SWANSWAN

source drain

Moore’s Law

No exponential is forever!

But can we delay “forever”?

SWANSWANCavin, Hutchby, Zhirnov, Bourianoff

SWAN

SWAN

Cavin, Hutchby, Zhirnov, Bourianoff

SWAN

A=0

Precession of phase

+ C

x

B=0

A=0, B=0 C=0

A=0, B=1 C=1

A=1, B=0 C=1

A=1, B=1 C=0

A

B

C

Out

A

B

C

Out

DMS: A&M, Maryland, UTMQCA:ND

Phasetronics: UT Path Integral Monte Carlo: ASU, UT

Pseudospintronics on Graphene: UT, UTD, Maryland

Future of Microelectronics: The beginning of the end or the end of the beginning?

Sanjay Banerjee, Univ. of Texas

Task 5: Nanoscale CharacterizationUTD

Task 4: Nano plasmonic interconnectsRice

Task 3: Nanoscale Thermal ManagementUIUC, NCSU

Γ ΓK MPho

no

n F

req

uen

cy (

cm-1)

Graphene Monolayer

Task 2:Spintronics in DMSTask 1: Logic Devices with Alternate State Variables

SWAN

South West Academy of Nanoelectronics

TI, Intel, IBM, Micron, AMD, Freescale,

NIST

Texas ETF

SWANSWAN

DNA~2-1/2 nm diameter

Things NaturalThings Natural Things ManmadeThings Manmade

Fly ash~ 10-20m

Atoms of siliconspacing ~tenths of nm

Head of a pin1-2 mm

Quantum corral of 48 iron atoms on copper surfacepositioned one at a time with an STM tip

Corral diameter 14 nm

Human hair~ 60-120m wide

Red blood cellswith white cell

~ 2-5 m

Ant~ 5 mm

Dust mite

200 m

ATP synthase

~10 nm diameterNanotube electrode

Carbon nanotube~1.3 nm diameter

O O

O

OO

O OO O OO OO

O

S

O

S

O

S

O

S

O

S

O

S

O

S

O

S

PO

O

The Challenge

Fabricate and combine nanoscale building blocks to make useful devices, e.g., a photosynthetic reaction center with integral semiconductor storage.

Mic

row

orld

0.1 nm

1 nanometer (nm)

0.01 m10 nm

0.1 m100 nm

1 micrometer (m)

0.01 mm10 m

0.1 mm100 m

1 millimeter (mm)

1 cm10 mm

10-2 m

10-3 m

10-4 m

10-5 m

10-6 m

10-7 m

10-8 m

10-9 m

10-10 m

Visib

le

Na

no

wo

rld

1,000 nanometers = In

frare

dUl

travio

let

Micr

owav

eSo

ft x-

ray

1,000,000 nanometers =

Zone plate x-ray “lens”Outer ring spacing ~35 nm

Office of Basic Energy SciencesOffice of Science, U.S. DOE

Version 10-07-03, pmd

The Scale of Things – Nanometers and MoreThe Scale of Things – Nanometers and More

MicroElectroMechanical (MEMS) devices10 -100 m wide

Red blood cellsPollen grain

Carbon buckyball

~1 nm diameter

Self-assembled,Nature-inspired structureMany 10s of nm

More is different!

Smaller is different!

SWANSWAN

SWAN

Subthreshold leakage is diffusion

current from S to D (as in BJT)

S= ln10 kT/q (1 + Cd/Cox)

SWANSWAN

)(1

1][ TG

c

cTODSAT VV

r

rWvCI −⎟⎟

⎠

⎞⎜⎜⎝

⎛

+−

=

( ) 20

1

2D X G T D D

WI C V V V V

Lμ

⎡ ⎤= − −⎢ ⎥⎣ ⎦

( )2

0

1

2DSAT X G T

WI C V V

Lμ

⎡ ⎤= −⎢ ⎥⎣ ⎦

( ) satvD OX G TI WC V V≈ −

SWANSWAN

Bandstructure effective mass, m*, is inversely related to curvature of bands, and depends on crystal orientation and strain.Density of states m* is related to geometric mean of bandstructure m*.

