Western Digital desktop drives in 1980 ss:Failureinayearorso : Failure in a year or so => Found Improper Design Rules in an IC controller (Hard Disk Drives require 1 – 2 Amperes of Current) 전자정보대학 김영석 7 Electromigration: Theory Ftotal = Fdirect + Fwind Fdirect : Direct Electrostatic Force from the Electric Field Fwind : Force on metal ions from momentum transfer from the conduction electrons (Electron Wind) Fdirect << Fwind due to High Current conduction => Metal Atoms (Ions) go to the Anode 전자정보대학 김영석 8 Electromigration: Theory Mass Balance Continuity Equation: describes the atom concentration evolution through some interconnect segment ∂N + ∇⋅ J = 0 ∂t N : atom concentration J = J c + JT + Jσ + J N :total atomic flux NqZDρ J = j :atomic flux induced by electric current c kT NDQ J = − ∇⋅T :atomic flux induced by temp gradient T kT 2 NDΩ J = ∇ ⋅ H :atomic flux induced by mechnical stress σ kT J N = −D∇ ⋅ N :atomic flux induced by concentration gradient Electromigration due to Electric Field, Mechanical Stress, Thermal GGadientradient 전자정보대학 김영석 9 Electromigration: Theory Effects of Electromigration in Metal Interconnects Depletion of Atoms (Voids) • Slow reduction of connectivity • ItInterconnec tFilt Failure Deposition of Atoms (Hillocks, Whisker) • Short Cuts 전자정보대학 김영석 10 Black’s Equation Mean time to Failure of a single wire due to electromigration Black’s Emirical Equation A E MTTF(Mean Time to Failure) = exp( a ) J n kT A: Cross section area dependent constant Jn: Current density Ea: Activation energy for electromigration (0.7eV for grain boundary in aluminium) K: Boltzmann constant T: Abso lu te tempera ture Jn and T are Deciding Factors 전자정보대학 김영석 11 Black’s Equation: Data J=1x105A/cm2 =1mA/um T=100 life >10year 전자정보대학 김영석 12 Temperature Dependency of Max Current Density A temp rise of 100K in Al reduces the max. Current Density by about 90% 전자정보대학 김영석 13 Atomic Transport Al, Cu Interconnects are Polycrystalline, i.e., consists of Grains of Lattice Atomic Transport occurs at metal-dielectric interface (surface), grain boundaries Grain, Grain Boundary, Triple Point Triple point(1 inbound, 2 outbounds) : Void Tr ip le po oint(2int(2 inboundinbound, 1 outbounds)outbounds) : HillockHillock 전자정보대학 김영석 14 Activation Energies Al Ea,grain=0.7eV Ea,bulk=1.2eV Ef08VEa,surface=0.8eV Dominant Diffusion: Grain/Surface Cu Ea,grain=1.2eV Ea,bulk=2.3eV Ea,surface=0.8eV Dominant Diffusion: Surface 전자정보대학 김영석 15 Electromigration-Aware Design 전자정보대학 김영석 16 Maximum Tolerable Current Densities Conventional metal wires (house wires) Al ~ 19,100A/cm2 Cu ~ 30,400A/cm2 =>R> Reac hing me lting tempera ture due to Jou le hea ting (Melting Temp of Al/Cu : 933K/1358K ) Metal Interconnet on ICs Al ~ 200,000A/cm2 Cu ~ 1,000,000A/cm2 => Reaching Failure due to Electromigration before reaching melting temperature Ex : IC Design Guide for Al Electromigration : J al =1mA/ μm Assume metal thickness = 0.5μm ' 2 2 J al =1mA/ 0.5μm = 200,000A/ cm 전자정보대학 김영석 17 Bamboo Wires Smaller Grains => Vulnerable to Electromigration What if we reduce wire width < grain size ? Resistive to Electromigration Bam boo Wires (Narrow Wires ) : Gra in Boun dar ies lie perpen dicu lar to width => No boundary diffusion => Less Electromigration 전자정보대학 김영석 18 Immortal Wires (Blech Length) High Current => Electromigration But, length < Blech Length Mechanical Stress by Hillcocks and Voids counteracts Electromigration 전자정보대학 김영석 19 Wires and Vias and Corner Bends Al Wire width < 1mA/um Current Density of Tungsten Via is higher => Use Multiple Vias Multiple Vias must be organized such that resulting current is distributed as evenly as possible Avoid 90-degree corner bends : use 135-degree bends 전자정보대학 김영석 20 EM-Aware (Analog) Physical Design Flow 전자정보대학 김영석 21 EM-Aware (Analog) Physical Design Flow Current-Driven Routing Routing with current-correct wire widths and via sizes Minimization of wire area CtCurrent-DitVifitiDensity Verification Automatic verification of actual current densities within arbitrarilyyp shaped la yout structures Current-Driven Layout Decompaction Post-routing adjustment of layout segments according to their actldittual density Homogenization of the current flow 전자정보대학 김영석 22 Summary Electromigration: Migration of atoms due to momentum transfer from conduction electrons Al : Grain Boundary Diffusion, Cu : Surface Diffusion Decisive Factors to Electromigration Current Density Temperature Soutions Cu instead of Al : Jmax(Cu) ~ 5*Jmax(Al) Bamboo Structures, Blech Length 전자정보대학 김영석 23.
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