Soft piezoresistive cantilevers for adhesion force measurements

Journal Pre-proof Soft piezoresistive cantilevers for adhesion force measurements K. Kwoka, K. Oroowska, W. Majstrzyk, A. Sierakowski, P. Janus, D. Tomaszewski, P. Grabiec, T. Piasecki, T. Gotszalk

PII:

S0924-4247(19)30956-2

DOI:

https://doi.org/10.1016/j.sna.2019.111747

Reference:

SNA 111747

To appear in:

Sensors and Actuators: A. Physical

Received Date:

3 June 2019

Revised Date:

5 November 2019

Accepted Date:

10 November 2019

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Soft piezoresistive cantilevers for adhesion force measurements K. Kwokaa,∗, K. Orlowskaa , W. Majstrzyka , A. Sierakowskib , P. Janusb , D. Tomaszewskib , P. Grabiecb , T. Piaseckia , T. Gotszalka a Wroclaw

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University of Science and Technology, ul. Z. Janiszewskiego 11/17, PL-50372 Wroclaw, Poland b Institute of Electron Technology, Al. Lotnik´ ow 32/46, PL-02668 Warszawa, Poland

Abstract

Micromechanical cantilevers are attractive devices for force measurements. We

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report the results obtained for SMMM (Soft MetMolMEMS) silicon cantilever fabricated on silicon on insulator (SOI) substrate with piezoresistive deflec-

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tion readout with the stiffness much lower than the typical piezoresistive silicon cantilever. The cantilever mechanical properties were characterised with laser vibrometer using the thermal noise technique (resonant frequency fres =

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5474.2 Hz, quality factor Q = 19.4 and stiffness k = 0.042 N m−1 ). The piezoresistive detection sensitivity was evaluated by measuring externally induced mechanical vibrations optically with laser vibrometer and electrically using current-

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to-voltage converter and lock-in amplifier simultaneously. We obtained deflection sensitivity DS = 11 V m−1 and force sensitivity F S = 263 V N −1 assuming typical bias voltage of 2 V . Such silicon cantilever may be successfully used in AFM investigation of fragile structures. Keywords: MEMS, doped, sensor, SOI, silicon

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2010 MSC: 00-01, 99-00

∗ Corresponding

author Email address: [email protected] (K. Kwoka)

Preprint submitted to Journal of LATEX Templates

November 5, 2019

1. Introduction In 1986 Gerd Binning with Calvin F. Quate and Christoph Gerber presented the very first atomic force microscope (AFM) [1]. In this device the cantilever with a scanning tip was used to measure the force interaction between the 5

tip and the sample. This technique started a significant advancement of the

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surface research and development of the cantilevers dedicated for small force measurements.

The invention of the AFM opened a whole new area for research on can-

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tilevers design [2] as using them as measurement device became more common.

Furthermore, the applications different than hard surface scanning appeared as

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well [3]. For example, it became possible to investigate DNA samples [4], to perform subsurface imaging [4], thermal imaging [5], liquid measurements [6] and to investigate living biological samples [7].

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The very first method of cantilever deflection detection in AFM was to use scanning tunneling microscope (STM) tip. Different methods emerged shortly

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after the invention such as optical beam deflection (OBD) [8], capacitive detection [9] and piezoresistive readout [10]. Each of these methods have their advantages and disadvantages.

Even with such a rapid development of AFM technique it is still challenging to perform measurements on soft, in example biological or polymer samples. In

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this case it is necessary to use very soft cantilevers to avoid sample deformation or even destruction [7]. Typical piezoresistive cantilevers exhibit relative large stiffness which is necessary to accumulate the strain in the area of the piezoresistor. Moreover application of the OBD technique may be difficult in some applications because of the complexity and size of the optical system.

