Physical Limits of Computing Dr. Mike Frank CIS 6930, Sec. #3753X Spring 2002 Lecture #22 Adiabatic Electronics & CMOS Fri., Mar. 1

Administrivia & Overview Don’t forget to keep up with homework!Don’t forget to keep up with homework! –We are  7 out of 14 weeks into the course. You should have earned  ~50 points by now.You should have earned  ~50 points by now. Course outline:Course outline: –Part I&II, Background, Fundamental Limits - done –Part III, Future of Semiconductor Technology - done –Part IV, Potential Future Computing Technologies - done –Part V, Classical Reversible Computing Fundamentals of Adiabatic Processes - Wed.Fundamentals of Adiabatic Processes - Wed. Adiabatic electronics & CMOS logic families - TODAYAdiabatic electronics & CMOS logic families - TODAY ( Spring Break ) Limits of adiabatics: Leakage and clock/power supplies. - Mon. 3/11Limits of adiabatics: Leakage and clock/power supplies. - Mon. 3/11 RevComp theory I: Emulating Irreversible Machines - Wed. 3/13RevComp theory I: Emulating Irreversible Machines - Wed. 3/13 RevComp theory II: Bounds on Space-Time Overheads - Fri. 3/15RevComp theory II: Bounds on Space-Time Overheads - Fri. 3/15 (plus ~7 more lectures…)(plus ~7 more lectures…) –Part VI, Quantum Computing –Part VII, Cosmological Limits, Wrap-Up

Terminology Shift The word “infropy” sounds a bit too goofy.The word “infropy” sounds a bit too goofy. –Unlikely to be accepted into widespread use. Shift in terminology used in this course: Before today:After today: “Infropy R”  “Physical Information I” (“Information”, “Pinformation”?) “Information I”  “Known information K” (“Kinformation”?) “Entropy S”  “Entropy S”Shift in terminology used in this course: Before today:After today: “Infropy R”  “Physical Information I” (“Information”, “Pinformation”?) “Information I”  “Known information K” (“Kinformation”?) “Entropy S”  “Entropy S”

Principles of Adiabatic Processes

Adiabatic Processes - overview Adiabatic steps in the reversible Carnot cycleAdiabatic steps in the reversible Carnot cycle Evolution of the meaning of “adiabatic”Evolution of the meaning of “adiabatic” Time-proportional reversibility (TPR) of quasi- adiabatic processesTime-proportional reversibility (TPR) of quasi- adiabatic processes Adiabatic theorem of quantum mechanicsAdiabatic theorem of quantum mechanics Adiabatic transitions of a two-state systemAdiabatic transitions of a two-state system Logic & memory in irreversible and adiabatic processes.Logic & memory in irreversible and adiabatic processes.

The Carnot Cycle In , Sadi Carnot analyzed the efficiency of an ideal heat engine all of whose steps were reversible, and furthermore proved that:In , Sadi Carnot analyzed the efficiency of an ideal heat engine all of whose steps were reversible, and furthermore proved that: –Any reversible engine (regardless of details) would have the same efficiency (T H  T L )/T H. –No engine could have greater efficiency than a reversible engine w/o producing work from nothing –Temperature itself could be defined on a thermodynamic scale based on heat recoverable by a reversible engine operating between T H and T L

Steps of Carnot Cycle Isothermal expansion at T HIsothermal expansion at T H Adiabatic (without flow of heat) expansion T H  T LAdiabatic (without flow of heat) expansion T H  T L Isothermal compression at T LIsothermal compression at T L Adiabatic compression T L  T HAdiabatic compression T L  T H V P TLTL THTH

Carnot Cycle Terminology Adiabatic (Latin): orig. “Without flow of heat”Adiabatic (Latin): orig. “Without flow of heat” –I.e., no entropy enters or leaves the system Isothermal: “At the same temperature”Isothermal: “At the same temperature” –Temperature of system remains constant as entropy enters or leaves. Both kinds of steps, in the case of the Carnot cycle, are examples of isentropic processesBoth kinds of steps, in the case of the Carnot cycle, are examples of isentropic processes –“at the same entropy” –I.e., no (known) information is transformed into entropy in either process But “adiabatic” has mutated to mean isentropic.But “adiabatic” has mutated to mean isentropic.

