Transcript Document

Basics of Scanning probe microscopy
A.K. Raychaudhuri
Unit for nanoscience and Theme Unit of
Excellence in Nanodevices
S.N. Bose National Centre for Basic Sciences
Kolkata-700098
SNBNCBS and Bruker School
December 14-15, 2011
www.bose.res.in
•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.
The Scanning Probe Microscope
What are the basic components of a SPM
A nano-positioning
mechanism that can
position the probe in
“close proximity”
Localized Probe
that has an
“interaction”with
the substrate to
be imaged
of the surface
SPM
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
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.
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.
•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.
The Scanning Probe Microscope (SPM) family
STM (Tunneling)
SFM (Force)
C-AFM
Atomic Force
Microscope (AFM)
STS,STP,Scanning
Electrochemical
Microscope
Lateral Force (LFM)
Magnetic Force
SPM
(MFM)
Electrostatic Force
(EFM)
Scanning Thermal
Microscope (Local
Temperature)
Scanning Near Field
Optical Microscope
(Optical imaging)
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
One can make a cantilever as a force measuring element
that can have the same order of k as that of a molecule.
w
Si elastic modulus (E)
L L
[111] Young's modulus= 185GPa
[110] Young's modulus=170 GPa
[100] Young's modulus= 130 Gpa
Si3N4 ~300 Gpa
For a Si cantilever :
3
k=
Et w
4L3
1
k
f=
2π m*
t = 5m, w= 20 m, L= 200 m
k=10N/m
It can be softer than atomic
spring constant
Engineering cantilevers with different spring
constant k- need for different applications
3
Et wb
k=
3
3
3
2b(L1 -L2 ) + 6wL2
L2
L1
t: thickness
m*~0.24(mass of the cantilever)
b
Advantages:
w
1.Less prone to vibrational
noise.
2. Can go to lower k or
resonance frequency.
Engineering cantilevers with different spring
constant k-a real triangular cantilever
Cantilever
What ever you do with SFM,
the cantilever is the “key”.
You need to know it.
Tip
Estimated radius of curvature of the tip Rt ~ 30 nm
Kc=0.1 N/m
Much softer than an
atomic spring !!!!
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
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)
QPD
Scan Piezo
Inertial drive piezo
X-Y micrometer stage
Electronics
Schematic of SFM
DEFLECTION
SENSOR
CANTILEVER
FEEDBACK
LOOP
COMPUTER
PROBE
TIP
XY-PIEZO SCANNER
Z-PIEZO
Keeps cantilever
deflection or oscillation
amplitude constant
Practical Considerations for AFM/SFM
1.
2.
3.
4.
Cantilever deflection detection system.
Type of cantilevers that can be used.
Coarse and fine approach mechanism.
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?
Basic schematic for SPM
Pre-Amplifier
A
Keeping “something”
constant, need for feed back
Laser
B
Tip &
Cantilever
A-B
Quadrant
Photo Detector
PID
Pixels
Feedback
DAC
Scanner
ADC
X-Y scanner
Z-scanner
bits
To Z-Piezo
Coarse approach vs fine approach
Need for
calibration
Calibration of scanning stage of SFM using commercial
2-D grating
The grating has 2160 lines/mm
1000µm/2160=0.46µm
The calibration: 40nm/V
Brar et.al
(2002)
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
Topography
Can take care of
image distortion
Soma Das
(2008)
Calibration in atomic rangeA freshly cleaved surface
7 nm x 7 nm
Mica
Freshly cleaved
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
Pre-Amplifier
A
Laser
B
Tip &
Cantilever
A-B
Quadrant
Photo Detector
Feedback
DAC
Scanner
To Z-Piezo
ADC
Main components of the optical
stage:
1. Laser diode
QPD is used as a position
sensitive detector, its output
signal is proportional to the
position of the laser spot.
2. Cantilever
3. Quadrant photo-detector (QPD)
4. Collimating lenses
5. Mirror
Why we need smaller cantilever ?
 L(Length of the laser path) 
Optical lever = 

l(Length
of
the
cantilever)


= 500 -100(for l=100mm)
Calibration of the optical stage.
A-B(V)
2
0
-2
Region of Gradient: 1000m
0
1
2
3
Z-displacement(cm)
•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
Often it is good to have a
cantilever –tip rest on a
surface and record the
output as a function of time
2
A-B(V)
We have the “base” response
of the QPD, need to enhance
optical lever and reduce
electrical noise to get better
resolution
0
-2
Region of Gradient: 1000m
0
1
2
3
Z-displacement(cm)
•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.
Quadrant photo-detectors
Why use 4 quadrant detector ?
Vertical deflection of cantileverTopography
Lateral deflection of cantileverLateral 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 resolution
For any oscillatory system we can apply
Equi-partition theorem


