Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers

Shen, Yu‐Lin; Suresh, S.; Blech, I. A.

doi:10.1063/1.362938

Cited by 145 publications

(61 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The generalized plane strain model realistically simulates the structure with long metal lines. It is also able to predict the overall wafer curvature in both the x and y directions for comparisons with experiments, 40 although this aspect is not specifically treated in the present paper. In some cases, comparisons of numerical results between the generalized plane strain and plane strain analyses are presented.…”

Section: Numerical Approachmentioning

confidence: 97%

Thermomechanical response and stress analysis of copper interconnects

Ege

Shen

2003

Journal of Elec Materi

View full text Add to dashboard Cite

This study is devoted to thermomechanical response and modeling of copper thin films and interconnects. The constitutive behavior of encapsulated copper film is first studied by fitting the experimentally measured stress-temperature curves during thermal cycling. Significant strain hardening is found to exist. Within the continuum plasticity framework, the measured stress-temperature response can only be described with a kinematic hardening model. The constitutive model is subsequently used for numerical thermomechanical modeling of Cu interconnect structures using the finite element method. The numerical analysis uses the generalized plane strain model for simulating long metal lines embedded within the dielectric above a silicon substrate. Various combinations of oxide and polymer-based low-k dielectric schemes, with and without thin barrier layers surrounding the Cu line, are considered. Attention is devoted to the thermal stress and strain fields and their dependency on material properties, geometry, and modeling details. Salient features are compared with those in traditional aluminum interconnects. Practical implications in the reliability issues for modern copper/low-k dielectric interconnect systems are discussed.

show abstract

Section: Numerical Approachmentioning

confidence: 97%

Thermomechanical response and stress analysis of copper interconnects

Ege

Shen

2003

Journal of Elec Materi

View full text Add to dashboard Cite

show abstract

“…[72][73][74] A comparison of Young's modulus E and the Poisson's ratio 68 of several materials frequently used in flexible electronics [e.g., singlecrystal Si, hydrogenated amorphous (a-Si:H), hydrogenated nanocrystalline Si (nc-Si:H), polycrystalline Si, Kapton V R , and polyethylene naphthalate (PEN)] is given in Table I. [75][76][77][78][79][80][81][82] The experimental techniques that have been used to study mechanical aspects of UTCs include (i) direct methods 83,84 such as xray diffraction 85,86 and micro-Raman spectroscopy 87,88 and (ii) indirect methods based on measuring the curvature 89 (e.g., optical interferometry, 90 laser scanning, 91,92 and microscope image monitoring in real time 43 ). The subsection below presents the uniaxial and biaxial bending in UTCs.…”

Section: Ultra-thin Chips and Mechanical Bendingmentioning

confidence: 99%

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

Heidari

Wacker

Dahiya

2017

Applied Physics Reviews

View full text Add to dashboard Cite

Electronics that conform to 3D surfaces are attracting wider attention from both academia and industry. The research in the field has, thus far, focused primarily on showcasing the efficacy of various materials and fabrication methods for electronic/sensing devices on flexible substrates. As the device response changes are bound to change with stresses induced by bending, the next step will be to develop the capacity to predict the response of flexible systems under various bending conditions. This paper comprehensively reviews the effects of bending on the response of devices on ultra-thin chips in terms of variations in electrical parameters such as mobility, threshold voltage, and device performance (static and dynamic). The discussion also includes variations in the device response due to crystal orientation, applied mechanics, band structure, and fabrication processes. Further, strategies for compensating or minimizing these bending-induced variations have been presented. Following the in-depth analysis, this paper proposes new mathematical relations to simulate and predict the device response under various bending conditions. These mathematical relations have also been used to develop new compact models that have been verified by comparing simulation results with the experimental values reported in the recent literature. These advances will enable next generation computer-aided-design tools to meet the future design needs in flexible electronics.

show abstract

“…A biaxial form of Stoney, appropriate for anisotropic film stresses, including different stress values at two different directions and non-zero, in-plane shear stresses, was derived by relaxing the assumption of curvature equi-biaxiality [2]. Related analyses treating discontinuous films in the form of bare periodic lines [4] or composite films with periodic line structures (e.g., bare or encapsulated periodic lines) have also been derived [5][6][7]. These latter analyses have also removed the assumption of equi-biaxiality and have allowed the existence of three independent curvature and stress components in the form of two, non-equal, direct components and one shear or twist component.…”

mentioning

confidence: 99%

Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures

Ngo

Rosakis

2005

ACTA MECH SINICA

View full text Add to dashboard Cite

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system's curvatures and the misfit strain. These relations feature a "local" part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a "non-local" part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a "non-local" dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.

show abstract

Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers

Cited by 145 publications

References 17 publications

Thermomechanical response and stress analysis of copper interconnects

Thermomechanical response and stress analysis of copper interconnects

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures

Contact Info

Product

Resources

About