Dynamic Atomic Force Microscopy: the quest of the - Iramis

Dynamic Atomic Force Microscopy:
from nonlinear regime to linear
operation
7th of July 2011, LBB, ETH Zürich
Jérôme Polesel Maris, PhD
CEA Saclay, France
[email protected]
7th of July 2011 | J. Polesel Maris | Page 1
Outline
• A.
• B.
• C.
Introduction
Elements for dynamic AFM
Dynamic AFM modes
– C.1.
– C.2.
– C.3.
AM-AFM
PM-AFM
FM-AFM
• D. Dynamic AFM in Liquids
• Outlooks
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 2
A. Introduction
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 3
Atomic Force Microscopy (AFM) or Surface Force
Microscopy (SFM)
Electrostatic Forces
(until micron)
Delayed Dispersive
Forces (hundred of nm)
Dispersive Forces
(tens of nm)
Chemical Forces
(some Angströms)
Repulsive Forces
(D<0)
Apex<10nm
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 4
CNT on gold electrodes
Living Cells
Force Spectroscopy
Transmembrane proteins
Graphene foils
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 5
The first SPM
by G. Binnig,
C. Quate and
Ch. Gerber
(1986)
Nanosurf (2002)
Omicron (2000)
IMT-UniBaselNanosurf (2008)
JPK (2005)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 6
Contact Mode AFM
PET in silica matrix
Topography
G. Meyer, 1988,
IBM Rüschlikon
Friction
But contact mode AFM could be perturbative for soft matter or isolated objects (polymers, cells, proteins, …)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 7
Towards dynamic AFM mode
AFM mode:
Contact
dynamique
dynamique
Polymer latex
particles on mica
Tip-surface
distance:
A.
Introduction
Contact
B. Elements
for Dynamic
AFM
1 nm
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
10 nm
7th of July 2011 | J. Polesel Maris | Page 8
Dynamic AFM
Surface Forces
•Amplitude
Tip-surface
distance
Apex
•Phase
•Frequency
Surface
Piezo
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 9
B. Elements for dynamic AFM
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 10
Dynamic equation of the oscillator
mz(t ) 
m0
z(t )  kc z (t )  w(t )  Fint z (t ), z(t ), D
Qc
w(t)= driving force
Fint [z(t),z(t),D]= Force(s) felt by the probe (tip surface
interaction, but also effects on the cantilever as in liquids)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 11
(1960)
See also Duffing oscillator: http://www.scholarpedia.org/article/Duffing_oscillator
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 12
mz(t ) 
m0
z(t )  kc z (t )  w(t )
Qc
Fint z (t ), z(t ), D  
L{f(t)}
Laplace
transform
HR
2
6D  z (t ) 
B. Elements
for Dynamic
AFM
S ( p)
1

W ( p) kc p 2
02
F.H.A.
F.H.A.= First Harmonic Approximation
A.
Introduction
C ( p) 
C. Dynamic
AFM Modes
N s1   
S ( p)

W ( p)
D. Dynamic
AFM in
Liquids
HR
1
3 D 2  s12

1
1
 N s1 
C ( p)
1

p
Qc0
1

3/ 2
Transfer function
of the AFM !!!
7th of July 2011 | J. Polesel Maris | Page 13
Example: Conservative Interaction
Let’s consider van der Waals force:
nl t  
H .R
2
6D  st 
with
st   s1 sinωt 
First Harmonic Approximation (FHA):
S ( p)

W ( p)
nl t   a1 sinωt   a1 cosωt 
1
1
 N s1 
C ( p)
With
ω 2ωπ
HR
s1
a1   nl t  sin ωt  dt  
π 0
3 D2  s 2
1


3
2
N s1   
ω 2ωπ
a1   nl t  cosωt  dt  0
π 0
HR
1
3 D2  s 2
1


3
2
J. Polesel-Maris et al., Phys. Rev. B 79, 235401 (2009)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 14
Transfer function of a dynamic AFM in interaction with a van der Waals force:
s1
1
 j   1
w0
kc   2 