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The most typical solution for the piezoresistive cantilever deflection sensing

is to fabricate four strain sensing piezoresistors forming a complete Wheatstone bridge circuit at the strain concentration area [11]. However to simplify the cantilever structure and to allow to reduce its size

30

the cantilevers with single piezoresistor can be manufactured as well. In that

2

a)

b)

c)

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I VOUT

VOUT

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VOUT

Figure 1: Schematic representation of cantilever circuits: cantilever with complete piezoresistive Wheatstone bridge (a), and reference and sensing cantilevers with single resistors in

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Wheatstone bridge (b) and Anderson loop (c) configuration.

case such cantilevers are typically used in pairs: sensing and reference can-

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tilever. Then they may be combined with two other separate resistor forming a Wheatstone bridge [12] or connected in Anderson’s loop configuration [13].

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All these methods provide high resistance change sensitivity and immunity to temperature changes and interference.

The goal of the presented research was to demonstrate the performance

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of soft, piezoresistive, silicon cantilever which may be used for adhesion force measurements. The piezoresistivity was induced by the slight gradient doping of the silicon resulting with the single, deflection-sensitive device to be used in

40

the Anderson’s loop or as a part of the Wheatstone bridge circuit.

2. Cantilever design

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The piezoresistive cantilevers were fabricated in ITE Warsaw from the SOI

wafer with (100) device layer. Its low thickness (1.5 µm) combined with the fact that the structure is relatively long (500 µm) and U-shaped design results

45

in very low stiffness. N-type device layer was p+ overcompensated using by Low Pressure Chemical Vapor Deposition (LPCVD) method to deposit boron doped layer making it highly conductive [14]. This process was conducted in 3

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Figure 2: Cantilever fabrication process: boron doping (a), gold sputtering (b), geometry defining (c), plasma etching (d) structures releasing (e). Z axis not in scale [15]

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.

two steps: at first boron doped layer was deposited at 270 ◦ C and then whole

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structure was annealed to lead to diffusion of boron into silicon. By controlling boron deposition time it is possible to control the surface boron concentration and by changing the temperature and duration of annealing it is possible to control dopant profile in the cantilever. Contact pads and cantilever shape were

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then defined using photolithography over sputtered gold layer. Cantilevers were released in a series of dry plasma etching processes (fig. 2). We described

55

fabrication process with details in previous paper [15]. The dopant distribution profile over cantilever thickness ensured the exis-

tence of the piezoresistive effect (fig. 3). The peak visible at the end of the graph

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is an unavoidable simulation artifact when the end of the cantilever is detected.

60

Finally, we decided on using the tip-less cantilever to be able to later test

its performance as adhesion force sensor with microball test sample and to try different shapes of tips in further investigations. The SEM images of the fabricated cantilevers were shown in Figure 4.

4

-3

[cm ]

20

of

20

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1x10

0 0,0

0,5

1,0

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Boron concentration B

con

2x10

1,5

2,0

m]

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Cantilever depth d [

(b)

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(a)

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Figure 3: Simulated dopant distribution across the thickness of the cantilever.

Figure 4: SEM images of the fabricated cantilevers: general view (a) and the close-up on the gold pad for the microball (b). The dimensions of the cantilever were as given: length 500 µm, width 100 µm, legs width 25 µm, thickness 1.5 µm and area over gold pad length 30 µm. Gold pad dimensions were 40 µm by 40 µm.

5

3. Measurement setup 65

We characterized the investigated cantilevers using two methods: thermomechanical noise actuation to determine stiffness and quality factor and piezostack actuation to evaluate the cantilever deflection sensitivity.

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3.1. Thermomechanical noise measurement We use the thermomechanical noise measurement to calculate the cantilever 70

resonant frequency, stiffness and the quality factor.

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According to Hutter and Bechhoefer [16] a simple harmonic oscillator (SHO), like cantilever, vibrates in response to the thermal noise, as long as it stays in

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the equilibrium with its surroundings. In this case it is possible to calculate stiffness of the oscillator from power spectrum of its thermomechanical noise using equipartition theorem. The power spectral density (PSD) of the thermo-

St (f ) =

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mechanical noise St (f ) of a SHO is given by: A 2

(

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(f02 − f 2 ) +

f f0 Q

)2

(1)

where A is the fitting parameter obtained from the PSD analysis, f is the frequency, f0 is the resonant frequency of the cantilever. From the Nyquist

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dissipation–fluctuation theorem we know that the power spectral density of the thermomechanical noise is given by: St (f ) =

