Download A Technology-Independent Model for Nanoscale Logic Devices

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.