Prof.arupKRaychaudhuri

8/2/2019 Prof.arupKRaychaudhuri

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Unit for nanoscience and Theme Unit ofExcellence in Nanodevices

S.N. Bose National Centre for Basic SciencesKolkata-700098

www.bose.res.in

Basics of Scanning probe microscopy

A.K. Raychaudhuri

SNBNCBS and Bruker School

December 14-15, 2011


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Basic concepts

Simple components of SPM

Cantilever Statics and Dynamics

The different modes of SPM


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I will assume:

You have used SPM in some form before andhave some acquaintance with it.

However, the talk is not for experts.


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SPM

The Scanning Probe Microscope

What are the basic components of a SPM

Localized Probethat has an

interactionwith

the substrate tobe imaged

A nano-positioningmechanism that canposition the probe in

close proximity

of the surface

A system tomeasure the

interaction of theprobe with the

substrate

A mechanism toscan the probe

relative to thesubstrate andmeasure the

interaction as

function of position


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STM- Quantum mechanical tunneling between atip and the substrate. The contrast comes fromspatial variation of local electronic desnsity of

states.

AFM- Localized mechanical (attraction orrepulsion) interaction between tip and surface.

Physical mechanism and contrast

Any microscopy will depend on some physicalmechanism to create a contrast spatially.

It will also need a way to measure the contrastwith spatial resolution.


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If the process of scanning does not measure thecontrast that has a spatial dependence you will not

get any image in any scanning microscope.

Being a computer operated system, any periodic

noise in the system can create images because thescanning process can add it up to the main signal.These are plain artifacts.

How to detect artifacts ? A quick thumb rule


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In contrast to TEM or Optical microscope there isno diffraction and reconstruction of diffracted wave

front in SPM.

Advantage:

Resolution is not diffraction limited.

Here the limitation comes from the tip size thatinterrogates and of course some fundamentallimitations on detection process and electronics.


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Different SPMs and different modesThe nature of the tip surface interaction gives

different types of microscopy.

The way we detect the response gives us thedifferent modes of SPM.


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SPM

The Scanning Probe Microscope (SPM) family

STM (Tunneling) SFM (Force)

Scanning ThermalMicroscope (Local

Temperature)

STS,STP,ScanningElectrochemical

Microscope

Scanning Near FieldOptical Microscope(Optical imaging)

Atomic ForceMicroscope (AFM)

Lateral Force (LFM)

Magnetic Force

(MFM)

Electrostatic Force

(EFM)

C-AFM


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Scanning Force Microscope

It is nothing but a spring balance (the cantilever)

that is scanned over a surface.

The cantilever is the precision force detectionelement- we can detect atomic forces

Type of force of interaction between the tip andsubstrate will determine what we are measuring andthe mechanism that makes the contrast.

How large are the atomic forces and can we reallydetect them by a cantilever that is much larger?


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How big is the Atomic Force

The atomic spring constant

What is the value of the springconstant of the bond connecting to

atoms ?

2 keff/M

- Is typically in IR range for atomic vibration

~ 1013 - 1014cps, M ~ 5 x 10-26 Kg,

keff= 2

M ~5 x (1-102

) N/m


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3

3

Et wk =

4L

1 kf =

2 m*

One can make a cantilever as a force measuring elementthat can have the same order of k as that of a molecule.

w

L L

Si elastic modulus (E)[111] Young's modulus= 185GPa

[110] Young's modulus=170 GPa

[100] Young's modulus= 130 Gpa

Si3N4~300 Gpa

For a Si cantilever :

t = 5m, w= 20 m, L= 200 mk=10N/m

It can be softer than atomic

spring constant


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L2

b

w

L1

t: thickness

m*~0.24(mass of the cantilever)

3 3 3

3

1 2 2

Et wbk =2b(L -L ) + 6wL

Engineering cantilevers with different springconstant k- need for different applications

Advantages:

1.Less prone to vibrationalnoise.

2. Can go to lower k orresonance frequency.


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Estimated radius of curvature of the tip Rt ~ 30 nm

Kc=0.1 N/m

Tip

Engineering cantilevers with different springconstant k-a real triangular cantilever

Much softer than an

atomic spring !!!!

Cantilever

What ever you do with SFM,the cantilever is the key.

You need to know it.


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Some feeling for numbers

We have a cantilever as a force measuring element.F = k.

If I want to measure F=1nN, k=1N/m. I should beable to measure a displacement =1 nm.

Entering the world of nano


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At the heart of all scanning probe microscope is thecantilever with a tip.

How we position the tip?How we scan the tip?How we measure deflection of the cantilever?


