MLT Rellablllty of semiconductor I CS plus spin-based electronics 6. 12J/3.155J Microelectronic processing Read Campbell, p. 425-428 and Ch. 20 Sec. 20.1, 20.2: Plummer, Sec. 11.5.6 IC reliability: Yield=( operating parts)/(total# produced) Particles on surface interrupt depositions, flaw devices Oxides, dielectrics fail by charging or dielectric breakdown. Metals fail by corrosion and Reliability in Spin-based electronics, spin valves and Nv.24,2003 Reliability of semiconductor I Cs Why is this an issue? Net yleld Is product: Y, x Y2 x Y3..(e.g., a 10-step process each 95%>60% yleld) and average over last 7 lots
M.I.T. Reliability of semiconductor I Cs plus spin-based electronics 6.12J / 3.155J Microelectronic processing Read Campbell, p. 425 -428 and Ch. 20. Sec. 20.1, 20.2; Plummer, Sec. 11.5.6 IC reliability: Yield = (# operating parts) / (total # produced) Failure of devices occurs over time (lifetime) by various mechanisms: w Particles on surface interrupt depositions, flaw devices w Oxides, dielectrics fail by charging or dielectric breakdown, w Metals fail by corrosion and Electro-migration: mass transport of one species along grain boundaries in metal toward one of the electrodes with subsequent failure there. (Ohring, p. 379 - 383) w Magnetic systems: interdiffusion, stress Reliability in Spin-based electronics, spin valves and magnetic random access memories (MRAM) N o v . 2 4 , 2 0 0 3 N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing Reliability of semiconductor I Cs Why is this an issue? “Learning curve”: yield vs. lot number : yield vs. lot number and average over last 7 lots. Defect density, D, has decreased with succeeding higher-density with succeeding higher-density dynamic random access memories dynamic random access memories … Net yield is product: Y1 x Y2 x Y3… (e.g., a 10-step process each 95% =>60% yield) 1
KIller defects fect areal density 6. 12J/3.155J Microelectronic processing Simplest yleld model assumes Independent, randomly-dIstrlbuted defects Polsson dlstrlbutlon) of defect Y D= defects/area p verlapping Particle control: Class(Max #/ft3)>0.5 um Nv.24,2003 Killer defects Defects are not randomly distributed spatially (e.g. stress concentrations generate dislocations, stacking fault Empirical distribution of defect sizes measure, ore Y (1-G exp(-AD) ■■■■■
Y = (1- G)e-AD(d ) Fraction of disk area in which all circuits fail N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing Killer defects Defect areal density Simplest yield model assumes independent, randomly-distributed defects, (Poisson distribution): Particle control: Class (Max #/ft3) > 0.5 mm 1 1 10 10 100 100 1000 1000 A = chip area D = defects/area Yield Y µe-AD AD AD = probability of defect overlapping chip N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing Killer defects Defect size Defects are not randomly distributed spatially (e.g. stress concentrations generate dislocations, stacking faults), or by size, d, i.e. D = D(d) D(d) = c dq d 0 q +1 ,0 < d < d 0 D(d) = c d 0 p-1 dp , d 0 < d < dmax Meander-line process control module 1- G Empirical distribution of defect sizes: Hard to measure, Therefore Y (1-G) exp(-AD) G is fractional area where all fail 2
Reliability definitions 6. 12J/3.155J Microelectronic processing e Cumulative fallure dlstrlbutlon function, F(t R(n F(D-fraction of fallures up to tlme, t. Survlval or rellablllty dlstrlbutlon function, R(t: R(t=1·F( Fallure probablity density function, f(t) f(n (This is key to predicting failure rates Mean time to fallure, MITF MTTF=ft·f(r)d Median time to fallure, tso: time after whIch half of devices have falled Nv.24,2003 Reliability definitions Fallure probabllity density/number remaInIng: ()=20)-k+a dF() Fallure rate in steady state: 4(0- const.-A,(fractional failure frequency) Steady-state survival R(t)∝e or reliability drops off exponentially with time steady state f( df dR
Reliability definitions 6.12J / 3.155J Microelectronic processing Cumulative failure distribution function, F (t): F (t) R (t) 1 F (t) = fraction of failures up to time, t. Survival or reliability distribution function, R (t): R (t)= 1 - F (t) 0 0 t 1 Failure probability density function, f (t): f (t) = dF/dt 0 (This is key to predicting failure rates) 0 t f (t) • Mean time to failure, MTTF: MTTF = Út ⋅ f(t)dt 0 Median time to failure, t50: time after which half of devices have failed. N o v . 2 4 , 2 0 0 3 Reliability definitions 6.12J / 3.155J Microelectronic processing 1 Failure probability density/number remaining: l(t) = f(t)/R(t) 0 0 t l(t) Failure rate during time dt, l(t): l(t) = R(t) - R(t +dt) dtR(t) = - 1 R(t) dR(t) dt 1 dF(t) = R(t) dt Failure rate l(t) = - 1 dR(t) = const. = l0 (fractional failure frequency) in steady state: R(t) dt Steady-state survival Hence: or reliability drops off R(t) µ e - l0 t exponentially with time steady state: • f (t) = dF = - dR µ l0e-l0 t MTTF = Ú t ⋅ f (t)dt = 1 ss dt dt ss 0 l0 N o v . 2 4 , 2 0 0 3 3