Conductivity m* is harmonic mean of bandstructure m*.

m* =31

m1* +

1m2

* +1

m3*

⎛

⎝⎜

⎞

⎠⎟

−1

=e τ

m *

m* = m1*m2

*m3*( )

13

( ) ( )212

3

2

*

4 cde

c EEh

mEg −⎟⎟

⎠

⎞⎜⎜⎝

⎛= π

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2

2

2*

dkEd

mh

Effective2 2 2

* *( ) ( ) ( )

2 2

p kE k V r V r

m m= + = +

h

SWAN

• Gapless, unless GNR• Electric field induced gap in bi-layer• Linear E(k) at K point; Dirac massless fermions

Min, Sahu, Banerjee, MacDonald, PRB (2007)

Uext=0 , Egap=0

Γ K

K′M

k space

Graphene Bandstructure Graphene Bandstructure

SWANSWAN

300

200

100

0Tunneling Conductance (10

-9Ω

-1)

-5 0 5 ( )Interlayer Voltage mV0

dIT/d

V

0

V

I. Spielman et al., Phys. Rev. Lett. 84, 5808 (2000)  

Charge-neutral superfluid: Bose-Einstein condensate of excitons! Electron-hole pairing enhanced interlayer conductance with NDR

Pseudospintronics in Bilayers at low T, high B Pseudospintronics in Bilayers at low T, high B

SWANSWAN

Atomic Levels:

Electrons in Magnetic

Field:

Electrons in Atomic Orbitals:

E0

E2

E1

E3B ħc

ħc

ħc

Electrons in a Magnetic Field: Landau Levels

(Landau levels) En = (n + 1/2) hc

c =eB

me

Macroscopic degeneracy: eB/h = 2.421010cm-2 T

SWANSWAN

Re

sist

ance

Magnetic Field

hc B

B BI

Vxy

• •

Filling factor = 2 = 1

(von Klitzing, 1980)

Quantum Hall Effect

SWAN

electron precession in magnetic field

Spin Precession Precession Starts on application of Magnetic Field B

Electron Spin

SPIN

MAGNETIC MOMENT

MAGNETIC FIELD

μ X H

mħ

11 12

21 22

H H

H H

⎛ ⎞⎜ ⎟⎝ ⎠

( )

( )z x y

x y z

B B iB

B iB B

− − −⎛ ⎞⎜ ⎟+ +⎝ ⎠

Polar angles (θ, φ)

H = - μ. B =

SWANSWAN

Quantum 2-Level Systems

cos(/2) +sin(/2) eiφ

cos(/2) +sin(/2) eiφ A B

cos(/2) +sin(/2) eiφ

top layer:

bottom layer: ↑

↓

SWAN

Pseudo-spintronic devices• Device consisting of two electron and/or hole layers in close proximity

• Inter-layer electron-electron interaction strong “layer” (pseudo-spin) degree of freedom uncertain

• Charge transport intimately determined by the dynamics of the pseudo-spin degree of freedom

zizj

wi wj

• ∏ ∏∏< <

= −−−Ψ=Ψji ji

jiji

jji wzwiwzz

,1111 )()()(~ν

= 1/2

= 1/2d ~ lB

SWAN

Intra-layer vs Inter-layer interaction

eB

hlB =

d

Einter=e2

d

Eintra=e2

lB

Eintra

Einter

d

lB=

Expect exciting physics when d/lb 1

B

B

A

eBl

o

B

256==

h

SWANQuantum Hall Effect-Counterflow transport in GaAs-AlGaAs

Vanishing counterflow longitudinal and Hall resistivities at =1 QHS Charge-neutral superfluid: Bose-Einstein condensate of excitons! Electron-hole pairing enhanced interlayer conductance

0.0 0.5 1.0 1.5 2.0 2.50

10

20

30

40

50

Vxy

I

I

Vxx

ρxx(kΩ/o)

ρxy(kΩ)

B(T)

pT=p

B=2.75?1010 cm-2

d/lB=1.3

T=30mK

0

10

20

30

40

50

4 2 ν=1

+

-

I

I

Vxx

Vxy

E. Tutuc et al., Phys. Rev. Lett. 93, 036802 (2004).

SWANSWANGraphene bilayer with excitons formed by MOS gate

Prediction of above room temperature existence of electron-hole condensate

holes in valence band

electrons in conduction band

•Room-Temperature Superfluidity in Graphene Bilayers?, • Min, Bistritzer, Su, MacDonald •How to make a bilayer exciton condensate flow,•Su, MacDonald

