A fresh look to amplitude-modulation AFM:Force minimization, interaction measurement, and the quest for high resolution

8/7/2019 A fresh look to amplitude-modulation AFM:Force minimization, interaction measurement, and the quest for high resolution

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Udo Schwarz Department of Mechanical Engineering Yale University

A fresh look to amplitude-modulation AFM:Force minimization, interaction measurement, and the quest for high resolution

Udo D. Schwarz and Hendrik Hlscher1

Department of Mechanical Engineering, Yale University1 Also: Center for Nanotechnology, University of Mnster

Frontiers of SPM Workshop, Purdue University, October 6th, 2006


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External oscillation of thecantilever

Driven at or close to resonance

Measured quantities:- Amplitude A- Phase

Amplitude-modulation AFM"dynamic force microscopy", "tapping mode"


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=> B. Anczykowski et al., Appl. Phys. A66, S885 (1998)

=> B. Anczykowski et al., Appl. Phys. A66, S885 (1998)

External oscillation of thecantilever

Driven at or close to resonance

Measured quantities:- Amplitude A- Phase

Additional driving with feedbackloop

Amplitude-modulation AFMwith Q-Control


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Conditions:

Sinusoidal oscillation

Optimal time delay t0 = 1/4f0(90)

=> active control of Q-value

( ) ( )4444444444 34444444444 21

&&&

driving-selfbydampingofoncompensati

0dd0 2cos)()(

2)( ttzgctfcatzctz

Q

mftzm zzz +=+

+ ( )0ttzgcz ( )tz

Q

mf&0

2

Compensation of damping by self-driving

=> B. Anczykowski et al., Appl. Phys. A

66, S885 (1998)

=> B. Anczykowski et al., Appl. Phys. A

66, S885 (1998)

0

1

1/effQ

Q g=

Basic principle of Q-Control


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J. Tamayo, A. D. L. Humphris, M. J. Miles, Appl. Phys. Lett. 77, 582 (2000)

S. Gao, L. Chi, S. Lenhert, B. Anczykowski, C. M. Niemeyer, M. Adler, H.Fuchs,

App. Phys. Lett. 82, 4821 (2001)

R. D. Jggi, A. Franco-Obregon, P. Studerus, K. Ensslin, Appl. Phys. Lett. 79,135 (2001)

B. Pignataro, L. F. Chi, S. Gao, B. Anczykowski, C. Niemeyer, M. Adler, H.

Fuchs, Appl. Phys. A. 74, 447 (2002)

A. Grant and L. McDonnell, Ultramicroscopy97, 2919 (2003)

R. W. Stark, G. Schnitter, A. Stemmer, Phys. Rev. B68, 085401 (2003)

T. R. Rodriguez, R. Garcia, Appl. Phys. Lett. 82, 4821 (2003). J. Kokavecz, Z. L. Horvth, A. Melcher, Appl. Phys. Lett. 85, 3232 (2004).

J. Tamayo, J. Appl. Phys. 97, 044903 (2005).

AM-AFM with Q-Control: Existing literature


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J. Tamayo, A. D. L. Humphris, M. J. Miles, Appl. Phys. Lett. 77, 582 (2000)

S. Gao, L. Chi, S. Lenhert, B. Anczykowski, C. M. Niemeyer, M. Adler, H.Fuchs,

App. Phys. Lett. 82, 4821 (2001)

R. D. Jggi, A. Franco-Obregon, P. Studerus, K. Ensslin, Appl. Phys. Lett. 79,135 (2001)

B. Pignataro, L. F. Chi, S. Gao, B. Anczykowski, C. Niemeyer, M. Adler, H.

Fuchs, Appl. Phys. A. 74, 447 (2002)

A. Grant and L. McDonnell, Ultramicroscopy97, 2919 (2003)

R. W. Stark, G. Schnitter, A. Stemmer, Phys. Rev. B68, 085401 (2003)

T. R. Rodriguez, R. Garcia, Appl. Phys. Lett. 82, 4821 (2003). J. Kokavecz, Z. L. Horvth, A. Melcher, Appl. Phys. Lett. 85, 3232 (2004).

