Gopal, Ashwin ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Esposito, Massimiliano ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Freitas, Nahuel
External co-authors :
yes
Language :
English
Title :
Large deviations theory for noisy nonlinear electronics: CMOS inverter as a case study
Publication date :
2022
Journal title :
Physical Review. B, Condensed Matter and Materials Physics
Semiconductor Industry Association, ITRS 2.0 Executive Report (2015), accessed: 2021-08-02.
G. Schrom and S. Selberherr, Ultra-low-power CMOS technologies, in 1996 International Semiconductor Conference, 19th Edition, CAS'96 Proceedings, Sinaia, Romania, Vol. 1 (IEEE, 1996), pp. 237-246.
A. Wang, B. H. Calhoun, and A. P. Chandrakasan, Sub-Threshold Design for Ultra Low-Power Systems (Springer, New York, 2006), Vol. 95.
V. Chandra and R. Aitken, Impact of technology and voltage scaling on the soft error susceptibility in nanoscale cmos, in 2008 IEEE International Symposium on Defect and Fault Tolerance of VLSI Systems, Cambridge, MA, USA (IEEE, 2008), pp. 114-122.
N. Freitas, K. Proesmans, and M. Esposito, Reliability and entropy production in nonequilibrium electronic memories, Phys. Rev. E 105, 034107 (2022) 10.1103/PhysRevE.105.034107.
L. B. Kish, Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states, Phys. Lett. A 373, 911 (2009) 0375-9601 10.1016/j.physleta.2008.12.068.
T. J. Hamilton, S. Afshar, A. van Schaik, and J. Tapson, Stochastic electronics: A neuro-inspired design paradigm for integrated circuits, Proc. IEEE 102, 843 (2014) 0018-9219 10.1109/JPROC.2014.2310713.
K. Y. Camsari, R. Faria, B. M. Sutton, and S. Datta, Stochastic (Equation presented)-Bits for Invertible Logic, Phys. Rev. X 7, 031014 (2017) 2160-3308 10.1103/PhysRevX.7.031014.
N. Freitas, J.-C. Delvenne, and M. Esposito, Stochastic Thermodynamics of Nonlinear Electronic Circuits: A Realistic Framework for Computing Around (Equation presented), Phys. Rev. X 11, 031064 (2021) 2160-3308 10.1103/PhysRevX.11.031064.
P. R. Gray, P. J. Hurst, S. H. Lewis, and R. G. Meyer, Analysis and Design of Analog Integrated Circuits (John Wiley & Sons, Hoboken, NJ, 2009).
K. Nepal, R. I. Bahar, J. Mundy, W. R. Patterson, and A. Zaslavsky, Designing logic circuits for probabilistic computation in the presence of noise, in Proceedings of the 42nd Annual Design Automation Conference (Association for Computing Machinery, New York, NY, 2005), pp. 485-490.
J. L. Wyatt and G. J. Coram, Nonlinear device noise models: Satisfying the thermodynamic requirements, IEEE Trans. Electron Devices 46, 184 (1999) 0018-9383 10.1109/16.737458.
M. S. Gupta, Thermal noise in nonlinear resistive devices and its circuit representation, Proc. IEEE 70, 788 (1982) 0018-9219 10.1109/PROC.1982.12405.
L. Brillouin, Can the rectifier become a thermodynamical demon? Phys. Rev. 78, 627 (1950) 0031-899X 10.1103/PhysRev.78.627.2.
G. J. Coram, Thermodynamically valid noise models for nonlinear devices, Ph.D. thesis, Massachusetts Institute of Technology, 2000.
R. Sarpeshkar, T. Delbruck, and C. A. Mead, White noise in MOS transistors and resistors, IEEE Circuits and Devices Mag. 9, 23 (1993) 8755-3996 10.1109/101.261888.
R. Landauer, Solid-state shot noise, Phys. Rev. B 47, 16427 (1993) 0163-1829 10.1103/PhysRevB.47.16427.
Y. Cui, G. Niu, A. Rezvani, and S. S. Taylor, Measurement and modeling of drain current thermal noise to shot noise ratio in 90 nm CMOS, in 2008 IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems, Orlando, FL, USA (IEEE, 2008), pp. 118-121.
P. Hanggi and P. Jung, Bistability in active circuits: Application of a novel Fokker-Planck approach, IBM J. Res. Dev. 32, 119 (1988) 0018-8646 10.1147/rd.321.0119.
