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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
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20063
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
??
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20064
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)
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20065
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
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20066
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)
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20067
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
~
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20068
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)
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 20069
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
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 200610
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
25.09.2006 International Workshop on Nanoscale Energy Conversion and Information Processing Devices, Nice 200611
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?