+

SWANBi-layer pseudoSpin Field Effect Transistor (BiSFET)

Banerjee, Register, Tutuc and Macdonald

“Bilayer pseudoSpin Field Effect Transistor (BiSFET): a proposed new logic device” S.K. Banerjee, L.F. Register, E.Tutuc, D.Reddy and A. Macdonald., IEEE EDL, accepted (2008); also patent disclosure

SWAN

0 5 10 15 20 250

1

2

VG'

ViL (mV)

I (A)

VG

BisFET simulated output characteristics as a function of interlayer bias and gate bias. VG’ puts the device in an unbalanced state, leading to lower currents

44

max

max

)/||1exp(

/)(1)(

−

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−−

+−=VVV

VVVVVGI

np

npnpo max max, exp( 10 | | /( ))oV V p n n p= − Δ −Δ +

Layer1:Electrons [n]

Inter layer bias

Many body tunneling

Layer2:Holes [p]

Bose condensation of excitons [e-h pairs]

Tc = 0.1Ef/kB; Tc = 300K implies n=p=4.9x1012 cm-2 which is possible by gating

Inter layer current

1~

F

sJ

ok

ρλ⎛ ⎞⎜ ⎟Δ⎝ ⎠

j

seGVI

λρ

h== maxmax π h

FF

F Ekk

h

eG == ;4

2

SWANInverter layout with complementary BisFETs and SPICE simulation

0

25

0

25

0 50 100 150 2000

25

Output (mV)

Input (mV)

Vsupply

(mV)

00 0

1

1 1

10 01

Time (ps)

1.0 nm EOT, gate L=10 nm, corresponding to the Josephson length, and W=20 nm. Clock frequency= 100 GHz and Vclock,peak 25 mV with 2.5 ps rise time. Input and output signals were subject to a fan-in and fan-out of 4 inverters. Current MOSFETs consume ~100 aJ per switching and 2020 “end of the roadmap CMOS will consume ~5 aJ [www.itrs.net]. Energy consumed per switching operation per BiSFET= 0.008 aJ! (2X Landauer limit)

SWAN

pGpC

nGnC

A

( )tVclock

B

C

mV 52−+

−

pGpC

nGnC

8=LW

2=LW2=

LW

pGpC

nGnC

+

−

switchV

BACmVVIf

BACmVVIf

switch

switch

•=−=

+==

,25

,0

• Clock: – Vlow = 0mV ; Vhigh= 25mV– Rise time= 2.5 ps– Fall time = 2.5 ps– Pulse width = 2.5ps– Pulse period =10 ps– Frequency of cock = 100 GHz– Delay between clock and input signal is 2.5 ps

• Maximum number of inverters the OR gate can drive: 6• Energy per operation:

– For OR GATE (load = 4 inverters) total energy for 4 operations: 133.7 x 1E-21 J

– Average Energy per operation 33.4 x 1E-21 J– For NAND GATE(load = 4 inverters) total energy for 4

operations: 121.81x1E-21 J– Average Energy per operation 30.45 x 1E-21 J

OR and NAND Gate

SWAN

0

25

0

25

0

25

0 10 20 30 400

25

Vclock

(mV)

A (mV) 0 0 1 1

B (mV) 00 1 1

Time (ps)

C (mV) 0

mVVswitch 25−=

BAC •=

NAND gate operation

SWANSWAN

The Collective FET vision

kBT/nq ~ about 25mV/n

SWAN

Graphene MOSFET Fabrication and Modeling

Carrier density in the channel induced by VTGCarrier density in the channel induced by VTG

Quantum Capacitance in GrapheneQuantum Capacitance in Graphene

VTG and carrier density, n, relationVTG and carrier density, n, relation

SWANR vs (VTG-VDirac) with model: 15nm Al2O3 Top-gated FET

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0500

1000

1500

2000

VBG

= +40 VV

BG= +10 V

VBG

= 0 VV

BG= - 10 V

R R R R R R R R R Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1 Fit Curve 1

Resistance

(Ω)

