a novel spm system for determining quantum electronic

A Novel SPM System for Determining Quantum

Electronic Structure at the Nanometer-scale

Joseph A. Stroscio, NIST Fellow

Electron Physics Group

2011 Nanoelectronics Metrology, May 25, 2011

Presentation Outline

2

B

Microscopy Honeycomb Lattices Magnetic Fields

Graphene“Quartet” Graphene Devices

Some History of Microscopy

Occhiolino “Little Eyes” – 16th Century

First microscope was the optical microscope

Compound microscopes end of 16 century

Galileo Galilei's compound microscope in 1625

Occhiolino “Little Eyes”

3

18th century microscopes

Musée des Arts et Métiers, Paris http:/www.eatechnology.com

Wikipedia

Some History of Microscopy: Scanning Tunneling

Microscope a “Quantum” Microscope

Invented by Gerd Binnig and Heinrich Rohrer in 1981

Nobel Prize in Physics in 1986 with Ersnt Ruska (electron microscope)

4

Quantum Mechanical Tunneling

Distance

Current

2 dI e

from Wikipedia

Scanning Tunneling Microscopy

A “Quantum” Microscope

STM is an electron probe, sensitive to the energy resolved

local density of electron states (LDOS) – seeing in “color”

5

2

( , ) ( , )

( , ) ( ) ( )

( , )

F

F

E V

t

E

t t

t

I r E T E V dE

r E r E E

dIr E

dV

J. A. Stroscio, R. M. Feenstra, and A. P. Fein, PRL

57, 2579 (1986)

R. M. Feenstra, J. A. Stroscio, J. Tersoff, and A. P.

Fein, PRL 58, 1192 (1987)

GaAs(110)

,B ,Vg

Evolution of Cryogenic Scanning Tunneling

Microscopes

6

Exponential tunneling transmission selects out the last

atom on the probe tip

Allows to “see”, “feel”, and “hear” in the nanometer

scale world

Evolution of Cryogenic Scanning Tunneling

Microscopes

Desire stability and higher energy resolution

Resolution limited by the thermal Fermi-Dirac

distribution ~ 3kBT

Solution: Go to lower temperatures

Not so easy!

7

1990

1981

2004

2010

T = 4 K T = 295 K

T = 0.6 K

T = 10 mK

Competing Requirements to Achieve High

Resolution at Low Temperatures

Tunneling current changes by x10 with 1 Å change

< 1 picometer displacement fluctuation is required

Isolate from the environment to achieve small

fluctuations

Poor thermal transport

Bond strongly to environment to achieve good thermal

contact

Poor isolation

Solution is to do both!

8

Developing High-Energy Resolution SPM

Measurements

9

Processing Lab

ULTSPM Lab at NIST

Stage 1

Stage 2

Stage 3

Vibration Isolation


Measurements

Refrigeration to 10 mK using 3He-4He mixture

10

Magnet

IVC

UHV

≈700 mK

STILL

Shield ≈50 mK

ICP

Shield

STM

Silver rods

Mixing

Chamber

≈10 mK3He dilute

3He rich

STILL

3He Pumping

Station

3He

Pump

4LHe

1K pot

3He

Z3 Z1

Z2

E3 E1

E2

E4

E5

Comp

3He-4He Gas Handling System

(GHS)

1.5 K

4 K

700 m K

50 mK

10 m K

Vladimir Shvarts

Zuyu Zhao Y. J. Song et al. RSI (2010)


Measurements

11

Young Jae Song

Alexander F. Otte

Young Kuk

Joseph A. Stroscio


Measurements

Excellent performance down to lowest temperatures

JT is better than 1K pot

Z noise < 1 pm Hz1/2

I noise < 100 fA Hz1/2

12

Y. J. Song et al. RSI (2010)

Er atoms on CuN

8 nm

Graphene/SiC

5 nm

T=13 mK


13

B



From Honeycombs to the Dirac Hamiltonian

Graphene – Light-like Electrons

14

Savage, N., "Researchers pencil in graphene

transistors." IEEE Spec. 45, 13 (2008).

From Pencil Drawings to High Speed Transistors to iPAD?

Or Galaxy Tab?