2kB T f03 πkQ

1 (f02 −

2 f 2)

( +

f f0 Q

)2

(2)

where kB is the Boltzmann constant, T is the absolute temperature , k is the

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stiffness and Q is the quality factor. Combining acquired fitting parameter with foregoing equation we can obtain stiffness with the formula [17]: k=

2kB T f03 πAQ

(3)

The PSD of the cantilever was measured using a SIOS SP120 laser vibrometer. It allowed us to measure vibrations with 100 f m/Hz −1/2 noise floor and

6

PC

Keithley 428 IDC

Gain

IDC

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Laser Vibrometer IAC

IAC

Lock-in

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Cantilever UB

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Piezostack

Gen

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Figure 5: Block diagram of the measurement setup for the cantilever deflection and force sensitivity measurement.

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sub-nanometer resolution. To ensure proper deflection measurement we also used digital camera attached to vibrometer head and software analyzing de75

flected signal power to adjust the laser spot exactly on the golden pad at the

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end of the cantilever.

3.2. Cantilever sensitivity

The cantilever deflection and force sentitivities were measured in the setup

shown in Figure 5. During the measurement the cantilever was actuated using

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the piezostack Piezomechanik GmbH PSt 150hTc/7x7/18. It allowed to obtain

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large vibrations amplitude at low actuation voltages which reduces the possible crosstalk between the actuator and electric readout. The piezostack resonant frequency was 20 kHz which was much higher than expected resonant frequency of the cantilever (around 5 kHz).

85

The Signal Recovery 7280 DSP lock-in amplifier allowed us to perform voltage measurement with 15 µV uncertainty (0.3 % of 5 mV range that we used

7

during the measurements [18]). We used a Keithley 428 current amplifier for two purposes: firstly, to amplify signal generated by the cantilever to make it easier to measure with lock-in amplifier and secondly, to minimize DC voltage influence on measurement and make it possible to use more accurate sensitivity range in lock-in amplifier. We know that the resistance of the sample is changing due to the induced vibrations

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and is given by the equation:

(4)

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R(t) = RDC + ∆R(t)

where R(t) - total calculated resistance during measurement, ∆R(t) - resistance component varying in time due to the piezoresistive effect, RDC - resistance

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of the cantilever. The current I(t) flowing through the measurement system is equal to:

UB UB UB · (RDC − ∆R(t)) = = 2 R(t) RDC + ∆R(t) RDC − ∆R2 (t)

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I(t) =

(5)

where: UB - voltage bias set of the current amplifier. Splitting the equation into

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alternating and direct parts and after assuming that that ∆R2 (t) is negligible 2 when compared to RDC we get:

UB UB · ∆R(t) = IDC + IAC (t) − 2 RDC RDC

(6)

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I(t) ∼ =

To allow for high gain and as best as possible lock-in amplifier sensitivity

setting without input overload we suppress IDC using Keithley 428 current

90

suppression function, which introduce additional direct current subtracting from the current generated by UB applied to the cantilever.

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The voltage at the output of the current–to–voltage converter is then given

by UAC (t): UAC (t) = G · IAC (t)

(7)

where G is the gain set in the current amplifier. Combining (6) and (7) we

obtain: ∆R(t) =

2 UAC (t) · RDC G · UB

8

(8)

which allows to calculate the resistance changes. While using the Anderson’s loop configuration two cantilevers (as a sensor and a reference) would be placed in the current loop. In the sensitivity calculations we assume that the current would be set to the value resulting in voltage at the cantilever at the 2 V level. This assumption allows us to compare results with the often used Wheatstone brigde biased by ±2 V voltage. Since the out-

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put voltage of the Anderson’s Bridge would be difference of voltage on reference

∆U = I · ∆R

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and sensing cantilevers the measured ∆U would be given by equation:

(9)

∆U ∆y

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DS =

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Finally we calculated cantilever sensitivities using (10) and (11):

FS =

∆U ∆F

(10)

(11)

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where ∆U is the voltage signal at Anderson’s loop output induced by ∆y or ∆F which are the deflection of the cantilever and force applied to the cantilever, respectively. DS and FS are also connected by stiffness value. This correlation

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is given by the following equation:

DS = F S · k

(12)

4. Results

95

The thermomechanical noise power spectral density of the cantilever vibra-

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tion was obtained by averaging the spectra for over 1500 measurements to reduce the influence of thermal noise. By fitting the result with the curve described by (2) we calculated the cantilever mechanical properties: the quality factor Q=19.4, resonance frequency fres =5474.2 Hz and stiffness k=0.042 N m−1 (fig.

