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Apply Tapping Mode Atomic Force Microscope

with CD/DVD Pickup Head in FluidShih-Hsun Yen, Jim-Wei Wu, and Li-Chen Fu

AbstractThis paper proposes a tapping mode scanningsample type Atomic Force Microscope (AFM) equipped with

a CD/DVD pick-up-head (PUH) used to measure the

deflection of the cantilever beam of the probe in the liquid.

To start with, we build an adaptive Quality-Factor-controller

(Q-controller) to modulate the interaction force between the

tip and the sample. To implement the above systems, we have

designed a novel AFM mechanism and proposed an adaptive

sliding-mode controller for it. For testing the system

capability and analyzing the biomorphic change of the

sample in liquid, we have conducted a series of experiments,

and the results can help us to understand more about the

mechanism of the sample in liquid.

I.INTRODUCTION

Biological samples can be imaged with AFM in eitherof the two imaging modes: contact mode or tapping mode

[1][2]. For AFM studies, biological materials are often

both delicate and tenuously immobilized on a surface,

even more so in fluid than in air. As a result, the vertical

and shear forces exerted on the sample via the tip in

contact mode can damage the sample by compressing,

tearing, or removing it from the surface[3].

Applications of fluid tapping mode AFM [4] [5] in

biology are constantly growing and the data obtained with

this technique are improving, especially in terms of

resolution. Even dynamic processes can be observed

almost as they would occur in vivo [6]. So far, in the

literature there exists an AFM which is developed using

CD/DVD PUH [7] [8] [9]. A PUH is light enough to becarried for rapid scan so that the sample can remain fully

stationary. Besides, a cost-effective, and lightweight

system with good scanning performance will be needed

for scientific development and is valuable in industrial

applications. The goal of this research is to design an AFM

with the aforementioned features. Utilizing an optical

pickup device as the measuring system and developing an

advanced feedback controller are the appropriate methods

to realize such a system [10][11]. For the former, there

still exists difficulty in employing CD/DVD PUH in liquid,

namely, the measuring system will encounter refraction

problem when the light has to go through different media,

and hence a novel mechanical design has been herebydesigned to solve this tough situation. As for the latter, this

research build an adaptive Qcontrol, for adjusting the Q

factor of a piezo-actuated bimorph probe dynamicallyduring scanning when necessary [12][13][14]. Specifically,

in our approach the Q factor of the probe is modified

adaptively depending on the profile of the surface being

scanned.

There are four sections in this paper. Section II

describes the system design from the viewpoint of

hardware/software. Then, in section III adaptive Qcontrol

and adaptive sliding- mode control are proposed and

analyzed to assure satisfactory operating performance of

the designed AFM. Numerical simulation and extensive

experiments are also provided in this chapter to validate

our design. In the final section, wewill make a conclusionsummarizing the hereby obtained achievements.

II. SYSTEM DESIGN

A schematic diagram of the experimental setup of an

AFM driven in the amplitude modulation mode (tapping

mode) is shown in Fig. 1. The cantilever is driven at a

fixed frequency by a constant sinusoidal signal originating

from the lock-in amplifier, and the resulting oscillating

amplitude is also detected by the lock-in amplifier. The

PC-based controller we have designed will use that signal

to adjust the z-scanner. The piezoelectric tube scanner is

driven by a homemade high voltage amplifier, whose

operation range is -200 V to +200 V. The scanning range

is 35 m 35 m 9 m in x-direction, y-direction, and

z-direction, respectively.

Figure 1. Schematic drawing of the experimental setup of the AFM

system using the constant excitation mode. A PC-based controller is used

to compensate the xy-trajectory and to reduce the tracking error in z-axis.

Unlike other commercial AFM, we use CD/DVD PUH

to detect the cantilevers oscillation amplitude in this work.

It is worthy to note that positions of all elements of the

entire AFM setup may change due to heat or other factors,

and therefore we should properly adjust our system to

make sure the laser beam focuses on the tip. When we

S. H. Yen and J. W. Wu are with the Department of Electrical

Engineering, National Taiwan University, Taipei, Taiwan, ROC.(e-mail:d96921004@ntu.edu.tw)

L. C. Fu is with the Department of Electrical Engineering and

Department of Computer Science and Information Engineering,National Taiwan University, Taipei, Taiwan, ROC.

