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Research Papers

Delamination-Based Measurement and Prediction of the Adhesion Energy of Thin Film/Substrate InterfacesOPEN ACCESS

[+] Author and Article Information
Liangliang Zhu

International Center for Applied Mechanics
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
International Center for Applied Mechanics,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China;
Columbia Nanomechanics Research Center
Department of Earth and
Environmental Engineering,
Columbia University,
500 West 120th Street,
New York, NY 10027
e-mail: zhu.liangliang@stu.xjtu.edu.cn

Xi Chen

Fellow ASME
Columbia Nanomechanics Research Center,
Department of Earth and
Environmental Engineering,
Columbia University,
500 West 120th Street,
New York, NY 10027
e-mail: xichen@columbia.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 10, 2016; final manuscript received October 4, 2016; published online February 9, 2017. Assoc. Editor: Taehyo Park.

J. Eng. Mater. Technol 139(2), 021021 (Feb 09, 2017) (4 pages) Paper No: MATS-16-1223; doi: 10.1115/1.4035497 History: Received August 10, 2016; Revised October 04, 2016

Abstract

With the rapid emerging of two-dimensional (2D) micro/nanomaterials and their applications in flexible electronics and microfabrication, adhesion between thin film and varying substrates is of great significance for fabrication and performance of micro devices and for the understanding of the buckle delamination mechanics. However, the adhesion energy remains to be difficult to be measured, especially for compliant substrates. We propose a simple methodology to deduce the adhesion energy between a thin film and soft substrate based on the successive or simultaneous emergence of wrinkles and delamination. The new metrology does not explicitly require the knowledge of the Young's modulus, Poisson's ratio, and thickness of the 2D material, the accurate measurement of which could be a challenge in many cases. Therefore, the uncertainty of the results of the current method is notably reduced. Besides, for cases where the delamination width is close to the critical wrinkle wavelength of the thin film/substrate system, the procedure can be further simplified. The simple and experimentally easy methodology developed here is promising for determining/estimating the interface adhesion energy of a variety of thin film/soft substrate systems.

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Introduction

Buckling of stiff thin films adhered to soft compliant substrates are a commonplace phenomenon in nature, e.g., wrinkles of aged human skin or dried apples [1], wrinkled fingertips immersed in water [2], and a group of fruits like ribbed pumpkins [3]. In the area of engineering technology, though historically viewed as a structural failure mechanism, in recent years buckling thin films have found many advanced applications in flexible electronics [47] and micro/nanofabrication [8,9], especially nowadays with the emergence of 2D materials.

Many previous theoretical studies assume that the interface between the film and substrate is either perfectly bonded or perfectly unattached, while the real interface strength (adhesion energy) could be crucial for structural integrity and wrinkle-to-delamination transitions [10,11]. Determination of adhesion strength is important for transferring of 2D materials to a substrate, such as graphene nanomechanical switches which involves transferring the suspended graphene to an underlying electrode [12,13]. Another example is the graphene manufacturing that transfers graphene from one substrate to another [14,15]. Furthermore, adhesion also plays an important part in the fabrication and performance of stretchable electronics [16,17].

The interface properties of emerging 2D materials have attracted much interest about their adhesion to different substrates. For example, using nanoparticles as point wedges at the graphene–silicon interface, adhesion energy was calculated by measuring the particle height and blister radius [18]. Through a blister test, Koenig et al. measured the adhesion energy of the graphene/silicon oxide interface [19], and Cao et al. analyzed the adhesion of large-scale graphene/copper interfaces [20]. These measurements focused on thin film/stiff substrate interfaces. On the other hand, measurement of the interface adhesion energy of thin film and soft substrate still remains a challenge [21]. Brennan et al. [16] recently reported a buckling-based methodology to measure the adhesion energy between a 2D material and its underlying compliant substrate, although with moderate uncertainties.

