A physics-based multi-scale simulation methodology that analyses die stress variations generated by package fabrication is employed for warpage study. The methodology combines coordinate-dependent anisotropic effective properties extractor with finite element analysis (FEA) engine, and computes mechanical stress globally on a package-scale, as well as locally on a feature-scale. For the purpose of mechanical failure analysis in the early stage of a package design, the warpage measurements were used for the tool's calibration. The warpage measurements on printed circuit board (PCB), interposer and chiplet samples, during heating and subsequent cooling, were employed for calibrating the model parameters. The warpage simulation results on full package represented by PCB-interposer-chiplets stack demonstrate the overall good agreement with measurement profile. Performed study demonstrates that the developed electronic design automation (EDA) tool and methodology can be used for accurate warpage prediction in different types of IC stacks at early stage of package design.

A recently proposed methodology for electromigration (EM) assessment in on-chip power/ground grid of integrated circuits has been validated by means of measurements, performed on dedicated test grids. IR drop degradation in the grid is used for defining the EM failure criteria. Physics-based models are involved for simulation of EM-induced stress evolution in interconnect structures, void formation and evolution, resistance increase of the voided segments, and consequent re-distribution of electric current in the redundant grid paths. A grid-like test structure, fabricated with a 65 nm technology and consisting of two metal layers, allowed to calibrate the voiding models by tracking voltage evolution in all grid nodes in experiment and in simulation. Good fit of the measured and simulated time-to-failure (TTF) probability distribution was obtained in both cases of uniform and non-uniform temperature distribution across the grid. The second test grid was fabricated with a 28 nm technology, consisted of 4 metal layers, and contained power and ground nets connected to "quasi-cells" with poly-resistors, which were specially designed for operating at elevated temperatures ~350°C. The existing current distributions resulted in different behavior of EM-induced failures in these nets: a gradual voltage evolution in power net, and sharp changes in ground net were observed in experiment, and successfully reproduced in simulations.

The paper presents a multiscale simulation methodology and EDA tool that assesses the effect of thermal mechanical stresses arising after die assembly on chip performance. Existing non uniformities of feature geometries and composite nature of on-chip interconnect layers are addressed by developed methodology of the anisotropic effective thermomechanical material properties (EMP) that reduces complexity of FEA simulations and enhances the accuracy and performance. Physical nature of the calculated EMP makes it scalable with the simulation grid size, which enables resolution of stress/strain at different scales from package to device channel. With feature-scale resolution, the tool enables accurate calculation of stress components in the active region of each device, where the carrier mobility variation results in deviations of circuits performance. The tool's capability of back-annotation of the hierarchic Spice netlist with the stress values allows a user to perform circuit simulation in different stress environments, by placing the circuit block in different locations in the layout characterized by different distances from the stress sources, such as die edges and C4 bumps. Both schematic and post-layout netlists can be employed for finding optimal floorplan minimizing the stress impact at early design stages, as well as for the final design sign-off. Electrical measurements on a specially designed test-package were used for validation of the methodology. Good agreement between measured and simulated variations of device characteristics has been demonstrated.

A recently proposed theoretical methodology for the assessment of the electromigration (EM) induced IR-drop degradation in on-chip power/ground grids has been validated by means of measurements performed on real silicon. A voltage tapping technique was employed for the direct measurement of voltage variations at 162 nodes of the power net, stressed with 10 mA constant source current at an elevated temperature of 350 °C. A voltage drop between cathode and anode pads exceeding a specified threshold was considered as a failure. Times-to-failure (TTF) was measured on 19 packaged test grids and used for computing the mean TTF (MTTF). The EM-induced voltage degradation in this grid was also analyzed with an assessment methodology based on a simulation of stress evolution everywhere in the grid, resulting in a voiding in some of grid branches and corresponding resistance increase. A set of voiding compact models for different grid segments was developed and used in the simulations. The stochastic nature of the EM phenomenon was captured by introducing random distributions of atomic diffusivities and critical stresses across the grid and iterating them with Monte Carlo loops. A good fit between the measured voltage evolution kinetics at different grid nodes and that predicted by simulation, and the good agreement between measured and simulated failure distributions can be considered as the ever first experimental validation of this EM assessment methodology for on-chip power/ground (p/g) grids.

This paper presents a novel approach and techniques for physics-based electromigration (EM) assessment in power delivery networks of very large scale integration systems. An increase in the voltage drop above the threshold level, caused by EM-induced increase in resistances of the individual interconnect branches, is considered as a failure criterion. It replaces a currently employed conservative weakest branch criterion, which does not account an essential redundancy for current propagation existing in the power-ground (P/G) networks. EM-induced increase in the resistance of the individual grid branches is described in the approximation of the recently developed physics-based formalism for void nucleation and growth. An approach to calculation of the void nucleation times in the group of branches comprising the interconnect tree is implemented. As a result, P/G networks become time-varying linear networks. A developed technique for calculating the hydrostatic stress evolution inside a multibranch interconnect tree allows to avoid over optimistic prediction of the time-to-failure made with the Blech-Black analysis of individual branches of interconnect tree. Experimental results obtained on a number of International Business Machines Corporation benchmark circuits show that the proposed method will lead to less conservative estimation of the lifetime than the existing Black-Blech-based methods. It also reveals that the EM-induced failure is more likely to happen at the place where the hydrostatic stress predicted by the initial current density is large and is more likely to happen at longer times when the saturated void volume effect is taken into account.

A novel methodology for the post placement leakage reduction based on employment of the stress-enhanced filler (SEF) cells was developed. Desired reduction of sub-threshold leakage in test chip silicon was achieved by placement of SEF cells close to the most leaking devices. In the standard cell rows the “optimization zones”, representing portions of the row located between two consecutive fixed cells (clock cells, etc.), were defined. Mentor Graphics' stress assessment tool was used to find the optimal locations for SEF insertion inside each zone, providing the maximal increase of threshold voltage of the leakiest transistors. Measurements performed on the processed silicon test chip have confirmed the predicted leakage reduction of 10–15 percent while keeping same electrical performance.