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Nanodevices & Maxwell’s demon
Channel
Source Drain
V I
McCoy Lecture, Purdue
September 26, 2006
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Nanodevices & Maxwell’s demon
“Gate”
VG
Insulator
Channel
Source Drain
V I
Transistor
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Nanodevices & Maxwell’s demon
Channel
Source Drain
V I
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Top-down view
V=IR or I=VG
Channel Drain
Conductance, G = 1/R
I
V G = ! A/ L
Conductivity
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Top-down view
V=IR or I=VG
Channel Drain
Conductance, G = 1/R
G = ! A/ L
I
V
Conductivity
CHANNEL 2
" = q n! /m
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Top-down view
V=IR or I=VG
Channel Drain
Conductance, G = 1/R
G = ! A/ L
I
V
Conductivity
2
CHANNEL " = q n! /m
m=? n=?
! =? “Very
complicated”
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Bottom-up View “Top”
Ohm’s law
Source Channel Drain I = GV , G = ! A/ L
I
V
" ! escape rate
2
G = (q / h) (" D ! )
CHANNEL
G = ( q 2 / h)
123
1 / 25.8 K! “Bottom”
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S Channel D VG 0
PTY
EM
µ No states
LED
FIL
Electrochemical
S Channel D
Potential
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S Channel D
V
µ1
µ2 µ1
µ2
I I
V V
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Escape rate
! / h : Escape Rate
! has dim ensions of energy
!1 / h "2 /h
S Channel D
µ1
µ2
Small "1
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S Channel D 1
q "1
Normalized
2h
Current
0.8
0.6
V
0.4
0.2
0
!
-0.2
-0.2 0 0.2 0.4 0.6
V"
!1 / h !1 / h
µ2
µ1 µ2
!
I µ1
V !
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0.25
!1 / h "1 / h
0.2
0.15 1
q "1
Normalized
0.1
2h
Current
µ2
0.8
0.05
0
0.6
-0.05
-0.1
0.4
!µ
-0.15
1 -0.2
-0.25
0.2
! -0.2 0 0.2 0.4 0.6 0.8 1
0
!
-0.2
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 V"
0.7
dI q"1 /2h
! ~
dV 4k T 1
Conductance
Normalized
0.8
!
0.6
0.4
! 0.2
0
-0.2
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
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!1 / h "1 / h 1
q "1
Normalized
2h
Current
µ2
0.8
0.6
0.4
!µ 1 0.2
! 0
!
-0.2
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 V"
0.7
dI q"1 /2h
! ~
dV 2"1 + 4k T 1
Conductance
Normalized
0.8
!
0.6
~ q 2 /4h if "1 >> k T 0.4
! 0.2
Conduc tance quantum 0
2 -0.2
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
! ~ q /2 " h ~ 1/25.8 K#
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U 0 : Increase in !1 / h "1 /h !1 / h "1 /h !1 / h "1 /h
potential due to µ2
SINGLE electron µ2
>> " , k T ! µ1 µ2 ! µ1 ! µ1
!
“Self-interaction
!
Correction” Non-interacting
! !
! ! q "1
1 1 *2
0.8 0.8 2h
Normalized
Current
0.6 0.6
0.4 0.4
0.2 0.2
0 0
!
-0.2 -0.2
-0.1 -0.1 0 0 0.1 0.1 0.2 0.2 0.30.3 0.4
0.4 V"
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! /h ! /h
q"
µ1 I ~ D qV
2
13
2h
{
D qV
Current
Number
of states
µ2 per state
I q2
= " D!
D: Density! V 2" h 123
of states
{ Transmission
Conduc tan ce
Quantum
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! /h Cross-section A ! /h
I q2 µ1
= " D!
V 2" h
D qV
µ2
D
{ = N0
{ AL
{
/eV 3 m3
/eV "m
Ballistic Diffusive
Can
show
that hv 2hD
! ~ " D! ~ A ! ~ " D! ~ A / L
L L2
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Power = V I " "
qV {
Source Channel Drain
! ! " ! "
I
V
Dissipation Dissipation
! !
Contacts assumed
to remain in equilibrium Newton’s law
Schrodinger equation
Thermodynamics
Dynamics
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Power = V I " "
qV {
Source Channel Drain
! ! " ! "
I
V
Dissipation Dissipation
! !
" !s "
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! !
