Unit for nanoscience and Theme Unit of Excellence in NanodevicesS.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

•Basic concepts

•Simple components of SPM

•Cantilever Statics and Dynamics

•The different modes of SPM

I will assume:

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

However, the talk is not for experts.

SPM

The Scanning Probe Microscope

What are the basic components of a SPM

Localized Probe that has an

“interaction”with the substrate to be imaged

A nano-positioning mechanism that can position the probe in “close

proximity”

of the surface

A system to measure the

interaction of the probe with the

substrate

A mechanism to scan the probe relative to the substrate and measure the

interaction as function of

position

STM- Quantum mechanical tunneling between a tip and the substrate. The

contrast comes from spatial variation of local electronic desnsity of states.

AFM- Localized mechanical (attraction or repulsion) interaction between tip and

surface.

Physical mechanism and contrast

Any microscopy will depend on some physical mechanism to create a contrast

spatially.

•It will also need a way to measure the “contrast” with spatial resolution.

•If the process of scanning does not measure the contrast 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 the scanning process can add it up to the main signal. These are plain artifacts.

•How to detect artifacts ? – A quick thumb rule

In contrast to TEM or Optical microscope there is no diffraction and reconstruction of diffracted wave front in SPM.

Advantage:

Resolution is not diffraction limited.

Here the limitation comes from the “tip size” that interrogates and of course some fundamental limitations on detection process and electronics.

Different SPM’s and different modes

•The nature of the tip –surface interaction gives different types of microscopy.

•The way we detect the “response” gives us the different modes of SPM.

SPM

The Scanning Probe Microscope (SPM) family

STM (Tunneling) SFM (Force)

Scanning Thermal

Microscope (Local

Temperature)

STS,STP,Scanning

Electrochemical Microscope

Scanning Near Field Optical Microscope

(Optical imaging)

Atomic Force Microscope (AFM)

Lateral Force (LFM)

Magnetic Force

(MFM)

Electrostatic Force (EFM)

C-AFM

Scanning Force Microscope

•It is nothing but a spring balance (the cantilever) that is scanned over a surface.

•The cantilever is the precision force detection element- we can detect “atomic forces”

•Type of force of interaction between the tip and substrate will determine what we are measuring and the mechanism that makes the contrast.How large are the atomic forces and can we really detect them by a cantilever that

is much larger?

How big is the “Atomic Force”

The atomic spring constant

What is the value of the spring constant 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

3

3

Et wk =

4L

1 kf =

2π m*

One can make a cantilever as a force measuring element that 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 m

k=10N/mIt can be softer than atomic spring constant

L2

b

w

L1

t: thicknessm*~0.24(mass of the cantilever)

3 3 3

3

1 2 2

Et wbk =

2b(L -L ) + 6wL

Engineering cantilevers with different spring constant k- need for different

applications

Advantages:

1.Less prone to vibrational noise.

2. Can go to lower k or resonance frequency.

Estimated radius of curvature of the tip Rt ~ 30 nm

Kc=0.1 N/m

Tip

Engineering cantilevers with different spring constant 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.

Some feeling for numbers

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

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

δ=1 nm.Entering the world of nano

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

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

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.Raychaudhuri“Design and development

of the scanning force microscope for imaging and force measurement with sub-nanonewton

resolution”

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

Schematic of SFM

DEFLECTION SENSOR

FEEDBACK LOOP

CANTILEVER

Z-PIEZO

PROBE TIP

COMPUTER

XY-PIEZO SCANNER

Keeps cantilever deflection or

oscillation amplitude constant

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 size

scanner.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?

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

Calibration of scanning stage of SFM using commercial 2-D grating

The grating has 2160 lines/mm 1000µm/2160=0.46µmThe calibration: 40nm/V

Brar et.al (2002)

TopographyCan 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)

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

Other calibrations:

•Z-Calibration- large scale vs small scale

•Force calibration-detection of exact k?

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

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 lenses

5. 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 ?

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 1000μm movement

•1mV electrical noise , positional reolution~1/4μm

•Using optical lever of 100, we can detect cantilever deflection of ~ 1/400 µm=2.5 nm.

