Reliability of semiconductor I Cs. Reliability of semiconductor I Cs plus

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1 M.I.T. Reliability of semiconductor I Cs plus spin-based electronics Read Campbell, p and Ch. 20. Sec. 20.1, 20.2; Plummer, Sec 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 ) w Magnetic systems: interdiffusion, stress Reliability in Spin-based electronics, spin valves and magnetic random access memories (MRAM) Reliability of semiconductor I Cs Why is this an issue? Net yield is product: Y 1 x Y 2 x Y 3 (e.g., a 10-step process each 95% =>60% yield) Learning curve : : yield vs. lot number and average over last 7 lots. Defect density, D,, has decreased with succeeding higher-density dynamic random access memories 1

2 Killer defects Defect areal density Simplest yield model assumes independent, randomly-distributed defects, (Poisson distribution): Yield Y µe -AD A = chip area D = defects/area AD = probability of defect overlapping chip AD Y = (1 - G)e -AD(d ) Fraction of disk area in which all circuits fail Particle control: Class (Max #/ft 3 ) > 0.5 mm 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) Empirical distribution of defect sizes: D(d) = c d q d, 0 < d < d q D(d) = c d p-1 0 d, d < d < d p 0 max Meander-line process control module 1- G Hard to measure, Therefore Y (1-G) exp(-ad) G is fractional area where all fail 2

3 Reliability definitions Cumulative failure distribution function, F (t): F (t) = fraction of failures up to time, t. 1 R (t) F (t) Survival or reliability distribution function, R (t): R (t)= 1 - F (t) 0 0 t Failure probability density function, f (t): 1 f (t) f (t) = df/dt 0 (This is key to predicting failure rates) 0 t Mean time to failure, MTTF: MTTF = Ú t f (t)dt 0 Median time to failure, t 50 : time after which half of devices have failed. Reliability definitions Failure probability density/number remaining: l(t) = f(t)/r(t) 1 l(t) 0 0 t Failure rate during time dt, l(t): R(t) - R(t +dt) l(t) = =- 1 dr(t) 1 df(t) = dtr(t) R(t) dt R(t) dt Failure rate l(t) =- 1 dr(t) = const. = l 0 (fractional failure frequency) in steady state: R(t) dt Steady-state survival Hence: or reliability drops off R(t) µ e - l 0 t exponentially with time steady state: f (t) = df =- dr µ l 0 e -l 0 t MTTF = Ú t f (t)dt = 1 ss ss dt dt 0 l 0 3

4 Different failure processes Failure rate: l (t) l(t) = l 0 0 Infant mortality Steady state t Wearout Different failure processes have different thermally activated rates: r = r 0 e E a - k B T More realistic example: log-normal distribution s = standard deviation = time for 50% of devices to fail t Ï ln(t) 1 Ô [ ] 2 Ô f (t) = expì- st 2p ÔÓ 2s 2 Ô s = ln(t 50 / t 16 ) and MTTF = exp{ln(t 50 + s 2 /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: 4

5 log-normal distribution 1 Ï f (t) = st 2p exp Ô - [ ln(t) Ì ]2 Ô ÓÔ 2s 2 Ô Log-normal distribution can represent any of the 3 regimes by varying s s > 1 could represent infant mortality Failure rate: l (t) Wearout s < 1 could represent wearout 0 Infant mortality Steady state t 5

6 Log-normal distribution s = ln(t 50 / t 16 ) If data are linear on lognormal plot, then s can be found 6

7 Mean time to failure The mean time to failure (MTTF) (related to inverse of rate): MTTF µ J -n e + E a / k B T n 2to3. (Most activated mechanisms of failure have a form like this) Expressed in log form as: ln < t fail >=ln( A) - nln(j) + E n k B T Plotted vs Log(J), right in which case the slope gives the power, -n. Log(MTTF) For increased operating current, MTTF drops off as the -n th power of J. For higher operating temperatures, lifetime curve is shifted down, quicker failure. log(j) Or, ln(mttf - 1 ), mean failure rate, could be plotted vs. 1/T (Arrhenius plot) Mitigating thermally activated failure Thermally activated failure rates: Caution on accelerated aging: r = r 0 e E a - k B T Operate at lower temp., Ln(r) Accel. aging test RT lower current density Operating temperature Use burn-out to elim. early fails 1/k B T you may get wrong activation energy. Example: electromigration... 7

8 Electromigration: electron wind moves atoms 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 but also mass transport of charged particles, e s or h s. J = nqv 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, j A = c A v drift, requires the force on an ion A due to the electric current: (Z*q. X nq v ) r Ion - carrier * * interaction F = qz A E = qz A Jr Here q is the electronic charge, Z A * 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 lbs/ micron 2 8

