University of Notre DameCenter for Nano Science and Technology Gregory L. Snider Department of Electrical Engineering University of Notre Dame Nanoelectronic

University of Notre Dame Center for Nano Science and Technology

Gregory L. SniderDepartment of Electrical Engineering

University of Notre Dame

Nanoelectronic Devices


What are Nanoelectronic Devices?

A rough definition is a device where:

• The wave nature of electrons plays a significant

(dominant) role.

• The quantized nature of charge plays a significant

role.


Examples

• Quantum point contacts (QPC)

• Resonant tunneling diodes (RTD)

• Single-electron devices

• Quantum-dot Cellular Automata (QCA)

• Molecular electronics (sometimes not truly nano)


References

• Single Charge Tunneling, H. Grabet and M. Devoret, Plenum

Press, New York, 1992

• Modern Semiconductor Devices, S.M. Sze, John Wiley and Sons,

New York, 1998

• Theory of Modern Electronic Semiconductor Devices, K. Brennan

and A. Brown, John Wiley and Sons, New York, 2002

• Quantum Semiconductor Structures, Fundamentals and

Applications , C. Weisbuch and B. Vinter, Academic Press, Inc.,

San Diego, 1991


When does Quantum Mechanics Play a Role?

W & V, pg. 12, Fig. 5


More Realistic Confinement

W & V, pg. 13, Fig.6


Quantum Point ContactsOne of the earliest nanoelectronic devices QPCs depend on ballistic, wave-like transport of carriers through a constriction.

In the first demonstration surface split- gates are used to deplete a 2D electron gas. The confinement in the constriction produces subbands.


Quantized Conductance

When a bias is applied from source to drain electrons travel ballisticly.Each spin-degenerate subband can provide 2e2/h of conductance.

Va Wees, PRL 60, p. 848, 1988


What About Temperature?Thermal energy is the bane of all nanoelectronic devices.

As the temperature increases more subbands become occupied, washing out the quantized conductance.

T2 > T1

All nanoelectronic devices have a characteristic energy that must be larger than kT


Resonant Tunnel DevicesIn a finite well the wavefunction penetrates into the walls, which is tunneling

€

ψn (z) ≈ e−κ n zIn the barrier:

€

κn =2m(Vo − En )

hwhere

Transmission through a single barrier goes as:

€

T ≈ e−2κ nLB


Two Barriers

Semiclassically a particle in the well oscillates with:

€

vz =hkzm

It can tunnel out giving a lifetime n and:

€

ΔEn =h

τ n

Now make a particle incident on the double barrier:

If Ei ≠ En then T = T1T2 which is small


If Ei = En then the wavefunction builds in the well, as in a Fabry-Perot resonator:

€

T(E i = En ) =4T1T2

(T1 + T2)2

Which approaches unity for T1 = T2:


In Real Life!Things are, of course, more complicated:

- No mono-energetic injection- Other degrees of freedom

In the well:

€

E = En +h2k⊥

2

2m*

In the leads:

€

n3D (E) = η 3D (E)dE

expE − EF

KT

⎛

⎝ ⎜

⎞

⎠ ⎟

∫

€

η3D (E) =(2m*)3 / 2

2π 2h3E1/ 2

€

J =q

2πhN(E z)T(E z)dE z∫ where

€

N(E z) =kTm *

πh2ln 1+ exp

EF − E zkT

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟


In k Space No One Can Hear You Scream!

For Transmission:

€

kzo =2m * (Eo − Ec

L )

h

To get through the barriers electrons must have E > Ec but must also have the correct kz. Only states on the disk meet these criteria.


J is proportional to the number of states on the disk, and therefore to the area of the disk:

€

Area = πR2 = π kF2 − kzo

2( )

€

⇒ J ∝ kF2 − kzo

2 ∝ EFL − Ec

L( ) − Eo − Ec

L( ) = EF

L − Eo

€

∴ J ∝V

EcL is above Eo, so no

states have the correct kz

Note: we have ignored the transmission probability


ScatteringScattering plays an important but harmful role, mixing in-plane and perpendicular states

B&B p236


Single Electron DevicesThe most basic single-electron device is a single island connected to a lead through a tunnel junction

The energy required to add one more electron to the island is:

EC = e2

2C This is the Charging Energy

If EC > kT then the electron population on the island will be stable. Usually we want Ec > 3-10 times kT. For room temperature operation this means C ~ 1 aF.


If the temperature is too high, the electrons can hop on and off the island with just the thermal energy. This is uncontrollable.

An additional requirement to quantize the number of electrons on the island is that the electron must choose whether it is on the island or not.

This requires RT > RK

Where RK = h/e2 ~ 25.8 kΩ

Usually 2-4 times is sufficient


What is an Island?

