Elastic property determination of nanostructured W/Cu multilayer films on a flexible substrate

Wei He·Meidong Han·Shibin Wang·Philippe Goudeau·Eric Le Bourhis·Pierre Olivier Renault

Abstract An experimental method for a single layer is extended to determine the elastic properties of nanostructured W/Cu multilayers on a flexible substrate. The strain difference between the W/Cu-polyimide-W/Cu composite and the uncoated substrate,measured by dual digital image correlation, allows us to extract the effective Young’s modulus of W/Cu multilayers (20 periods)equaling 216±13 GPa.Finite element method is then performed,which agrees well with the experiment and classical rule of mixture(ROM)theory demonstrating that the extension to multilayers is effective and reliable.The numerical analysis also interestingly shows that the strain difference is linearly related to the thickness ratio (W/Cu), periods and sublayer thickness, respectively. In contrast to ROM theory, this approach could potentially be used for the evaluation of properties and design of emerging/unknown functional multilayers,whether or not they are crystalline or amorphous.

Keywords Nanostructured multilayers·Young’s modulus·Dual digital image correlation·Finite element method

1 Introduction

In the future micro-/nano-electro-mechanical systems(MEMS/NEMS) and flexible electronics, nanostructured metallic multilayers (NMMs) may play a leading role due to their desirable mechanical properties and performance,such as superior strength [1], relatively high deformability/adhesion [2], excellent electrical/thermal conductivity[3], great radiation/magnet tolerance [4], and dramatically improved fatigue life [5], making them unique multifunctional materials to satisfy special needs. Among these NMMs, W/Cu multilayer films have attracted much interest. One concern is to integrate Cu (high ductility, thermal conductivity)and W(high strength,low thermal expansion coefficient)in thermal management applications,such as the heat sink for high density integrated circuits[6].Moreover,introducing Cu as an immiscible interlayer for W thin films enables a controllable microstructure, which could be used to improve the mechanical properties of W films[7].

Young’s modulus is one of the most important properties in the performance design and reliability evaluation of those functional multilayers. Because of the nanoscale film thickness and complex multilayered structure,accurate experimental characterization is a real challenge. Although there have already been many techniques for a single layer[8],such as X-ray tensile testing[9],rule of mixture(ROM)[10,11] and bulge test [12], there are much fewer applications to investigate multilayers. Noticeably, some of those techniques have been effectively extended to study the elastic moduli of multilayers, which include indentation [13],vibrational approach [14] and ROM. Especially, ROM is widely adopted due to its simplicity and non-requirement of crystallinity of materials.There are two ways to use ROM for multilayers. One is to theoretically predict the effective Young’s modulus using a governing equation based on the fact that the elastic moduli of each monolayer is known[15,16].The other is to extract the properties of nanocomposites by subtracting the properties of substrate from the overall experimental measurement of a film-substrate structure[17].To do this, one must assume a uniform one-dimensional stress distribution through the film thickness, and a complete strain transfer at the interface is extremely important,which has been proved in many cases [18–20]. However,the theoretical approach is limited in the case of emerging/unknown materials or when a size effect of a sublayer is present [21,22]. Furthermore, the corresponding experimental approach to study the periodic multilayers, such as many periods of W/Cu nanostructured bilayers,is still lacking although it is of utmost importance.

Recently,we have proposed an original approach[23]for a single layer allowing higher precision and simpler process of experiments compared to ROM. In this study, we provide a brief overview of this approach including theory and experiment based on dual digital image correlation(DIC). Combined with finite element method (FEM), we extend this method to probe the effective elastic properties of W/Cu multilayers(20 periods)on a flexible substrate,and the relationships between the strain difference and important parameters of multilayers are analyzed.

2 Theoretical and experimental background

For a single continuous layer or film symmetrically coated on both sides over a half-surface of the substrate in tension,as shown in Fig.1(enlarged view of the dogbone specimen,film is highlighted in silver white),a simple formula can be acquired[23]

Fig. 1 Experimental setup combining the dual DIC system with the Deben Microtest.Reproduced from our previous work[23]

where E, t, ε, f and s represent the Young’s modulus,thickness, strain, film and substrate, respectively. The subscripts u,c and 11 correspond to the uncoated substrate,the film-substrate-film composite and the longitudinal (tensile)direction,respectively.It is not difficult to measure tf,Esand ts;therefore,to obtain the Young’s modulus of a thin film Ef,the key consideration is to simultaneously measure the tensile strain of the uncoated substrateand the compositeFurthermore, the experimental error analysis of the Young’s modulus determination can be found in Ref. [24].For better understanding of the rule of experimental design,herein,we give a brief overview of the error analysis.Defining a non-dimensional ratio,,

the uncertainty of the Young’s modulus measurement can be calculated:

