Stress-Induced Delamination Of Through Silicon Via Structures

Continuous scaling of on-chip wiring structures has brought significant challenges for materials and processes beyond the 32 nm technology node in microelectronics. Recently three-dimensional (3-D) integration with through-silicon-vias (TSVs) has emerged as an effective solution to meet the future interconnect requirement. Thermo-mechanical reliability is a key concern for the development of TSV structures used in die stacking as 3-D interconnects. This paper examines the effect of thermal stresses on interfacial reliability of TSV structures. First, the three-dimensional distribution of the thermal stress near the TSV and the wafer surface is analyzed. Using a linear superposition method, a semi-analytic solution is developed for a simplified structure consisting of a single TSV embedded in a silicon (Si) wafer. The solution is verified for relatively thick wafers by comparing to numerical results obtained by finite element analysis (FEA). Results from the stress analysis suggest interfacial delamination as a potential failure mechanism for the TSV structure. Analytical solutions for various TSV designs are then obtained for the steady-state energy release rate as an upper bound for the interfacial fracture driving force, while the effect of crack length is evaluated numerically by FEA. Based on these results, the effects of TSV designs and via material properties on the interfacial reliability are elucidated. Finally, potential failure mechanisms for TSV pop-up due to interfacial fracture are discussed.Aerospace Engineerin

Automated Netlist Generation for 3D Electrothermal and Electromagnetic Field Problems

We present a method for the automatic generation of netlists describing general three-dimensional electrothermal and electromagnetic field problems. Using a pair of structured orthogonal grids as spatial discretisation, a one-to-one correspondence between grid objects and circuit elements is obtained by employing the finite integration technique. The resulting circuit can then be solved with any standard available circuit simulator, alleviating the need for the implementation of a custom time integrator. Additionally, the approach straightforwardly allows for field-circuit coupling simulations by appropriately stamping the circuit description of lumped devices. As the computational domain in wave propagation problems must be finite, stamps representing absorbing boundary conditions are developed as well. Representative numerical examples are used to validate the approach. The results obtained by circuit simulation on the generated netlists are compared with appropriate reference solutions.Comment: This is a pre-print of an article published in the Journal of Computational Electronics. The final authenticated version is available online at: https://dx.doi.org/10.1007/s10825-019-01368-6. All numerical results can be reproduced by the Matlab code openly available at https://github.com/tc88/ANTHE

Some Key Developments in Computational Electromagnetics and their Attribution

Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution

Exact 3D solution for static and damped harmonic response of simply supported general laminates

The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [-15/15], [0/30/0] and [-10/0/40] laminates are studied for various length-to-thickness ratios

Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip Packaging

This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses numerical challenges due to the presence of different geometric scales. The necessity of very fine grids is relaxed by solving and embedding a 1D sub-problem along the wire into the surrounding 3D geometry. The arising singularities are described using de Rham currents. It is shown that the problem is related to fluid flow in porous 3D media with 1D fractures [C. D'Angelo, SIAM Journal on Numerical Analysis 50.1, pp. 194-215, 2012]. A careful formulation of the 1D-3D coupling condition is essential to obtain a stable scheme that yields a physical solution. Elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates. Additionally, the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented.Comment: all numerical results can be reproduced by the Matlab code openly available at https://github.com/tc88/ETwireSi