1
k BT  k z 2  m * V 2
2
harm onic system, k z 2  m* V 2 ,
z
2 1/ 2
1/ 2
 k BT 


 k 
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
Simple ball and spring model
2
d z
dz
jt
m 2 
 kz  Fe
dt
dt
Any force  velocity will
add to damping and
reduce amplitude of
vibration-dissipation
Driving term
for dynamic
mode
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
Static mode (contact mode)
AFM
d 2z
dz
m 2 
 kz  Fe jt
dt
dt
kz  F
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.
HRt
fTS ( z )  
6z 2
a0~Atomic dimension (hard sphere)
E*~ Effective elastic constant
Rt- Tip radius of curvature.
HRt 4
1.5
fTS ( z )  

E
*
R
(
a
0

z
)
t
6a 0 2 3
H=Hamakar cosntant
HRt 4
1.5
fTS ( z )  

E
*
R
(
a
0

z
)
t
6a 0 2 3
Elastic force wins
over. The deformation
of the surface should
be larger than the
features you would
like to see
HRt
fTS ( z )  
6z 2
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
 total   cantilever   substrate 
Fappl
kcantilever

Fappl
k substrate
1
1
1


keff kcantilever k substrate
The softer spring wins

Fappl
keff
.
A thumb rule to select cantilever in contact
mode imaging
The softer spring wins
,k
k
cantilever eff
cantilever
k
 k
,k
k
substrate
cantilever eff
substrate Will image the
elastically
deformed surface
k
substrate
 k
Correct
condition
for
topography
in
contact mode
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
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
Dynamic mode
2
d x
dx

m

 kx  Fe
dt
dt
j t
2
Force of interaction of
tip with substrate and
surrounding
Driving force
Controlled by
experimenter
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)
HRt
fTS ( z (t ))  
6 z (t ) 2
HRt 4
1.5
fTS ( z ( t ))  
 E * Rt (a 0  z (t ))
2
6a 0
3
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
d 2z
dz
j t
m



kz

Fe
d t2
dt
j
z (t )  z 0 e
( F / m )( 02   2 )
Re( z 0 ) 
2
2 2
2
2
( 0   )   
( )(F / m)
Im (z 0 ) 
2
2 2
2
2
( 0   )   
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
Start with a cantilever that is free
 k eff  k 0
o 
k0
meff
 2U
f
U
(
)  k0 
, f  
2
z
z
z
Shift in resonance frequency when the interaction is turned on
 
'
0
keff
meff
'
'

f
1
f
2
 0 
 0 1 
 2  2m
meff
0 eff

'
1
f
'
  0  0 
2 02 meff




Force derivative is the
important parameter in
dynamic mode
Tapping
NC
55
Force Derivative
Tapping
NC
Two paradigms of dynamic mode
Detection by amplitude modulation
If 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)
Non-contact
The set frequency is somewhat larger than the free
resonance frequency.
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)
Sample: Mica
K= 0.68N/m
Resonance Frequency = 86KHz
Sample:Mica
80.000003800
70.000003325
Amplitude (nm)
60.000002850
50.000002375
40.000001900
30.000001425
approach(41nm)
retract(41nm)
approach(70nm)
retract(70nm)
approach(90nm)
retract(90nm)
20.000000950
10.000000475
0.000000000
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Tip-sample separation (m)
Amplitude vs. distance curves for mica for three different free vibration amplitude of
the cantilever.
61
Amplitude vs Height
(in absence of feedback)
Application of Non-contact mode
Magnetic Force Microscopy
MFM
Measuring long-range force
Any force that decays slower than
inverse square
A
f long ( z )   n , n  2
z
HRt
fTS ( z )  
6z 2
HRt
fTS ( z )  
2
6z
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
'
1
F
  0'  0 
2 02 meff
The shift in frequency the
MFM detects is the gradient
of the magnetic force
Magnetic Force Microscopy of hard disk
(No applied field)
Stored data in a
hard disk
MFM maps the
magnetic domains on
the sample surface
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
Ordinary tip
Mono-domain
tip
Stray field line scan
Observed
Simulated
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