Characterization of materials' nanomechanical properties by force modulation and phase imaging atomic force microscopy with soft cantilevers

Materials Characterization 48 (2002) 147 – 152

Characterization of materials’ nanomechanical properties by force modulation and phase imaging atomic force microscopy with soft cantilevers V. Snitka*, A. Ulcinas, V. Mizariene Research Center for Microsystems and Nanotechnology, Kaunas University of Technology, Studentu 65, LT-3031 Kaunas, Lithuania

Abstract Soft cantilevers, although having good force sensitivity, have found limited use for investigating materials’ nanomechanical properties by conventional force modulation (FM) and intermittent contact (IC) atomic force microscopy. This is due to the low forces and small indentations that these cantilevers are able to exert on the surface, and to the high amplitudes required to overcome adhesion to the surface. In this paper, it is shown that imaging of local elastic properties of surface and subsurface layers can be carried out by employing electrostatic forcing of the cantilever. In addition, by mechanically exciting the higher vibration modes in contact with the surface and monitoring the phase of vibrations, the contrast due to local surface elasticity is obtained. D 2002 Elsevier Science Inc. All rights reserved. Keywords: Atomic force microscopy; Nanomechanics; Dynamic AFM

1. Introduction Continuous development in materials science and technology has raised the demands for the control of materials’ properties on the nanometer scale. The atomic force microscope (AFM), which is based on the sensing of interaction between the atomically sharp tip and the surface, has become the instrument of choice for the characterization of the surface nanomechanical properties. The dynamic modes of the AFM, such as force modulation (FM), intermittent contact (IC, or ‘‘tapping’’ mode), or scanning acoustic microscopy, by employing different character of tip – surface contact (constant or periodic) or cantilever dynamics regimes, have greatly expanded the capabilities of nanomechanical mapping in com* Corresponding author. Tel.: +370-7-451-588; fax: +370-7-451-593. E-mail address: [email protected] (V. Snitka).

parison with the static mode AFM. In FM-AFM [1], the cantilever basis is low frequency modulated via piezo while the tip is in contact with the surface. The cantilever exerts the force on the surface and the stiffer areas of the surface will deform, giving a higher amplitude of cantilever deflection. At the same time, the surface topography is determined from the feedback circuit output, which tries to keep the average cantilever deflection constant. This technique has been used to measure quantitatively the Young’s modulus of soft and compliant polymeric materials [2]. However, stiff cantilevers with spring constants of several tens of newtons per meter are required to obtain contrast on materials that have a Young’s modulus in the gigapascal range. As an alternative to mechanical forcing, the electrostatic interaction has been used to evaluate surface hardness [3]. To circumvent some of the problems of the soft cantilevers for nanomechanical surface characterization, the operating frequencies above the first can-

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tilever resonance have been employed. The theoretical and experimental studies of the high-frequency dynamics of the AFM [4], and applications for the surface properties mapping have been reported [5,6]. Higher eigenmodes of the AFM cantilever with dominant torsional vibration have been used to image the surface shear stiffness [7]. This paper describes an investigation into probing elastic properties of materials employing soft cantilevers (spring constant k < 0.2 N/m), by using electrostatic excitation and cantilever dynamics at high frequencies.

respectively; S ( = ab) is the cross-sectional area; r is the mass density of the cantilever; and Adr and w are the driving amplitude and frequency, respectively. The equation is solved by considering the boundary conditions at both the clamped and the nonclamped end. As the cantilever contacts the surface, the boundary condition at the nonclamped end is changed. In the simple limiting case of constant linear contact, characterized by the contact stiffness K, and the sine driving force, the amplitude of nonclamped end is [9]: A ¼ Adr

2. Theory

! cosha þ cosa
 1 1 þ cosha cosa þ aM3 sina  aM3 cosasinha

 sinwt;

To describe the cantilever dynamics in the wide frequency range, the elastic beam model should be considered. By using the corrective factors, analysis using the same dynamic equations can be extended for cantilevers with triangular geometry [8]. The vibrations of a beam are excited by harmonically driving its clamped end, which corresponds to the driving of the cantilever via forces of inertia distributed over the beam surface. The displacement z(x,t) of a beam in the absence of damping will be described in Eq. (1) @ 4 zðx; tÞ @ 2 zðx; tÞ EI þ rS ¼ rSw2 Adr sinwt; @x4 @t2

4

where E is the elastic modulus of the cantilever material; I ( = ab3/12) is the area moment of inertia; a and b are the width and thickness of the cantilever,

ð2Þ

rSw

0i where M = KL3/EI, a ¼ EI L, and w0i is the resonance frequency of the eigenmode of beam vibration. The equality to zero of the denominator of Eq. (2) describes the condition for resonance, from which the resonance frequencies can be calculated. If the deflection of the cantilever end remains harmonic to a good approximation, the phase shift can be described in terms of resonance frequency shift (Eq. (3)) [10]:

Dj ¼ 2Q ð1Þ

qffiffiffiffiffiffiffi2ffi

Dw ; w0

ð3Þ

where Q is the cantilever quality factor. Using this relationship, the phase shift can be expressed through a and related to the material properties. By choosing the appropriate contact model, the contact stiffness K

Fig. 1. Dependence of the phase shift on the Young’s modulus of the surface. Numbers indicate the eigenmode of rectangular cantilever vibrations.