HR
1
1  2   j

Q0 3kc D 2  s 2
 0 
1


3
2
Expression of amplitude and phase resonance curves:
  0

 w0Qc

 k s
 c 1





2


2

 HR
1
 1 
2   w0



1

1

4
Q
1

Q


c
c
 2Q
 3k
  k s
c
c 1
c D2 s 2



1








  arctan 

  f  2 HR
1
 0Qc 1    
  f  3k
2

c D2  s
1
  0


A.
Introduction
B. Elements
for Dynamic
AFM
 
 
3  
2 
 
2







3 
2 


C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 15
Attractive interaction
1.0n
Force (Newtons)
500.0p
0.0
-500.0p
-1.0n
-1.5n
vdW
-2.0n
-2.5n
-3.0n
1
2
3
4
5
6
Distance (nm)
J. Polesel Maris et al., Nanotechnology 14, 1036 (2003)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 16
Access to Hamaker constant
analytical
experimental

HR
1
3kc D 2  A2


3/ 2
→ Integration on one period of the interaction
• Hamaker constant H of dipolar coupling  1eV
J. Polesel Maris et al., Nanotechnology 14, 1036 (2003)
J. Polesel Maris et al., Nanotechnology 15, S24 (2004)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 17
Repulsive interaction
1.0n
Force (Newtons)
500.0p
0.0
-500.0p
-1.0n
-1.5n
Morse
-2.0n
-2.5n
-3.0n
1
2
3
4
5
6
Distance (nm)
M. H. Korayema and N. Ebrahimi, J. Appl. Phys. 109, 084301 (2011)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 18
Both Attractive and Repulsive interaction
1.0n
Force (Newtons)
500.0p
0.0
-500.0p
-1.0n
-1.5n
Morse+vdW
-2.0n
-2.5n
-3.0n
1
2
3
4
5
6
Distance (nm)
L. Wang, Appl. Phys. Lett. 73, 3781 (1998)
M. H. Korayema and N. Ebrahimi, J. Appl. Phys. 109, 084301 (2011)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 19
Master Equations, general treatment:
Expression of amplitude and phase resonance curves:

2

2
 


Qc   w0 Qc 
 w0 Qc    
    
1 14 2 1

 

 k s    2Q
 
   kc s1  
c
 c 1


 


2
2
f  f0






f
  arctan 

  f 2




 f 0Qc 1       
f

  0
 
J. Polesel-Maris et al., Phys. Rev. B 79, 235401 (2009)
General treatment of the forces:


s1kc
2 / 
 F s(t ), Dsint dt
Conservative part
int
0
Qc
  1
s1kc
2 / 
 F s(t ), Dcost dt
Dissipative part
int
0
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 20
C.1. AM-AFM
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 21
AM-AFM (Amplitude Modulation), also called
Tapping AFM
• For a constant excitation frequency and a constant drive signal
• Tracking of the amplitude modulation
w(t)=w0.cos(2.π.fexc.t)
A.
Introduction
B. Elements
for Dynamic
AFM
s(t)=A(t).cos( 2.π.fexc.t+φ(t) )
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 22
AM-AFM
Light Source
Photodiode
Lock-In
A
Frequency
Generator
Drive Out
ADC
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 23
40
-/2
32
-
amp. exp. 0nma
amp. exp. 2nma
amp. exp. 4nma
amp. exp. 6nma
amp. exp.8nma
amp. exp. 10nma
amp. exp. 12nma
amp. exp. 14 nma
amp. exp. 16nma
amp. exp. 120nmr
A (nm)
24
16
8
0
-10
 (radians)
0
48
-/4
48
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
-/2
10
Df (Hz)
44
-3/4
40
A (nm)
36
From resonance curves to… Distance curves
32
28
24
20
0
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
8
16
24
DD-120Hz (nm)
32
7th of July 2011 | J. Polesel Maris | Page 24
Hysteresis between net attractive and net repulsive
regime
0.6
0.4
0.0
-0.2
-0.4
-0.6
0.990
0.992
0.994
0.996
0.998
1.000
1.002
Phase (radians)
A0=3nm
D=3nm
Q=400
k=25N/m
0.2
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1.004
NC = Non Contact regime,
<attractive>T
IC = Intermittent Contact regime,
<repulsive>T
normalized Frequency
0.6
0.4
0.2
0.0
IC
-0.2
-0.4
-0.6
NC
-0.8
fdown=0. 99144
-1.0
0
1
1.0
normalized
Amplitude
0.8
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
Phase (radians)
normalized
Amplitude
1.0
2
0.8
0.6
0.4
0.2
0.0
IC
-0.2
-0.4
-0.6
NC
-0.8
0
Distance (D/A0)
A.
Introduction
B. Elements
for Dynamic
AFM
fdown=0. 99744
-1.0
1
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
Phase (radians)
normalized
Amplitude
0.8
2
Distance (D/A0)
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 25
Hysteresis effect and non-linearity
Contact mode AFM
(Force curve)

