Crack Arrest on Brittle Film

Controlled crack arrest in brittle thin films: The effect of embedded voids Ling Liu, Xi Chen * Department of Civil Engineering and Engineering Mechanics, Columbia University, 500 West 120th Street, New York, NY 10027-6699, USA Received 3 April 2008; received in revised form 15 August 2008; accepted 17 August 2008 Available online 25 September 2008 Abstract Controlled crack arrest is useful for controlling self-assembled crack paths in micro-fabrication, as well as limiting crack length in toughening composites. Compliant inclusions and voids can effectively attract and arrest cracks, thereby controlling the crack pattern. Analytical stress solution indicates that when the inclusion is about 10 times more compliant than its matrix, it may be effectively mod- eled as a void. The crack arrest capability is expressed in terms of the critical angle of the initial crack path, as the inclusion size, shape, crack origin and film properties are varied. Simple criteria are established to maximize the crack arrest ability and to determine the critical crack angle. The effectiveness of using different void patterns to arrest cracks is also explored. The results are useful for both controlling and restricting cracks in brittle thin films, through the utilization of compliant or void-like inclusions as crack arrestors. 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Thin films; Fracture; Toughness; Kinetics self-organiz ation & patter ning; Simulation 1. Introduction Thin films are often subjected to residual stresses inher- ited from deposition and/or thermal expansion mismatch with substrates. In many technolog ically important thin films, large equibiaxial tensile stress is developed as the sys- tem is cooled from an elevated deposition temperature or as the film is dried; when such tensile stress exceeds a critical value in brittle thin films (e.g. NiAl film on Si substrate [1] or SiO 2 film on Si wafer [2]), fracture occurs and various channel crack patterns have been observed [3], including mud cracks [4] , spiral cracks [5] and sinusoidal cracks [6] . Conventionally, cracks are regarded as a threat to sys- tem integrity and should be avoided if possible. However, cont rolled fr actur e in thin fil ms may also be us ef ul: in recent years, mechanical self-assembly based on ordered crack patterns has emerged as a competitive approach for fabric atin g nanowires and nanochannels [2,7–10]. In essence, various crack initiators and arrestors are embedded in a film, whose shape and alignment are adjusted so as to guide the spontaneous formation of a highly ordered, stre ss-ass iste d fra ctur e pat ter n. Since the typical cra ck opening (gap) is on the order of nanometers, a network of nanochannel is formed. Based on such a template, various deposition methods may be employed to fill the crack channels with a different material. Upon removal of the original film material, the fillers become ordered nanowire pattern [2,9]. Compared to the conventional photolithogra- phy, such mechanical self-assembly is arguably more eco- nomical and efficient, and it also involves rich mechanics problems. One of the key challenges of the self-assembly of fracture is to guide the crack growth along an expected path. Var ious types of cra ck initiators and arrestors may be employed [2], which are regular-shaped dent-like features (e.g . square , cir cul ar, ann ula r, hea rt, etc.) pat ter ned on the substr ate surfac e pri or to film deposi tion, stre ssin g and cracking. In essence, the crack initiators and arrestors in thes e expe riments are voids (vacant ‘‘i nclusio ns ) embedded in thin films. While there are various ways to initiate cracks along a given path (e.g. using a void or inclusion with sharp tips [2] , or applying pyramidal indentatio n to nucleate radial cracks [11]), a comprehensive study on the controlled crack arrest is still scarce. How large is the 1359-6454/$34.00 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.08.038 * Corresponding author. Tel.: +1 212 854 3787; fax: +1 212 854 6267. E-mail address: [email protected] (X. Chen). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 56 (2008) 6214–6223

Crack Arrest on Brittle Film

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