J. Tamayo, J. Appl. Phys. 97, 044903 (2005).

AM-AFM with Q-Control: Existing literature


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improve your signal-to-noise ratioJ. Tamayo, J. Appl. Phys. 97, 044903 (2005).

improve your feedback loop (D-A curves has same slope)J. Kokavecz, Z. L. Horvth, A. Melcher, Appl. Phys. Lett. 85, 3232 (2004).

So why would anybody want to use Q-Control to enhance Q?

Sales pitch: Lower tip-sample interaction forces

Better "contrast"

Q-Control does NOT


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Procedure:Solve the equation of motion

Ansatz: z(t) = d+ A cos(2fdt+ )

( ) ( )[ ] ( ) ( )0exitationexternal

ddts0 2cos,)()(

2)( ttzgctfcatztzFtzctz

Q

mftzm zzz ++=+

+

44 344 21&&&& ( )

43421control

0

Q

z ttzgc( ) ( )[ ]4434421&

ninteractio

ts , tztzF

( ) ( ) ( )( ) ( ) ( )( )20d00d2

0d20

20

2d

d

2sinf2cos, tfgQftfgAdIfff

aA

++++=

( )0d2sin tfg ( )0d2cos tfg ( )AdI ,

( ) [ ] ( ) =d1

0

dtsd 2cos...

2,

f

z

dttfFAc

fAdI => H. Hlscher, D. Ebeling, U. D. Schwarz,

J. Appl. Phys. 99, 084311 (2006)

=> H. Hlscher, D. Ebeling, U. D. Schwarz,J. Appl. Phys. 99, 084311 (2006)

For conservative forces:

Analysis of Q-Control with conservativetip-sample interaction


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Tip-sample interaction in airCombines van der Waals forces and DMT-M model


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Instability and hysteresis prevented by Q-Control!

symbols = simulation, dashed line = analytical solutionA

0

= 10 nm, cz

= 40 N/m, E* = 1 GPa

Amplitude curve with tip-sample interaction


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silicon cantilever (300 kHz, 40 N/m) on DPPC filmData: D. Ebeling, University of Mnster

20

15

10

5

0

amplitude(nm)

Q = 1040approachretraction

AM-AFM with Q-control20

15

10

5

0

amplitude(nm)

Q = 306approachretraction

conventional AM-AFM("tapping")

-120

-90

-60

phase(deg)

20151050

distance (nm)

-120

-90

-60

phase(deg)

20151050

distance (nm)

Prevention of instability by Q-Control in airExperimental data


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=> H. Hlscher, D. Ebeling,and U. D. Schwarz,J. Appl. Phys. 99, 084311 (2006)

=> H. Hlscher, D. Ebeling,

and U. D. Schwarz,J. Appl. Phys. 99, 084311 (2006)

Interaction forces likely

too low for molecularresolution!

Amplitude curve with tip-sample interaction


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Procedure:Solve the equation of motion

Ansatz: z(t) = d+ A cos(2fdt+ )

( ) ( )[ ] ( ) ( )0exitationexternal

ddts0 2cos,)()(

2)( ttzgctfcatztzFtzctz

Q

mftzm zzz ++=+

+

44 344 21&&&& ( )

43421control

0

Q

z ttzgc( ) ( )[ ]4434421&

ninteractio

ts , tztzF



cos2

0

22

0

A

aI

f

ffd

even

d +=

sin1

00A

aIff

Q

d

odd

d +=

General analysis of AM-AFM (I)


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Coupled equations:

Definition of integrals:

cos2

0

22

0

A

aI

f

ffd

even

d +=

sin1

00A

aI

f

f

Q

d

odd

d +=

( ) ( )

1/

0, ( )

2

cos 2

d

ts

f

deven d

z

f

I F z f t dt tc tA z + = &

( ) ( )1/

0

2s, ( ) in 2

d

t

f

dodd d

z

sF z t zf

I f t dt c A

t + = &

2

3/ 2

2 tsD A

z Ddzc A z D

F

+

2

z

c A

E

=



General analysis of AM-AFM (II)


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Iodd is related to energy dissipation:

Energy dissipation per cycle:

see also Cleveland et al. Appl. Phys. Lett 72, 2613 (1998)

2

Ac

EI

z

odd

=

2

0

sin1

AcA

a

f

f

QE

z

dd

+=

Analysis of the integral Iodd


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Definition of an integral equation:

Invertion yields:

H. Hlscher,Appl. Phys. Lett.,

in press.