AM-AFM
Due to adhesion forces !
Due to nonlinearities !
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 26
Nonlinearity and AM-AFM imaging
1
L state
2
3
H state
1
2
L state
3
Instabilities due to the non-linear behavior of the oscillator
R. Garcia et al., Phys. Rev. B 61, 13381 (2000)
and not to a bad tip !
R. Garcia et al., Surf. Sci. Rep.47, 197 (2000)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 27
0.2
0.0
-0.2
-0.4
-0.6
0.990
0.992
0.994
0.996
0.998
1.000
1.002
0.6
0.4
-0.2
-0.4
-0.6
-0.8
-1.0
0.0
-0.4
-0.6
0.990
0.992
0.994
0.996
0.998
1.000
1.002
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1.004
B. Elements
for Dynamic
AFM
0.6
0.4
0.2
-0.2
normalized Frequency
A.
Introduction
0.8
0.0
Phase (radians)
A0=10nm
D=8nm
Q=400
k=25N/m
-0.2
1.5
C. Dynamic
AFM Modes
2.0
2.5
Change frequency → change NC/IC distance
normalized
Amplitude
normalized
Amplitude
0.6
0.0
1.0
1.0
0.8
0.2
0.5
Distance (D/A0)
normalized Frequency
0.4
fdown=0. 99744
f0=1
fup=1.00256
0.2
0.0
Phase (radians)
A0=3nm
D=3nm
Q=400
k=25N/m
0.4
A0=3nm
-0.4
-0.6
-0.8
-1.0
0.0
0.5
1.0
1.5
6.0
5.5
5.0
4.5
4.0
3.5
A0=10nm 3.0
2.5
A0=5nm
2.0
A0=3nm
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
2.0
2.5
Phase (radians)
0.6
normalized
Amplitude
normalized
Amplitude
0.8
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1.004
0.8
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
Phase (radians)
1.0
Distance (D/A0)
Change drive amplitude → change NC/IC regime ratio
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 28
<Repulsive>T = IC
<Attractive>T = NC
<Repulsive>T
<Attractive>T
R. Garcia et al., Phys. Rev. B 60, 4961 (1999)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 29
Some advices to optimize AM-AFM
• The choice of the excitation frequency and also the driving amplitude is
critical to obtain stable conditions of imaging
• Only A(D) cannot give the net repulsive or net attractive regime of the
interaction → We need the phase φ(D) !
• Use the phase signal to optimize your setpoint for imaging !
• The choice of an excitation frequency lower than f0 contribute to stable
imaging in liquid with no destroying of soft materials (e.g. cells)
• Noncontact (NC) operation in liquids is more difficult than in air ambient due
to weak van der Waals interaction → check the phase φ(D) to be in IC !
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 30
How to convert dynamic data into force values ?
A. J. Katan et al., Nanotechnology 20, 165703 (2009)
J. E. Sader and S. P. Jarvis, Appl. Phys. Lett. 84, 1801 (2004)
with:
with (for ωd = ωc):
kc : spring constant
ωd : Excitation frequency
ωc : resonance frequency
Qc : quality factor
ad : Excitation amplitude
afree : free amplitude at ωc
a(d) : amplitude vs. distance
φ(d): phase vs. distance
ΩAM : normalized frequency shift
And also for the dissipated energy:
F. Montagne, J. Polesel-Maris et al., Langmuir 25, 983 (2009)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 31
Calibration is necessary to quantify forces and
energy
• Amplitude calibration
– Force curve, but be careful to the bandwith ! (DC and AC response)
– A(d) curves but with high A0, high Q factor (in air, not in liquid), stiff surface
4.0
0.8
3.5
0.6
3.0
0.4
2.5
0.2
0.0
2.0
-0.2
1.5
-0.4
1.0
-0.6
0.5
-0.8
-1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0
2.0
Phase (radians)
normalized
Amplitude
1.0
Distance (D/A0)
• Spring constant calibration
1
1
k
.
T

