Dissipation and Entropy Flow in Logic Fundamental Limits and Engineering Challenges

1Systems Technology Lab, Intel Research Berkeley2Mechanical Engineering, Stanford University

Dissipation and Entropy Flow in LogicFundamental Limits and Engineering Challenges

Sanjiv SinhaSanjiv Sinha11 and Ken Goodson and Ken Goodson22

25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20062

Minimal Energy in Logic

SNL theory ~ kT ln 2 ~ 17 meVPractical ~ 40 kT ~ 1 eV

0 1 0

00

0

01

1

1

11 1 0 0

Cramer et al., Science 288, 640(2000)

~ O (10 kT) per nucleotide1

Landauer, IBM J Res Dev, 5, 183 (1961)Bennett, Int. J. Theor. Phys., 21, 905 (1982)

Intel Dothan

106 kT ~ 10 keV

Intel

Electronic irreversible computing produces Joule

heat


Length Scales in Internal Energy Flow

Characteristic Length

1mm1 m0.1 m10 nm1 nm5 A°

FourierFourierDiffusionDiffusion

Semi-Semi-ClassicalClassical

AtomisticAtomistic

StronglyStronglyQuantumQuantum

ContinuumContinuum

Pro

ble

m L

ev

el

1 cm

Devices

Circuits

Die/Chip

System

Heat Flow Path

T_die

??


Time Scales in Internal Energy Flow

timePow

er

40

50

60

70

80

0.0001 0.01 1 100 10000

Time (sec)

Jun

ctio

n T

emp

erat

ure

Ris

e (C

) 90

Thermal Mass die

package

systemheat sink

T_die ( ~ 1-10ms)

T_HS ( ~ 100s)

T_pkg ( ~ 1s)

T_sys ( ~ 1000s)

0.1 ps

1-100 ps

100 s

Hot Electrons

Hot Phonons

Thermal Phonons

Heat Sink0 100 200 300 400

10

20

30

40

50

60

70

80

90

100

t (ps)

r (n

m)

ON OFF

=15.4 THz

Hotspot

Sinha et al, J. Heat Transfer, 128 (2006)


Electron-Phonon Interactions

Buried Oxide

Source Draingate

18 nm4 nm65 W/m3

T(K)

20 40 60 80 10020

40

60

80

100

120

140

x [nm]

y [

nm

]

390 400 410 420 430 440 450 460

S D

BOX

Temperature field using phonon Boltzmann Transport model

05

1015

400

500

600

0

1

2

[THz]

Time [ps]E

[eV

]

LOLA1TA1

3-phonon decay

kx

ky

kz

Sinha et al., J. Appl. Phys., 97, 23702 (2005)

Intervalley Electron Scattering


Minimal Energy Dissipated Per Switch

Landauer’s 1-particle-in-a-bistable-well model

E = kT (ln2)

Bate’s 2 level multi-particle QM logic gate model

E = kTc ln2

For comparison, <E> = PDYNAMIC x tDELAY ~ 1 fJ today

1

0

Landauer, IBM J Res Dev, 5, 183 (1961)

Bate, VLSI Electronics, 5 (1982)


The Heat Transfer Limited Power Density

Tswitch

Tcontact

Tdie

Tatm

Phonon conduction limited

Technology limited

Interface physics limited

Switch

Die and Package

System

32ln

2

Tk

mtA

EP

AAPTTT

B

switchswitch

switch

chip

chip

switch

switchatmswitch

Sinha et al, Under Review, IEEE Trans. Electron Devices

xSWITCH px

~


Conduction Across The -n Interface

th

Tswitch

Nano to Micro bridge

Switch Microscale

contactHeat flow

KW

e

dxex

h

Tk

m

Tk

Tk

x

xB

BRIDGE

B

m

B

m

/103~

1

10

2

22

max,

min,

Micro to Nano Address Block

(MNAB)


Estimate Including Macroscopic Heat Flow

Always will need to reject to the ambient

Convection/radiation limits will remain dominant

fgVAPMAXVAP

apaSATDIE

fgfDIEMACRO

hcnmq

CmTT

hm

~4/,

,

K125ΔT@kW/cm6.3 2 MAXP


Comments

Not quite a fundamental limit nor a technological figure; Somewhere in the middle

Essential challenge is how do we enhance rejection to the sink

Assumption of local equilibrium in the switch may not hold

Comparisons

SNL based theory - > ~ MW/cm2

Best case demonstrated -> ~ 300 W/cm2


In Summary• Logic devices are “inefficient” by several orders of magnitude above

the SNL limit

• Irreversible Joule heating creates hotspots on the order of 10 nm and power density on the order of 10 W/m3

• Conduction from the transistor is complicated due to phonon relaxation and interfaces

• We estimate an optimistic power density ~ kW/cm2

• How close can we get to this?

Documents

Dissipation and Entropy Flow in Logic Fundamental Limits and Engineering Challenges