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Demystifying AFM-A simple AFM(Home made)

Laser

QPD

Inertial drive piezo

Scan Piezo

Electronics

L. K. Brar, Mandar Pranjape,Ayan Guha and

A.K.RaychaudhuriDesign and development of

the scanning forcemicroscope for imaging and

force measurement with

sub-nanonewtonresolution

Current Science , 83,1199 (2002) X-Y micrometer stage

h i f


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Schematic of SFM

DEFLECTION

SENSOR

FEEDBACK

LOOP

CANTILEVER

Z-PIEZO

PROBE

TIP

COMPUTER

XY-PIEZO SCANNER

Keeps cantileverdeflection or oscillation

amplitude constant


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Practical Considerations for AFM/SFM

1. Cantilever deflection detection system.

2. Type of cantilevers that can be used.3. Coarse and fine approach mechanism.4. No net relative motion between sample, cantilever and

detection system.

5. Scanner range and type of encoder for large sizescanner.6. Data acquisition system ,processing and display

software.7. Accessibility to all the parts of the SFM and capability of

using image processing software on stored data.

Where do the SPM sold by different vendors

differ?

B i h ti f SPM


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Scanner

Feedback

A-B

Pre-Amplifier

A B

Quadrant

Photo Detector

Tip &

Cantilever

Basic schematic for SPM

To Z-Piezo

Laser

ADC

DAC

Need for

calibration

Keeping something

constant, need for feed back

X-Y scanner

Z-scanner

Coarse approach vs fine approach

Pixels

bits

PID

C lib i f i f SFM i i l


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Calibration of scanning stage of SFM using commercial2-D grating

The grating has 2160 lines/mm

1000m/2160=0.46mThe calibration: 40nm/V

Brar et.al

(2002)


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Topography

Can take care of

image distortion

Arranging spheres of PS in an array by self-assembly

Sub 500nm level calibration, works fine to 20nm

Can find the size by Electron microscope or DLS

Soma Das

(2008)

C lib ti i t i


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Mica

Freshly cleaved

7 nm x 7 nm

Calibration in atomic range-A freshly cleaved surface

Can we assume a linear calibration ?

The piezo -scanner is non-linear and

has hysteresis


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Other calibrations:Z-Calibration- large scale vs small scale

Force calibration-detection of exact k?

O ti l h d d D t ti l t i f i


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Optical head and Detection electronics for scanning

Scanner

Feedback

A-B

Pre-Amplifier

A B

Quadrant

Photo Detector

Tip &

Cantilever

To Z-Piezo

Laser

ADC

DAC


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Optical lever =

= 500 -100(for l=100mm)

L(Length of the laser path)

l(Length of the cantilever)

Main components of the optical

stage:

1. Laser diode

2. Cantilever

3. Quadrant photo-detector (QPD)

4. Collimating lenses5. Mirror

QPD is used as a position

sensitive detector, its output

signal is proportional to the

position of the laser spot.

Why we need smaller cantilever ?

C lib ti f th ti l t


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Calibration of the optical stage.

0 1 2 3

-2

0

2

A-B(V)

Z-displacement(cm)

Region of Gradient: 1000m

Detects 4V for 1000m movement

1mV electrical noise , positional reolution~1/4m

Using optical lever of 100, we can detect cantilever deflectionof ~ 1/400 m=2.5 nm.

Source of noise in AFM


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Atomically resolved steps in Ti terminated SrTiO3substrate-reaching the limits

Size of step (1/2 unit cell) ~0.38nm

Courtesy Dr. Barnali Ghosh.

Taken in CP-II

Resolution from optical detection


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Resolution from optical detection

0 1 2 3

-2

0

2

A-B(V)

Z-displacement(cm)

Region of Gradient: 1000m

Detects 4V for 1000m movement, 1mV electrical noise~1/4m.

Reduce noise to 0.1 mV,

Using optical lever of 100, we can detect cantilever deflection

of ~ 1/4000 m=0.25 nm.

Often it is good to have acantilever tip rest on asurface and record the

output as a function of time

We have the base responseof the QPD, need to enhance

optical lever and reduceelectrical noise to get better

resolution


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Quadrant photo-detectors

Why use 4 quadrant detector ?

Vertical deflection of cantilever-Topography

Lateral deflection of cantilever-

Lateral Force Microscopy (LFM)


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Thermal Noise limited resolution

If k is reduced the force sensitivity is increased

Cantilever displacement = Force/k

K ~ 0.1N/m , displacement of 1nm will come from aforce of 100pN

Does any thing limit us ?

Yes it is the thermal noise.