After taking typical values of δR = ±0.01, Es= 4±0.2 GPa,ts=125± 0.5 μm,and t f =359± 3 nm,used in our experiments,we obtain

Figure 1 schematically illustrates the dual DIC system that we used for the synchronous strain measurement during a tensile test of the dogbone specimen by Deben Microtest.The tensile speed was 0.2 mm/min corresponding to a strain rate of 4.1×10-5s-1.One two-dimensional (2D)DIC system mainly comprises a telecentric lens,a charge-coupled device(CCD)camera and illumination.The 0.5X gold series telecentric lens from Edmund is selected to measure the strain of the film-substrate-film composite due to its large depth of field and constant magnification, which allows focusing on the image side up to±2.1 mm at f/10.Meanwhile,the 1.0X gold series telecentric lens from Edmund is selected to measure the strain of the uncoated substrate with a depth of field being±0.6 mm at f/10.The camera for 0.5X lens is a digital 8-bit complementary metal-oxide semiconductor(CMOS)camera(2560×1920 pixels),and the one for 1.0X lens is 1392×1040 pixels with a real size of 9 mm×7 mm.The illumination for 0.5X lens is a flexible fiber optic light called model 21 dc from TechniQuip, and the one for the 1.0X lens is an AI standard working distance LED ring light from Edmund. It should be noted that two polarizers and a flexible fiber light with a low incidence angle is imperative to significantly reduce the mutual influence oflights on each DIC system considering the fact that the uncoated substrate is translucent.

For the high precision strain measurement, DIC [25,26]is a widely adopted method owing to its simplicity,versatility and robustness.In principle,DIC is an optical technique based on digital image processing and numerical computing.It directly provides full-field displacements to sub-pixel accuracy and full-field strains by a comparison of digital images of a specimen surface before and after deformation.Notice that DIC can achieve different scales of deformation(from nano-scale to macro-scale),depending on the observation devices,such as the high-spatial-resolution microscopes and scanning electron microscope(SEM).Furthermore,with special considerations and speckle (a carrier or “sensor” of deformation information)fabrication methods[27],DIC can be even applied in extreme environments [28,29], such as 1600°C high temperature. Herein, we use the typical paint spraying technique to fabricate random speckle patterns on the specimen surface and to obtain the macroscopic strains by selecting the region of interest of uncoated substrate and composite, and then calculate using the software Deftak[30].

3 Experiment with dual DIC

Extending Eq. (1) to a multilayer structure and defining a dimensionless quantity,R =-1,the effective elastic modulus of the multilayer thin films could be obtained as:

Fig. 2 Young’s modulus determination of W/Cu nanocomposites:longitudinal strain of the uncoated substrate as a function of that of W/Cu-polyimide-W/Cu composite. The continuous red line corresponds to the linear regression in the elastic domain, and the inset schematically illustrates the dual DIC tensile testing of the as-deposited specimen

To verify its effectiveness and to study the elastic properties of substrate-supported W/Cu multilayers, a tensile test combined with dual DIC system is performed. The dogbone-shaped substrate is a flexible polyimide,Kapton HN 125 μm thick,with a nominal in-plane gauge section dimensions of 34 mm ×12 mm.This polymer substrate exhibits a large elastic region (about 4% ) and its elastic modulus is 4.0 ± 0.2 GPa. After cleaning the substrate ultrasonically with acetone and ethanol,and thanks to a homemade mask[23], W (6 nm) and Cu (18 nm) single layers are sputtered alternately on both sides over the half-surface of the substrate with an Ar flow rate of 19 and 3 standard cubic centimeters per minute(SCCM),respectively.This mask is designed so that the region of interest for deformation measurement is large with a constant film thickness and is far away from the film-substrate boundary. Thin films are deposited with 20 periods(n =20)that should result in a total thickness of 2×480 nm,as shown in the inset of Fig.2,while the measured thickness is smaller(2×359±3 nm)due to the overestimated deposition speed. The comprehensive crystallographic and residual stress analyses of similar W/Cu multilayers can be found in Refs.[7,31].Herein,we emphasize that it is strongly recommended to coat on both sides instead of one side,because with this symmetric configuration,regardless of the residual stress and the Poisson’s ratio mismatch between the composite and the uncoated substrate(surface curvature evolution appears with only one side coated[18]),the specimen remains flat during the tensile testing,which is an important assumption for this method[23].A dual DIC system is then applied to simultaneously measure the longitudinal strain of the uncoated substrate and the W/Cu-polyimide-W/Cu composite in tension.Figure 2 also shows the tensile strain of the uncoated substrate as a function of that of the film-substrate film composite, which clearly indicates a significant strain difference (R = 0.31). Notice that the curve deviates from linearity at a strain of about 0.9% showing that the dual DIC system is sufficiently precise to capture the yield point of a thin film[23].Moreover,the elastic limit of the multilayers is much larger than pure W films (about 0.3% in general),which may due to the introduction of a large amount of ductile Cu sublayers.From the recorded digital images,no cracks are observed.However,the cracks may exist considering the insufficient magnification of the telecentric lens. Since we focus on the elastic domain, even small cracks exist in the inelastic region,they have no influence on the Young’s modulus determination, and even appear in the elastic region,the effect of cracks is negligible based on the fact that the linearity of the entire elastic domain is excellent.