Source of noise in AFM

Atomically resolved steps in Ti terminated SrTiO3 substrate-reaching the limits

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

Courtesy Dr. Barnali Ghosh.

Taken in CP-II

Resolution from optical detection

0 1 2 3

-2

0

2

A-B

(V)

Z-displacement(cm)

Region of Gradient: 1000m

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

•Reduce noise to 0.1 mV,

•Using optical lever of 100, we can detect cantilever deflection of ~ 1/4000 µm=0.25 nm.

Often it is good to have a cantilever –tip rest on

a surface and record the output as a function

of time

We have the “base” response of the QPD,

need to enhance optical lever and reduce

electrical noise to get better resolution

Quadrant photo-detectors

Why use 4 quadrant detector ?

Vertical deflection of cantilever-Topography

Lateral deflection of cantilever-Lateral Force

Microscopy (LFM)

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 a force of 100pN

Does any thing limit us ?

Yes it is the thermal noise.

It can be very high for “soft” cantilevers (those with very small k)

Thermal Noise limited resolutionFor any oscillatory system we can apply

Equi-partition theorem

2/12/12

2*2

2*2

,,

2

1

k

Tkz

Vmzksystemharmonic

VmzkTk

B

B

For a 0.1N/m cantilever the thermal noise induced root mean-square amplitude 0.14 nm.For a deflection of 1nm of the cantilever it is a substantial amount. Force uncertainty~(100±14)pN

I have discussed some of the basic concepts of the SFM 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 of noise

It will be best if your reflect upon your experience of using SFM and connect to

this presentation

Cantilever Statics and Dynamics

The different modes of SPM

Source: PhD thesis Soma Das , SNBNCBS

Statics and Dynamics of cantilever

• Interaction between the tip and the substrate will decide the nature of force and

hence the statics and dynamics of the cantilever

Tip sample interaction model

Dynamics of cantilever

Any force velocity will add to damping and reduce amplitude of vibration-dissipation

Any force displacement will change the frequency of vibration

Different types of force microscopy depends on the dynamics of cantilever and

the mode of detection

tjFekzdt

dz

dt

zdm

2

2

Simple ball and spring model

Driving term for dynamic

mode

Static mode (contact mode) AFM

tjFekzdt

dz

dt

zdm

2

2

Fkz ω=0

Static mode:

Mostly for contact-mode – the cantilever deflection is such that the bending force is balanced by the force of interaction:

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

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

26)(

z

HRzf t

TS

5.10

0)( )(*

3

4

6 2zaRE

a

HRf t

tzTS

a0~Atomic dimension (hard sphere)

E*~ Effective elastic constant

Rt- Tip radius of curvature.

H=Hamakar cosntant

26)(

z

HRzf t

TS

5.10

0)( )(*

3

4

6 2zaRE

a

HRf t

tzTS

Elastic force wins over. The

deformation of the surface should be

larger than the features you would

like to see

Si tip pressing on Si

substrate

One can evaluate the

contact radius

Herzian contact

The contact area depends on

Elastic modulus

A thumb rule to select cantilever in contact mode imaging

Cantilever touching a surface is like two springs connected back to back, The

force applied is balanced by displacement

The softer spring wins

substratecantilevereff

eff

appl

substrate

appl

cantilever

applsubstratecantilevertotal

kkk

k

F

k

F

k

F

111

.

A thumb rule to select cantilever in contact mode imaging

A surface with mixed k (elastic constants) like a composite of soft and hard matter will not image the topography. What you image is actually a “mixture” of both

substratek

effk

cantileverk

substratek

cantileverk

effk

cantileverk

substratek

,

,

Correct condition for topography in contact mode

The softer spring wins

Will image the elastically deformed surface

Some tips for good contact mode imaging

•Get a soft cantilever that is realistically needed.

•Do a force spectr0scopy (F-d) curve

•Have some idea about the elastic modulus of the surface you image.