Different failure processes 6. 12J/3.155J Microelectronic processing Fallure rate 0 Steady mortality" state Different failure processes have different thermally activated rates r=e Nv.24,2003 More realistic example: log-normal distribution 6. 12J/3.155J Microelectronic processing ge standard devlation tIme for 50% of devices to fall f() OTv/T O=In(tso/t16) and MTTF =exp(In(tsn +0/2) Log-normal dlstrlbutlon: If In of fallure time Is plotted Vs. fractlon of chlps falling within a range of tlmes glves a normal, L.e. Gausslan dlstrlbutlon, then the dlstrlbutlon Is log-normal Lognormal dIstrbution is hard to handle analytically but can be represented more simply on a log-normal scale
Different failure processes mortality” state Wearout 6.12J / 3.155J Microelectronic processing l(t) = l0 l (t) t 0 “Infant Steady Failure rate: Ea Different failure processes have - k B T different thermally activated rates: r = r 0e N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing More realistic example: log-normal distribution s = standard deviation t = time for 50% of devices to fail 50 Ï ln(t) ¸ 1 Ô [ ]2 Ô f (t) = expÌ- ˝ st 2p Ô 2s2 Ô Ó ˛ s = ln(t50 / t 16 ) and MTTF = exp{ln(t50 + s2 /2) Log-normal distribution: if ln of failure time is plotted vs. fraction of chips failing within a range of times gives a normal, i.e. Gaussian distribution, then the distribution is log-normal. Lognormal distribution is hard to handle analytically but can be represented more simply on a log-normal scale: N o v . 2 4 , 2 0 0 3 4
g-normal distribution 6. 12J/3.155J Microelectronic processing sigma =05 Bognor mal PDP(sigm= 2) Bognor mal PDF(sigma a 5) http://www.itl.nistgov/div898/handbook/eda/section3/eda3669.htm N口w24,2003 Log-normal dlstrlbutlon can represent any of the 3 regimes by varying o 6. 12J/3.155J Microelectronic processing The lognormal distributio could Infant mortallty Fallure rate: Wearout
s 1 could represent infant mortality l (t) t 0 Infant mortality Steady state Wearout Failure rate: 5
Log-normal distribution 6. 12J/3.155J Microelectronic processing o=In(tso/t16) n time Cumulative failure percentage on a lognormal scale If data are near on lognormal plot, then o can be found Nv.24,2003
Log-normal distribution 6.12J / 3.155J Microelectronic processing If data are linear on lognormal plot, then s can be found s = ln(t50 / t 16 ) N o v . 2 4 , 2 0 0 3 6
Mean time to fallure 6. 12J/3.155J Microelectronic processing The mean time to fallure (MTF) (related to inve MTF∝Je+hnkr Most actiated mech of faiure have a form like Expressed In log form as: 10 Plotted vs For Increased operating current, ifetime curve Is shifted down, quicker fallure. 1±mA logo) Or, I(MTTF.), mean fallure rate, could be plotted vs, 1/T (Armhenlus plot Nv.24,2003 Mitigating thermally activated failure Thermally activated failure rates: Caution on accelerated aging: ● Operate at lower temp lower current density temperatur e Use"burn-out"to elim. early fails wrong activation energy
Mean time to failure 6.12J / 3.155J Microelectronic processing Expressed in log form as: Plotted vs Log(J), right in which case the slope gives the power, -n. For increased operating current, MTTF drops off as the -nth power of J. For higher operating temperatures, lifetime curve is shifted down, quicker failure. Log(MTTF) log(J) ln = ln( A) - nln(J) + En kBT The mean time to failure (MTTF) (related to inverse of rate): n 2 to 3. (Most activated mechanisms of failure have a form like this) MTTF µ J -n e + Ea / kB T O - r, ln(MTTF 1), mean failure rate, could be plotted vs. 1/T (Arrhenius plot)… N o v . 2 4 , 2 0 0 3 Mitigating thermally activated failure 6.12J / 3.155J Microelectronic processing Thermally activated failure rates: Caution on accelerated aging: Ea - k B T Operating temperature Accel. aging r = r 0e test Ln(r) RT Operate at lower temp., lower current density Use “burn-out” to elim. early fails 1/kBT …you may get wrong activation energy. Example: electromigration. . . N o v . 2 4 , 2 0 0 3 7
Electromigration: electron wnd moves atoms ElectromIgration: mode of fallure In hlgh-current-density heterostructures. Most literature on electromigration deals with metallic conductors in semiconductor devices not only charge transport J-ngv harged particles, es or h When charge carlers colde with atoms(electron wind) hey Impart a small momentum to atom sweeping them In the dIrection of the carrier drift. Expression for the electromigration flux of specles A, JA- CAVon ( v)p equlres the force on an lon a due to the electric current ZE=qZJP Here g is the electronic charge, ZA' is the effective ion valence and E is the electric field (force per unit charge) producing the electric current density, J=E/p o=Flareas2x10-2Ibs/micron 8