Herein,Eq.(4)can be modified as:

Fig. 3 Three-dimensional quarter-symmetric FEM model of the multilayer-substrate-multilayer structure and the calculated longitudinal strain field.The inset clearly indicates the strain difference between the composite and uncoated substrate

where n is the period number,tWand tCudenote the thickness of W and Cu sublayers, respectively. Equation (5) is the ultimate governing equation that we used to determine the effective Young’s modulus of W/Cu multilayers to be 216± 13 GPa.

On the other hand,the theoretical effective elastic modulus of W/Cu multilayers can be obtained from a classical isostrain model of ROM as expressed by[16]:

where EW, ECuare the Young’s moduli of W and Cu sublayers,respectively,and ρ is the thickness ratio of W to Cu monolayers,i.e.ρ = tW/tCu= 1/3.Since the exact values of the elastic moduli of W and Cu sublayers are unknown,EW= 411 GPa and ECu= 130 GPa from Ref. [32] are used. The effective Young’s modulus of W/Cu multilayer thin films is then obtained as 200 GPa, which agrees well with the experimental result showing a good reliability of extending Eq.(1)to multilayers.

4 Finite element method

To further demonstrate the feasibility of extending Eq. (1)to experimentally study the Young’s modulus of W/Cu nanocomposite thin films, a numerical simulation (FEM)is performed using ABAQUS v6.14 (Dassault systems).Considering the structural symmetry and to improve the calculation efficiency, one quarter of the specimen is modeled(X Z and X Y planes of symmetry)as shown in Fig.3,where the X-axis denotes the loading or longitudinal direction,Y-axis the transverse direction,and Z-axis the out-of-plane direction.The total film thickness is 2×359=718 nm,i.e.the measured deposition thickness(ρ =1/3,n =20).

Based on the structural characteristics, the polyimide substrate (the grey part in Fig. 3) is modeled with a threedimensional(3D)solid part meshed in C3D8 elements,while the W/Cu nanocomposites (the yellow part in Fig. 3) are modeled with a 2D shell part meshed in S4 elements, i.e.a 4-node doubly curved general-purpose shell, and its section is defined using the “composite type” in the software,by which we can define the 20 W/Cu nanocomposites on both sides of the substrate. Furthermore, the nanocomposites and the substrate are bonded together at their coincident nodes using a tie constraint to simulate the perfect strain transfer at the interface.The force is applied directly on the right end of the substrate with the left end constrained in the X-direction,and the central planes of the substrate have been exerted the symmetric boundary conditions (X Z and X Y planes of symmetry)to avoid rigid body motions. Both the films and substrate are assumed as isotropic elastic materials while taking account of geometric non-linearity effects in all steps.The Young’s modulus and Poisson’s ratio of W and Cu monolayers are set to be 411 GPa,0.28 and 130 GPa,0.34,respectively[32],and the polyimide substrate are 4 GPa and 0.34,respectively.Notice that there is a Poisson’s ratio mismatch between W monolayers(0.28)and Cu monolayers(0.34)and polyimide substrate(0.34).