C. Y. Gao and D. T. Limmer, Principles of low dissipation computing from a stochastic circuit model, Phys. Rev. Res. 3, 033169 (2021) 2643-1564 10.1103/PhysRevResearch.3.033169.
H. Li, J. Mundy, W. Patterson, D. Kazazis, A. Zaslavsky, and R. Bahar, A model for soft errors in the subthreshold CMOS inverter, in Proceedings of Workshop on System Effects of Logic Soft Errors, San Jose, CA, USA (Citeseer, 2006).
E. Rezaei, M. Donato, W. R. Patterson, A. Zaslavsky, and R. I. Bahar, Fundamental thermal limits on data retention in low-voltage CMOS latches and SRAM, IEEE Trans. Device Mater. Reliab. 20, 488 (2020) 1530-4388 10.1109/TDMR.2020.2996627.
H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478, 1 (2009) 0370-1573 10.1016/j.physrep.2009.05.002.
B. Derrida and J. L. Lebowitz, Exact Large Deviation Function in the Asymmetric Exclusion Process, Phys. Rev. Lett. 80, 209 (1998) 0031-9007 10.1103/PhysRevLett.80.209.
J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, J. Stat. Phys. 95, 333 (1999) 0022-4715 10.1023/A:1004589714161.
C. Giardina, J. Kurchan, and L. Peliti, Direct Evaluation of Large-Deviation Functions, Phys. Rev. Lett. 96, 120603 (2006) 0031-9007 10.1103/PhysRevLett.96.120603.
L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Macroscopic fluctuation theory, Rev. Mod. Phys. 87, 593 (2015) 0034-6861 10.1103/RevModPhys.87.593.
J. M. Horowitz and T. R. Gingrich, Proof of the finite-time thermodynamic uncertainty relation for steady-state currents, Phys. Rev. E 96, 020103 (R) (2017) 2470-0045 10.1103/PhysRevE.96.020103.
D. Ruelle, Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 2004).
R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics (Taylor & Francis, London, 2006), Vol. 1431.
M. Assaf and B. Meerson, WKB theory of large deviations in stochastic populations, J. Phys. A: Math. Theor. 50, 263001 (2017) 1751-8113 10.1088/1751-8121/aa669a.
T. Herpich, T. Cossetto, G. Falasco, and M. Esposito, Stochastic thermodynamics of all-to-all interacting many-body systems, New J. Phys. 22, 063005 (2020) 1367-2630 10.1088/1367-2630/ab882f.
J. N. Freitas and M. Esposito, Emergent second law for non-equilibrium steady states, Nat. Commun. 13, 5084 (2022) 10.1038/s41467-022-32700-7.
R. L. Jack, Ergodicity and large deviations in physical systems with stochastic dynamics, Eur. Phys. J. B 93, 74 (2020) 1434-6028 10.1140/epjb/e2020-100605-3.
C. Flindt and J. P. Garrahan, Trajectory Phase Transitions, Lee-Yang Zeros, and High-Order Cumulants in Full Counting Statistics, Phys. Rev. Lett. 110, 050601 (2013) 0031-9007 10.1103/PhysRevLett.110.050601.
H. Vroylandt, M. Esposito, and G. Verley, Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition, Phys. Rev. Lett. 124, 250603 (2020) 0031-9007 10.1103/PhysRevLett.124.250603.
A. Lazarescu, T. Cossetto, G. Falasco, and M. Esposito, Large deviations and dynamical phase transitions in stochastic chemical networks, J. Chem. Phys. 151, 064117 (2019) 0021-9606 10.1063/1.5111110.
J. Meibohm and M. Esposito, Finite-Time Dynamical Phase Transition in Nonequilibrium Relaxation, Phys. Rev. Lett. 128, 110603 (2022) 0031-9007 10.1103/PhysRevLett.128.110603.
A. C. Barato and U. Seifert, Thermodynamic Uncertainty Relation for Biomolecular Processes, Phys. Rev. Lett. 114, 158101 (2015) 0031-9007 10.1103/PhysRevLett.114.158101.
J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020) 1745-2473 10.1038/s41567-019-0702-6.
D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81, 2340 (1977) 0022-3654 10.1021/j100540a008.
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992), Vol. 1.
D. A. Bagrets and Y. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade systems, Phys. Rev. B 67, 085316 (2003) 0163-1829 10.1103/PhysRevB.67.085316.
M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009) 0034-6861 10.1103/RevModPhys.81.1665.