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Spin Valves
Source Channel Drain
Source Channel Drain
Insulating substrate
Insulating substrate
Parallel (P)
Anti-parallel (AP)
Source Current P
AP
Perfect
AP
Voltage
Drain
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Spin
flip
+ve
Source Channel Drain
Insulating substrate - +
Source Drain
Spin
flip Current with spin-flip
w/o spin-flip
+ - Voltage
Source Drain
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Spin
flip
+ve
Source Channel Drain
Insulating substrate
- +
Source Drain
Spin Current
flip
+ - Voltage
Source Drain
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1
current --->
Normalized
Source Channel
0.5
Drain
0
-0.5
Current
-1
-0.1 -0.05 0 0.05 0.1
Voltage --->
Voltage
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1
current --->
Normalized
0.5
0
Source Channel Drain
-0.5
-1
-0.1 -0.05 0 0.05 0.1
Voltage --->
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Source Channel Drain Source Channel Drain
Where did the energy come from ?
Answer: From the contacts
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Source Channel Drain Source Channel Drain
S = k ln W
S=0 S = Nk ln 2
Energy upto T "S may be extracted
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No energy needed
Source Channel Drain
Source Channel Drain
Need > N kT to “Erase”
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Energy needed to1
VG Transistor switch from one
0.9
minimum to
Flipping a spin another ?
0.8
Insulator
0.7
Normalized Energy
Channel increases energy 0.6
0.5
0.4
Source Drain 0.3
0.2
0.1
V I 0
0 50 100 150 200 250 300
Angle of magnetization from plane of magnet
350
P = 104
electrons
x (40 kT) = 1 µW / switch
x 109 Hz
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Transistor
VG Nanoelectronics Research
Initiative (NRI)
Insulator
Launched by SIA & NSF
Channel
Objective: Explore
Source Drain options for producing a
low power switch
V I
P = 104 Mark Lundstrom
electrons Ashraf Alam
Kaushik Roy
x (40 kT) = 1 µW / switch Gerhard Klimeck
x 109 Hz
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S = Nk ln 2 S=0
No energy needed
Source Channel Drain
Source Channel Drain
Need > N kT to “Erase”
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S = k log W
All
“blue”
Source Channel Drain
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“Reservoir” “System”
Down > Up
E
"s
µ1 H µ2
Density
of states
! "1 "2
! !
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! !
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Macroscopic Ho
0.1 dimensions
mm t
Source Channel Drain
10 µm Diffusion
1µm
"s
0.1 µm Boltzmann
µ1 H µ2
10 nm
1 nm “Quantum ! "1 "2
Boltzmann”
0.1 nm Atomic
! Nanowires, nanotubes, molecules …..
!
dimensions
Switches, energy conversion, cooling …
!
!
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Entangled !
+
*A *B
Source Channel Drain
A B2
2
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Macroscopic “Even simple things .. work .. in
0.1 dimensions
mm only one direction because it
has some ultimate contact with
10 µm Diffusion the rest of the universe ..”
Feynman lectures, Vol.1, 46-8
1µm
0.1 µm Boltzmann
Ho Entangled !
10 nm t
1 nm Quantum
Boltzmann
Source Channel Drain
0.1 nm Atomic
dimensions
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nanoHUB.org Acknowledgements
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Thanks to Purdue and
to all my outstanding
students and colleagues,
supportive friends and family.
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Questions & Answers
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Macroscopic Ho
0.1 dimensions
mm t
Source Channel Drain
10 µm Diffusion
1µm
"s
0.1 µm Boltzmann
µ1 H µ2
10 nm
1 nm “Quantum ! "1 "2
Boltzmann”
0.1 nm Atomic
! Nanowires, nanotubes, molecules …..
!
dimensions
Switches, energy conversion, cooling …
!
!
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U 0 : Increase in !1 / h "1 /h !1 / h "1 /h !1 / h "1 /h
potential due to µ2
SINGLE electron µ2
>> " , k T ! µ1 µ2 ! µ1 ! µ1
!
“Self-interaction
!
Correction” Non-interacting
! !
! ! q "1
1 1 *2
0.8 0.8 2h
Normalized
Current
0.6 0.6
0.4 0.4
0.2 0.2
0 0
!
-0.2 -0.2
-0.1 -0.1 0 0 0.1 0.1 0.2 0.2 0.30.3 0.4
0.4 V"
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Spin Valves
Source Channel Drain
Source Channel Drain
Insulating substrate
Insulating substrate
Parallel (P)
Anti-parallel (AP)
Source Current P
AP
Perfect
AP
Voltage
Drain
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