K . z (t )
– Thermal noise analysis (in air !) : 2 B
2
2
– Cleveland method, reference cantilever method,
geometrical determination
E.w.t 3
K
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
3.L3
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 32
Conclusions for AM-AFM
Good:
• Very easy instrumentation
• Very easy to set (only one loop: ADC)
Drawbacks:
• Bi-stabilities non-linear jump
• Limited to low Q factor operation (τ=Q/π.f0)
• No direct access to conservative and dissipative contributions
of the tip-surface forces
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 33
C.2. PM-AFM
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 34
PM-AFM (Phase Modulation)
• For a constant excitation frequency and a constant oscillation
amplitude
• Tracking of the phase shift between w(t) and s(t)
w(t)=K.(A(t)-A0).cos( 2.π.fexc.t )
A.
Introduction
B. Elements
for Dynamic
AFM
s(t)=A(t).cos( 2.π.fexc.t+φ0+Δφ(t) )
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 35
PM-AFM
Light Source
Photodiode
Lock-In
D
AGC
Dissipation
.
Drive Out
ADC
AGC= Automatic Gain
Controller
A.
Introduction
Frequency
Generator
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 36
Linearization by constant amplitude operation







   arctan 
.
2
 Q0  

1  2    


 0
 
And the driving force:
w0 
s1kc 
1

Q 0 sin  
to maintain the amplitude S1 constant
,  = constant for a given distance D, with s1=A0 → no longer nonlinearities !!!
Example with pure conservative van der Waals interaction:




  arctan 
2

  
1
 0Qc 1   f   HR



f
3kc D 2  s 2

1
  0


B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes

Constant oscillation
amplitude (PM-AFM,
FM-AFM)
Constant drive force
(AM-AFM)
A.
Introduction






3 
2 

D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 37
PM-AFM imaging
Y. Sugawara et al., Appl. Phys. Lett. 90, 194104 (2007)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 38
10.0n
5.0n
0.0
-5.0n
A0=10nm
A0=3nm
-10.0n
-15.0n
-20.0n
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
2.4
Phase (radians)
Force (Newtons)
Approach curves in PM-AFM
Distance (D-A0)
• Higher is A0, lower is the phase shift
• Bi-stabilities have disappeared (smooth transition)
• Phase curves “resembles” to the Force curves, but…
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 39
How to convert dynamic data into force values ?
The same equations as for AM-AFM !
Keep in mind:
Phase shift approach curves mixes conservative and dissipative parts
of the interaction …
Not so easy analytical treatment …
A. J. Katan et al., Nanotechnology 20, 165703 (2009)
J. E. Sader and S. P. Jarvis, Appl. Phys. Lett. 84, 1801 (2004)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 40
Conclusions for PM-AFM
Good:
• Easy instrumentation
• Easy to set (two loops: AGC, ADC)
• No instabilities of the signal (linearization with A=constant)
• “Instantaneous” change of phase shift Δφ for a change in Force
→ Fastest dynamic AFM, ready for “video rate AFM” !!!
• More sensitive than AM-AFM
following “N. Kobayashi et al., Jap. J. Appl. Phys. 45, L793 (2006)”
Drawbacks:
• No directly accessible on commercial AFM machine (until now!)
• No direct access to conservative and dissipative contributions of the
tip-surface forces
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 41
C.3. FM-AFM
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 42
FM-AFM (Frequency Modulation), also called
non contact AFM
• For a constant phase shift (-π/2) and a constant oscillation
amplitude A0
• Tracking of the frequency shift Δf(t)
w(t)=K.(A(t)-A0).cos( 2.π.(f0+Δf(t)).t-π/2 )
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
s(t)=A(t).cos( 2.π. .( f0+Δf(t)).t )
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 43
FM-AFM
Light Source
Photodiode
PLL
Df
AGC
Dissipation
.
PLL= Phase Locked
Loop (frequency
shift )
Drive Out
ADC
ADC= Automatic
Distance Controller
A.
Introduction
Phase
shifter
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 44
Two signals for Conservative/Dissipative parts