IBM and HRL

GHz Transistors

Nature Nanotech. (2010) SKKU, Korea

New Materials and State Variables

Graphene, TIs; Spin and Pseudo-Spin as State Variables

Electron spin

Graphene sub-lattice pseudo-spin

Graphene bilayer – layer pseudo-spin

Topological Insulator – spin locked to momentum

15

Graphene Dirac Fermions

Graphene Basics

16

Top View (real space)

Carbon with 4 valence electrons

Two atom basis in the unit cell

→ pseudo-spin


17

Figure from droid-life.com

kx

ky

Ener

gy

Figure from P. Kim

Wallace (1947)

kx' ky'

K K’

Energy is linear with

momentum massless particles


Low Energy Expansion: Dirac Hamiltonian

18

y

x

Real space: For behavior away from Dirac point, make an expansion:

Paul Dirac

4

0, ,3

y xK K K k ka

kx' ky'

E

/2

, /2

3

2

0

0

1 ( )

2

arctan

F nn

x y

F F

x y

i

F i

x

y

av

k ikH v v

k ik

eE v k

e

k

k

k

k

K

K

k

σ k

k

Reciprocal space:

The Independent Two Valleys

19

kx' ky'

E

kx' ky'

E

K

K’

0

0

x y

F

x y

k ikH v

k ik

K

0

0

x y

F

x y

k ikH v

k ik

K

Leads to additional degeneracy

Consequences of Dirac Hamiltonian

Pseudo-spin; reduced

backscattering

20

kx' ky'

E

Klein tunneling;

transmission through

potential barriers

Katsnelson et al. Nature Physics 2006


21

B



Geim & Novoselov Nature 2007

Landau Quantization in Graphene

Cyclotron motion in a magnetic field

Quantized orbits and energy levels

22

“Standard” Landau level spacing Graphene Landau level spacing

10 K@10 T

1000 K@10 T

Relativistic:

2sgn( ) 2nE n e c n B

Standard Model:

*( 1/ 2)n

eE E B n

m

Lev Landau

1908 - 1968

B

Scattering in the graphene

landscape

Effects of disorder and

interactions

http://upload.wikimedia.org/wikipedia/en/5/52/Lev_Davidovich_Landau.jpg

Landau Quantization in Graphene

The Graphene Quartet

23

Four-fold degenerate

due to spin and valley

symmetries

STS provides direct

measure of energy gaps

and interaction effects

STS vs Transport Measurements

STS

24

http://en.wikipedia.org/wiki/Quantum_Hall

Wide energy spectrum

Localized states in the

mobility gaps

Spatial properties of

extended and localized

states

Energy gaps when

degeneracies are lifted

Correlation effects

Transport

http://en.wikipedia.org/wiki/Quantum_Hall


25

B



Epitaxial Graphene on C-face SiC – Weak Disorder

26

C-Face termination

Si-Face termination

SiC SiC

4 - 100 ML

1 - 5 ML

(0001)

(0001)

Graphene layers

n~1012/cm2

n~1010/cm2

E

E

SiC

Induction Furnace Method

J. Hass et al., PRL 100, 1255504 (2008) Berger et al., J. Phys. Chem B 108, 19912 (2004) Berger et al., Science 312, 1191 (2006) de Heer et al., Sol. St. Commun., 143, 92 (2007)

Magnetic Quantization C-face Graphene at 4K

Direct measurement of graphene quantization

Weak disorder

27

Quantization obeys

graphene scaling

Full quantization of DOS

into Landau levels

Very sharp LLs

High mobility

-300 -200 -100 0 100 200 300

0

1

2

3

4

5

dI/

dV

(nS

)

Sample Bias (meV)

B= 5 T

-7-6-5

-4

-3

-2 -1

n=0

12

3 4 56

7

D. L. Miller, et al., Science 324, 924 (2009).

Resolving the Graphene Quartet

Tunneling Spectroscopy at ~10 mK

28

0 2 4 60

100

200

300

-200 -100 0 100 200

0

10

20

30

Linear Fit

B=2 T

B=3 T

B=4 T

EN-E

0 (

meV

)

(NB)1/2

N=1

B=0 T

B=2 T

B=3 T

B=4 T

dI/d

V (

nS

)

Sample Bias (mV)

N=0

Zero field Dirac point is at -125 meV

indicating a doping of ~1 x 1012 cm-2

Graphene on C-face SiC

Y. J. Song et al. Nature (2010)



29


-25 -20 -15 -10 -5 0 5-1

0

1

2

3

4

5

dI/d

V (

nS)

Sample Bias (mV)

B = 11.5 T

-200 -100 0 100 200

0

1

2

3

dI/d

V (

nS

)

Sample Bias (mV)

B= 2 TN=1

Weak disorder in graphene

on C-face SiC allows fine

features to be observed

ΔVrms = 1 mV

ΔVrms = 50 μV



30


-25 -20 -15 -10 -5 0 5-1

0

1

2

3

4

5

dI/d

V (

nS)

Sample Bias (mV)

B = 11.5 T




ΔVrms = 50 μV

Smaller peak separation

– electron spin?