• Anywhere that an electron wants to sit can be used as an island– Metals– Semiconductors

• Quantum dots• Electrostatic confinement


Single Electron Box

Assume a metallic island

The energy of the configuration with n electrons on the island is :

E(n) = (ne - Q)2

2(Cs + Cj)

Q = Cs U


At a charge Q/e of 0.5 one more electron is abruptly added to the island.

What does it mean to have a charge of 1/2 and electron?


Single - Electron Transistor (SET)

Now the gate voltage U can be used to control the island potential. The source - drain Voltage V is small but finite.

When U=0, no current flows.

Coulomb Blockade

When (CGU)/e = 0.5 current flows.

Why?

One more electron is allowed on the island.


These are called Coulomb blockade peaks.

Is the peak the current of only one electron flowing through the island?

No, but they flow through one at a time!


What about Temperature?

G&D p181

As the temperature increases the peaks stay about the same, while the valleys no longer go to zero. This is the loss of Coulomb blockade. Finally the peaks smear out entirely.

This shows the classical regime, such as for metal dots. In semiconductor dots resonant can cause an increase in the conductance at low temperatures (the peak values increase).


SET Stability DiagramYou can also break the Coulomb blockade by applying a large drain voltage.


Ultra-sensitive electrometers

Dot Signal

Add an electron

Lose an electron

GD GE

VG VE

dot electrometer

Sensitivity can be as high as 10-6 e/sqrt(Hz)


Single Electron Trap

G&D p123

This non-reversible device can be used to store information.


Single Electron Turnstile

G&D p124

This is an extension of the single electron trap that can move electrons one at at time


Turnstile Operation

G&D page 125Why does it need to be non-reversible?

Can this be used as a current standard?

Issues:Co-tunnelingMissed transitionsThermally activated events


Single Electron Pump

G&D p128Here there are two coupled boxes, and an electron is moved from one to the other in a reversible process.

Same Issues:Missed transitionsThermally activated eventsCo-tunneling


e-

Vg

SET

Con

duct

ance

Vg

• Nanometer scaled movements of charge in insulators, located either near or in the device lead to these effects.

• This offset charge noise (Q0) limits the sensitivity of the electrometer.

Background charge effect on single electron devices


Background charge insensitive single electron memory

A bit is represented by a few electron charge on a floating gate.

SET electrometer used as a readout device.

Random background charge affects only the phase of the SET oscillations.

The FET amplifier solves the problem of the high output impedance of the SET transistor.

K. K. Likharev and A. N. Korotkov, Proc. ISDRS’95


Plasma oxide – fabrication technique

A

To diffusion pump

Gas inlet


Plasma oxide device

• Two step e-beam lithography on PMMA/MMA.

• Oxidation after first step in oxygen plasma formed by glow discharge.

• Oxide thickness characterized by VASE technique.

CG FG

Ground

BG

SET

• 6 nm of oxide grown after 5 min oxidation in 50 mTorr oxygen plasma at 10 W.


Hysteresis Loops

• SET conductance monitored on the application of a bias on the control gate.

• A back gate bias cancels the direct effect of the control gate on the SET.

• The change in the operating point of the SET is due to electrons charging and discharging the floating gate.


on=“1”

Zuse’s paradigm• Konrad Zuse (1938) Z3 machine

– Use binary numbers to encode information

– Represent binary digits as on/off state of a current switch Telephone

relay Z3 Adder

The flow through one switch turns another on or off.

Electromechanicalrelay

Exponential down-scaling

Vacuum tubes Solid-state transistors CMOS IC

off=“0”


Problems shrinking the current-switch

Electromechanicalrelay

Vacuum tubes Solid-state transistors CMOS IC

New idea

Valve shrinks also – hard to get good on/off

Current becomes small - resistance becomes high Hard to turn next switchCharge becomes quantized

Power dissipation threatens to melt the chip.

Quantum Dots


New paradigm: Quantum-dot Cellular Automata

Revolutionary, not incremental, approach

Beyond transistors – requires rethinking circuits and architectures

Represent information with charge configuration.

Zuse’s paradigm• Binary• Current switch • Charge configuration


Quantum-dot Cellular Automata

Represent binary information by charge configuration

A cell with 4 dots

Tunneling between dots

Polarization P = +1Bit value “1”

2 extra electrons

Polarization P = -1Bit value “0”

Bistable, nonlinear cell-cell response

Restoration of signal levels

Robustness against disorder

cell1 cell2

cell1 cell2

Cell-cell response function

Neighboring cells tend to align.Coulombic coupling


Variations of QCA cell design

4-dot cell 2-dot cell 5-dot cell 6-dot cell

Middle dot acts as variable barrier to

tunneling.

Indicates path for tunneling


Clocking in QCA

0 1

0

en

erg

y

xClock

Small Input Applied

Clock Applied

Input Removed

but Information is preserved!

