1 Systems Technology Lab, Intel Research Berkeley 2 Mechanical Engineering, Stanford University Dissipation and Entropy Flow in Logic Fundamental Limits and Engineering Challenges Sanjiv Sinha 1 and Ken Goodson 2

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Minimal Energy in Logic SNL theory ~ kT ln 2 ~ 17 meV Practical ~ 40 kT ~ 1 eV Cramer et al., Science 288, 640(2000) ~ O (10 kT) per nucleotide 1 Landauer, IBM J Res Dev, 5, 183 (1961) Bennett, Int. J. Theor. Phys., 21, 905 (1982) Intel Dothan 10 6 kT ~ 10 keV Intel Electronic irreversible computing produces Joule heat

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Length Scales in Internal Energy Flow Characteristic Length 1mm 1  m0.1  m 10 nm1 nm5 A° FourierDiffusionSemi-Classical Atomistic StronglyQuantum Continuum Problem Level 1 cm Devices Circuits Die/Chip System Heat Flow Path T_die ?

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Time Scales in Internal Energy Flow time Power Time (sec) Junction Temperature Rise (C) 90 Thermal Mass die package system heat sink T_die (  ~ 1-10ms) T_HS (  ~ 100s) T_pkg (  ~ 1s) T_sys (  ~ 1000s) 0.1 ps ps 100 s Hot Electrons Hot Phonons Thermal Phonons Heat Sink =15.4 THz Hotspot Sinha et al, J. Heat Transfer, 128 (2006)

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Electron-Phonon Interactions Buried Oxide Source Drain gate 18 nm 4 nm 65 W/  m 3 T(K) SD BOX Temperature field using phonon Boltzmann Transport model LO LA1 TA1 3-phonon decay Sinha et al., J. Appl. Phys., 97, (2005) Intervalley Electron Scattering

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Minimal Energy Dissipated Per Switch Landauer’s 1-particle-in-a-bistable-well model E = kT (ln2) Bate’s 2 level multi-particle QM logic gate model E = kT c ln2 For comparison, = P DYNAMIC x t DELAY ~ 1 fJ today 1 0 Landauer, IBM J Res Dev, 5, 183 (1961) Bate, VLSI Electronics, 5 (1982)

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice The Heat Transfer Limited Power Density T switch T contact T die T atm Phonon conduction limited Technology limited Interface physics limited Switch Die and Package System Sinha et al, Under Review, IEEE Trans. Electron Devices

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Conduction Across The -n Interface  th T switch Nano to Micro bridge Switch Microscale contact Heat flow Micro to Nano Address Block (MNAB)

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Estimate Including Macroscopic Heat Flow Always will need to reject to the ambient Convection/radiation limits will remain dominant

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice Comments Not quite a fundamental limit nor a technological figure; Somewhere in the middle Essential challenge is how do we enhance rejection to the sink Assumption of local equilibrium in the switch may not hold Comparisons SNL based theory - > ~ MW/cm 2 Best case demonstrated -> ~ 300 W/cm 2

International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice In Summary Logic devices are “inefficient” by several orders of magnitude above the SNL limit Irreversible Joule heating creates hotspots on the order of 10 nm and power density on the order of 10 W/  m 3 Conduction from the transistor is complicated due to phonon relaxation and interfaces We estimate an optimistic power density ~ kW/cm 2 How close can we get to this?