1. A Technology-Independent Model for Nanoscale Logic Devices Motivation / problem description: Candidate nanocomputing technologies operate in a wide variety of different physical domains. –E.g., electronic, mechanical, optical, chemical. Even just the all-electronic technologies differ by: –Conductivity class: Semiconductors, conductors, superconductors. –Operating principles: Field effect transistors, resonant tunneling diodes/transistors, Josephson junctions, etc. –Confinement dimensions: Quantum dots, wires, wells. –Materials: Metals, silicon crystals, other semiconductors, hybrid materials, carbon nanotubes, organic molecules, … –Information encoding: In position, voltage, current, phase, or spin states. –Particles manipulated: Just electrons, or also holes, ions, dopants, nuclei, charged molecules, … The long-term winner is still completely unclear… –Yet, we would like a theoretical foundation for future nanocomputer systems engineering and architecture! Proposed solution: Develop generic models of nano logic devices –Independent of the device technology domain. This is feasible because, in the end: –All domains are subject to the same underlying laws! E.g. quantum electrodynamics subsumes virtually all of nanoscale physics (except for nuclear reactions). The Standard Model of particle physics appears to encompass all accessible phenomena except gravity. The generic model will thus be based on: –Universal physical considerations, such as: Entropy, energy, heat, temperature, momentum, etc. –And universal computer engineering considerations: Capacity, frequency, performance, throughput, latency, bandwidth, BW density, energy dissipation, heat flux, size, cost, etc. Any particular nanocomputing technology then just fills in the parameters of the generic model! –Technology is an interfacial “glue” layer between universal physical and computational domains. The generic model is useful because: –It is sufficient as a basis for higher-level architecture. In which we don’t care about the technology details anyway. –We don’t have to guess which devices will win. Any guess we made would probably be wrong anyway. –It can be easily adapted to fit whichever does win. To make the model more precise later. –Results obtained from the generic model will never become obsolete! Assuming the core principles of physics don’t change. –Model can help device physicists to optimize their designs Tells them what low-level device parameter values lead to the best system- level figures of merit. Fundamental Physical Limits of Computing: A 100 watt computer expelling its waste heat into a room- temperature environment can perform no more than: A single-electron device where electrons may be at most 1 volt above their ground state can perform no more than: Any system whose internal computational degrees of freedom are at a generalized temperature no greater than room temperature can update its logical bits at a frequency of no more than: Device Model Parameters T g – Avg. generalized temperature for ops. in the coding subsystem. E lb – Energy per amt. of coding-state info. representing 1 logical bit. t lbop – Elapsed time for carrying out one logical bit-operation (transition of a logical bit-system). t d – Avg. time btw. decoherence events per bit in coding subsystem. P lk – Leakage power per stored logical bit. S t – Rate of parasitic entopy generation per bit. Minimum Entropy Generation per Bit-op I lb = E lb /T g – Physical info. per logical bit. r = I lb /b ≥ 1 – Redundancy factor (no units). E pb = E lb /r = k B T g ln 2 – Energy per physical bit. C lb = I b ·(op/b)/t tr = (E lb /T g )t tr (op/bit) – Rate of physical computation per logical bit. P tr = E lb /t tr – Power transfer in switching a bit. t tr ≥ h/2bT g – Margolus-Levitin theorem. S t = I lb /t d + P lk /T – Rate of parasitic entropy gen. Minimum entropy generated per reversible bit-operation: Michael P. Frank, University of Florida, Depts. of CISE and ECE, CSE Bldg., Box 116120, Gainesville, FL 32611, mpf@cise.ufl.edu Physical QuantityComputational InterpretationComputational Units EntropyPhysical information that is incompressible (non-decomputable) Information (log #states), e.g., nat = k B, bit = k B ln 2 ActionNumber of (quantum) operations of motion & interactionOperations or ops: r-op = , π-op = h/2 Angular MomentumNumber of operations taken per unit angle of rotation ops/angle (1 r-op/rad = 2 π-ops/  ) Proper Time, Distance, Time Number of internal-update ops, spatial transition ops, total ops if trajectory taken by a Planck-mass reference system ops, ops, ops Velocity 2 Frac. of total ops of system effecting net spatial translationops/ops = unitless, max. = 100% (c 2 ) EnergyRate of (quantum) computation, total ops ÷ timeops/time = ops/ops = unitless Rest mass-energyRate of internal opsops/time = unitless MomentumSpatial translation ops/distanceops/dist. = unitless Generalized Temp.Update freq., avg. rate of complete parallel update stepsops/time/info = info −1 HeatEnergy in subsystems whose information is entropyops/time = unitless Thermal Temper.Generalized temp. of subsystems whose info. is entropyops/time/info = info −1 Reconstructing Physical Quantities in Computational Terms Hierarchical System Design/Optimization Methodology Faithful Generic Models of Physical Computation where c = T g /T (overdrive factor) where q = t d /t tr = T g /T d (quantum quality factor) (Some example implications) Conclusion: The generalized temperature of the computational degrees of freedom must be >> both the prevailing decoherence & thermal temps. in order to permit << kT energy dissipation per rev-op.