Method to analyze dislocation injection from sharp features in strained silicon structures

Zhang, Zhen; Yoon, Jung‐Sik; Suo, Zhigang

doi:10.1063/1.2424665

Cited by 18 publications

(8 citation statements)

References 23 publications

(25 reference statements)

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“…The b coefficients for different lengths of the chip remain unchanged. This conclusion recovers a previous result [32]: the stress intensity factor reaches a plateau when L/h is greater than 10. That is, when the length of the chip exceeds several times the thickness of the chip, the stress field near one edge of the chip can no longer be affected by the presence of the other edge.…”

Section: Geometric Effectssupporting

confidence: 80%

Singular stress fields at corners in flip-chip packages

Zhang

Yoon

et al. 2012

Engineering Fracture Mechanics

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An electronic device integrates diverse materials, and inevitably contains sharp features, such as interfaces and corners. When the device is subject to thermal and mechanical loads, the corners develop intense stress and are vulnerable sites to initiate failure. This paper analyzes stress fields at corners in flip-chip packages. The stress at a corner is a linear superposition of two modes of singular fields, with one mode being more singular than the other. The amplitudes of the two modes are represented by two stress intensity factors of dissimilar dimensions. To determine the stress intensity factors, we analyze the flip-chip structures under two loading conditions: stretching of the substrate and bending of the substrate. We show that the less singular mode may prevail over the more singular mode for some stretching-bending combinations. The relative significance of the two modes of stress fields also varies with materials, and with the substrate to chip thickness ratio.

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Section: Geometric Effectssupporting

confidence: 80%

Singular stress fields at corners in flip-chip packages

Zhang

Yoon

et al. 2012

Engineering Fracture Mechanics

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“…Recently, a method was described to predict conditions under which such sharp features do not emit dislocations [4]. The method is further developed in the present report to account for split singularities [5,6].…”

Section: Introductionmentioning

confidence: 97%

Split singularities and dislocation injection in strained silicon

Feron¹,

Zhang²,

Suo³

2007

Journal of Applied Physics

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The mobility of charge carriers in silicon can be significantly increased when silicon is subject to a field of strain. In a microelectronic device, however, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular, and is often a linear superposition of two modes of different exponents.The relative contribution of the two modes is characterized by a mode angle, and the critical slip systems are determined as the amplitude of the load increases. Critical residual stress is calculated in a thin-film stripe bonded on a silicon substrate for different geometries and material conditions. In particular, the effect of elastic mismatch between island and substrate is studied, yielding a profound understanding of the importance of the two modes describing the singular stress field.

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“…For instance, the mobility of charge carriers in the integrated electronic structures, if strained, can be significantly enhanced. The great potential of the development of strained nano-electronics, however, is weakened by its susceptibility to dislocation injection, which can act as electrical leakage paths and fail the devices (Kammler et al, 2005;Zhang et al, 2006;Feron et al, 2007;Li et al, 2009). The critical condition for the dislocation injection near the stress concentration sites such as the edges or other geometric sharp features in these interconnected structures requires a knowledge of the dislocation nucleation process.…”

Section: Introductionmentioning

confidence: 99%

“…As will be shown in Section 2, regardless of how stresses are introduced in this structure, the stress fields near the edge root are singular and can be characterized by two parameters: the stress intensity factors (SIFs) and the transverse T-stress. Because of the asymptotic nature of the stress field, the linear elastic fracture mechanics shows that when an appropriate measure of the SIFs reaches a critical value, the dislocation will be nucleated (Zhang et al, 2006). This is essentially equivalent to the Rice-Thomson criterion, which states that a Volterra dislocation will be nucleated if the total driving force at a critical distance away from the stress singularity is larger than the lattice resistance (Rice and Thomson, 1974;Yu et al, 2007;Gao et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects

Lee

Gao

2011

International Journal of Solids and Structures

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a b s t r a c tDislocations can be nucleated from sharp geometric features in strained interconnects due to the thermal expansion coefficient mismatch, lattice mismatch, or stresses that arise during material processing. The asymptotic stress fields near the edge root can be described by mixed-mode singularities, which depend on the dihedral angle and material properties, and a transverse T-stress, which depends on how residual stress is realized in the interconnects. The critical condition for stress nucleation can be determined when an appropriate measure of the stress intensity factors (SIFs) reaches a critical value. This method, however, does not offer an explicit picture of the dislocation nucleation process so that it has difficulties in studying complicated structures, mode mixity effects, and more importantly the temperature effects. Using the Peierls concept, a dislocation can be described by a continuous slip field, and the dislocation nucleation occurs when the total potential energy reaches a stationary state. Through implementing this ad hoc interface model into a finite element framework, it is found that dislocation nucleation becomes more difficult with the increase of mode mixity, or the decrease of the T-stress, or the decrease of the length-to-height ratio of the surface pad, while the shape of the surface pad, being a square or a long line, plays a less important role. The Peierls dislocation model also allows us to determine the activation energy, which is the energy needed for the thermally activated, mechanically assisted dislocation nucleation when the applied load is lower than the athermal critical value. The calculated saddle point configuration agrees well with the molecular simulations in literature. Suggestions on making immortal strained interconnects are made.

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Method to analyze dislocation injection from sharp features in strained silicon structures

Cited by 18 publications

References 23 publications

Singular stress fields at corners in flip-chip packages

Singular stress fields at corners in flip-chip packages

Split singularities and dislocation injection in strained silicon

Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects

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