It is worth noting that the above proposed methods may strongly depend on the accurate characterization of the thickness of 2D membrane and require the knowledge of the film's Young's modulus and Poisson's ratio [16,18]. Besides, both buckle delamination and wrinkle deformation must coexist in the same experimental sample concomitantly [16]. However, the value of 2D material's Young's modulus and Poisson's ratio may vary in a relatively large range according to different characterization methods [2224]. And different layers of the 2D material may result in quite different Young's modulus. For example, the Young's modulus of a monolayer MoS2 is ∼270 GPa, whereas for a bilayer MoS2 it is ∼200 GPa [22]. In addition, measurement of the thickness of monolayer or few-layer 2D material with atomic force microscopy is very challenging [1618]. Furthermore, to the same substrate, 2D material with different layers may have quite different adhesion energy [19]. And different synthesis, preparation, and transferring methods of the 2D material may lead to different surface properties which strongly influences the interface adhesion energy. Therefore, a simple and experimentally easy methodology is still in demand for determining/estimating the interface adhesion energy of thin film/soft substrate systems.

The current work proposes a new delamination-based methodology to calculate the adhesion energy between a thin film and soft substrate, where the successive or simultaneous emergence of wrinkles and delamination is required. In the present method, it is not necessary to accurately determine the film's thickness, nor to explicitly know the Young's modulus or Poisson's ratio of the film. Because of these simplifications, the uncertainty of the resulting adhesion energy is reduced significantly. Furthermore, in some cases where the delamination width is close to the critical wrinkle wavelength, the delamination configuration alone may be sufficient to estimate the adhesion energy with the present method, without the coexistence of wrinkles.

Method

As mentioned above, the successive or concomitant emergence of wrinkles and delamination is needed for calculating the adhesion energy. The configure (morphological) parameters (i.e., height and width of the delamination, amplitude and wavelength of wrinkles) are employed for determining the interface adhesion energy. Using MoS2/polydimethylsiloxane (PDMS) in Brennan et al.'s work [16] as a representative example, this section describes the experimental acquisition of successive or concurrent emergence of wrinkles and delamination, and the measurement of configure parameters.

Concomitant wrinkles and delamination were created in the same MoS2 film/PDMS substrate system in Ref. [16] through pressing down firmly on the MoS2/PDMS system during the transfer process. In this method, an indent was created in the PDMS, resulting in a slight local surface expansion which may be different at varying locations depending on the distance away from the pressing center. When the pressure was released, the nonuniform compressive force from PDMS substrate may lead to concurrent formation of wrinkle and buckle delamination of the MoS2 film. Besides, the successive appearance of wrinkles and delamination may be achieved through prestretching the substrate before transferring the film to it, which is known as wrinkle-to-delamination transition [10,11]. Depending on the critical strain needed for delamination, prestrain of the substrate may also be induced through the thermally expanded substrates.

It is worth noting that different testing methods and/or conditions may to some extent influence the resultant adhesion energy because of the effect of the surface roughness on the adhesion of film/substrate interfaces [25]. Besides, the interface friction (sliding) [26] may also vary in different testing methods and/or conditions, which may also affect the tested adhesion energy. Nevertheless, the effect of testing methods and conditions on interface adhesion is not a focus in this work, and thus is left for future studies.

For successive or concomitant wrinkles and delamination in Fig. 1, the delamination height δ and width λd can be obtained by fitting of the experimental delamination profile (Fig. 1(b)) with a cosine form [10] with the coordinate centered at Point O

Display Formula

(1)$y=δ2[1+cos 2πxλd]$

Similarly, fitting the wrinkle profile (Fig. 1(a)) can lead to the wrinkle amplitude A and wavelength λw with the following cosine form: Display Formula

(2)$y=A cos 2πxλw$

In Sec. 3.1, δ, λd, A, and λw will be used to deduce the interface adhesion energy.

Results and Discussion

Methodology for Determining the Adhesion Energy.

