Predicted Response of the Die-Carrier Assembly in Flexible Electronics to the Combined Action of Tension and Bending Applied to the Carrier

Suhir, Ephraïm

doi:10.1115/1.4005191

Cited by 9 publications

(7 citation statements)

References 18 publications

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“…5(c)) can be obtained using the theory of lap-joints. [106][107][108] It can be noticed that Eq. (4) considers only the effect of M, and the effect of q is ignored.…”

Section: A Uniaxial Bending Of Utcsmentioning

confidence: 99%

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

Heidari

Wacker

Dahiya

2017

Applied Physics Reviews

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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.

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“…5(c)) can be obtained using the theory of lap-joints. [106][107][108] It can be noticed that Eq. (4) considers only the effect of M, and the effect of q is ignored.…”

Section: A Uniaxial Bending Of Utcsmentioning

confidence: 99%

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

Heidari

Wacker

Dahiya

2017

Applied Physics Reviews

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“…and has an horizontal asymptote λ ∞ k = λ e + kλ −1 e as y → +∞. Equilibrium paths predicted by (8) are traced out in the plane (y = max (w) , λ) by gradually incrementing y and evaluating λ k , k and a 0 being fixed. Predictions are compared with a numerical solution of (6), using MATLAB's boundary value solver bvp4c [this is a finite difference code that implements a collocation formula, details of which can be found in 29].…”

Section: Solving Methodsmentioning

confidence: 99%

“…The usual way to model the interaction between the beam and the foundation is to replace the latter with a set of independent springs whose restoring force is a linear [see e.g. [1][2][3][4][5][6][7][8] or a nonlinear [see e.g. 9-19] function of the local deflection of the beam.…”

Section: Introductionmentioning

confidence: 99%

Limit point buckling of a finite beam on a nonlinear foundation

Lagrange

2021

Preprint

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In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases.Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics.

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“…The system is symmetric about the axes x 1 and x 2 , therefore only half of it is examined. The solution is obtained by solving the equilibrium, kinematic and constitutive equations, together with the boundary conditions, well-known in literature [11][12][13][14][15][16][17]. The applied uniform load q can be decomposed into a uniform axial stretching load (F) acting along the x 1 -axis, and a lateral load that creates a bending moment (M) about the x 2 -axis [18].…”

Section: Analytical Solutionmentioning

confidence: 99%

Stress analysis of ultra-thin silicon chip-on-foil electronic assembly under bending

Wacker

Richter

Hoang

et al. 2014

Semicond. Sci. Technol.

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In this paper we investigate the bending-induced uniaxial stress at the top of ultra-thin (thickness ⩽20 μm) single-crystal silicon (Si) chips adhesively attached with the aid of an epoxy glue to soft polymeric substrate through combined theoretical and experimental methods. Stress is first determined analytically and numerically using dedicated models. The theoretical results are validated experimentally through piezoresistive measurements performed on complementary metal-oxide-semiconductor (CMOS) transistors built on specially designed chips, and through micro-Raman spectroscopy investigation. Stress analysis of strained ultra-thin chips with CMOS circuitry is crucial, not only for the accurate evaluation of the piezoresistive behavior of the builtin devices and circuits, but also for reliability and deformability analysis. The results reveal an uneven bending-induced stress distribution at the top of the Si-chip that decreases from the central area towards the chipʼs edges along the bending direction, and increases towards the other edges. Near these edges, stress can reach very high values, facilitating the emergence of cracks causing ultimate chip failure.

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Predicted Response of the Die-Carrier Assembly in Flexible Electronics to the Combined Action of Tension and Bending Applied to the Carrier

Cited by 9 publications

References 18 publications

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

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

Limit point buckling of a finite beam on a nonlinear foundation

Stress analysis of ultra-thin silicon chip-on-foil electronic assembly under bending

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