100

6). We simulated the mechanical properties: stiffness and resonant frequency and the results match measurements (the differences are consistent with our 9

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Q=19,4 f

2,0x10

-22

res

=5674,2 Hz

k=0,042 N/m

5,0x10

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1,0x10

-22

-22

ro

1,5x10

-23

0,0 4,0k

4,5k

5,0k

5,5k

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Thermomechanical Noise N

th

(m^2/Hz)

2,5x10

6,0k

6,5k

7,0k

re

Frequency f (Hz)

Figure 6: Thermomechanical noise power spectral density of the tested cantilever (dots) fitted

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with the curve resulting from eq. (2).

experience with simulation-measurement comparison). Simulated resonant frequency fres =6407 Hz and stiffness k=0.071 N m−1 . The quality factor and

105

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resonance frequency are relatively low for typical silicon cantilever but this is the consequence of extremely low stiffness of our structure which may be useful in certain applications and is much safer for the fragile samples. As it was mentioned before, for convenience the electric measurements were

done in single cantilever configuration. These measurements as such were influenced by unwanted crosstalk induced by electric field caused by the actuation voltage applied to the piezostack. Because cantilever area is relatively small

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110

in comparison to the piezostack and the necessary strict mechanical connection it was impossible to eliminate crosstalk even though electromagnetic shielding was used. Such phenomena would be greatly reduced in Wheatstone bridge or Anderson loop configurations. In this case the amplitude A of the SHO response

115

as the function of the actuation is the sum of the pure SHO response ASHO (f )

10

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(b) 1.0

apparent

0.5

SHO

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magnitude (a.u)

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(a)

0.0 990

995

1000

1005

1010

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frequency f (Hz)

Figure 7: Illustration of the crosstalk influence on the resonance measurement: complex plane trajectory of the SHO (f0 = 1000 Hz, Q = 1000) complex amplitude with frequency

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dependent crosstalk (a) and the apparent magnitude influenced by the crosstalk compared to the true SHO magnitude (b).

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and frequency dependent crosstalk B(f ) [19] and is given by:

f2 A(f ) = ASHO (f ) + B(f ) = Amax 02 Q

√ Q2 −

1 3 + B(f ) (13) 2 2 16 f0 − f − j fQf0

where: A(f ) is the complex amplitude describing both magnitude and phase,

Amax is the maximal amplitude and B(f ) is the function describing the un-

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wanted crosstalk. The model example of such a situation is shown in Figure 7a.

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In this case the simple measurement of the magnitude would be strongly

distorted. The described phenomenon is shown in figure 7b in the model example and as the hollow dots in figure 8. In the latter one we present the data measured for the investigated cantilever where both mechanical vibrations and electrical

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5

100m

R with compensation

A

Fit

R

=2.05

max

R

80m

=38 m

max

3

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60m

2

ro

40m

1

0

m

)

=5630 Hz

Q=17

20m

4000

4500

5000

5500

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y(f) (m) Vibrations amplitude

4

res

R without compensation

R (

f

Fit vibrations

Resistance change

Vibrations

6000

6500

0 7000

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Frequency f (Hz)

Figure 8: Measured (dots) and fitted (lines) resonance peaks of the mechanically actuated cantilever obtained optically (black) and electrically (red) after crosstalk compensation and

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raw measured resistance change (red circles).

resistance changes were measured simultaneously. As mentioned by Niedermayer [19] this crosstalk can be represented as con-

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ductance and susceptance with both being first order functions in given frequency. In order to compensate the crosstalk we assumed that the B(f ) would change linearly between the Bstart and Bend which are the first and the last

130

points of the measurement, respectively. Such simple calculations allowed to achieve a good correlation between vibrations magnitudes measured optically

