Almost all practical engineering applications are multi-physics in nature, and various physical phenomena usually interact and couple with each other. For instance, the resistivity of most conducting metals increases linearly with increases in the surrounding temperature resulting from Joule heating by electrical currents flowing through conductors. Therefore, in order to accurately characterize the performance of high-power integrated circuits (ICs), packages and printed circuit boards (PCBs), it is essential to account for both electrical and thermal effects and the intimate couplings between them. In this paper, we present non-conformal, non-overlapping domain decomposition methods (DDMs) for thermal-aware direct current (DC) IR drop co-analysis of high-power chippackage-PCBs. Here, IR stands for the finite resistivity (R) of metals and current (I) drawn off from the power/ground planes. The proposed DDM starts by partitioning the composite device into inhomogeneous sub-regions with temperature-dependent material properties. Subsequently, each sub-domain is meshed independently according to its own characteristic features. As a consequence, the troublesome mesh-generation task for complex ICs can be greatly subdued. The proposed thermal-aware DC IR drop co-analysis applies the non-conformal DDM for both conduction and steady-state heattransfer analyses with a two-way coupling between them. Numerical examples, including an IC package and a chip-package-PCB, demonstrate the flexibility and potential of the proposed thermal-aware DC IR-drop co-analysis using non-conformal DDMs.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2011.0708

Thermal-aware DC IR-drop co-analysis using non-conformal domain decomposition methods

In this paper, we present a non-conformal, non-overlapping domain decomposition method (DDM) for the IR drop analysis of high-power integrated circuit (IC) package in which both dielectrics and non-ideal conductors coexist. The proposed non-conformal DDM starts by partitioning the composite device into inhomogeneous sub-regions. Subsequently, each sub-domain is meshed independently according to its own characteristic features. As a consequence, the troublesome mesh generation task for complex ICs can be greatly relaxed. The proposed non-conformal DDM has been applied to analyze the IR drops in the power delivery networks (PDNs) of complex ICs. Numerical results of a product-level IC package demonstrate the flexibility and potentials of the non-conformal DDM.

Analysis of IR-drop in 3-D IC packaging using a non-conformal domain decomposition method

Combination Approach of FEM and Circuit System in IR Drop Analysis and Its Applications

Worst case graphics core power delivery noise is a major indicator of graphics chip performance. The design of good graphics core power delivery network (PDN) is technically difficult because it is not easy to predict a worst case current stimulus during pre-silicon design stage. Many times, the worst case power delivery noise is observed when graphics benchmark software is run during post-silicon validation. At times like this, it is too late to rectify the power delivery noise issue unless many extra capacitor placeholders are placed during early design stage. To intelligently optimize the graphics core power delivery network design and determining the right amount of decoupling capacitors, this paper suggests an approach that setup a working platform to capture the worst case power delivery noise; and later re-construct the worst case power delivery current using Thevenin's Theorem. The measurement is based on actual gaming application instead of engineering a special stimulus that is generated thru millions of logic test-vectors. This approach is practical, direct and quick, and does not need huge computing resources; or technically skilled logic designers to design algorithms to build the stimulus.

Measurement of worst-case power delivery noise and construction of worst case current for graphics core simulation

A control-volume numerical method is developed for package IR drop analysis. By meshing conductors and solving the governing equations using a finite-volume method with multigrid linear solver, steady-state volumetric currents resulted based IR drop can be accurately and efficiently computed for power delivery analysis.

A finite-volume method for on-package IR drop characterization

A power delivery modeling and design methodology for a programmable logic device package is presented in this paper. Both the DC IR drop and high frequency power ground input impedance have been analyzed by commercial available power integrity software and calibrated with measurements. Design modifications have then been carried out for power delivery system improvement of the package for next generation products.

Jin Zhao

Papers

Power delivery modeling and design methodology for a programmable logic device package