(e-mail:lichen@ntu.edu.tw)

This work was supported by National Science of Council under the

grant NSC 98-2218-E-002-014.

2010 American Control ConferenceMarriott Waterfront , Baltimo re, MD, USAJune 30-July 02, 2010

FrC08.5

978-1-4244-7425-7/10/$26.00 2010 AACC 6549

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operate the AFM in liquid, the laser beam can be refracted

or scattered and its hard to focus it at a focal point. As a

result, we construct a mechanism to ensure the laser beam

does focus on the tip without suffering from refraction or

scattering. Besides, this mechanism can prevent

movement of the laser spot when the scanner is moved

upward and downward.

The kernel element of the designed AFM system is thepickup head (as shown in Fig. 4), which is used to

measure the cantilever deflection. As mentioned earlier,

the relative positions of different components may change

due to temperature variation or other factors, but the laser

beam always needs to focus on the tip exactly. Besides,

the probe may be worn away by scanning [15], thereby a

precision tuning mechanism (see Fig. 2) needs to be

incorporated to solve this problem. The mechanism

includes a precision miniature linear stage, a piezoelectric

element (bimorph), a magnet, and a magnetic mount. The

piezoelectric element [16][17][18] is to oscillate the

cantilever in tapping mode operation; the magnetic mount

is to fix the probe; the rest are to enable preciserepositioning of the probe which is just newly installed,

replacing the previous obsolete one. In normal situation,

the cantilever should reveal high Q-factor property in the

frequency response so that a slight shift in the driving

frequency may induce significant decrease in oscillation

amplitude. To prevent this from happening, a function

generator based on direct digital synthesized (DDS)

technology is incorporated in the system. During the

calibration process, the focusing error (FE) signal is

monitored to confirm at the middle the linear region of

operation.

The precision miniature linear stage is to establish theability to reposition the probe whenever the probe is

shifted, and resolution and weight of the stage are 0.01mm and 0.1 kg, respectively. The above arrangement

implies that the repositioning accuracy is improved

significantly and the total weight of the AFM platform is

still kept light. Overall speaking, the precision miniature

linear stage can offer more robust and steadier

performance while reducing operational inconvenience.

Figure 2. The view of the precision tuning mechanism.

In order to scan the sample immersed in the water, one

special novel mechanism has been designed (see Fig. 3(a)),

so that a cover slip can be inserted between the probe and

the CD/DVD PUH lens through the guiding chamfers

located at the two inner edges of the above mechanism

(see Fig. 3(b)). By resorting to water capillary

phenomenon, a good environment for liquid scanning has

been created. Such a novel design can fit the liquid

environment well since we can prevent the probe while

scanning the sample from back-and-forth motion between

liquid and air media causing excessive disturbance to the

path of the laser beam shed on the back of the tip. Another

advantageous feature of this design is that we can alleviatethe problem with variation of the focal point of the laser

beam due to refraction caused by immersing of the probe

in liquid medium. The last but not the least, such design

also makes the process of calibrating the probes light path

quite easily in liquid experiment.

(a)

(b)

Figure 3. (a) The view of reduced refraction design, (b) the views of

the enlarged kernel parts of the AFM system.

Figure 4. The view of the DVD PUH.

III. TAPPING MODE TYPE AFM

A. Operation Scheme

Tapping mode is a very useful technique. The cantileverof the probe is oscillated vertically by a small

piezoelectric element near it is resonance frequency. The

amplitude and phase of the cantilever during the scanning

process is usually measured by a lock-in amplifier, and the

topography image is obtained by monitoring these

changes. Because of the short intermittent contact, tapping

mode AFM greatly reduces irreversible destructions on

sample surfaces, so that it has been widely used for

non-destructive imaging of soft and fragile materials such

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as polymers and biological samples. The lateral force is

also greatly reduced in contrast with the case of contact

mode, but the resolution of the imaging is still limited by

the tip radius.

