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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
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:
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
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
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)
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
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
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
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 !!!!!
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