Nanoelectronic Transport Basics

Bhaskaran Muralidharan Department of EE, IITB

22/02/2016

School on electronic transport and magnetism

HRI Allahabad

The Building block of digital age

S D

Nanoelectronics

How far can we scale transistors?

New physics emerges at these lengthscales

CHARGE Spin

Energy

Emerging Electronics Landscape

Charge is only the beginning!

Outline of this workshopPart I: Nanoscale charge transport and low dimensional systems Theory: B. Muralidharan - basics A Ghosh -basics S Datta- overview of lessons on nanoelectronics !Modeling and simulation: A Ghosh – predictive modeling S Mahapatra – predictive modeling A Sengupta – predictive modeling + demo !Experiments: T. Kalarikkad – low dimensional conductance K Dasgupta – 2 D systems and quantum Hall effect S Lodha – 2 D Systems K Majumdar – 2 D systems !Part II: Nanomagnetism and Spintronics P Majumdar - Magnetism P Sen – Magnetism K Raman – Spin devices and molecular spintronics A Tulapurkar- Spin devices and spin transport S Bandyopadhyay – Frontiers of spintronics !Part III: Nano-energy S. D. Mahanti – Thermoelectric energy conversion B. Muralidharan – Thermoelectric energy conversion !Part IV: Frontier topics B. Muralidharan – Information viewpoint of transport S. Ganguly – Bio memetics

!

Modeling device electronics

Bulk Solid (“macro”) (Classical Drift-Diffusion)

~ 1023 atoms

Bottom Gate

Source

Channel

Drain

Clusters (“meso”) (Semiclassical Boltzmann Transport)

80s ~ 106 atoms

Molecules (“nano”) (Quantum Transport)

Today ~ 10-100 atoms

(“Traditional Engg”)

(“Nano Engg”)

Nanoelectronics: New Paradigms and Possibilities

8

Part 1: Key concepts: !•Elastic resistor model, basic concepts of current flow, role of contacts, ballistic transport basics !

•Bottom up view point, Landauer approach, connection with diffusive transport, Concepts regarding conductivity !

•Role of electrostatics, case of nano transistor, drift-diffusion, Boltzmann transport formalism

Bottom up view point of transport

Drift Diffusion

Quantum theory

Quasi-Ballistic/Ballistic

( )∫∞

∞−

−Ξ= )()()( EfEfEdEI DS

“Top Down” … (EE 620/normal way of thinking)

Vd20 µm

Vd

2 nm

Solid State Electronics/ Mesoscopic Physics

Molecular Electronics

“Bottom Up” ... (EE 724)

Vd20 µm

Vd

2 nm

Solid State Electronics/ Mesoscopic Physics

Molecular Electronics

Bottom Up fabrication

Build pyramidal quantum dots from InAs atoms (Gerhard Klimeck, Purdue)

Bottom up architecture Chepren Pyramid, Giza (2530 BC)

Full quantum theory of nanodevices !• Carbon nanotubes, Graphene • Atomic wires, nanowires, • Point contacts, quantum dots, • thermoelectrics, • molecular electronics • Single electron Transistors (SETs) • Spintronics

Bottom up view point of transport

Diffusive

Quantum theory

0.1 mm !10 µm !1 µ m !0.1 µm !10 nm !1 nm !0.1 nm

Macroscopic dimensions

Atomic dimensions

��

€

γ /h

qVD(E)

€

µ2,T2

€

µ1,T1

�2/)()()( EEDE γ→Ξ

hEMLEvEDE /)(2/)()()( ≡→Ξ

22 /)()()()( LEEvEDE τ→Ξ

Anatomy of Nano-Devices: Point to Point

0µ1µ 2µ

Contacts/Leads Source/Drain electrodes

Channel

e-e-

Dynamics+ Dissipation

A possible evolution path?

Strained Si, SiGe (µ ~ 270cm2/Vs)

Bottom Gate

Source DrainTop Gate

Channel

15 nm

CNTs (µ ~ 10,000cm2/Vs) Hard to align into a circuit!