Old and New “Adiabatic” Consider a closed system where you just lose track of its detailed evolution:Consider a closed system where you just lose track of its detailed evolution: –It’s adiabatic (no heat flow), –But it’s not “adiabatic” (not isentropic) Consider a box containing some heat, flying ballistically out of the system:Consider a box containing some heat, flying ballistically out of the system: –It’s not adiabatic, because heat is “flowing” out of the systembecause heat is “flowing” out of the system –But it’s “adiabatic” (no entropy is generated) Hereafter, we bow to the 20 th century’s corrupt usage: let adiabatic :  isentropicHereafter, we bow to the 20 th century’s corrupt usage: let adiabatic :  isentropic Box o’ Heat “The System”

Quasi-Adiabatic Processes No real process is completely adiabaticNo real process is completely adiabatic –Because some outside system may always have enough energy to interact with & disturb your system’s evolution - e.g., cosmic ray, asteroid  Evolution of system state is never perfectly known  Evolution of system state is never perfectly known –Unless you know the exact quantum state of the whole universe –Entropy of your system always increases. Unless it is already at a maximum (at equilibrium)Unless it is already at a maximum (at equilibrium) –Can’t really be at complete equilibrium with its surroundings »unless whole universe is at utterly stable “heat death” state. Systems at equilibrium are sometimes called “static.”Systems at equilibrium are sometimes called “static.” Non-equilibrium, quasi-adiabatic processes are sometimes also called quasi-staticNon-equilibrium, quasi-adiabatic processes are sometimes also called quasi-static –Changing, but near a local equilibrium otherwise

Degree of Reversibility The degree of reversibility (a.k.a. reversibility, a.k.a. thermodynamic efficiency) of any quasi- adiabatic process is defined as the ratio of:The degree of reversibility (a.k.a. reversibility, a.k.a. thermodynamic efficiency) of any quasi- adiabatic process is defined as the ratio of: –the total free energy at the start of the process –  by the total energy spent in the process Or, equivalently:Or, equivalently: –the known, accessible information at the start –  by the amount that is converted to entropy This same quantity is referred to as the (per- cycle) “quality factor” Q for any resonant element (e.g., LC oscillator) in EE.This same quantity is referred to as the (per- cycle) “quality factor” Q for any resonant element (e.g., LC oscillator) in EE.

The “Adiabatic Principle” Claim: Any ideal quasi-adiabatic process performed over time t has a thermodynamic efficiency that is proportional to t,Claim: Any ideal quasi-adiabatic process performed over time t has a thermodynamic efficiency that is proportional to t, –in the limit as t  0. We call processes that realize this idealization time-proportionally reversible (TPR) processes.We call processes that realize this idealization time-proportionally reversible (TPR) processes. Note that the total energy spent (  E spent ), and the total entropy generated (  S), are both inversely proportional to t in any TPR process.Note that the total energy spent (  E spent ), and the total entropy generated (  S), are both inversely proportional to t in any TPR process. –The slower the process, the more energy-efficient.

Proving the Adiabatic Principle (See RevComp memo #M14) Assume free energy is in generalized kinetic energy of motion E k of system through its configuration space. E k = ½mv 2  v 2 = ( /t) 2  t  2 for m, const.Assume free energy is in generalized kinetic energy of motion E k of system through its configuration space. E k = ½mv 2  v 2 = ( /t) 2  t  2 for m, const. Assume that every t f time, on average (mean free time), a constant fraction f of E k is thermalized (turned into heat)Assume that every t f time, on average (mean free time), a constant fraction f of E k is thermalized (turned into heat) Whole process thermalizes energy f(t/t f )E k  t  t  2 = t  1. Constant in front is ½ fm 2 /t f  :  2, whereh  =½fm/t f is the effective viscosity.Whole process thermalizes energy f(t/t f )E k  t  t  2 = t  1. Constant in front is ½ fm 2 /t f  :  2, whereh  =½fm/t f is the effective viscosity.