   arctan 
.
2
 Q0  

1  2    


 0
 
And the driving force:
w0 
s1kc 
1

Q 0 sin  
to maintain the amplitude S1 constant
,  = constant for a given distance D, with s1=A0 → no longer nonlinearities !!!
 2  02


2.D





02
Q0 tan 
0

   = tracked by the PLL
2
→ Frequency shift proportional to conservative part of the force:
D
 
0

2
B. Elements
for Dynamic
AFM

2
→ Driving force (or damping, dissipation signal) proportional to
dissipative part of the force:
Ak
w0 
A.
Introduction

C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
0 c
Q

7th of July 2011 | J. Polesel Maris | Page 45
FM-AFM imaging
F=0.1 nN
<F>=0.3 nN
k=0.1N/m
F=0.3 nN
Contact AFM
f0=107kHz, Q=6.2 k=46N/m, A0=0.64 nm
<F>= 0.8 nN
FM-AFM
• FM-AFM operation reduces lateral friction
forces and small sensitivity to drift
• Very small-amplitude operation overcomes
the large frequency noise due to the low Q
factor in water
• Small amplitude possible only for stiff lever !
kc A  Fint
Purple membrane in buffer solution
B. W. Hoogenboom et al., Appl. Phys. Lett. 88, 193109 (2006)
T. Fukuma et al., Appl. Phys. Lett. 87, 034101 (2005)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 46
10.0n
20.0m
18.0m
16.0m
5.0n
14.0m
12.0m
0.0
10.0m
8.0m
-5.0n
6.0m
A0=10nm
A0=3nm
-10.0n
4.0m
2.0m
0.0
-15.0n
Df/f0
Force (Newtons)
Approach curves in FM-AFM
-2.0m
-20.0n
0.6
-4.0m
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Distance (D-A0)
• Higher is A0, lower is the frequency shift
• Bi-stabilities have disappeared (smooth transition)
• Frequency shift curves is very similar to the Force curves, but…
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 47
How to convert dynamic data into force values ?
For any amplitude A:
with:
D ( z )
0

T. Uchihashi et al., Appl. Phys. Lett. 85, 3575 (2004)
( z )
 ( z )
2

For small amplitude A~λ (Angströms) :
Fsmall z   k   ( z ' ) dz '
Force gradient constant during
one oscillation period
z
F. Giessibl, Rev. Modern Phys. 75, 949 (2003)
J. E. Sader and S. P. Jarvis, Appl. Phys. Lett. 84, 1801 (2004)
For large amplitude A>10.λ :

1
d( z ' ) 1
Flarge z   
.k. A03 / 2 
dz '
dt
2
z'-z
z
Dissipated Energy:
A.
Introduction
with:
kA02  w0 ( z ) 
kA02  ( z ) 


E z   
 1  
 1
Q  w0 () 
Q   () 
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
 z   k. A03 / 2
( z )
2
A.A. Farell et al., Phys. Rev. B 72,
125430 (2005)
7th of July 2011 | J. Polesel Maris | Page 48
Conclusions for FM-AFM
Good:
• Direct access to conservative and dissipative contributions of
the tip-surface forces
• Adapted for high quality factor (τ=1/f0)
• No instabilities of the signal (linearization with A=constant)
Drawbacks:
• Heavy instrumentation
• Not so easy to set (three loops: AGC, PLL, ADC)
• Delayed response for Δf (electronics) …
• Instabilities of the signal (double solution for Δf) …
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 49
D. Dynamic AFM in Liquids
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 50
Resonance determination in liquid
Acoustic excitation
spectrum
Thermal noise
spectrum
The thermal noise spectrum analysis allows to focus on the correct resonance peaks of
the cantilever.
But, what to do if cantilever peak is inside the liquid cell peaks ?
→ Change liquid cell configuration, Active driving, Q Control
A. Maali et al., Appl. Phys. Lett. 88, 163504 (2006)
T. E. Schäffer et al., J. Appl. Phys. 80, 3622 (1996)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 51
Effects of the added mass of liquid
 