VTG-V

DIRAC(V)

Parameters Extracted Values

n0 (cm-2) 3.19– 4.28 x 1011

Mobility (cm2/Vs)

4,434- 6,190

Rcontact (ohm) 552 - 1579

Thinner dielectric layer

lower remote charge impurities in oxide

Lower initial carriers less carrier scattering

Higher mobility

Mobility independent of T

Thinner dielectric layer

lower remote charge impurities in oxide

Lower initial carriers less carrier scattering

Higher mobility

Mobility independent of T

60 80 100 120 140 160 180 200 220 240 260 280 300 3200

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Mobility (cm

2/Vs)

Temperature (K)

God made solids; surfaces on the other hand are the work of the devil. (Pauli)

SWAN All Graphene Electronics

DARPA Carbon Era Rf Applications (CERA) program with IBM

LNA, interconnects, …

SWAN

Tight Binding Model of Graphene

Nearest neighbor (NN) tight binding Hamiltonian:

, for NN, 0 otherwise. self-consistent potential.

ij ij i ijH tN qφδ= −1ijN =

iφPerfect armchair graphene ribbon showing equal no. of atoms in successive slices.

Corresponding band structures:

No. of atoms in the slice = 7, 8 and 9

SWAN

T(E) vs. E [different roughness (identical Wch)]

T(E) vs. E for a 7.63 nm wide graphene channel having different roughness. r = 0.5 » random, r = 1 » perfect.

SWAN

A=0

Precession of phase+ C

Phasetronics: AB device with Rashba Effect Register, Banerjee

Phasetronics: AB device with Rashba Effect Register, Banerjee

x

B=0

EX OR Gate

A=0, B=0 C=0

A=0, B=1 C=1

A=1, B=0 C=1

A=1, B=1 C=0

State 0: Electron transmission is suppressed State 1: Electron transmission is permitted

SWANResonant Injection Enhanced Field-Effect Transistor

Patent disclosure, Register, Banerjee

SWAN

ON/OFF states of RIEFET

ON state (Vg=150mV in following examples):

The multiple quantum-wells below the gate serve as a nearly transparent high-order band pass filter for electrons;

OFF state (Vg=0mV):

The gate not only raises the channel potential directly beneath the gate relative to the source, but destroys the inter-well resonances and reduce access to the channel even for electrons with sufficient thermal energy.

Energy levels of quantum states

Energy levels of quantum states

Aligned

Misaligned

Transport direction

Transport direction

Top gate

Top gate

SWANSpintronics- Datta-Das Transistor

Electrons quantum mechanically can be viewed as a spinning top which can point “up” or “down”!

SWAN

1 10 0

A

B

C

Out

-11 10

Binary wire

InverterMajority gate

MA

B

C

Programmable 2-input AND or OR gate.

Nanomagnet-Based Logic- MQCAWolfgang Porod and Gary Bernstein, Univ. Notre Dame

SWAN

ITRS, 2005

SWANWhat is needed in the new switch?

Speed = CV/I

Active Power = CV2f

Stand-by Power = Sub-VT, gate leakage

Desirable Attributes

•Energy efficiency

•Speed (performance, noise)

•Room T operation (non-equilibrium devices?)

•Size (device/ wafer): capacitance, fan-out

•Gain; uni-directional signal flow (I/O isolation)

•Reliability, manufacturability, cost

•CMOS compatibility (process, topology)

CMOS CMOS caca 2020 2020Energy ~ 10 aJ/op; power~ 10Energy ~ 10 aJ/op; power~ 1077 W/cm W/cm22

Speed ~ 0.1 ps/op (10 THz fSpeed ~ 0.1 ps/op (10 THz fTT; 100 GHz circuit); 100 GHz circuit)Size ~ LSize ~ Lgg 5 nm; cell ~ 100 nm, I 5 nm; cell ~ 100 nm, IDNDN~ 3 mA/~ 3 mA/µµmmDensity ~ 10Density ~ 101010 cm cm-2-2; BIT ~100 GBit/ns/cm; BIT ~100 GBit/ns/cm22

Cost ~ 10Cost ~ 10-12-12 $/gate $/gate

0.01 aJ/op

100GHz

Yes

10 nm, FO=4

???

Yes

???