H. Hlscher,Appl. Phys. Lett.,

in press.

Reconstruction of the tip-sample force


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-4

-2

0

2

4

tip-sam

pleforce(nN

)

2.01.51.00.50.0-0.5

tip-sample distance (nm)

DMT modelreconstructed

40

30

20

10

0

energyd

issipation(eV

)

2.01.51.00.50.0-0.5

tip-sample distance (nm)

dissipation modelreconstructed

10

9

8

7

6

5

amplitude(nm)

121086

cantilever position (nm)

-120

-110

-100-90

-80

-70

-60

-50-40

phas

e(degree)

121086

cantilever position (nm)

Numerical simulation of the method


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integration restricted until first instability occurs!

Limited integration range!


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parameters: fd = f0 = 328.61 kHz, cz = 33.45 N/m, Q= 537

Experimental application on silicon in air


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height increaseswith Q-Control!

AM-AFM:Q= 39height: 3.3 0.4 nm

Q-Control:Q= 209height: 5.2 0.4 nm

silicon cantilevercz = 3 N/mf0 = 75 kHz

A0=0.67 VAset=0.5 V

D. Ebeling, H. Hlscher, B. Anczykowski, H. Fuchs, and U. D. Schwarz,

Nanotechnology 17, S221 (2006)



DPPC bilayer in water


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height increaseswith Q-Control!

AM-AFM:Q= 26height: 0.9 0.2 nm

Q-Control:Q= 223height: 1.6 0.2 nm

silicon cantilevercz = 3 N/mf0 = 75 kHz

A0=0.53 VAtap=0.48 VAQ=0.27 V

DNA in liquid (EB buffer)

A li d d l i AFM i li id


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Esubstrate = 20 GPaEisland = 1 GPa

Amplitude-modulation AFM in liquidsSoft island on hard substrate: Model interactions

A lit d d l ti AFM i li id


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symbols = simulation

red = active Q-Control

blue = conventional AM-AFM

Esubstrate = 20 GpaEisland = 1 GPa

1.8 nm

1.1 nm

Amplitude-modulation AFM in liquidsAmplitude vs. distance curves

Th f Q C l i li id


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driving at eigenfrequency (fd = f0)

optimal time delay (90) => increased Qeff

Hertz model with large amplitude approximation

Bielefeldt, Giessibl, Surf. Sci. Lett. 440, L863 (1999)

reduction of indentation depth with Qeff

( )2 2

0*

2( ) z

eff

A A AcD AQ E R

=

=> H. Hlscher and U. D. Schwarz,Appl. Phys. Lett. 89, 073817 (2006).

=> H. Hlscher and U. D. Schwarz,Appl. Phys. Lett. 89, 073817 (2006).

Theory of Q-Control in liquids

Dynamic force microscopy in liquids


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Esubstrate = 20 GPa; Eisland = 1 GPa

Red: active Q-Control

Blue: without Q-Control

Symbols: simulation

Lines: analytical model

=> H. Hlscher andU. D. Schwarz,

Appl. Phys. Lett. 89,073817 (2006).

=> H. Hlscher and

U. D. Schwarz,Appl. Phys. Lett. 89,

073817 (2006).

1.1 nm 1.8 nm

Dynamic force microscopy in liquidsSoft island on hard substrate: Indentation depth

Dynamic force microscopy in liquids


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Esubstrate = 20 GPaEisland = 1 GPa

Red: active Q-Control

Blue: without Q-Control

Symbols:simulation

Lines:analytical model

Dashed lines:soft island

Solid lines:hard substrate

Dynamic force microscopy in liquidsSoft island on hard substrate: Interaction force

C l i


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AM-AFM:Reconstruction of interaction force possible

Q-ControlActive modification of apparent Qvalue

Ambient conditions:

Q-Control prevents repulsive forces, butresulting attractive forces might be too lowfor molecular resolution

Operation in liquids:Reduced interaction forces, but still too high

( )2 20*

2( ) z

eff

A AcD A

Q E R

=

Conclusions

Documents

A fresh look to amplitude-modulation AFM:Force minimization, interaction measurement, and the quest for high resolution