0

Keyes and Landauer, IBM Journal of Res. Dev. 14, 152, 1970


Quasi-Adiabatic Switching• Clocking Schemes for Nanoelectronics:

•Keyes and Landauer, IBM Journal of Res. Dev. 14, 152, 1970•Lent et al., Physics and Computation Conference, Nov. 1994•Likharev and Korotkov, Science 273, 763, 1996

• Requires additional control of cells.• Introduce a “null” state with zero polarization which encodes no

information, in contrast to “active” state which encodes binary 0 or 1.

Clocking achieved by modulating energy of third state directly (as in metallic or molecular case)

P= +1 P= –1 Null State

Clocking achieved by modulating barriers between dots (as in semiconductor dot case)

Clocking signal should not have to be sent to individual cells, but to sub-arrays of cells.


Power Will Be a Limiter

5KW 18KW

1.5KW 500W

40048008

80808085

8086286

386486

Pentium®

0.1

1

10

100

1000

10000

100000

1971 1974 1978 1985 1992 2000 2004 2008

Pow

er

(Watt

s)

Microprocessor power continues to increase exponentially

Power delivery and dissipation will be prohibitive !

P6

Transition from NMOS to CMOS

Source: Borkar & De, IntelSlide author: Mary Jane Irwin, Penn State University


Power Density will Increase

40048008

8080

8085

8086

286 386 486Pentium®

P6

1

10

100

1000

10000

1970 1980 1990 2000 2010

Pow

er

Den

sit

y (

W/c

m2)

Hot Plate

Nuclear

Reactor

Rocket

Nozzle

Power densities too high to keep junctions at low temps

Source: Borkar & De, Intel

Sun’s

Surface

Slide author: Mary Jane Irwin, Penn State University


QCA power dissipation

QCA architectures can operate at densities above 1011 devices/cm2 without melting the chip.

QCA Operation Region


0 01 1

01 10

A

B

C

Out

Binary wire

InverterMajority gate

MABC

Programmable 2-input AND or OR gate.

QCA devices


Metal-dot QCA implementation

“dot” = metal island70 mK

electrometers

Al/AlO2 on SiO2

Metal tunnel junctions

1 µm


Tunnel junctions by shadow evaporation

First aluminum depositionOxidation of aluminumSecond aluminum depositionThin Al/AlOx/Al tunnel junction


Metal-dot QCA cells and devices

• Demonstrated 4-dot cell

A.O. Orlov, I. Amlani, G.H. Bernstein, C.S. Lent, and G.L. Snider, Science, 277, pp. 928-930, (1997).

Input Double Dot

(1,0) (0,1)

Switch Point

Top Electrometer

Bottom Electrometer


Switching of 4-Dot Cell


Majority Gate

MABC

Amlani, A. Orlov, G. Toth, G. H. Bernstein, C. S. Lent, G. L. Snider, Science 284, pp. 289-291 (1999).


QCA Latch Fabrication


Gtop

Gbotelectrometers

VIN+

VIN–

VCLK

QCA Clocked Latch (Memory)


QCA Shift Register

Gtop

Gbotelectrometers

VIN+

VIN–

VCLK1 V

CLK2


Fan-Out

Vin+

Vin–

VClock1

VClock2

VClock2


From metal-dot to molecular QCA

“dot” = metal island70 mK

Mixed valence compounds

“dot” = redox center

Metal-dot QCA established proof-of-principle.but …low T, fabrication variations

Molecular QCA: room temp, synthetic consistency

room temperature+

Metal tunnel junctions


Charge configuration represents bit

“1”

isopotential surface

“0”

Gaussian 98 UHF/STO-3G

HOMO


Double molecule

Considered as a single cell, bit is represented by quadrupole moment.

Alternatively: consider it a dipole driving another dipole.


“0”

HOMO Isopotential (+)

“1”

Double molecule


Core-cluster molecules

Five-dot cell


Core-cluster moleculesTheory of molecular QCA bistability Allyl group

Variants with

“feet” for surface bindingand orientation


Electron Switching in QCAMetal Dots

Measure conductance

Molecular Dots

Measure capacitance

C

Voltage


Electron Switching Demonstration

Capacitance peaks correspond to “click-clack” switching within the molecule

JACS 125, 15250-15259, 2003


Clocked molecular QCA


Summary

• QCA may offer a promising paradigm for nanoelectronics– binary digits represented by charge configuration – beyond transistors– general-purpose computing– enormous functional densities– solves power issues: gain and dissipation– Scalable to molecular dimensions

• Single electron memories represent the ultimate scaling

Documents

University of Notre DameCenter for Nano Science and Technology Gregory L. Snider Department of Electrical Engineering University of Notre Dame Nanoelectronic