Zurich Research Laboratory Fundamental graphene interface studies motivated by nano ... · 2016-11-07 · © 2015 IBM Corporation Zurich Research Laboratory Fundamental graphene interface

© 2015 IBM Corporation

Zurich Research Laboratory

Fundamental graphene interface studies

motivated by nano-electromechanical

switchesUrs Duerig, Elad Koren (cQOM fellow 2013 – 2014), IBM Research Zurich

cQOM ITN Diavolezza Workshop, 31 January - 4 February 2016


Mechanical relay

High on/off ratio

Leakage-free switching

Low on-resistance

Large adhesion (hysteresis)

Variable contact parameters

Low reliability

ITN Project: Physics and materials of nanoscale electrical

contact for NEM switches

Original Motivation

Graphene based nanopillar switch for energy efficient

(low adhesion, high conductance) NEMS logic

Graphite nanopillar switch

HOPG

Au top electrode

Easy to implement

HOPG easily shears

along a 0001 plane

preferredconductorpoor

masseffective

densityelectronFc

Challenge: Quantitative data on adhesion,sliding friction, and conductance in Graphite is lacking

Switching energy determined

by electrical contact forces

- nm size Au contact:

Ron ~ 2 kΩ Fc ~ 5 nN Es 150 eV

- Graphite could provide 10x improvement

of overall switching energy required to

substantially surpass CMOS scaling

predictions


Fabrication process

2.5 mm

1 mm

2.5 mm

250 nm

0.5 mm

250 nm


Electrical transport in graphite is a complex subject

Stacking faults are abundant because of the

low energy difference ~ 0.25 meV/atom with

respect to AB stacking

They acts as high resistance barriers for

c-axis electrical transport

ρc ~ 4.1 x 10-7 Ωm

stacking fault density 1/10 nm

ideal graphite

ρc ~ 4.1 x 10-5 Ωm

>> in-plane resistivity

ρa ~ 4.1 x 10-3 Ωm

Shusuke Ono, J. Phys. Soc. Jpn 40, 498 – 504 (1976)

Accurately predicts

the measured resistance

in meso-scale graphite

structures (our work)


Electrical transport measurements in graphite (HOPG) pillars

Pillar height: h = 20 – 90 nm, Pillar radius: r = 100 – 500 nm

Huge resistance scatter decreasing

with pillar height

Highly non-linear I/V characteristics

at high field > 5mV/nm

Statistical analysis

stacking fault density 0.25 nm-1

Hopping across stacking fault barriers

stacking fault density 0.25 nm-1

stacking fault resistance

107 Ωnm2 as predicted by Ono

~ 300 Ω for r=100 nm

barrier height ~ 0.3 eV

consistent with energy of

localized Tamm states at the

interface

Koren et al. Nat. Commun. 5:5837 (2014)


Sliding Graphite “Potentiometer”

Measured quantities:

- Shear force F

- Pillar current I

Electric field effect of

adhesion energy

30% of the voltage drop across the

sheared interface!

Current not proportional to overlap area

as naively expected

Sheared interface disturbs

current transport by more

than one order of magnitude

compared to a stacking fault !

0 1

0 20 3

0 40 50

Interface potential (V)


Electrical transport across twisted graphene interface

Koren et al., under review Nature Nanotechnol.

rotation axis stabilized

by adhesive forces

Better than 0.1 deg control of the

rotation angle

Moiré superstructure

in general incommensurate with

graphene lattice

“Magic” angles, e.g. 21.768o, Moiré superstructure is

commensurate with graphene lattice

Two flavors: SE-odd SE-even


Electrical transport across twisted graphene interface

incommensurate Moiré superstructure commensurate Moiré superstructure

Momentum conservation

via Umklapp scattering:

2D electronic state confined

to the twisted interface

with the symmetry of the

Moiré superstructure

enables current transport

across the interface

Momentum mismatch

quenches current transport

dramatically (basically tunneling

between pz-orbitals)

hard to be handled by standard k-space

methods

phonon scattering could provide

a sidestep for momentum conservation


Electrical transport across twisted graphene interface: Experiments

Observed peak splitting

consistent with interface

band structure

Overall dependence of interface conductivity

accurately modelled by phonon scattering

process including Fermi-velocity renormalization

at low twist angles. Tunneling contribution is negligible

First experimental confirmation of 2D interface

state settling a long standing theoretical debate.

