Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 32: November 24, 2010 Uncorrelated Noise Sources Ionizing, Thermal, Shot

Today Ionizing Particles Thermal Noise Shot Noise Penn ESE370 Fall DeHon 2

Ionizing Particles Alpha Particles (He nucleus=He 2+ ) Impact with mega-electron-volts of energy (3—10MeV) Penn ESE370 Fall DeHon 3

Ionizing Particles Alpha Particles (He nucleus=He 2+ ) Can penetrate microns into Si Creating 2×10 6 electron-hole pairs Penn ESE370 Fall DeHon 4

Ionizing Particles Alpha Particles (He nucleus=He 2+ ) Can be generated by decay in packaging materials –Lead common one including some fraction of radioactive isotopes 210 Pb Penn ESE370 Fall DeHon 5 Src:

Comparisons How many electrons in: –Capacitor: 1fF charges to 1V –e = 1.6× Coulombs Recall C 0 = 0.01fF, – typical load around 10-20C 0 How large a capacitor to withstand loss of 2×10 6 electrons? Penn ESE370 Fall DeHon 6

Disrupt Alpha particle will disrupt DRAM Cell Can disrupt undriven nodes –Latch –Dynamic node –Memory bit Penn ESE370 Fall DeHon 7

Ionizing Particles There are other particles with different energies –Neutrons from cosmic rays 10x energy of alpha particles Penn ESE370 Fall DeHon 8

Particle Flux Differs with location –Altitude Denver vs. Philadelphia Ground vs. aircraft at 30,000 feet Space (outside atmosphere) –Near poles Changes upset rate seen by chips Penn ESE370 Fall DeHon 9

LLNSD October 2005 [Quinn and Graham/FCCM2005]

LLNSD October 2005 Soft Error Failure Rate Projections [Heather Quinn 2005] 1 FIT = 1 Failure per 10 9 hours of operation

Scaling Charge holding memory decreases –More susceptible Cross-sectional area of bit decreases –Each bit less likely to be hit –Hit may be large enough to take out multiple bits at a time More bits on the chip –More targets!  more likely something gets hit Penn ESE370 Fall DeHon 12

Driven Node What happens if the alpha particle impacts a driven node? Will recover –Creates a glitch –May slow down node –Only a problem if latched into register Penn ESE370 Fall DeHon 13

Driven Failure Driven input to latch -- value failure? –When is it a problem? Occurs at end of cycle –Right at last transition time for node Occurs earlier –Not expecting value to have settled Occurs later –May not propagate to latch Penn ESE370 Fall DeHon 14

Logic Failure Rate Probability will see increases with increasing frequency T upset ~ picoseconds? Penn ESE370 Fall DeHon 15

Frequency Dependence Penn ESE370 Fall DeHon 16 Gill (Intel), IEEE International Reliability Physics Symposium 2009

Penn ESE370 Fall DeHon 17 Scaling and Error Rates Source: Carter/Intel Increasing Error Rates Technology (nm) SEU/bit Norm to 130nm cache arrays logic 2X bit/latch count increase per generation

Thermal Noise Penn ESE370 Fall DeHon 18

Thermal Background Except at absolute 0 (Temperature) –Particles are moving around randomly Thermal bath means free energy around Electron can be borrow the thermal energy to hop over barrier –Out of an energy well, bond cite –…Out of a capacitor Penn ESE370 Fall DeHon 19

Doping with P End up with extra electrons –Donor electrons Not tightly bound to atom –Low energy to displace –Easy for these electrons to move Penn ESE370 Fall DeHon 20 Day 8

Doped Band Gaps Addition of donor electrons makes more metallic –Easier to conduct Penn ESE370 Fall DeHon 21 EvEv EcEc Semiconductor 1.1ev EDED 0.045ev Day 8

Electron Conduction Penn ESE370 Fall DeHon 22 Day 8

Thermal Background Except at absolute 0 (Temperature) –Particles are moving around randomly Thermal bath means free energy around Electron can be borrow the thermal energy to hop over barrier Are doing it all the time to give us our semiconductors Penn ESE370 Fall DeHon 23

Rising above the Thermal Noise Must apply more energy than background noise to –Hold electron in place –Move an electron from place to place Charge/discharge a node with some reliability Penn ESE370 Fall DeHon 24

Minimum Energy Single bit gate output –Set from previous value to 0 or 1 –Reduce state space by factor of 2 –Entropy:  S= k×ln(before/after)=k×ln2 –Energy=T  S=kT×ln(2) Setting a bit costs at least kT×ln(2) Penn ESE370 Fall DeHon 25

Probability of Noise Error This minimum energy around kT is just to have 50% probability of setting bit correctly Probability exponential in energy –Not exactly this…but basic dependence Penn ESE370 Fall DeHon 26

Implication To keep error rate sufficiently low –Need energy of operation (of storage) to be some multiple of kT Penn ESE370 Fall DeHon 27

Where are we today? How does kT compare to switching 10C 0 at 1V? –k=1.4× J/K –T=300K (Room Temperature) Penn ESE370 Fall DeHon 28

Where are we today? How does kT compare to switching 10C 0 at 1V? –k=1.4× J/K –T=300K (Room Temperature) kT=4.2× J E switch =CV 2 = 0.1fJ= J E switch ~=2×10 4 kT Penn ESE370 Fall DeHon 29

Scaling E switch ~=2×10 4 kT 45nm to 4.5nm  impact on E switch ? –reduce capacitance by 10x –reduce voltage by 2x –E switch ~=500 kT Penn ESE370 Fall DeHon 30

Relate kT to electrons If we arrange the capacitor to hold a single electron –What storage/switching just equals 1 kT? Penn ESE370 Fall DeHon 31

Chip Reliability Chip has many transistors …And many switching events Each of which may fail Penn ESE370 Fall DeHon 32

Chip Upset Rates Penn ESE370 Fall DeHon 33 Kish, Physics Letters A —149 (2002)

Shot Noise Penn ESE370 Fall DeHon 34

Shot Noise Actual electron transport is probabilistic Current is a statement about average rate of electron flow For large numbers of electrons –Law of large numbers convergence to mean –  ~= Sqrt(N) –Large N  sqrt(N)/N small Small percentage variation Penn ESE370 Fall DeHon 35

Shot Noise For small number of electrons (N) –  ~= Sqrt(N) –sqrt(N)/N not so small –Higher variation –Noise in switching time Penn ESE370 Fall DeHon 36

Electron Counts How many electrons (N) –in 0.1fF, 1V switching event? –in 0.01fF, 0.5V switching event?  ? How many  out to only get 50% of electrons moving? Penn ESE370 Fall DeHon 37

Will we see? Large chips, fast clock rates  many events….samples far out on curve Penn ESE534 Spring DeHon 38 From:

Gaussian Distrubution Penn ESE370 Fall DeHon 39 Number Sigma1 in How many K 51.7 M 6510M

Admin Class Monday Lab on Wednesday or Friday (TBD) –Class other day Penn ESE370 Fall DeHon 40

Idea Many sources cause upsets –Ionizing particles, thermal, shot noise Tend to depend on charge –Of node, of switching even Scaling decreases charge –Lower voltage, lower capacitance Also increases susceptible nodes –Also increases frequency susceptibility Penn ESE370 Fall DeHon 41