Following Vella et al. [10], the adhesion energy of the delamination profile can be obtained as Display Formula

(3)$Γ=2π4Bfδ2λd4=π46δ2λd4hf3E¯f$

where Bf, hf and $E¯f$ are the bending stiffness, thickness, and plane-strain modulus of the 2D material (film), respectively, and $E¯f=Ef/(1−vf2)$, where Ef and vf are the Young's modulus and Poisson's ratio of the film. On the other hand, from nonlinear analyses of a thin film/soft substrate system [27,28], the critical wavelength of the film at the onset of wrinkles is Display Formula

(4)$λ0=2πhf(E¯f3E¯s)1/3$

where $E¯s=Es/(1−vs2)$, and Es and vs are, respectively, the Young's modulus and Poisson's ratio of the substrate which are usually easy to obtain. Substituting Eq. (4) into Eq. (3), we have Display Formula

(5)$Γ=π16δ2λ03λd4E¯s$

where λ0 can be calculated easily from the wrinkle wavelength λw and amplitude A, assuming a constant contour length of the film [29] Display Formula

(6)$λ0=∫0λw1+(2πAλw)2 sin2(2πλwx) dx$

The advantages of the current formulation are the following. First, Eqs. (5) and (6) do not explicitly contain the parameter hf, thus, largely eliminating the uncertainties of the adhesion energy caused by AFM measurement of the 2D material's thicknesses [17,18]. Second, Eqs. (5) and (6) do not require the explicit knowledge of the film's Young's modulus and Poisson's ratio which may be difficult to obtain in some cases. In Eqs. (5) and (6), the wrinkle wavelength λw and amplitude A is used instead of the film thickness hf, Young's modulus Ef, and Poisson's ratio vf, since usually λw and A are much easier to be experimentally obtained or measured than hf, Ef, and vf [16]. Besides, the measurement uncertainties of λw and A are relatively much smaller than that of hf, Ef, and vf (see Ref. [16] and Sec. 3.3). The metrology of experimentally obtaining λw and A is introduced in Sec. 2 with surface profile fitting in cosine forms.

Finally, it has been shown that the delamination spreading in its two sides is limited by the increase of delamination width and mode-mixity [30,31], though the energy release rates are much larger for compliant substrates [32] compared to their rigid counterparts. As wrinkles precede delamination “blisters” upon substrate compression [10], in some 2D material/compliant substrate systems with moderate interface adhesion energy, the delamination width λd may be close to the critical wrinkle wavelength, i.e., $λd≈λ0$. In this case, Eq. (6) can be further simplified to Display Formula

(7)$Γ≈π16δ2λdE¯s$

In this case, the adhesion energy can be estimated through the delamination width λd and height δ, thus not requiring the coexistence of wrinkles and buckle delamination. Note that Eq. (7) must be used with care for the range of systems with appropriate adhesion energy with $λd≈λ0$, which may not be widely available for many 2D material/compliant substrate systems [10].

Validation of the Present Metrology.

Using relevant experimental results from the literature, and taking the MoS2/PDMS system as an example, with $δ=163 nm$, $λd=816 nm$, $A=25.5 nm$, and $λw=814 nm$, Ref. [16] gives the adhesion energy as 15.74 mJ/m2, whereas Eqs. (5) and (6) yield 15.67 mJ/m2, and Eq. (7) predicts 15.34 mJ/m2. For another system with $δ=143 nm$, $λd=611 nm$, $A=4.7 nm$, and $λw=653 nm$, Ref. [16] gives the adhesion energy as 19.27 mJ/m2, and the present equations (5) and (6) deduce 19.28 mJ/m2, and Eq. (7) yields 15.77 mJ/m2. The differences between results of Ref. [16] and that of the new Eqs. (5) and (6) are less than 0.5% for both examples.