Incommensurate transport cannot be

addressed using commensurate supercells


Adhesion and friction: Lateral force measurements

Self-

retracting

structure0

25

50

75

-75

-50

-25

-100 -50 0 50 100

Lateral cantilever motion (nm)x

La

tera

l fo

rce

(n

N)

F

25

50

75

R

L

L LL L L L

R R R R R R

Koren et al., Science 348, 679 – 683 (2015)

All mechanical surface

energy measurement

avoiding calibration ambiguities

Hysteresis: Energy dissipation


Overlap area

2212 )2/(2/

2/cos 2 xrx

r

xrA

dx

dAF

Restoring force

σ: surface energy of 0001 planes

2

2)2/(12

r

xrF

Conservative adhesion force measurements

Why important:

- Benchmark for theoretical models

- Determines energetics of nano-actuation

- Enables engineering of arbitrary potential

landscapes for realizing e.g. bi-stable structures


Mesoscale friction in HOPG

0

25

50

75

-75

-50

-25

-100 -50 0 50 100

Lateral cantilever motion (nm)x

La

tera

l fo

rce

(n

N)

F

25

50

75

I

II

III

Measured shear force

Trace / Re-tracePillar radius:

100 nm

Friction = Energy dissipation

dxFFdsFE

l

tracetrace

pathclosed

sfr 0

frF

Friction force = blue - green


Statistical analysis

for Δx > 20 nm

Gaussian distribution

+ Central limit theorem

Random statistically

independent events

with finite correlation

length

Variance >> mean value

Friction force can be

negative over some range

Energy is recovered

Correlation length ~ 20 nm

co

rre

lati

on

sta

t. i

nd

ep

en

den

t

nmxfr 20/1 Random walk characteristics

Signature of

lattice structure

in the PSD


Friction Scaling

Amonton’s law

PFfr

m

Nra

P m 242

0

(for r = 100nm)

5107 xm

AreaFfr

Experiment

NFFfr

0

Small force oscillations i.e. <F> from 1.5 - 4.5 nN,

expected > mN.

Clear sign for structural superlubricity of

non-commensurate lattices.

Cancelation of lateral forces except at

periphery sites.

Fractional scaling factor = 0.35.

(m ≈ 0.1…0.3 typical for dry conditions)

Binding force per atomApplied load

Number of interface atoms

Genuine superlubricity due to incommensurate lattice interaction


Adding fluctuations: Compliant sliding

- Experimental set-up is compliant allowing for

off-axis movements Δy and rotations ΔΦ of the mobile pillar section

- Complex adhesion energy E(x,y,Φ) landscape randomness due to bifurcations

- Pillar trajectory maps a minimum energy path:

Δy(x) and ΔΦ(x) evolve such that

- Thermal fluctuations included by allowing paths to locally violate the minimum energy

condition with a probability given by the Botzmann statistics enhanced randomness

.min)(),(, xxyxE

X [Å]

Y [Å]

Example of x-y adhesion energy

landscape

Minimum energy path indicated

by dashed line

Note that each saddle point in the

energy landscape is a potential

bifurcation point


Compliant sliding simulation at room temperature

Pillar radius: 5nm

Initial conditions: y0 = 0, Φ0 = 10o

Adhesion energy landscape probed on a mesh with Δx=0.002 nm, Δy=0.01 nm, ΔΦ=0.3o

Energy map

Atomic positions


y- path - path resulting force

Adding fluctuations: Compliant sliding

Pseudo random walk in the y-Φ plane

Excellent agreement with experimental data


Outlook

Understanding of the current flow

enhanced at the edge due to symmetry breaking in

incomplete Moiré tiles?

In-plane transport in few layer systems

Devices can be fabricated

Low temperature studies quenching phonon

mediated transport

Magnetic fields


Acknowledgements

Elad Koren,

Armin Knoll,

Colin Rawlings,

Emanuel Loertscher,

(IBM Research Zurich)

Michel Despont (CSEM)

Daniel Grogg (Tyco electronics)

Funding

Fabrication: Meinrad Tschudy, Ute Drechsler

(IBM Research Zurich)

http://www.snf.ch/de

http://www.snf.ch/de


Thank you !

Documents

Zurich Research Laboratory Fundamental graphene interface studies motivated by nano ... · 2016-11-07 · © 2015 IBM Corporation Zurich Research Laboratory Fundamental graphene interface