V. Snitka et al. / Materials Characterization 48 (2002) 147–152

can be determined. For Hertz contact (see Eqs. (4) and (5)) [4]:

K¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 6RE * F0 ;

" #1 1  p2 1  t2 * E ¼ þ ; Ep Et

ð4Þ

ð5Þ

where R is the tip radius, Ex and nx are the Young’s modulus and the Poisson’s ratio of the sample and tip, respectively, and F0 is the average interaction force. It is evident that both the amplitude and the phase of the cantilever vibrations depend on the surface mechanical properties. Fig. 1 shows the dependence of the phase shift on the Young’s modulus of the surface for first three eigenmodes. The cantilever is assumed to be in contact with the surface with Ep = 10 GPa. The equation parameters were as follows: L = 180 mm, a = 25 mm, b = 0.8 mm, nt = 1.81, np = 0.3, Et = 130 GPa, r = 2330 kg/m3, E = 169 GPa, R = 10 nm, and F0 = 10 nN. It is seen that for elasticity contrast, it is necessary to excite the cantilever near contact resonance. The third mode has the steepest slope for chosen conditions, providing superior sensitivity.

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3. Experimental procedures The experimental setup was based on the Quesant Instrument contact mode AFM Q-Scope 250, modified for dynamic operating modes. Cantilever vibrations were excited electrostatically by applying modulated voltage between the cantilever and the electrode placed under the sample, or mechanically via the driving piezo glued onto a custom cantilever holder (Fig. 2). A custom signal access module, an absolute amplitude detector, and a fast ‘‘flip-flop’’ phase detector were used to process the cantilever deflection signal in order to obtain its amplitude and phase. A triangular V-shaped Si3N4 gold-coated cantilever (static stiffness k = 0.01 N/m and tip radius R = 50 nm) was used for the electrostatically forced FM-AFM, while a triangular silicon cantilever (static stiffness k = 0.16 N/m, tip radius R = 10 nm and geometry L = 180 mm, a = 25 mm and b = 0.8 mm, as reported by manufacturers) was used for the IC-AFM. The third flexural vibration mode of Si cantilever had a frequency f3 = 710 kHz and a quality factor of 20, in reasonable agreement with calculations. In the electrostatic FM-AFM, the average cantilever deflection was kept constant and the vibration amplitude recorded simultaneously with the topography. An excitation voltage of 5 – 15 V and a frequency of 12 kHz were chosen. In FM-AFM at high frequencies, the constant deflection feedback was also used, and the error and cantilever vibration

Fig. 2. Schematic diagram of the experimental setup.

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phase shift images were recorded simultaneously with the topography image.

4. Results 4.1. Electrostatically driven FM-AFM The electrostatically forced FM-AFM at low forcing amplitudes is to be interpreted differently from the conventional FM-AFM. Since the electrostatic force is distributed over the area of cantilever, while the position of cantilever base is constant, lower stiffness material (deeper indentation depth) will correspond to the higher deflection amplitude. The softer areas should appear as bright spots on the image. Fig. 3 shows the FM-AFM images of a multilayered integrated circuit surface. Fig. 3a corresponds to the topography image, in which the silicon sub-

strate and aluminum interconnections are distinguishable. Fig. 3b, c and d shows cantilever vibration amplitude images taken with increasing forcing amplitude. The low forcing amplitude image does not reveal the distribution of elastic properties on the surface, because the tip does not indent the surface considerably. The slight contrast in the image is caused by surface topography variations. With increasing forcing amplitude (Fig. 3c), the inversion of contrast takes place, the softer Al-coated areas appearing dark, and the harder Si areas appearing bright. This contrast inversion arises when the electrostatic interaction becomes strong enough to induce bending in the middle of the cantilever. This bending increases with the surface stiffness, thus producing higher deflection. Although providing contrast of the surface elastic properties, such bending can be undesirable since it is difficult to control the amount of force acting on the

Fig. 3. Electrostatically driven FM-AFM images of a multilayered integrated circuit. (a) Topography; (b – d) absolute vibration amplitude images taken with increasing forcing amplitude. Scan size 40 mm.

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Fig. 4. High-frequency FM-AFM images of a laser-treated polyimid on glass. (a) Topography; (b) phase. Excitation frequency 710 kHz, scan size 5 mm.

cantilever. In principle, the conductive cantilevers with conductive tips would enable the concentration of electrostatic force near the tip, avoiding the bending in the middle. 4.2. FM-AFM at high frequencies As it was shown in Section 2, the high-frequency vibration parameters of the cantilever in contact with the surface change due to the surface elastic properties. This effect was used to image the surface with

elastic inhomogeneities. Fig. 4 shows the images of laser-treated polymer polyimid on glass obtained with constant deflection feedback and mechanically excited 710-kHz cantilever vibration. In Fig. 4a, the topography image, the edge of the laser-burned hole is seen, where the transition from polymer to glass is present. The phase image reveals the surface areas with varying stiffness. Fig. 5 was obtained on the polyethylene surface using a cantilever of the same type, which had the resonant frequency of the third eigenmode at 750

Fig. 5. High-frequency FM-AFM images of polyethylene. (a) Topography; (b) phase. Excitation frequency 850 kHz, scan size 10 mm.

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kHz. In contact with polyethylene surface, the resonance was found at 850 kHz. Again, the phase image reveals elastic inhomogeneity of the surface.

5. Conclusions In this paper, it has been shown that the elastic properties of a wide range of materials can be characterized using the FM-AFM by employing the electrostatic forcing. In addition, since the dynamics of the cantilever at high frequencies depend on the contact parameters, by monitoring the changes in cantilever vibration amplitude and phase, the elastic properties of the surface material can be characterized and measured. From Fig. 1, it is evident that the sensitivity of the method decreases as the contact resonance frequency is shifted further from the driving frequency. The optimal way to operate the instrument would be to drive the cantilever always at contact resonance frequency. This could be realized by using the phasecontrolled generator to excite the cantilever vibrations, in a manner similar to noncontact mode AFM.

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