0 2 4 6 8 10 12 140.0

0.5

1.0

1.5

2.0

E

S(m

eV

)

Magnetic Field B (T)

gS = 2.26 0.05



31


-25 -20 -15 -10 -5 0 5-1

0

1

2

3

4

5

dI/d

V (

nS

)

Sample Bias (mV)

B = 11.5 T




ΔVrms = 50 μV

Valley splitting is ten

times larger than

smaller energy splitting

~1 meV/T

Many Body Effects in Graphene

Polarizing Landau Levels

32

-15 -12 -9 -6 -3 0 3 5

0

3

6

9

0

3

6

90

5

10

0

5

10

0

5

10

15

0

5

10

15

B=11.75 T

B=11 T

B=11.5 T

B=11.375 T

B=11.25 T

ESL

ESR

Sample Bias (mV)

=6

EV

B=11.125 T

=11/2

1/2 filled LL

ESF

ESF

ESE

=5

dI/d

V (

nS)

=5

1/2 filled LL =9/2

=4

-6 -3 0 3 6 9 12

0

3

6

9

1/2 filled LL

B=14 T

=7/2

-15 -12 -9 -6 -3 0 3 5

0

3

6

9

dI/d

V (

nS)

B=11 T

ESL

ESR

Sample Bias (mV)

=6

Filling factor = 6

Fermi Level


Polarizing Landau Levels

33

-15 -12 -9 -6 -3 0 3 5

0

3

6

9

0

3

6

90

5

10

0

5

10

0

5

10

15

0

5

10

15

B=11.75 T

B=11 T

B=11.5 T

B=11.375 T

B=11.25 T

ESL

ESR

Sample Bias (mV)

=6

EV

B=11.125 T

=11/2

1/2 filled LL

ESF

ESF

ESE

=5

dI/d

V (

nS)

=5

1/2 filled LL =9/2

=4

-6 -3 0 3 6 9 12

0

3

6

9

1/2 filled LL

B=14 T

=7/2

-15 -12 -9 -6 -3 0 3

0

5

10

Sample Bias (mV)

B=11.25 T

ESE

=5

dI/d

V (

nS)

Filling factor = 5

Enhanced spin splitting at

odd filling factors Enhanced valley splitting

at v=4


Enhanced Exchange Interaction

For polarized LL, symmetric spin and antisymmetric

space wavefunction leads to enhanced exchange

interaction

34

Pauli Exclusion Principle

Wolfgang Pauli


35

B



Developing SPM Measurements for Devices

Graphene is Not Ideal in Real Devices

36

Y. Zhang et al. Nature (2010)

K. Novoselov et al. Nature (2005)

SPM Measurements in Graphene Devices

Potential Disorder in Graphene/SiO2

37

SiO2

Graphene

Impurities

EF @ Vg2

EF @ Vg1

Disorder potential variation

Vg2 > Vg1

Puddle size @ Vg2

Gate Electrode

N. M. R. Peres et al. PRB (2006)

E. H. Hwang et al. PRL (2007)

J. Martin et al. Nature Phys. (2008), (2009)

E. Rossi and S. Das Sarma PRL (2009)

Y. Zhang et al. Nature Phys. (2009)

Etc……

• Mobility

• Minimum conductivity

• Localization…

How does disorder affect:

SPM Measurements in Graphene Devices

Device Fabrication / Experimental Set-up

38

- Mechanically exfoliated graphene on SiO2/ Si substrate - Single / bilayer confirmed by Raman spectroscopy - Stencil mask evaporation

200 μm

Optical viewing and probe alignment in

CNST STM

S. Jung et al. Nature Physics (2010)

LDOS vs Transport Measurements

Gate Mapping Tunneling Spectroscopy

39

Vary density with

applied back gate

Spatially map density

fluctuations

Examine interaction

effects at EF

Vg = V1

Gate insulator Gate electrode

Vg = V2

Map dI/dV(E,Vg)

-300

-200

-100

0

100

200

300S

ampl

e B

ias

(mV

)

dI/dV (nS)-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

Gate Voltage (V)

SPM Measurements of Graphene Devices

Gate Mapping Tunneling Spectroscopy (simulation)

40

LL0

LL1

LL0

LL-1

0

D F

G

E v n

n V V

LL-1

5 10 15 20 25 30 35-300

-200

-100

0

100

200

300

Gate Voltage (V)