A. Lazarescu, The physicist's companion to current fluctuations: One-dimensional bulk-driven lattice gases, J. Phys. A: Math. Theor. 48, 503001 (2015) 1751-8113 10.1088/1751-8113/48/50/503001.
H. Touchette and R. J. Harris, Large deviation approach to nonequilibrium systems, in Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond, edited by R. Klages, W. Just, and C. Jarzynski (Wiley-VCH Verlag, Weinheim, Germany, 2013).
R. Chetrite and H. Touchette, Nonequilibrium Markov processes conditioned on large deviations, Annales Henri Poincaré 16, 2005 (2015) 10.1007/s00023-014-0375-8.
N. Wiener, Differential-space, J. Math. Phys. 2, 131 (1923) 0097-1421 10.1002/sapm192321131.
M. Herman, E. Bruskin, and B. Berne, On path integral Monte Carlo simulations, J. Chem. Phys. 76, 5150 (1982) 0021-9606 10.1063/1.442815.
J. Lehmann, P. Reimann, and P. Hänggi, Surmounting oscillating barriers: Path-integral approach for weak noise, Phys. Rev. E 62, 6282 (2000) 1063-651X 10.1103/PhysRevE.62.6282.
É. Roldán and S. Gupta, Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement, Phys. Rev. E 96, 022130 (2017) 2470-0045 10.1103/PhysRevE.96.022130.
C. Gardiner, Stochastic Methods (Springer, Berlin, 2009), Vol. 4.
H. S. Wio, Path Integrals for Stochastic Processes: An Introduction (World Scientific, Singapore, 2013).
P. C. Martin, E. Siggia, and H. Rose, Statistical dynamics of classical systems, Phys. Rev. A 8, 423 (1973) 0556-2791 10.1103/PhysRevA.8.423.
L. Peliti, Path integral approach to birth-death processes on a lattice, J. Phys. France 46, 1469 (1985) 0302-0738 10.1051/jphys:019850046090146900.
T. Cossetto, Problems in nonequilibrium fluctuations across scales: A path integral approach, Ph.D. thesis, University of Luxembourg, 2020.
S. H. Strogatz, Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering (CRC Press, Boca Raton, FL, 2018).
S. Saryal, H. M. Friedman, D. Segal, and B. K. Agarwalla, Thermodynamic uncertainty relation in thermal transport, Phys. Rev. E 100, 042101 (2019) 2470-0045 10.1103/PhysRevE.100.042101.
G. Falasco, M. Esposito, and J.-C. Delvenne, Unifying thermodynamic uncertainty relations, New J. Phys. 22, 053046 (2020) 1367-2630 10.1088/1367-2630/ab8679.
K. Ptaszyński, Nonrenewal statistics in transport through quantum dots, Phys. Rev. B 95, 045306 (2017) 2469-9950 10.1103/PhysRevB.95.045306.
N. Ubbelohde, C. Fricke, F. Hohls, and R. J. Haug, Spin-dependent shot noise enhancement in a quantum dot, Phys. Rev. B 88, 041304 (R) (2013) 1098-0121 10.1103/PhysRevB.88.041304.
B. R. Bułka, Current and power spectrum in a magnetic tunnel device with an atomic-size spacer, Phys. Rev. B 62, 1186 (2000) 0163-1829 10.1103/PhysRevB.62.1186.
S. Itzkovitz, R. Levitt, N. Kashtan, R. Milo, M. Itzkovitz, and U. Alon, Coarse-graining and self-dissimilarity of complex networks, Phys. Rev. E 71, 016127 (2005) 1539-3755 10.1103/PhysRevE.71.016127.
A. A. Abidi, Phase noise and jitter in CMOS ring oscillators, IEEE J. Solid-State Circuits 41, 1803 (2006) 0018-9200 10.1109/JSSC.2006.876206.
J. Han and M. Orshansky, Approximate computing: An emerging paradigm for energy-efficient design, in 2013 18th IEEE European Test Symposium (ETS), Avignon, France (IEEE, 2013), pp. 1-6.
C. C. Enz and E. A. Vittoz, Charge-Based MOS Transistor mmodeling: The EKV Model for Low-Power and RF IC Design (John Wiley & Sons, Hoboken, NJ, 2006).
Y. Tsividis, Operation and Modeling of the MOS Transistor (McGraw-Hill, Inc., New York, 1987).
M. F. Weber and E. Frey, Master equations and the theory of stochastic path integrals, Rep. Prog. Phys. 80, 046601 (2017) 0034-4885 10.1088/1361-6633/aa5ae2.