VG VD

INSULATOR

DRAIN

SOURCE

I

< 10 nm

Silicon Nanowires (Low µ < 100 cm2/Vs)

5 nmOrganic Molecules ?

(Reproducibility/ Gateability)

2 nm

Quantum transport: •Schoedinger equation, Hamiltonian, density of states, basic semiconductor physics from quantum mechanical viewpoint !•Examples of equilibrium calculations: concept of band structure, quantum wells, nanowires, carbon nanotubes, graphene, electrostatics, quantum capacitance !•Non-equilibrium transport: elastic resistor model re-visited from quantum transport perspective, introducing “contacts” to the Schroedinger equation, Green’s functions, self-energy, Non-equilibrium Green’s function (NEGF) formalism !•Application of the NEGF formalism to concrete examples: a) molecular electronics, b) nanowire transport, c) resonant tunnelling diodes

Nanoscale Devices: DOS determines everything!

( )∫∞

∞−

−Ξ= )()()( EfEfEdEI DS

�/γ

qVD(E)

€

µ2,T2

€

µ1,T1

Transport Function

Driving Force

DSDSqV µµ −=

I

V

Quantum Transport: DOS is the main thing!

��

€

γ /h

qVD(E)

€

µ2,T2

€

µ1,T1

S D S D

Effective mass + Poisson Equation

Tight Binding + Poisson Equation

Semi-empirical /Ab initio

The material ‘zoo’ !!

Strained Si, SiGe (µ ~ 270cm2/Vs)

Bottom Gate

Source DrainTop Gate

Channel

15 nm

CNTs (µ ~ 10,000cm2/Vs) Hard to align into a circuit!

VG VD

INSULATOR

DRAIN

SOURCE

I

< 10 nm

Silicon Nanowires (Low µ < 100 cm2/Vs)

5 nmOrganic Molecules ?

(Reproducibility/ Gateability)

2 nm

24

Molecular ElectronicsAviram-Ratner Diode: an acceptor-bridge-donor molecule Chem.Phys.Lett. (1974) 29, 277.

1. Electrode charge-injection to donor 2. Donor-Acceptor ET 3. Acceptor-electrode charge-injection

A molecular rectifier

Quantum Transport

��

€

γ /h

qVD(E)

€

µ2,T2

€

µ1,T1

S D S D

Effective mass + Poisson Equation

Tight Binding + Poisson Equation

Semi-empirical /Ab initio

CHARGE Spin

Energy

Part III: Charge Spintronics

Charge + SPIN degree of freedom

SPINTRONICS

Spintronics

Brief History

SV/MTJ DW NLSV QD

BUILDING BLOCKS

ULTRAFAST MAGNETIZATION DYNAMICS

SPINTRONIC INTERONNECTS

LOGIC MEMORY

BUILDING BLOCKS

Nanomagnetic logic

• Energy-efficient • Non-volatile • Fast • Radiation resistant

GMR technology

MRAM: Reading/writing process

Spin transfer torque (STT)

Future MRAM Improvements

Spin Torque Transfer !• No applied magnetic field

• Utilizes heavily spin polarized current • The magnetization of nano-elements is flipped back and forth • Still has challenges in basic physics and materials to overcome

MTJ DW NLSV QD

BUILDING BLOCKS

ULTRAFAST MAGNETIZATION DYNAMICS

SPINTRONIC INTERONNECTS

LOGIC MEMORY

CHARGE Spin

Energy

Part IV: Charge + Energy

Energy transport: •Introduction to nanoscale energy conversion devices, basics of thermoelectrics and photovoltaics !•Thermoelectric transport, energy conversion efficiency, low dimensional thermoelectrics !•Energy, entropy and heat currents, connection with second law

Nanocaloritronics Energy Conversion at nanoscale!