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and electrically (Fig. 8), but this simplification by using linear function might be inaccurate for higher ∆f . The resonance peaks whose frequency corresponded to the results of the ther-

135

momechanical noise measurements were fitted with the SHO model (1) to determine the amplitudes of the mechanical vibrations ∆y and resistance changes ∆R. The apparent resonant peak at lower frequency was related to the second

12

resonance in the actuation system. Investigation of this problem shows that it is caused by another cantilever in the matrix. 140

Investigated cantilever resistance RDC was 2035 Ω which results in the I = 983 µA as the current polarizing the cantilever to 2 V. Based on (9) we obtained the voltage change on our cantilever at ∆Rmax read from fitting on Figure 8. Then, using (10) we calculated the deflection sensitivity DS=11 V m−1 and

5. Summary

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145

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using (12) force sensitivity FS=263 V N−1 .

The presented manufacturing process allowed to fabricate very soft silicon

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piezoresistive cantilever, with DS and FS comparable to these of the polymer cantilevers with thin film strain sensor, suitable for the adhesion investigations. Piezoresistive effect is realized by creating dopant gradient in the SOI substrate. It is important to note that at the same time the gradient is small enough to not

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150

cause a thermal actuation of the cantilever [15]. Due to the low stiffness of the

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SMMM cantilever it should be possible to measure fragile structures without the risk of destroying them. The fabrication of the complete array of such cantilevers would make it possible to reduce the influence of the structure drift 155

and unwanted crosstalk by arranging the cantilevers in Wheatstone bridge or

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Anderson loop configurations and to increase the measurement throughput by simultaneous measurement of multiple cantilevers. It was possible to conduct the measurements and to verify the parameters of the cantilever however the tipless solution is appropriate only at the development stage. Without a tip

160

or microball at the end of the cantilever it is vulnerable to parasitic effects

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when approaching the surface. In further experiments the microball should be mounted on the device to introduce additional distance from the sample. The comparison of the results obtained for presented SMMM cantilever with

the parameters reported by other groups (Table 1) shows the benefits of the pro-

165

posed design. The stiffness of SMMM cantilever is one order of magnitude softer than the softest silicon cantilever found in literature [12, 20] with simultaneous

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Table 1: Comparison of the cantilever parameters: stiffness k, force sensitivity F S and deflection sensitivity DS.

cantilever

k

(N ) m

FS

(V ) N

DS

(V ) m

Fres (kHz)

0.042

434

18.2

5.5

Sierakowski [25]

20.57

561

11500

36.9

Biczysko [26]

75

190

14300

56

Pandya [20]

0.14

0.0027

0.00038

N/A

Rangelow [27]

12.9

271

3500

42.6

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SMMM

very high force sensitivity. Low value of the quality factor, resonant frequency

the purpose of adhesion force measurements. 170

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and DS result from extremely low stiffness and are not significant factors for

It is possible to manufacture cantilevers softer as well as more sensitive than

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SMMM but it is important to notice, that shape, size and technology is also important factor. Cantilevers designed by other groups like for example reported

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by Harley et al. [21] and Tosolini et al. [22] are softer and in case of the latter much more sensitive but are also very prone to thermal deflection due to the 175

bimetallic effect. Another example of the device with similar spring constants was reported by Arlett et al. [23] but it is very short and thin, which would make

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it impossible to for example mount microball for biological measurements and it is most efficient when used in cryogenic temperatures. Another noteworthy example is the cantilever reported by Takahashi et al [24] which has very big

180

area very convenient for the flow sensing but in general it is unsuitable for any

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SPM measurements.

Acknowledgements The electromagnetic cantilevers were fabricated in the OPUS project “Metrol-

ogy of molecular interactions using electromagnetically actuated MEMS force

185

sensors-MetMolMEMS” (Grant No. 2015/17/B/ST7/03876) and the investigations presented here were supported by the National Science Center (NCN) Pre14

ludium Grant “Mechanical impedance measurements of MEMS structures with the use of the photon force reference, PF-MEMS” (Grant No. 2017/25/N/ST7/02780).

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