With the help of the adaptive Q-Control module [19], it

is possible to reduce the damping of the dynamic system,

i.e.to increase the effective quality factor of the oscillating

cantilever and thereby to enlarge the regime ofnet-attractive interaction forces. Therefore, delicate and

highly sensitive surface structures that originally can not

be scanned with a standard scanning force microscope can

now be characterized with high resolution after applying

adaptive Q-Control. As a result, the effective quality (Q)

factor of the probe increases momentarily which in turn

increases the oscillation amplitude of the probe. This

causes a sudden increase in the magnitude of the error

signal and the control signal sent to the vertical direction

actuator adjusting the position of the sample with respect

to the probe tip. The scanning system responds faster to

the downward steps, leading to scan speeds faster than the

conventional PI controller with or without standard Q

control.

B. Adaptive Sliding-Mode Controller

In order to design a controller which can properly

handle piezoelectric nonlinearity and system uncertainty,

and meanwhile can gain high robustness and self-tuning

property, we propose an adaptive sliding-mode controller

for the tapping mode type AFM operation[20] [21]. To

start with, a linear second order model can be used to

represent the actuators nominal dynamics:

1 0z a z a z bu+ + = , (1)

wherez stands for the displacement of the vertical actuator

moving the sample, b is the forcing coefficient of thecontrol input u, a1 and a0 represent the damping and the

stiffness of the system, respectively. The parameters a1, a0

and bcan be well estimated via an off-line identification

test.

We assume thatzdis a desired constant height between

tip and sample, and the control goal is to change z to

maintain the tip-sample distance at a desired valuezd. Thetracking error can then be defined as:

de z z (2)Substituting eq. (1) into eq. (2), we have :

1 0

1 0

( )d

d

e z a z a z bu

a z a z bu

= +

= + +

(3)

Nevertheless, we have made some assumptions to simplify

the model of the plant. Those assumptions may result in

some inaccuracies of the plant model. Thus, two

additional disturbance terms need to be added into eq. (3)

yielding a model more closer to the real plant, which can

be expressed as:

1 0d c ve z a z a z bu w w= + + + + (4)

where wcrepresents a constant system uncertainty, and wvrepresents a varying system uncertainty. Note that we here

assume that the varying uncertainty term is bounded and

satisfies || c vw w+ ||wmax, where wmax is a constant.

Then, a sliding surface variable,s, is chosen as:

s e e= + (5)

where is positive parameter to be designed.

The sliding surface variable is designed such that the

system is exponentially stable when the system state

constantly lie on the sliding surface. Therefore, the

problem is reduced to guaranteeing that the state of the

system can reach the sliding surface, or in the case of

bounded tracking some region around the surface. The

purpose is to force the tracking error to zero or to some

very small residual set. Then, taking the time derivative of

eq. (5), we have, i.e.,

1 0( )d c v

s e e

z a z a z bu w w e

= +

= + + + + +

(6)

Based on eq. (6), the control law is designed as:

1

1 0 ( ( ))

AS d cu b a z a z z w e s sat s = + + + + + + (7)

where > 0and > |wmax|. Moreover, b and cw are the

estimated values of band wc, respectively, andsat(.) is the

saturation function with boundary layer width definedas:

1

( )

1

sat if

s

ss s

s

>

<

, (8)

Substituting eq. (7) into eq. (4), we can obtain

1 0

( )

c v AS e a z a z w w bu e

s sa t s

= + + +

(9)

where the estimation errors are defined as:

1 1 1 0 0 0 ,

, c c c

a a a a a a

b b b w w w

= =

= =

(10)

By applying appropriate gains , , and , we canaccelerate the convergence and force the error to a small

residual error set in a shorter period of time.In the following stability analysis, the adaptation law

has to be proposed in order to eliminate the estimation

errors as much as possible. Based on adaptive control

theory, we define a Lyapunov function candidate V, which

is a positive definite function:

2 2 1 2 1 2 1 2 1

1 1 0 0 2 3

1 1 1 1 1

2 2 2 2 2 c

V s a a b w = + + + +

(11)

where 0, 1, 2, and 3, are positive constants. In the

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next step, differentiating the Lyapunov function candidate,

we obtain:

1 1 1 1

1 1 1 0 0 2 3

c cV ss a a a a bb w w

= + + + + (12)

Substituting eqs. (6) and (9) into eq. (12), we can derive

the following:

[ ]

12

1 1 1

1 1 1

0 0 0 2 3

( ) ( )

( ) ( ) ( )

v

AS c c

V s sat s w s a a sz

a a sz b b su w w s

= + +

+ + + + +

(13)

By the latent purpose to make 0V , we design theadaptation law as

1 1 1 1 1 1

0 0 0 0 0 0

2 2 2

3 3 3

AS

c c c

a a sz a

a a sz a

b b su b

w w s w

= =

= =

= =

= =

(14)

Substituting eq. (14) and the inequality > |wmax| into eq.