Electronic Maxwell’s demon

Batteries, Fuel cells and Nano-heat engines

Battery Operation Schematic

1µ 2µ

0µ

Active Region

Electrodes

fuel!cell

H2OO2H2

heat

work

Battery Operation Basics

Electrolysis (Chemistry)

fuel!cell

H2OO2

H2

heat

work

The familiar process of electrolysis requires work to proceed, if the process is put in reverse, it should be able to do work for us spontaneously. !The most basic “black box” representation of a fuel cell in action is shown below:

Figure 2

Battery Operation Basics

Electrolysis (Chemistry)

Figure 3

Battery Operation Basics

Fuel cells: Putting all together!

Figure 3

Battery Operation Basics

Some types!

What is the connection with nanoelectronic devices?

RECALL: Anatomy of Nano-Devices

0µ1µ 2µ

Contacts/Leads Source/Drain electrodes

Channel

e-e-

I

V

0=ΔT I

V

0>ΔT

Sapp VV =

Nanoscale Devices/Heat Engines?

00

≤Δ−Δ=Δ

≥Δ

STEFStot

1µ 2µ

MsappQ

nnn

JT

JVT

JT

S

JFS

TSEFHMNpVTSE

µ

µ

Δ−−Δ=

=

−=

++−=

∑11)1(�

�

21

2211 0NNNN

−=

≥+ µµ

12

2

2

1

1

NNT

ET

E

−=

−≥

− µµOnsager-Callen theory

1µ 2µ

T1 T2

50

POWER GENERATION: USING SEEBECK EFFECT REFRIGERATION:

USING PELTIER EFFECT

• Discovered in early 1800s –Seebeck and Peltier !

• Theory by Onsager-Callen -1930s !• Practical energy conversion ideas after 1950s—Ioffe !• Nanoscale energy conversion –after 2000s!

Thermoelectric energy conversion

Thermoelectric applications

T_H T_CV

TE

MacroscopicSeebeck effect

C H

I

TE

Peltier effect

T_H T_C

Ef

Seebeck effectMicroscopic

D(E)

C H

Peltier effect

Electron Engineering: Microscopic viewpoint

• Asymmetry in DOS results in a better TE material • Barriers create better TE cooling systems

What nano-world does?

• Distort ing the smooth DOS- DOS engineering !• Superlattices – Electron filtering

Engineering the Nanoscale-Basics

• Hicks and Dresselhaus: Sharp features in DOS (quantum wells, wires) would enhance zT due to energy filtering

• Sofo and Mahan: Delta-like DOS best for reaching Carnot efficiency

Hot Contact Cold Contact Channel

54

• Hicks and Dresselhaus: Sharp features in DOS (quantum wells, wires) would enhance zT due to energy filtering

• Sofo and Mahan: Delta-like DOS best for reaching Carnot efficiency

Hot Contact Cold Contact Channel

55

Engineering the DOS-Basics

• Hicks and Dresselhaus: Sharp features in DOS (quantum wells, wires) would enhance zT due to energy filtering

• Sofo and Mahan: Delta-like DOS best for reaching Carnot efficiency

Hot Contact Cold Contact Channel

56

Engineering the DOS-Basics

Modeling device electronics

Bulk Solid (“macro”) (Classical Drift-Diffusion)

~ 1023 atoms

Bottom Gate

Source

Channel

Drain

Clusters (“meso”) (Semiclassical Boltzmann Transport)

80s ~ 106 atoms

Molecules (“nano”) (Quantum Transport)

Today ~ 10-100 atoms

EE 620 (“Traditional Engg”)

ECE 724 (“Nano Engg”)

Bottom up view point of transport

Diffusive

Quantum theory

0.1 mm !10 µm !1 µ m !0.1 µm !10 nm !1 nm !0.1 nm

Macroscopic dimensions

Atomic dimensions

��

€

γ /h

qVD(E)

€

µ2,T2

€

µ1,T1

�2/)()()( EEDE γ→Ξ

hEMLEvEDE /)(2/)()()( ≡→Ξ

22 /)()()()( LEEvEDE τ→Ξ