It can be very high for soft cantilevers (those withvery small k)

Th l N i li i d l i


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Thermal Noise limited resolutionFor any oscillatory system we can apply

Equi-partition theorem

2/12/1

2

2*2

2*2

,,

2

1

k

Tkz

Vmzksystemharmonic

VmzkTk

B

B

For a 0.1N/m cantilever the thermal noise inducedroot mean-square amplitude 0.14 nm.For a deflection of 1nm of the cantilever it is asubstantial amount.

Force uncertainty~(10014)pN


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I have discussed some of the basic concepts of theSFM and the main components that go with it and

their functions as well as limitations.

Cantilevers and force detection, Scanner

calibrations, Optical detections and sources ofnoise

It will be best if your reflect upon your experienceof using SFM and connect to this presentation


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Cantilever Statics and Dynamics

The different modes of SPM


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Source: PhD thesis Soma Das , SNBNCBS


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Statics and Dynamics of cantilever

Interaction between the tip and the substrate willdecide the nature of force and hence the statics and

dynamics of the cantilever

Tip sampleinteraction model

D i f til


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Dynamics of cantilever

Any force velocity willadd to damping andreduce amplitude of

vibration-dissipation

Any force displacement will change

the frequency ofvibration

Different types of force microscopy depends onthe dynamics of cantilever and the mode of

detection

tjFekzdtdz

dtzdm 2

2

Simple ball and spring model

Driving term

for dynamicmode


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Static mode (contact mode)

AFM

tjFekz

dt

dz

dt

zdm

2

2

Fkz=0


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Static mode:

Mostly for contact-mode the cantilever deflection

is such that the bending force is balanced by theforce of interaction:

F(z) =-U/z=-k.z

U = Total energy that includes the surface as well aselastic deformation energy.

26)(

z

HR

zf

tTS

5.10

0

)( )(*3

4

62

zaREa

HRf t

tzTS

a0~Atomic dimension (hard sphere)

E*~ Effective elastic constant

Rt- Tip radius of curvature.

H=Hamakar cosntant


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26

)(z

HRzf tTS

5.10

0

)( )(*3

4

62

zaREa

HRf t

tzTS

Elastic force winsover. The deformation

of the surface shouldbe larger than thefeatures you would

like to see


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Si tip pressingon Si substrate

One can evaluatethe contact radius

Herzian contact

The contact areadepends on Elastic

modulus

A th b l t l t til i t t


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A thumb rule to select cantilever in contactmode imaging

Cantilever touching a surface is like two springsconnected back to back, The force applied isbalanced by displacement

The softer spring wins

substratecantilevereff

eff

appl

substrate

appl

cantilever

appl

substratecantilevertotal

kkk

kF

kF

kF

111

.

A th b l t l t til i t t


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A thumb rule to select cantilever in contactmode imaging

A surface with mixed k (elastic constants) like acomposite of soft and hard matter will not image thetopography. What you image is actually a mixtureof both

substratekeffkcantileverksubstratek

cantileverk

effk

cantileverk

substratek

,

,

Correctcondition fortopography incontact mode

The softer spring wins

Will image theelasticallydeformed surface


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Some tips for good contact mode imaging

Get a soft cantilever that is realistically needed.

Do a force spectr0scopy (F-d) curveHave some idea about the elastic modulus of the

surface you image.

For soft materials when you cannot have verysoft cantilever use LFM


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ODT self-assembled monolayer on Ag

Sai and AKR, J.Phys.D Appl. Phys. 40, 3182 (2007)


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Some useful applications of

contact mode AFM

Force spectroscopy

Piezo-force spectroscopy

Conducting AFM

Local charge measurements


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tj

Fekxdt

dx

dt

xdm

2

2

Dynamic mode

Driving force

Controlled byexperimenter

Force of interaction oftip with substrate and

surrounding


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Dynamic mode (all non-contact modes):

Cantilever is modulated at resonance frequency and

the shift in resonance frequency , phase oramplitude measures the force gradient

-F/z=-k+(2U/z2)

2)(6

))((tz

HRtzf tTS

5.10

0

))(( ))((*3

4

62

tzaREa

HRf t

ttzTS

i d h d d


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Dynamic mode -what do we do ?