Example: Electrical Resistance We know P spent =I 2 R=(Q/t) 2 R, or E spent =Pt = Q 2 R/t.  Note scaling with 1/tWe know P spent =I 2 R=(Q/t) 2 R, or E spent =Pt = Q 2 R/t.  Note scaling with 1/t –Charge transfer through a resistor obeys the adiabatic principle! Why is this so, microscopically?Why is this so, microscopically? –In most situations, conduction electrons have a large thermal velocity relative to drift velocity.  Scatter off of lattice-atom cross-sections with a mean free time t f that is fairly independent of drift velocity  Scatter off of lattice-atom cross-sections with a mean free time t f that is fairly independent of drift velocity –Each scattering event thermalizes the electron’s drift kinetic energy - a frac. f of current’s total E k Therefore assumptions in prev. proof apply!Therefore assumptions in prev. proof apply!

The Adiabatic Theorem A result in basic quantum theoryA result in basic quantum theory –Proved in many quantum mechanics textbooks Paraphrased: A system initially in its ground state (or more generally, its nth energy eigenstate) will, after subjecting it to a sufficiently slow change of applied forces, remain in the corresponding state, with high probability.Paraphrased: A system initially in its ground state (or more generally, its nth energy eigenstate) will, after subjecting it to a sufficiently slow change of applied forces, remain in the corresponding state, with high probability. –Result has been recently shown to be very general. Amount of leakage out of desired state is proportional to speed of transition, at low speeds.Amount of leakage out of desired state is proportional to speed of transition, at low speeds. –  Quantum systems obey the adiabatic principle!

General Principles of Adiabatic Logics

Two-state Systems Consider any system having an adjustable, bistable potential energy surface (PES) in its configuration space.Consider any system having an adjustable, bistable potential energy surface (PES) in its configuration space. The two stable states form a natural bit.The two stable states form a natural bit. –One state represents 0, the other 1. Consider now the P.E. well having two adjustable parameters:Consider now the P.E. well having two adjustable parameters: –(1) Height of the potential energy barrier relative to the well bottom –(2) Relative height of the left and right states in the well (bias) 01

Possible Parameter Settings We will distinguish six qualitatively different settings of the well parameters, as follows…We will distinguish six qualitatively different settings of the well parameters, as follows… Direction of Bias Force Barrier Height

Possible Adiabatic Transitions Catalog of all the possible transitions in these wells, adiabatic & not...Catalog of all the possible transitions in these wells, adiabatic & not... Direction of Bias Force Barrier Height N (Ignoring superposition states.) leak “1” states “0” states

Ordinary Irreversible Logics Principle of operation: Lower a barrier, or not, based on input. Series/parallel combinations of barriers do logic. Major dissipation in at least one of the possible transitions.Principle of operation: Lower a barrier, or not, based on input. Series/parallel combinations of barriers do logic. Major dissipation in at least one of the possible transitions Example: CMOS logics

Ordinary Irreversible Memory Lower a barrier, dissipating stored information. Apply an input bias. Raise the barrier to latch the new information into place. Remove input bias.Lower a barrier, dissipating stored information. Apply an input bias. Raise the barrier to latch the new information into place. Remove input bias N Example: DRAM

Input-Bias Clocked-Barrier Logic Cycle of operation:Cycle of operation: –Data input applies bias Add forces to do logicAdd forces to do logic –Clock signal raises barrier –Data input bias removed N Input “0” Input “1” Retract input Clock barrier up Clock up Can amplify/restore input signal in clocking step. Can reset latch reversibly given copy of contents. Examples: Adiabatic QDCA, SCRL latch, Rod logic latch, PQ logic, Buckled logic

Input-Barrier, Clocked-Bias Retractile Cycle of operation:Cycle of operation: –Inputs raise or lower barriers Do logic w. series/parallel barriersDo logic w. series/parallel barriers –Clock applies bias force which changes state, or not N * Must reset output prior to input. * Combinational logic only! Input barrier height Clocked force applied  Examples: Hall’s logic, SCRL gates, Rod logic interlocks

Input-Barrier, Clocked-Bias Latching N Cycle of operation:Cycle of operation: –Input conditionally lowers barrier Do logic w. series/parallel barriersDo logic w. series/parallel barriers –Clock applies bias force; conditional bit flip –Input removed, raising the barrier & locking in the state-change –Clock bias can retract Examples: Mike’s 4-cycle adiabatic CMOS logic

Adiabatic electronics & CMOS implementations