f 
Damping
Thermal noise,
in water
(I) D=41.6 um, f0=27.134 kHz, Q=3.45
(II) D=1.2 um, f0=23.506 kHz, Q=1.4
(IV) D=0.025 um, f0=19.967 kHz, Q=1.09
Effects of the fluid:
• Lowering of the resonance frequency
• Reducing of the quality factor
A. Maali et al., J. Appl. Phys. 99, 024908 (2006)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 52
Ways for analytical treatment for liquid AFM
Shear stress
20 um
Surface
M. H. Korayem et al., J. Appl. Phys. 109, 084301 (2011)
S. Basak et al., J. Appl. Phys. 99, 114906 (2006)
New force term in dynamic equation:
Fint z(t ), z(t ), D  Ftipsamplez(t ), z(t ), D  Fliquid[ x, t ]
To obtain :
 2 wx, t 
wx, t 
Such as: Fliquid[ x, t ]    a

c
a
t 2
t
2 liq
3
2
b
With:  a  liqb 
12
4


and:
Added mass of liquid
A.
Introduction
B. Elements
for Dynamic
AFM


s1kc
2 / 
F
int
sin t dt
0
Q
  1 c
s1kc
2 / 
F
int
cost dt
0
3
b3
ca  3 
b 2 liq 
4
H x, t 
Free hydrodynamic damping Surface Squeezing damping
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 53
Conclusions for dynamic AFM in liquid
Good:
• Use High frequency and the smallest cantilever with long tip to
reduce the hydrodynamics and squeezing force (↘ ρa and ↘ ca )
• Active excitation of the cantilever
• Very small amplitude operation increase the SNR… but needs
stiff lever
Drawbacks:
• Optical artefacts and limitations (interfringes, non-transparent
solution, diffraction limit to ~5um for cantilever dimension,
problem with photosensitive samples)
A.
Introduction
B. Elements
for Dynamic
AFM
C. Dynamic
AFM Modes
D. Dynamic
AFM in
Liquids
7th of July 2011 | J. Polesel Maris | Page 54
Outlooks
• Why not to implement self-sensing cantilevers !
1 um
Caltech 1 MHz piezoresistive self-sensing SPM cantilever
with tip (M.L.. Roukes, 2006)
Tuning fork with tip (CEA Saclay, J. Polesel, 2010)
7th of July 2011 | J. Polesel Maris | Page 55
Last question ?
(A)
(B)
7th of July 2011 | J. Polesel Maris | Page 56
Suggestions for reading:
• L. Nony et al., "Nonlinear dynamical properties of an oscillating tip–
cantilever system in the tapping mode", J. Chem. Phys. 111, 1615
(1999)
• F. Giessibl, "Advances in atomic force microscopy ", Rev. Modern
Phys. 75, 949 (2003)
• M. Lantz et al., "Dynamic Force Microscopy in Fluid", Surf. Interface
Anal. 27, 354-360 (1999)
• M. H. Korayem et al., "Nonlinear dynamics of tapping-mode atomic
force microscopy in liquid", J. Appl. Phys. 109, 084301 (2011)
• B. Gotsmann et al., "Conservative and dissipative tip-sample
interaction forces probed with dynamic AFM", Phys. Rev. B 60, 11051
(1999)
7th of July 2011 | J. Polesel Maris | Page 57
Thank you for you attention !
And I’m sure that you have many questions ;-)
[email protected]
7th of July 2011 | J. Polesel Maris | Page 58
7th of July 2011 | J. Polesel Maris | Page 59