As mentioned in Sec. 1, measuring the adhesion energy between a 2D material and a soft substrate is very challenging, thus, there are only limited reports of the adhesion of thin film/soft substrate systems. For example, to the best of our knowledge, for graphene/soft substrate system, there are only two reported attempts to data [16,21,33]. Table 1 summarizes a comparison of the adhesion energies from the present metrology and some other methods up to date. It can be seen that Eqs. (5) and (6) lead to very close results to the previous study [16], where the wrinkle wavelength λw and amplitude A are available. And when λw and A are absent, estimated values of the adhesion energy from Eq. (7) are within the same order of magnitude of results determined via alternative methods. Despite the consistency of the results from Eq. (7) and previous studies [10,16], and that Eq. (7) requires the minimum information to estimate the adhesion energy, again we note that Eq. (7) should be used with caution for systems with $λd≈λ0$.

Uncertainties of the Present Metrology.

With Eqs. (5) and (6) to calculate the adhesion energy, the overall uncertainty lies in the measured values of the delamination height δ and width λd, and the critical wrinkle wavelength λ0 (calculated from fitted parameters A and λw). Based on the above analysis, the total error in determining the adhesion energy can be written as [16,34] Display Formula

(8)$σΓ=Γ(3σλ0λ0)2+(2σδδ)2+(4σλdλd)2$

where $σΓ$, $σλ0$, $σδ$, and $σλd$ are the uncertainties of the adhesion energy, critical wrinkle wavelength, delamination height, and delamination width, respectively. Uncertainties of the film's Young's modulus and Poisson's ratio are eliminated here. Since the measurement uncertainties for the morphological parameters are small [16], the uncertainty for determining the adhesion energy $Γ$ is reduced notably. With reference to Table 1, the metrology of Brennan et al. [16] gives the uncertainties of the adhesion energy as ±5.1 mJ/m2, while the present work leads to ±3.7 mJ/m2.

Conclusions

A simple framework is proposed to deduce the adhesion energy of thin film/soft substrate systems based on wrinkles and delamination. The wrinkles and delamination can be concomitantly or successively created in one experimental sample. The wrinkle wavelength and amplitude, as well as the delamination width and height, are obtained from surface profile fitting in cosine forms. The proposed metrology does not require the explicit knowledge of the film's thickness, Young's modulus, and Poisson's ratio, thus are much simpler and more convenient for relevant applications, since these values can be difficult to obtain accurately in some cases. And for cases where the delamination width is close to the critical wavelength, the formulation can be further simplified, and the delamination profile alone is sufficient for estimating the adhesion energy. Experimental values for thin film/soft substrate systems from the literature are employed to validate the new framework with good consistency. It is expected that the present methodology may be easily applicable to a range of thin film/soft substrate systems concerning their interface adhesion.

Acknowledgements

The authors acknowledge additional financial support from the National Natural Science Foundation of China (Grant Nos. 11372241 and 11572238).

