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Fracture, Delamination, and Buckling of Elastic Thin Films on Compliant Substrates

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Fracture, Delamination, and Buckling of Elastic Thin Films on Compliant Substrates FRACTURE, DELAMINATION, AND BUCKLING OF ELASTIC THIN FILMS ON COMPLIANT SUBSTRATES Haixia Mei, Yaoyu Pang, Se Hyuk Im, Rui Huang Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin 1 University Station, C0600 Austin, Texas 78712 Phone: (512) 471-7558 Fax: (512) 471-5500 Email: [email protected] ABSTRACT Greek symbols A series of studies have been conducted for mechanical fracture toughness (J/m2) behavior of elastic thin films on compliant substrates. Under first Dundurs parameter (dimensionless) tension, the film may fracture by growing channel cracks. The second Dundurs parameter (dimensionless) driving force for channel cracking (i.e., the energy release opening displacement (m) rate) increases significantly for compliant substrates. phase angle of mode mix (radian) Moreover, channel cracking may be accompanied by Poisson’s ratio (dimensionless) interfacial delamination. For a film on a relatively compliant 2 substrate, a critical interface toughness is predicted, which stress (N/m ) separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with Subscripts no delamination when the interface toughness is greater than a f film critical value. An effective energy release rate for the steady- i interface state growth of a channel crack is defined to account for the s substrate influence of interfacial delamination on both the fracture ss steady state driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. Alternatively, when the film is under compression, it tends to INTRODUCTION buckle. Two buckling modes have been observed, one with interfacial delamination (i.e., buckle-delamination) and the Integrated structures with mechanically soft components have other without delamination (i.e., wrinkling). By comparing the recently been pursued over a wide range of novel applications, critical stresses for the onset of buckling, we give a criterion from high performance integrated circuits in microelectronics for the selection of the buckling modes, which depends on the [1] to unconventional organic electronics [2] and stretchable stiffness ratio between the film and the substrate as well as the electronics [3,4], along with the ubiquitous integration of hard interface defects. A general conclusion from these studies is and soft materials in biomedical systems [5]. In particular, the that, whether tension or compression, the interfacial properties integration of low dielectric constant (low k) materials in are critical in controlling the morphology and failure of elastic advanced interconnects of microelectronics has posed thin films on compliant substrates. significant challenges for reliability issues due to compromised mechanical properties. Two common failure KEY WORDS: fracture, delamination, buckling, interface modes have been reported, one for cohesive fracture [6] and the other for interfacial delamination [7]. The former pertains NOMENCLATURE to the brittleness of the low-k materials subjected to tension, and the latter manifests due to poor adhesion between low-k E elastic modulus (N/m2) and surrounding materials. Furthermore, a thin film layer G energy release rate (J/m2) under compression can buckle, which leads to failure due to K stress intensity factor (N m1/2) uneven surfaces, buckle-driven delamination and/or fracture W fracture energy (J/m2) [8,9]. These failure mechanisms are schematically illustrated b half width of buckle-delamination (m) in Figure 1. In this paper, the influence of interfacial d delamination width (m) delamination on fracture and buckling of elastic thin films is h thickness (m) investigated, with an emphasis on applications with compliant substrates. 978-1-4244-1701-8/08/$25.00 ©2008 IEEE 762 CHANNEL CRACKING the film and the substrate or the buffer layers are assumed to remain perfectly bonded as the channel crack grows in the One common cohesive fracture mode for thin films under film (Figure 1a). Under this assumption, the energy release tension is channel cracking (Figure 1a). Previous studies have rate for the steady-state growth of a channel crack in a thin shown that the driving force (i.e., the energy release rate) for elastic film bonded to a thick elastic substrate is: the steady-state growth of a channel crack depends on the 2 h constraint effect of surrounding layers [10-12]. For a brittle f f , (1) Gss Z( , ) thin film on an elastic substrate, the driving force increases for E f increasingly compliant substrates. The effect of constraint can where is the tensile stress in the film, is the film be partly lost as the substrate deforms plastically [13] or f h f viscoelastically [14,15]. More recent studies have investigated 2 thickness, and E f E f 1 f is the plane strain modulus of the effects of stacked buffer layers [16,17] and patterned film the film with Young’s modulus E and Poisson’s ratio . The structures [6]. In most of these studies, the interfaces between f f dimensionless coefficient Z depends on the elastic mismatch between the film and the substrate, through the Dundurs’ parameters Gss Film E E f s , (2) E f Es h f f E (1 )(1 2 ) E (1 )(1 2 ) f f s s s f . (3) 2(1 f )(1 s ) E f Es Substrate When the film and the substrate have identical elastic (a) moduli, we have 0 and Z 1.976 . The value of Z decreases slightly for a compliant film on a relatively stiff substrate ( E f Es and 0 ). A more compliant substrate Film ( 0 ), on the other hand, provides less constraint against film cracking. Thus, Z increases as increases. For very compliant substrates (e.g., low-k dielectrics, polymers, etc.), Z increases rapidly, with Z 30 for 0.99 [11,12]. The effect of is secondary and often ignored. hf In general, the steady-state energy release rate of channel dd cracking can be calculated from a two-dimensional (2D) Gd model [10-12] as follows: 1 h f Substrate G O (z)dz , (4) (b) ss 0 f 2hf where (z) is the opening displacement of the crack surfaces far behind the channel front. Due to the constraint by the substrate, the crack opening does not change as the channel front advances and the energy release rate attains a steady state, independent of the channel length. Three-dimensional (c) substrate analyses have shown that the steady state is reached when the length of a channel crack exceeds two to three times the film thickness for a relatively stiff substrate [18], but the crack length to reach the steady state can be significantly longer for more compliant substrate materials [13]. The present study 2b focuses on the steady state. (d) substrate INTERFACIAL DELAMINATION FROM CHANNEL Fig. 1: Schematic illustration of common failure mechanisms While some experimental observations clearly showed in thin film structures: (a) channel cracking; (b) concomitant channel cracks with no delamination [16,19], others observed channel cracking and interfacial delamination; (c) wrinkling; delamination of the interface [16,20]. There are two questions (d) buckle-delamination. to be answered: First, under what condition would the growth 763 of a channel crack be accompanied by interfacial where depends on the elastic mismatch and can be delamination? Second, how would the interfacial delamination determined by solving the equation [23] (if occurring) affect the fracture condition or reliability in 2 2 integrated thin film structures? To answer these questions, we cos 1 2 . (8) consider in this section interfacial delamination emanating 1 1 2 from the root of a channel crack (Fig. 1b). For a long, straight Here we discuss three scenarios at the short crack limit, channel crack, we assume a steady state far behind the channel which would eventually determine the condition for channel front, where the interfacial crack has a finite width, d. The cracking with or without interfacial delamination. First, when energy release rate for the interfacial crack can be written in a similar form as Eq. (1): 0 (no elastic mismatch), we have 0.5 . In this case, approaches a constant as . An analytical Zd d / h f 0 C d S 2 h G Z D ,, T f f , (5) solution [21] predicts that Z (0,0,0) 0.9878 , which d d D h T E d E f U f compares closely with the numerical results (Fig. 2). When 0 , we have 0.5 . Consequently, Z as d / h 0 . where Zd is a dimensionless function that can be determined d f from a two-dimensional plane strain problem [21]. In the As shown in Figure 2, for both 0 and 0 , the present study, a finite element model is constructed to interfacial energy release rate monotonically decreases as the calculate the interfacial energy release rate. The finite element delamination width increases. On the other hand, when 0 , package ABAQUS is employed. The method of J-integral is we have 0 0.5 , and thus, Zd 0 as d / h 0 . adopted for the calculation of the interfacial energy release f Interestingly, the numerical results in Figure 2 show that, rate. In all calculations, we set 1/3 such that f s instead of a monotonic variation with respect to the crack 4 , while the mismatch parameter is varied. length, the interfacial energy release rate oscillates between 1.2 the short and long crack limits for the cases with 0 . Such β α α=−0.99 an oscillation leads to local maxima of the interfacial energy 1.1 = /4 α=−0.6 release rate, which in some cases (e.g., 0.6 ) can be greater than the steady state value at the long crack limit. 1 α=0 α 0.9 =0.2 65 α=0.6 d β α 0.8 = /4 Z 60 0.7 0.6 55 0.5 (deg) 0.4 ψ 50 α=−0.99 0 1 2 3 α=−0.6 d/h f 45 α=0 Fig.
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