(13), we can then derive:

[ ] 2 1 1 1 0 0 0 2

3

?= ( )

(15)

v

c c

V s sat s w s a a a a bb

w w

+ + +

+

From eq. (19), the range of each term is derived from:

2

1 1 1 1 1 1 1 1 1 1 1 1

2

1 1 1 1 1

2 22

1 1 1 1 1

2 211 1

( )

1 1 1[ ( ) ]2 2 2

[ ]2

a a a a a a a a

a a a

a a a a

a a

= = +

+

= +

(16)

Substituting inequalities (16) into (14), we can derive:

[ ]2 2 2 201

1 1 0 0

2 2 2 232

( ) [ ] [ ]2 2

[ ] [ ] (17)2 2

v

c c

V s sat s w a a a a

b b w w

If { }0 1 2 30 min 2 , , , , < < is chosen, then we

focus on the following two cases:

Case 1. > ,s

[ ] 2 2 2 21 1 0 0 2 3

2 2 2 2

1 1 0 0 2 3

2 2 2 2

1 1 0 0 2 3

1( )

2

1 =

2

1 =

2

v c

v c

v c

V s sat s w V a a b w

ss w V a a b w

s

s sw V a a b w

+ + + +

+ + + +

+ + + + +

2 2 2 2

max 1 1 0 0 2 3

2 2 2 2

1 1 0 0 2 3

2 2 2 2

1 1 0 0 2 3

1

2

1 = ( )

2

1 (18)

2

c

msx c

c

s s w V a a b w

s w V a a b w

V a a b w

+ + + + +

+ + + +

+ + + +

Case 2. ,s

[ ] 2 2 2 21 1 0 0 2 3

2 2 2 2

1 1 0 0 2 3

2 2 2 2 2

1 1 0 0 2 3

2 2 2 2 2

max 1 1 0 0 2 3

2

1( )

2

1 =

2

1 =

2

1

2

=

v c

v c

v c

c

V s sat s w V a a b w

ss w V a a b w

s sw V a a b w

s s w V a a b w

s

+ + + +

+ + + +

+ + + +

+ + + + +

2 22 2 2 2max max

max 1 1 0 0 2 3

22 2 2 2 max

1 1 0 0 2 3

1

4 4 2

1 (19)

2 4

c

c

w ww s V a a b w

wV a a b w

+ + + + + +

+ + + + +

From the above discussions in Case 1 and Case 2, we can

conclude that for:2

2 2 2 2 max

0 1 1 0 0 2 3

1, 0

2 4c

wV V a a b w V

= + + + +

which implies that V and V L

. Finally, we can

further show that the tracking error will converge to a

residual set. The plant with uncertainties and the bounded

disturbance can be controlled by this adaptive

sliding-mode controller stably. According to the control

theory, the tracking error will converge to a residual set in

order of , 0.3 andi i = .

C. Numerical simulation

Referring to sweep-sine identification experiment, the

parameters of the plant are listed below: 80 1.02 10a = ,

2

1 5.25 10a =

, and 2.38b = . The parameters of theadaptive sliding-mode controller are listed as follows:

0 1 2 350, 10, 1, 10, 5, 1, 50 = = = = = = =

The sliding-mode controller can reduce the tracking

error quickly. On the other hand, the adaptive law enables

the controller to be equipped with self-correcting

capability that may improve performance significantly. As

seen in Fig. 5, the controlled z position approaches thedesired value, and after 1.4 seconds the error is suppressed

within 2 nm.

The frequency response can give an overview of the

oscillation properties of the system. The resonance curve

of the cantilever of the AFM probe will be changed in

shape while changing the Q factor. As shown in Fig. 6,with the phase shift set to 90

o,Gset = 50, G0 = 10, and the

effective Q factor, Qeff, increased to 300, the resonance

peak of the amplitude curve is significantly enhanced.

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Figure 5. Numerical simulation of z-scanner tracking a standard

grating. The reference (blue line) step height is 200 nm. (a) is thesimulation result and (b) is the enlargement.