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References

Genzer, J. , and Groenewold, J. , 2006, “ Soft Matter With Hard Skin: From Skin Wrinkles to Templating and Material Characterization,” Soft Matter, 2(4), p. 310.
Yin, J. , Gerling, G. J. , and Chen, X. , 2010, “ Mechanical Modeling of a Wrinkled Fingertip Immersed in Water,” Acta Biomater., 6(4), pp. 1487–1496. [PubMed]
Yin, J. , Cao, Z. , Li, C. , Sheinman, I. , and Chen, X. , 2008, “ Stress-Driven Buckling Patterns in Spheroidal Core/Shell Structures,” Proc. Natl. Acad. Sci. U. S. A., 105(49), pp. 19132–19135. [PubMed]
Rogers, J. A. , Someya, T. , and Huang, Y. , 2010, “ Materials and Mechanics for Stretchable Electronics,” Science, 327(5973), pp. 1603–1607. [PubMed]
Xu, S. , Yan, Z. , Jang, K. I. , Huang, W. , Fu, H. , Kim, J. , Wei, Z. , Flavin, M. , McCracken, J. , Wang, R. , Badea, A. , Liu, Y. , Xiao, D. , Zhou, G. , Lee, J. , Chung, H. U. , Cheng, H. , Ren, W. , Banks, A. , Li, X. , Paik, U. , Nuzzo, R. G. , Huang, Y. , Zhang, Y. , and Rogers, J. A. , 2015, “ Materials Science. Assembly of Micro/Nanomaterials Into Complex, Three-Dimensional Architectures by Compressive Buckling,” Science, 347(6218), pp. 154–159. [PubMed]
Khang, D. Y. , Jiang, H. , Huang, Y. , and Rogers, J. A. , 2006, “ A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates,” Science, 311(5758), pp. 208–212. [PubMed]
Cao, Q. , Kim, H. S. , Pimparkar, N. , Kulkarni, J. P. , Wang, C. , Shim, M. , Roy, K. , Alam, M. A. , and Rogers, J. A. , 2008, “ Medium-Scale Carbon Nanotube Thin-Film Integrated Circuits on Flexible Plastic Substrates,” Nature, 454(7203), pp. 495–500. [PubMed]
Bowden, N. , Brittain, S. , Evans, A. G. , Hutchinson, J. W. , and Whitesides, G. M. , 1998, “ Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer,” Nature, 393(6681), pp. 146–149.
Moon, M. W. , Lee, S. H. , Sun, J. Y. , Oh, K. H. , Vaziri, A. , and Hutchinson, J. W. , 2007, “ Wrinkled Hard Skins on Polymers Created by Focused Ion Beam,” Proc. Natl. Acad. Sci. U. S. A., 104(4), pp. 1130–1133. [PubMed]
Vella, D. , Bico, J. , Boudaoud, A. , Roman, B. , and Reis, P. M. , 2009, “ The Macroscopic Delamination of Thin Films From Elastic Substrates,” Proc. Natl. Acad. Sci. U. S. A., 106(27), pp. 10901–10906. [PubMed]
Ebata, Y. , Croll, A. B. , and Crosby, A. J. , 2012, “ Wrinkling and Strain Localizations in Polymer Thin Films,” Soft Matter, 8(35), p. 9086.
Li, P. , You, Z. , Haugstad, G. , and Cui, T. , 2011, “ Graphene Fixed-End Beam Arrays Based on Mechanical Exfoliation,” Appl. Phys. Lett., 98(25), p. 253105.
Shi, Z. , Lu, H. , Zhang, L. , Yang, R. , Wang, Y. , Liu, D. , Guo, H. , Shi, D. , Gao, H. , Wang, E. , and Zhang, G. , 2011, “ Studies of Graphene-Based Nanoelectromechanical Switches,” Nano Res., 5(2), pp. 82–87.
Li, D. , Windl, W. , and Padture, N. P. , 2009, “ Toward Site-Specific Stamping of Graphene,” Adv. Mater., 21(12), pp. 1243–1246.
Yoon, T. , Shin, W. C. , Kim, T. Y. , Mun, J. H. , Kim, T. S. , and Cho, B. J. , 2012, “ Direct Measurement of Adhesion Energy of Monolayer Graphene as-Grown on Copper and Its Application to Renewable Transfer Process,” Nano Lett., 12(3), pp. 1448–1452. [PubMed]
Brennan, C. J. , Nguyen, J. , Yu, E. T. , and Lu, N. , 2015, “ Interface Adhesion Between 2D Materials and Elastomers Measured by Buckle Delaminations,” Adv. Mater. Interfaces, 2(16), p. 1500176.
Bunch, J. S. , and Dunn, M. L. , 2012, “ Adhesion Mechanics of Graphene Membranes,” Solid State Commun., 152(15), pp. 1359–1364.
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Figures

Fig. 1

Schematic diagram of substrate compression induced wrinkles (a) and delamination (b). Definition of the wrinkle amplitude A and wavelength λw, and delamination height δ and width λd are indicated. Wrinkles and delamination are not drawn to scale.

Tables

Table 1 Comparison of interface adhesion energy from the present work (Eqs. (5) and (6) or Eq. (7)) and previous studies with typical sizes of delamination and wrinkles from the literature

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