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A Technology-Independent Model for Nanoscale Logic Devices Michael P. Frank, University of Florida, Depts. of CISE and ECE, CSE Bldg., Box 116120, Gainesville, FL 32611, [email protected] Motivation / problem description: Reconstructing Physical Quantities in Computational Terms • Candidate nanocomputing technologies operate in a wide variety of different physical domains. Physical Quantity Entropy • Even just the all-electronic technologies differ by: Action Angular Momentum Proper Time, Distance, Time Computational Interpretation Physical information that is incompressible (non-decomputable) Number of (quantum) operations of motion & interaction Number of operations taken per unit angle of rotation Number of internal-update ops, spatial transition ops, total ops if trajectory taken by a Planck-mass reference system Velocity2 Energy Rest mass-energy Momentum Generalized Temp. Heat Thermal Temper. Frac. of total ops of system effecting net spatial translation Rate of (quantum) computation, total ops ÷ time Rate of internal ops Spatial translation ops/distance Update freq., avg. rate of complete parallel update steps Energy in subsystems whose information is entropy Generalized temp. of subsystems whose info. is entropy – E.g., electronic, mechanical, optical, chemical. – 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! P 100 W 3 10 bit erasures b T (kB ln 2)(300 K) second • A single-electron device where electrons may be at most 1 volt above their ground state can perform no more than: 14 2 E 2 eV 5 10 reversible state transitio ns h h second • 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: 22 2Tb 2 (300 K)(k B ln 2) 9 10 reversible state transitio ns h h bit second 9 THz clock frequency 12 • The generic model is useful because: – It is sufficient as a basis for higher-level architecture. – 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 systemlevel figures of merit. Hierarchical System Design/Optimization Methodology ops/ops = unitless, max. = 100% (c2) ops/time = ops/ops = unitless ops/time = unitless ops/dist. = unitless ops/time/info = info−1 ops/time = unitless ops/time/info = info−1 (Some example Fundamental Physical Limits of Computing: implications) • A 100 watt computer expelling its waste heat into a roomtemperature environment can perform no more than: – Technology is an interfacial “glue” layer between universal physical and computational domains. • In which we don’t care about the technology details anyway. Computational Units Information (log #states), e.g., nat = kB, bit = kB ln 2 Operations or ops: r-op = , π-op = h/2 ops/angle (1 r-op/rad = 2 π-ops/) ops, ops, ops Device Model Parameters • Tg – Avg. generalized temperature for ops. in the coding subsystem. • Elb – Energy per amt. of coding-state info. representing 1 logical bit. • tlbop – Elapsed time for carrying out one logical bit-operation (transition of a logical bit-system). • td – Avg. time btw. decoherence events per bit in coding subsystem. • Plk – Leakage power per stored logical bit. • St – Rate of parasitic entopy generation per bit. Minimum Entropy Generation per Bit-op • • • • Ilb = Elb/Tg – Physical info. per logical bit. r = Ilb/b ≥ 1 – Redundancy factor (no units). Epb = Elb/r = kBTgln 2 – Energy per physical bit. Clb = Ib·(op/b)/ttr = (Elb/Tg)ttr(op/bit) – Rate of physical computation per logical bit. • Ptr = Elb/ttr – Power transfer in switching a bit. • ttr ≥ h/2bTg – Margolus-Levitin theorem. where Ptr I trV I tr E pb / kT kTg ln 2 / kT Vq / kT c c = Tg/T e e e 2 (overdrive Plk I lkV I lk Faithful Generic Models of Physical Computation • St = Ilb/td + Plk/T – Rate of parasitic entropy gen. • Minimum t tr t tr S lbc St t tr I lb Plk entropy td T generated per reversible t tr Ptr t tr Elb I lbTg c c c I lb c bit-operation: Plk c T 2 T 2T 2T 2 1 c 1 c S lbc I lb c 1 bit c q 2 q 2 factor) where q = td/ttr = Tg/Td (quantum quality factor) 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.