Dissipation and Entropy Flow in Logic Fundamental Limits and Engineering Challenges

1. Dissipation and Entropy Flow in LogicFundamental Limits and Engineering Challenges Sanjiv Sinha1 and Ken Goodson2

2. SNL theory ~ kT ln 2 ~ 17 meV Practical ~ 40 kT ~ 1 eV 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 Electronic irreversible computing produces Joule heat ~ O (10 kT) per nucleotide1 Cramer et al., Science 288, 640(2000) 106 kT ~ 10 keV Intel Intel Dothan Minimal Energy in Logic Landauer, IBM J Res Dev, 5, 183 (1961) Bennett, Int. J. Theor. Phys., 21, 905 (1982) International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

3. System Die/Chip ? Circuits Problem Level T_die Heat Flow Path Devices Strongly Quantum Semi- Classical Fourier Diffusion Atomistic Continuum 5 A° 1 nm 10 nm 0.1 mm 1 mm 1mm 1 cm Characteristic Length Length Scales in Internal Energy Flow International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

4. 90 80 heat sink system package 70 T_sys (t ~ 1000s) Junction Temperature Rise (C) Thermal Mass 60 die 50 Power Hot Electrons 40 T_HS (t ~ 100s) 0.1 ps n=15.4 THz 0.0001 0.01 1 100 10000 Hot Phonons T_pkg (t ~ 1s) Time (sec) time Hotspot 1-100 ps Thermal Phonons T_die (t ~ 1-10ms) 100 s Heat Sink Sinha et al, J. Heat Transfer, 128 (2006) Time Scales in Internal Energy Flow International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

5. 18 nm 4 nm 65 W/mm3 gate Source Drain Buried Oxide S D BOX 3-phonon decay LA1 TA1 LO T(K) Temperature field using phonon Boltzmann Transport model Electron-Phonon Interactions Intervalley Electron Scattering Sinha et al., J. Appl. Phys., 97, 23702 (2005) International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

6. 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 = kTc ln2 • For comparison, <E> = PDYNAMIC x tDELAY~ 1 fJ today Landauer, IBM J Res Dev, 5, 183 (1961) 1 0 Bate, VLSI Electronics, 5 (1982) International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

7. Tcontact Switch Phonon conduction limited Tswitch Die and Package Interface physics limited Tdie Technology limited System Tatm The Heat Transfer Limited Power Density Sinha et al, Under Review, IEEE Trans. Electron Devices International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

8. Microscale contact Conduction Across The m-n Interface Tswitch Nano to Micro bridge ~lth Switch Heat flow Micro to Nano Address Block (MNAB) International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

9. 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 2006

10. 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/cm2 • Best case demonstrated -> ~ 300 W/cm2 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006

11. 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/mm3 • Conduction from the transistor is complicated due to phonon relaxation and interfaces • We estimate an optimistic power density ~ kW/cm2 • How close can we get to this? International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 2006