Electromigration: electron wind moves atoms 6.12J / 3.155J Microelectronic processing Electromigration: mode of failure in high-current-density heterostructures. (Most literature on electromigration deals with metallic conductors in semiconductor devices) Large current density, J => not only charge transport J = nqv but also mass transport of charged particles, e’s or h’s. When charge carriers collide with atoms (“electron wind”), they impart a small momentum to atoms, sweeping them in the direction of the carrier drift. Expression for the electromigration flux of species A, jA = cAvdrift, (Z*q . X nq v ) r requires the force on an ion A due to the electric current: Ion - carrier * * F interaction = qZAE = qZAJr Here q is the electronic charge, ZA* is the effective ion valence and E is the electric field (force per unit charge) producing the electric current density, J = E/r s = F / area ª 2 ¥10-2 lbs/ micron2 N o v . 2 4 , 2 0 0 3 8
Electromigration: graln-boundary dIffusion 6.12J/3. Most electromigration takes place along graIn boundarles D,=Dexp/-ea/(kgT)/ Da is the graln boundary dimesion coefficient of A (DA typically 0.5-0.8 ev vs bulk about 1. 4 ev) Flux of specles A, Jo bs proportional to the product volume concentration of A) x(velocity of A resulting from F-gZAJp): DF DzP CAVA=CA Here use Nernst-Einstein equation for drift velocity of a particle at temperature T under influence of force F: V= DAF/RT lectromlgratlon Is problematic at high current density, high resistivity(many electron-atom collisions for light metals (D is Inverse function of mass of A) Nv.24,2003 Electromigration damage: due to flux divergence or temperature gradients 6.12J/3.155J Microelectronic processing FIck's second law of diffusion states that change In concentration of specles A occurs as a result of a divergence In Jv Le. a varable concentration gradient: Add temperature-dependent term to time rate of change of concentration as follows: de a. a. dT othermal mas such as at grain boundary junctions couple with temperature NDw.242003
Electromigration: grain-boundary diffusion 6.12J / 3.155J Microelectronic processing Most electromigration takes place along grain boundaries. DA = DA o exp[-Ea /(kBT)] DA is the grain boundary diffusion coefficient of A . (DA typically 0.5 - 0.8 eV vs. bulk about 1.4 eV) Flux of species A, JA, is proportional to the product * (volume concentration of A) x (velocity of A resulting from F = qZA Jr ): J DAF DAqZA * Jr A = cAvA = cA = cA RT RT Here use Nernst-Einstein equation for drift velocity of a particle at temperature T under influence of force F: v = DAF/RT. Electromigration is problematic • at high current density, • high resistivity (many electron-atom collisions), • for large grain-boundary diffusion, • at high T (which is in exponent of DA), • for light metals (DA 0 is inverse function of mass of A) N o v . 2 4 , 2 0 0 3 N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing Add temperature-dependent term to time rate of change of concentration as follows: dcA dt = - ∂JA ∂x - ∂JA ∂T dT dx temperature gradients associated with local hot or cold spots couple with temperature dependence of JA. Isothermal mass transport due to flux divergence such as at grain boundary junctions. jA Fick's second law of diffusion states that change in concentration of species A occurs as a result of a divergence in JA, i.e. a variable concentration gradient: ∂cA ∂t = -∂JA ∂x = DA ∂ 2 cA ∂x 2 Electromigration damage: due to flux divergence or temperature gradients 9
Electromigration Vs linewidth/grain size 〔 hampson- Frost model 6. 12J/3.155J Microelectronic processing Yleld w/dso 3.0 1.-14乙p+a)wa13 Equal ,σ=-ax+b 0.3 4p Nv.24,2003 Electromigration summary electron wInd mass transp Voids, depletion Accumulation. hillocks GraIn boundarles that run parallel to current direction are most problematic. A factor cos (e is often attached to the atomic flux expresson to reflect this fact a Is the angle between the current and the graIn boundary. NDw.24,2003
N o v . 2 4 , 2 0 0 3 6.12J / 3.155J Microelectronic processing Electromigration vs. linewidth/grain size (Thompson-Frost model) w/d50 Yield JA = DAcA kBT (qZA * Jr + W ds dx ) ds dx = - qZA * Jr W s = -ax + b s max = ± Z* qJr W Ê Ë Á ˆ ¯ Lp 2 Equilibrium: , JLp < scrit 2W Z* qr w w/d50 3.0 d50 w/d50 0.3 w/d50 1.3 Lp Voids hillocks Mass flow Electromigration summary 6.12J / 3.155J Microelectronic processing electron wind, mass transport Voids, depletion Accumulation, hillocks 4 microns Most electromigration takes place along grain boundaries. Grain boundaries that run parallel to current direction are most problematic. A factor cos (q) is often attached to the atomic flux expression to reflect this fact; a is the angle between the current and the grain boundary. N o v . 2 4 , 2 0 0 3 10