•For soft materials when you cannot have very soft cantilever use LFM

ODT self-assembled monolayer on Ag

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

Some useful applications of contact mode AFM

Force spectroscopy

Piezo-force spectroscopy

Conducting –AFM

Local charge measurements

tjFekxdt

dx

dt

xdm

2

2

Dynamic mode

Driving force

Controlled by experimenter

Force of interaction of tip with substrate

and surrounding

Dynamic mode (all non-contact modes):

Cantilever is modulated at resonance frequency and the shift in resonance frequency , phase or amplitude measures the force gradient

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

2)(6))((

tz

HRtzf t

TS

5.10

0))(( ))((*

3

4

6 2tzaRE

a

HRf t

ttzTS

Dynamic mode -what do we do ?

•Oscillate the cantilever at close to resonance frequency

•Interaction with the substrate will change the resonance frequency and /or amplitude of oscillation (through the viscous force on

the surface)

•Detect the departure from resonance or damping detected by amplitude, phase or frequency shift as the cantilever scans the

surface

•This leads to contrast and the imaging

Dynamics of cantilever

222220

0

222220

220

0

0

2

2

)(

)/)(()Im(

)(

))(/()Re(

)(

mFz

mFz

eztz

Fekzdt

dz

dt

zdm

j

tj

In dynamic mode spectroscopy the resonance curve and its modifications during imaging

provides the image

what happens to resonance frequency in dynamic mode when there is additional force

z

Uf

z

fk

z

Ukkeff

,)( 02

2

0

effo m

k0Start 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

20

'

0'0

20

'

0

'20

'0

2

1

2

11

Force derivative is the important parameter in

dynamic mode

NC

Tapping

Force Derivative

55

NC

Tapping

Two paradigms of dynamic mode

Detection by amplitude modulationIf the resonant frequency of a cantilever shifts, then the amplitude of cantilever vibration at a given frequency changes. Near a cantilever’s resonant frequency, this change is 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 at some part of the swing)

The set frequency is somewhat larger than the free resonance frequency.

Non-contact

IC/tapping-mode

The set frequency is somewhat smaller than the free resonance frequency.

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

Das, Sreeram,AKR , Nanotechnology 18, 035501 (2007),Nanotechnology 21, 045706 (2010),Journal of

Nanoscience and Nanotechnology 7, 2167 (2007)

-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

Am

plitu

de (n

m)

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.

Sample: MicaK= 0.68N/mResonance Frequency = 86KHz

Amplitude vs Height (in absence of feedback)

61

Application of Non-contact mode

Magnetic Force Microscopy

MFMMeasuring long-range force

Any force that decays slower than inverse square

26)(

z

HRzf t

TS

2,)( nz

Azf

nlong

26)(

z

HRzf t

TS

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

•MFM is an important analytical tool whenever the near-surface stray-field variation of a magnetic sample is of interest.

•MFM can be used to image flux lines in low- and high-Tc superconductors . MFM have even extended local detection of magnetic interactions to eddy currents and magnetic dissipation phenomena .

•The interpretation of images acquired by magnetic force microscopy requires some basic knowledge about the specific near-field magnetostatic interaction between probe and sample.

•How to take care of the topography ???

The magnetic stray field produced by a magnetized medium and the “contrast” mechanism

effm

F20

'

0'0 2

1

The shift in frequency the MFM detects is the

gradient of the magnetic force

Magnetic Force Microscopy of hard disk

(No applied field)

MFM maps the magnetic domains

on the sample surface

Stored data in a hard disk

The stray field is maximum when the

anisotropy is perpendicular

Magnetic Force Microscopy (with applied field)

Requirements for MFM tips These tips can be coated with a thin layer of magnetic material for the purpose of MFM observations.

A lot of effort has been spent on the optimization of magnetic tips in order to get quantitative information from MFM data .

The problem is that in the coating of conventional tips, a pattern of magnetic domains will arrange, which reduces the effective magnetic moment of the tip. The exact domain structure is unknown and can even change during MFM operation. Best tip is the one that has a single “mono-domain” magnetic particle !!!!!

Lorentz Microscopy of field around a tip

Effect of tip sharpness

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

I have tried to give a basic introduction to SFM and some of its different modes and

shared my experience with you.

SFM images are not just picture gallery

The more knowledge you acquire and more quantitative you become you can get more

value from your SFM.

Thank you