9 Electromigration: grain-boundary diffusion Most electromigration takes place along grain boundaries. D A = D A o exp[-e a /(k B T)] D A is the grain boundary diffusion coefficient of A. (D A typically ev vs. bulk about 1.4 ev) Flux of species A, J A, is proportional to the product * (volume concentration of A) x (velocity of A resulting from F = qz A Jr ): D J A F D A qz * A Jr A = c A v A = c A = c A RT RT Here use Nernst-Einstein equation for drift velocity of a particle at temperature T under influence of force F: v = D A F/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 D A ), for light metals (D A0 is inverse function of mass of A) Electromigration damage: due to flux divergence or temperature gradients Fick's second law of diffusion states that change in concentration of species A occurs as a result of a divergence in J A, i.e. a variable concentration gradient: Add temperature-dependent term to time rate of change of concentration as follows: dc A dt c A t =- J A x = D 2 c A A x 2 =- J A x - J A dt T dx j A Isothermal mass transport due to flux divergence such as at grain boundary junctions. temperature gradients associated with local hot or cold spots couple with temperature dependence of J A. 9

10 Electromigration vs. linewidth/grain size (Thompson-Frost model) Yield w/d d 50 w w/d 50 J A = D c A A k B T (qz * AJr +W ds dx ) Equilibrium: w/d Voids Mass flow hillocks * ds dx =-qz A Jr, s =-ax + b W Ê s max =± Á Z* qjrˆ L p Ë W 2 w/d L p JL p < s crit 2W Z * qr Electromigration summary electron wind, mass transport Accumulation, hillocks Voids, depletion 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. 10

11 Grain growth Grain growth well described also by log-normal distribution 1 ÏÔ [ ln(d / d 50 ) f (d) = expì- sd 2p ÔÓ 2s 2 ] 2 Ô Ô d 50 = median grain diameter Spin-based electronic devices: background Semiconductor review E P Immobile e s N type E F type Mobile holes High mass holes Mobile e s Immobile holes E Low mass electrons E F Semiconductors have two distinct types of carriers (e s and h s) characterized by w w w different mobilities, concentrations, conductivities different Fermi energies for N and P carriers scattered into dopant sites become trapped 11

12 Spin-based devices Two carrier types: e s e s with spin parallel or antiparallel to local moments Mobile carrier e - e - e - Scatters from ion Spin-dependent resistivity r < r < r e - e - Spin memory is lost over x, t M (x) x M (x) x Spintronics = spin (magnetism)-based electronic devices Spin-up and spin-down electrons form the basis for a number of spin-based devices including spin valve (non-magnetic metal interposed) and the spin-tunnel junction (oxide layer interposed). Separator Device non-mag metal => low-impedance spin valve or spin switch insulator => high-impedance spin-tunnel junction (Messervey and Tedrow,, Phys. Rpts. 238,, 174 ( 96);( Moodera et al. Phys. Rev. Lett. 80,, 2941 ( 98))( Resistance H Unlike semiconductor devices, performance of spin-based devices improves as thickness decreases because screening lengths and spin diffusion lengths in metals << than in semiconductors. 12

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14 Magnetic Random Access Memory (MRAM) (based on spin valve or spin-tunnel junction) No moving parts, non-volatile bits but presently limited by lower density than hard disk Array of spin valves (or psuedo-svs, PSVs) connected by x and y electrode lines Magnetic Random-Access Memory (MRAM) Bit written by strong coincident current pulses (magnetic field) in specific x and y lines Bit read by weak current pulses (magnetic field) in specific x and y lines 14

15 High Density Magnetic Random Access Memories Magnetic nanostructures can be used in electronic components such as ultrasensitive magnetic field sensors, optical computing components, and a new class of spintronic devices. One example is an MRAM, which will replace the semiconductor memory chips in computers with faster, lower power, nonvolatile storage using magnetoresistive (MR) elements. Word line (W) Insulator (SiO2) MR element (Co/Cu/NiFe) Sense line (W) Spintronics: processing, reliability issues w Very large current densities ( (J > 10 7 A/cm 2 ) => high operating temperatures ( (T > C), electrothermal failure: MTTF µ J -n e + E a / k B T w Spin-valve magnetic layers < 8 nm thick w Oxide layers in spin-tunnel jcts < 3 nm thick w Track-width decreasing toward 100 nm w Chemical interaction of dissimilar metals 15