Figure 6. Amplitude vs. frequency curve with adaptive Q controland

IV.Experiments

A. Hardware Setup

The core parts of the experimental setup is illustrated in

Fig. 7. As shown in Fig. 7, the CD/DVD PUH is fixed on

the frame and relatively above the probe mount, and

furthermore the cover slip which are attached to the

precision tuning mechanism and cover slip holder.

The sample used in the following experiment is a test

grating (Calibration grating set TGS1 is intended for z-axis

calibration of the scanning probe microscope and

nonlinearity measurements, and is formed on the layer of

SiO2. The vertical depth is 107.5 nm, and the horizontal

pitch is 3 m, NT-MDT Inc.) with three-dimensional array

of small squares on the sample surface as shown in Fig. 8.

This calibration grating is a silicon step height standard

mounted on 15 mm puck.

To ensure the cantilever beam is totally immersed in the

liquid, a cover slip is placed over the probe. The liquid will

be absorbed between this cover slip and the sample, and

hence we can avoid operating the probe at the surface of

the liquid and be exempt from a significant force due to the

surface tension. This cover slip is 0.12 mm thick, which is

thin enough that the laser beam will not be refracted too

much. The fine layer of water between the cover slip and

the cantilever beam tends to make the laser beam focus on

different positions. But the novel design which can clip

cover slip can completely solve this problem.

Figure 7. The enlarged picture of the core parts of the AFM system.

Figure 8.Standard grating and depth: 107.5 nm, pitch: 3 m.

B. Scanning results in liquid

There are some resonant peaks appearing at different

frequencies while the tip is oscillating in liquid. Through

the amplitude-distance curve experiment, we can figure out

which one is the real resonant frequency. After these

pre-works, the scan experiment in liquid can be started.

Although the fine layer of water between the cover slip and

the cantilever beam will change the focal spot of the laserbeam. But the cover slip will be clipped by our novel

design during the sample approaching process, and then the

thickness of the water layer will not be altered so that the

light path calibration can be done before scanning. In other

words, the cantilever beam does oscillate at the focal point

exactly. Therefore, the signal read from the opto-electric

integrated circuit (OEIC) can represent the real bending

information of the cantilever, and the corresponding height

information can characterize the real topography.

The scanning results and the reconstructed 3D

topography images in liquid are shown in Figs. 9 and 10.

The morphology is clear and identifiable. The scanning

ranges are 12 m 12 m and 4.5 m 4.5 m,respectively. The scan speed is 8 seconds per line. The

expected result is seen in this figure. Through the above

experiments, this proposed system performs satisfactory

efficiency while scanning in liquid. Moreover, the

implemented mechanism and controllers realize most of the

design concept and solve previously encountered problems.

In the liquid experiment results, Fig. 10 shows that the

original standard rectangular forms become curving. All of

the observed discrepancies can be explained as that the

set 0G 50,G 10= =

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laser beam of the CD/DVD pickup head is refracting the

light more or less due to its motion between liquid and air

media. But high scanning quality cannot be denied by these

discrepancies. In addition, the holistic topography is clear

and stable which means this type AFM utilizing DVD

pickup head can be employed in the life science field and

may lead to significant contribution.

Fig. 9. Scanning topography and the virtual 3D topography image in

liquid. The total scanning range is 12 m12 m.

Fig. 10. Scanning topography and the virtual 3D topography image in

liquid. The total scanning range is 4.5 m4.5m.

V. Conclusion

A novel tapping mode atomic force microscopy

(AFM) applying a CD/DVD pickup head (PUH) operating

in liquid has been proposed in this paper. In addition, the

characteristics of the fluid and the influence of Q-factor onthe drag force also have been analyzed to overcome the

problem with significant drag force affecting the

performance of the cantilever beam applied to the fluid.

A model-based adaptive sliding-mode controller has

been designed for vertical z-scanner to reduce the tracking

error. In numerical simulation, the maximum transient

tracking error is less than 3 nm, and the steady state error

is less than 2 nm. These novel mechanism and controller

design are capable of investigating changes in local

surface properties with nano-scale spatial resolution.

Moreover, the clear topography and satisfactory scanning

performance of the calibration grating can be obtained

from our extensive experiments in liquid.

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