Fig.4 Effective Young’s modulus of W/Cu multilayers as a function of a thickness ratio ρ,c periods n,d thickness of Cu sublayer.b The effective elastic modulus by FEM versus that by ROM with the change of thickness ratio ρ.The continuous red line corresponds to the linear regression

After calculation,the full-field longitudinal strain contour of the uncoated substrate and the film-substrate-film composite is obtained,and the strain along the centerline(X Z plane of symmetry) is extracted in the inset as shown in Fig. 3.As can be clearly seen,there is a sharp strain jump(0.46% –0.60% ) from the composite to the uncoated substrate at a given load equaling 24 N, and the strain difference (R =0.30) is close to the one in the experiment (R = 0.31). It is worth mentioning that the strain of the film and the underling substrate is the same except for several singularities near the uncoated substrate-composite boundaries(not shown here),which indicates a full strain transfer at the multiple interfaces of the multilayered structure.Referring to Eq.(5),the effective elastic modulus is determined to be 211 GPa,which agrees well with the experimental result(216±13 GPa)and the theoretical ROM prediction(200 GPa).

As stated above,the feasibility and reliability of FEM to characterize the effective Young’s modulus of multilayer thin films have been verified by its good agreement with experimental and theoretical results.In order to further understand the underlying influence factors, we numerically study the relationship between the Emultilayer/strain difference(R)and the thickness ratio (ρ), period number (n), thickness of Cu sublayer (tCu), which can significantly reduce the cost of experiment and time. Figure 4a shows the effective elastic modulus of W/Cu multilayersas a function of thickness ratio ρ,while n and tCuremain constant, i.e. n = 20, tCu= 18 nm. When ρ is smaller than 1,increases dramatically,and then experiences a steady and slight growth (ρ ＞1). This is reasonable if we refer to Eq.(6),andalso shows an identical trend and similar values, which further proves the reliability of extending the method[23]for multilayers.It is particularly interesting to note thatpresents a linear relationship withwhen ρ is changed from 1:18 to 10:3,as shown in Fig.4b.Moreover,an acceptable discrepancy(about 10% ) betweenwhich arises from the Poisson’s ratio mismatch (W, Cu films and polyimide)and the intrinsic theoretical error,is evidenced.Figure 4c,d show the evolution of effective Young’s modulus as n and tCuvary,respectively,while ρ and tCu(ρ =1:3,tCu=18 nm),ρ and n(ρ =1:3,n =20)keep unvarying,respectively.As can be seen,andagree well with each other and keep almost constant.Therefore,the effective elastic modulus of multilayers is strongly related to ρ rather than n and tCu(only one variable in each case).Figure 5 shows the strain difference(R)as a function of ρ, n, tCu, respectively. It is also interesting to see that all have exhibited a nearly perfect linear relationship. In order to explain this behavior,we define a dimensionless quantity,φ =Combining Eqs.(5)and(6),we obtain

Fig.5 Strain difference(R)as a function of a thickness ratio ρ,b periods n,c thickness of Cu sublayer.The continuous red lines correspond to the linear regression

From Fig.4,it is obvious and imperative that φ remains constant whenρ,n,tCuare varying,respectively,although the values of φ in these three cases are different.Consequently,according to Eq. (7), the unvarying φ, EW, ECu, Esand tsin each case leads to a linear relationship between R and ρ,n,tCu,respectively,and the values of slopes from FEM data are reasonably compatible with Eq. (7). It should be noted that in all the analyses above (ROM and FEM), the elastic properties of single layers are assumed to be known,which are not applicable to multilayers comprising unknown materials.However,our experimental testing is promising,since it is based on the strain difference between the coated and uncoated parts so that the materials can be unknown.Furthermore, for the studied multilayers, the bulk Young’s moduli of W and Cu sublayers[32]could be considered acceptable due to the good agreement in above cases,which also indicates that little or no lengthscale size effect appears in the monolayers.It is worth mentioning that this method has the potential to be employed for multilayers working in extreme environment,such as high-temperature condition,based on some special considerations for DIC measurements[33,34].

5 Concluding remarks

In summary,we have studied the elastic properties of flexible substrate-supported W/Cu nanocomposites by a combination of theory, experiment and numerical simulation. The good agreement between the effective elastic moduli determined by the experiment and FEM/ROM(216±13 GPa and 211/200 GPa,respectively)shows the reliability of extending our previous method [23] from a single layer to multilayers(20 periods).In contrast to the typical ROM theory,the multilayer consisting of periodic sublayers with unknown properties can be characterized, especially when the ultrathin films present a size effect. Interestingly,is linearly related toalthough both show a nonlinear behavior as the thickness ratio (ρ) varies. Moreover, to the best of our knowledge, the linear relationship between the strain difference(R)and the separate ρ,n and tCuis reported for the first time.

AcknowledgementsThis research is financially supported by the National Natural Science Foundation of China(Grant 11802156),China Postdoctoral Science Foundation (Grant 2018M641331), and French Government Program “Investissements d’Avenir” (Labex Interactifs,Grant ANR-11-LABX-0017-01).