Sam

ple

Bia

s (

mV

)

-2 0 2 4 6Filling Factor


Gate Mapping Tunneling Spectroscopy in An Electron

Puddle

41

LL0

LL1

Potential Disorder Map

electron-rich hole-rich

0

2 nS

dI/d

V

B=8 T STS Measurement of Dirac

Point Fluctuations

S. Jung et al. Nature

Physics (2010)

0.4 dI/dV (nS) 1

Sa

mp

le B

ias (

mV

)

dI/dV (nS)

N=0

N=-2

N=-1

-10 0 10 20 30 40 50

-250

-125

0

125

250

Sam

ple

Bia

s (

mV

)

Gate Voltage (V)


Evolution of Localization in Graphene Devices

42

B = 0 T B = 2 T B = 4 T B = 5 T B = 6 T B = 7 T B = 8 T LL0

LL-1

LL-2

LL0

LL1

LL2


Graphene Quantum Dot Formation in High Field

Coulomb blockade – Groups of four diamonds due to spin and valley

degeneracy

43

E

Vb

STM tip Sample

QD

Vacuum

barrier

I.S.

26 27 28 29

Gate Voltage (V)

1 2 3 4

Double barrier tunneling due to vacuum

barrier and incompressible regions


Graphene QDs Formed in Disorder Potential

44

Si (back gate)

SiO2 Cg Vg

A

I STM tip

Vb

Landau level formed

(Compressible region)

Resistive region

(Incompressible strip) B > 0 T


Graphene QDs Formed in Disorder Potential

45

Si (back gate)

SiO2 Cg Vg

A

I STM tip

Vb

Landau level formed

(Compressible region)

Resistive region

(Incompressible strip) B > 0 T

EF

EF

Metallic

Compressible

Insulating

Incompressible

SPM Measurements of Bilayer Graphene Devices

STS Allows Direct Measurement of Bilayer Potentials

46

E

k

ΔU = 0

±LL0, 1

LL2

LL3

LL4

LL2

LL3

LL4

ΔU > 0

LL2

LL3

LL4

LL2

LL3

LL4

+LL0, 1 (top)

-LL0, 1 (bottom)

ΔU < 0

LL2

LL3

LL4

LL2

LL3

LL4

-LL0, 1 (bottom)

+LL0, 1 (top)

!STS Selects Layer

Polarized States

20 nm

STM topography image Disorder potential

Electron

puddle

Hole

puddle

20 nm

Probing Spatial Distribution of Disorder Potential

47

20 nm

Single Layer Bilayer

Electron puddle

Hole puddle

SPM Measurements of Bilayer Graphene Devices

Gate Mapping Allows Direct Measurement of Bilayer Gap

48

Quantitative determination of bilayer gap

Variation on a microscopic scale in both

magnitude and sign

G. Rutter et al. Nature Physics (2011)

0 10 20 30 40 50 60

-60

-40

-20

0

20

40

,

,

,

Gate Voltage (V)

Ene

rgy

Gap

, U

(m

eV)

Hole puddle

Electron puddle

8 T 6 T 0 T

What’s the Next in Atomic Scale Measurement

Development

Coordinated approach to combine new atomic-scale

measurement methods, synthesis, and device fabrication

Atomic scale and macroscale measurements on the same test devices

How does microscale properties from substrates/gate insulators, contacts

etc… determine macroscale performance

Develop measurements for new qraphene device concepts, i.e. Veslago lens

BiSFET device

Fabrication and measurement of topological insulators – more Dirac

MBE and bulk crystal growth, atomic characterization studies

Combined STM, AFM and spin-polarized STM on device geometries

New high-throughput STM/AFM/SGM system

Multi-terminal STM/STS measurements on devices that combine

simultaneous transport and atomic characterization measurements to

optimize device performance

Continue to seek collaborations that leverage our capabilities

49

Collaborators

50

Jeonghoon Ha Jungseok Chae Young Kuk

Sander Otte Young Jae Song

Graphene/TI mK Crew

Niv Levy Tong Zhang

Collaborators

51

Graphene Device Crew

Greg Rutter Suyong Jung Nikolai Klimov

Nikolai Zhitenev Dave Newell Angie Hight-

Walker

Collaborators

52

GT Epitaxial Graphene Crew Graphene Theory Crew

Yike Hu

Phil First

Walt de Heer Hongki Min Shaffique Adam

Mark Stiles Allan MacDonald Britt Torrance Eric Cockayne

a novel spm system for determining quantum electronic

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