Joseph A. Stroscio, NIST Fellow Electron Physics Group 2011 - - PowerPoint PPT Presentation

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 d

I 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 dI r 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

Developing High-Energy Resolution SPM 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 mK

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)

Developing High-Energy Resolution SPM Measurements

11

Young Jae Song Alexander F. Otte Young Kuk Joseph A. Stroscio

Developing High-Energy Resolution SPM 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

Presentation Outline

13

B Microscopy Honeycomb Lattices Magnetic Fields Graphene“Quartet” Graphene Devices

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

From Honeycombs to the Dirac Hamiltonian

17

Figure from droid-life.com

kx ky

Energy

Figure from P. Kim

Wallace (1947) kx' ky'

K K’ Energy is linear with momentum massless particles

From Honeycombs to the Dirac Hamiltonian

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 x

K K K k k a            

kx' ky' E

/2 , /2

3 2 1 ( ) 2 arctan

F nn x y F F x y i F i x y

a v k ik H v v k ik e E 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’

x y F x y

k ik H v k ik         

K x y F x y

k ik H 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

Presentation Outline

21

B Microscopy Honeycomb Lattices Magnetic Fields Graphene“Quartet” Graphene Devices

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:

2

sgn( ) 2

n

E n e c n B 

Standard Model:

*

( 1/ 2)

n

e E E B n m



  

Lev Landau 1908 - 1968 B

• Scattering in the graphene

landscape

• Effects of disorder and

interactions

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

Presentation Outline

25

B Microscopy Honeycomb Lattices Magnetic Fields Graphene“Quartet” Graphene Devices

Epitaxial Graphene on C-face SiC – Weak Disorder

26

C-Face termination Si-Face termination

SiC

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

100 200 300 1 2 3 4 5

dI/dV (nS) Sample Bias (meV)

B= 5 T

• 7-6
• 5
• 4
• 3
• 2
• 1

n=0 1 2 3 4 5 6 7

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

Resolving the Graphene Quartet

Tunneling Spectroscopy at ~10 mK

28

2 4 6 100 200 300

• 200
• 100

100 200 10 20 30

Linear Fit B=2 T B=3 T B=4 T

EN-E0 (meV) (NB)

1/2

N=1 B=0 T B=2 T B=3 T B=4 T

dI/dV (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)

Resolving the Graphene Quartet

Tunneling Spectroscopy at ~10 mK

29

• Y. J. Song et al. Nature (2010)
• 25
• 20
• 15
• 10
• 5

5

• 1

1 2 3 4 5

dI/dV (nS) Sample Bias (mV) B = 11.5 T

• 200
• 100

100 200 1 2 3

dI/dV (nS) Sample Bias (mV) B= 2 T N=1

Weak disorder in graphene

• n C-face SiC allows fine

features to be observed

ΔVrms = 1 mV ΔVrms = 50 μV

Resolving the Graphene Quartet

Tunneling Spectroscopy at ~10 mK

30

• Y. J. Song et al. Nature (2010)
• 25
• 20
• 15
• 10
• 5

5

• 1

1 2 3 4 5

dI/dV (nS) Sample Bias (mV) B = 11.5 T

Weak disorder in graphene

• n C-face SiC allows fine

features to be observed

ΔVrms = 50 μV

Smaller peak separation – electron spin?

2 4 6 8 10 12 14 0.0 0.5 1.0 1.5 2.0

ES(meV)

Magnetic Field B (T) gS = 2.26 0.05

Resolving the Graphene Quartet

Tunneling Spectroscopy at ~10 mK

31

• Y. J. Song et al. Nature (2010)
• 25
• 20
• 15
• 10
• 5

5

• 1

1 2 3 4 5

dI/dV (nS) Sample Bias (mV) B = 11.5 T

Weak disorder in graphene

• n C-face SiC allows fine

features to be observed

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

3 5 3 6 9 3 6 9 5 10 5 10 5 10 15 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/dV (nS)

=5 1/2 filled LL =9/2 =4

• 6
• 3

3 6 9 12

3 6 9

1/2 filled LL B=14 T =7/2

• 15
• 12
• 9
• 6
• 3

3 5 3 6 9

dI/dV (nS)

B=11 T ESL ESR

Sample Bias (mV)

=6

Filling factor = 6

Fermi Level

Many Body Effects in Graphene

Polarizing Landau Levels

33

• 15
• 12
• 9
• 6
• 3

3 5 3 6 9 3 6 9 5 10 5 10 5 10 15 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/dV (nS)

=5 1/2 filled LL =9/2 =4

• 6
• 3

3 6 9 12

3 6 9

1/2 filled LL B=14 T =7/2

• 15
• 12
• 9
• 6
• 3

3

5 10

Sample Bias (mV)

B=11.25 T ESE

=5

dI/dV (nS)

Filling factor = 5 Enhanced spin splitting at

• dd filling factors

Enhanced valley splitting at v=4

Many Body Effects in Graphene

• Enhanced Exchange Interaction
• For polarized LL, symmetric spin and antisymmetric

space wavefunction leads to enhanced exchange interaction

34

Pauli Exclusion Principle

Wolfgang Pauli

Presentation Outline

35

B Microscopy Honeycomb Lattices Magnetic Fields Graphene“Quartet” Graphene Devices

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
• n 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

100 200 300

Sample Bias (mV) dI/dV (nS)

• 30 -25 -20 -15 -10
• 5

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

D F G

E v n n V V     

LL-1

5 10 15 20 25 30 35

• 300
• 200
• 100

100 200 300

Gate Voltage (V) Sample Bias (mV)

• 2

2 4 6

Filling Factor

SPM Measurements of Graphene Devices

Gate Mapping Tunneling Spectroscopy in An Electron Puddle

41

LL0 LL1 Potential Disorder Map

electron-rich hole-rich

2 nS dI/dV B=8 T STS Measurement of Dirac Point Fluctuations

• S. Jung et al. Nature

Physics (2010)

0.4 dI/dV (nS) 1 Sample Bias (mV) dI/dV (nS)

N=0 N=-2 N=-1

• 10

10 20 30 40 50

• 250
• 125

125 250 Sample Bias (mV) Gate Voltage (V)

SPM Measurements of Graphene Devices

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

SPM Measurements of Graphene Devices

• 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

SPM Measurements of Graphene Devices

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

SPM Measurements of Graphene Devices

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)

10 20 30 40 50 60

• 60
• 40
• 20

20 40

, , ,

Gate Voltage (V) Energy Gap, U (meV)

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

• ptimize 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