Oscillate the cantilever at close to resonance

frequency

Interaction with the substrate will change theresonance frequency and /or amplitude of

oscillation (through the viscous force on thesurface)

Detect the departure from resonance or damping

detected by amplitude, phase or frequency shift asthe cantilever scans the surface

This leads to contrast and the imaging


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Dynamics of cantilever

22222

0

0

22222

0

22

00

0

2

2

)(

)/)(()Im(

)(

))(/()Re(

)(

mFz

mFz

eztz

Fekzdt

dz

dt

zd

m

j

tj

In dynamic mode spectroscopy the resonance curve


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In dynamic mode spectroscopy the resonance curveand its modifications during imaging provides the

image

what happens to resonance frequency in dynamic


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what happens to resonance frequency in dynamicmode when there is additional force

z

Uf

z

fk

z

Ukkeff

,)( 02

2

0

eff

omk0Start with a cantilever that is free

Shift in resonance frequency when the interaction is turned on

eff

effeffeff

eff

m

f

m

f

m

f

m

k

2

0

'

0

'

0

20

'

0

'

2

0

'

0

2

1

2

11

Force derivative is theimportant parameter in

dynamic mode


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NC

Tapping

55


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Force Derivative

NC

Tapping


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Two paradigms of dynamic mode

Detection by amplitude modulationIf the resonant frequency of a cantilever shifts, then theamplitude of cantilever vibration at a given frequencychanges. Near a cantilevers resonant frequency, this changeis large.

Non-contact (tip does not touch the substrate,) -This also encompasses the EFM and MFM.

Tapping or IC mode (the tip touches the surface atsome part of the swing)


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The set frequency is somewhat larger than the freeresonance frequency.

Non-contact

IC/tapping-mode


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The set frequency is somewhat smaller than the free

resonance frequency.

F i l ti f d t h t h t th


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From simulation of data-what happens to theresonance curve in Tapping mode

Das, Sreeram,AKR , Nanotechnology 18, 035501 (2007),Nanotechnology21, 045706 (2010),Journal of Nanoscience and Nanotechnology 7, 2167

(2007)

Sample: MicaK= 0 68N/m


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-1.0 -0.5 0.0 0.5 1.0 1.5 2.00.000000000

10.000000475

20.000000950

30.000001425

40.000001900

50.000002375

60.000002850

70.000003325

80.000003800

Sample:Mica

Amplitude(nm)

Tip-sample separation (m)

approach(41nm)

retract(41nm)

approach(70nm)

retract(70nm)

approach(90nm)

retract(90nm)

Amplitude vs. distance curves for mica for three different free vibration amplitude of

the cantilever.

K= 0.68N/mResonance Frequency = 86KHz

61


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Amplitude vs Height

(in absence of feedback)

Application of Non contact mode


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Application of Non-contact mode

Magnetic Force Microscopy

MFM

Measuring long-range force

Any force that decays slower than

inverse square

26

)(z

HRzf tTS

2,)( nz

Azf

nlong


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26

)(z

HRzf tTS

This mode is realized by employing suitable probes


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This mode is realized by employing suitable probes(magnetic tip) and utilizing their specific dynamicproperties.

MFM is an important analytical tool whenever thenear-surface stray-field variation of a magneticsample is of interest.

MFM can be used to image flux lines in low- andhigh-Tc superconductors . MFM have evenextended local detection of magnetic interactions

to eddy currents and magnetic dissipationphenomena .


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The interpretation of images acquired bymagnetic force microscopy requires some basicknowledge about the specific near-fieldmagnetostatic interaction between probe andsample.

How to take care of the topography ???

The magnetic stray field produced by a magnetized


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g y p y gmedium and the contrast mechanism

effm

F2

0

'

0

'

0

2

1

The shift in frequency the

MFM detects is the gradient

of the magnetic force

Magnetic Force Microscopy of hard disk


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g py

(No applied field)

MFM maps themagnetic domains on

the sample surface

Stored data in a

hard disk

The stray field is maximumwhen the anisotropy is

perpendicular

Magnetic Force Microscopy (with applied field)


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g py ( pp )

Requirements for MFM tips


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Requirements for MFM tipsThese tips can be coated with a thin layer of magneticmaterial for the purpose of MFM observations.

A lot of effort has been spent on the optimization ofmagnetic tips in order to get quantitative information fromMFM data .

The problem is that in the coating of conventional tips, apattern of magnetic domains will arrange, which reducesthe effective magnetic moment of the tip. The exact domainstructure is unknown and can even change during MFM

operation.Best tip is the one that has a single mono-domainmagnetic particle !!!!!


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Lorentz Microscopy of fieldaround a tip

Effect of tip sharpness


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Stray field line scan

Observed

Simulated

Ordinary tip Mono-domain

tip

In SFM , what ever you do the most significant

role is played by the tip and the cantilever


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I have tried to give a basic introduction to SFM andsome of its different modes and shared my

experience with you.SFM images are not just picture gallery

The more knowledge you acquire and morequantitative you become you can get more value

from your SFM.

Thank you

Prof.arupKRaychaudhuri

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