Jianyong Xie

Designing and Modeling for Power Integrity

After providing an overview of the state-of-the-art in power distribution design and modeling, this paper focuses on return path discontinuities (RPDs) for I/O signaling. After briefly describing their importance in the context of simultaneous switching noise, a specific case of RPD based on via discontinuities is discussed in detail in the context of both the frequency- and time-domain waveforms using a test vehicle. The modeling of RPD in practical packages and printed circuit boards is addressed along with substrate coupling due to nonideal reference planes. Finally, a high-impedance power distribution scheme for I/O signaling is presented that can potentially solve a number of RPD-related problems, followed by future challenges.

Electrical-Thermal Co-Simulation of 3D Integrated Systems With Micro-Fluidic Cooling and Joule Heating Effects

In this paper, the electrical-thermal co-simulation of 3D systems with Joule heating, fluidic cooling and air convection effects is proposed. The finite-volume method formulations of voltage distribution equation, heat equations for both fluid flow and solid medium with nonuniform mesh are explained in detail. Based on the proposed iterative co-simulation method, package temperature distribution and voltage drop with Joule heating and fluidic cooling effects can be estimated. Several packaging examples are simulated and the results show that with micro-channel fluidic cooling in high power density 3D integrated packages, the thermal effect on voltage drop is reduced by 10% which is much less than that of using a traditional heat sink.

Coupling analysis of through-silicon via (TSV) arrays in silicon interposers for 3D systems

This paper investigates the coupling effect between through-silicon vias (TSVs) in large TSV array structures. A coupling analysis method for large TSV arrays is proposed. Using this method the importance of coupling between TSVs for low resistivity silicon substrates is quantified both in the frequency and time domain. This has been compared with high resistivity silicon substrates. The comparison between the two indicates the importance of jitter and voltage analysis in TSV arrays for low resistivity silicon substrates due to enhanced coupling.

Electrical-thermal co-analysis for power delivery networks in 3D system integration

In this paper, an electrical-thermal co-analysis method for power delivery networks in 3D system integration is proposed. For electrical analysis, temperature-dependent electrical resistivity of conductors is taken into account. For thermal analysis, Joule heating effect due to the current flowing through conductors is considered. The proposed co-analysis method is carried out using Rgen and ChipJoule of IBM EIP Tool Suite. An example of 3D integration system including stacked chips, power delivery network, glass-ceramic substrate, through-silicon vias, controlled collapse chip connections (C4s), underfill material, and TIM is analyzed using the proposed method. The simulation results show that the temperature effect on IR drop can not be neglected. The error of not considering thermal effect on IR drop is about 20% in the example.

A Rigorous Model for Through-Silicon Vias With Ohmic Contact in Silicon Interposer

High-density through-silicon via (TSV) interconnects in silicon interposer require effective crosstalk-reduction signaling schemes and rigorous crosstalk modeling techniques. In this letter, we propose a rigorous model for grounded TSVs with ohmic contact. The proposed model takes into account contact resistance, doping density, and doping-region capacitance for the metal-silicon interface of grounded TSVs. The comparison between modeling results and full-wave simulations validates the accuracy of the proposed model for signal-ground-signal vias.

Simulation of power delivery networks with Joule heating effects for 3D integration

In this paper, we present the first work on simulation of power delivery network (PDN) with both Joule heating and convection effects. The finite volume formulations of DC voltage drop equation and thermal equation with convection boundary conditions are explained. In thermal simulation, both Joule heating effect from the PDN and convection effect are considered in solving the steady-state heat equation. In electrical DC voltage drop simulation, by updating the temperature-dependent electrical resistivity of the PDN, voltage distribution is obtained with temperature effects. By iterating between the electrical DC voltage drop and thermal simulations until results converge, the simulation not only enables accurate estimation of system level voltage drop with convection effects, but also provides accurate temperature distribution with convection and Joule heating effects. The simulation results show that even with natural convection effects, the temperature effect on system level IR drop is about 5 – 10%.

Effect of system components on electrical and thermal characteristics for power delivery networks in 3D system integration

In this paper, parameterized electrical-thermal co-analysis for power delivery networks (PDN) in 3D system integration is carried out. A 3D integrated system including glass-ceramic substrate, single and stacked dies, power delivery network, through-silicon vias (TSVs), controlled collapse chip connections (C4s), underfill material, and thermal interface material (TIM) is analyzed with several variable parameters. The analysis results show that temperature effects on DC IR drop can not be neglected. The TIM thermal conductivity, C4 density, stacking order of stacked dies, and voltage source location affect the final IR drop and hot spot temperature in the system.

Electrical–Thermal Cosimulation With Nonconformal Domain Decomposition Method for Multiscale 3-D Integrated Systems

Because of the multiple scales in 3-D integrated systems, numerical simulation methods that are able to handle multiscale problems efficiently are strongly required. In this paper, electrical-thermal cosimulation of multiscale integrated systems using Mortar finite element-based domain decomposition method is proposed. Using the nonconformal domain decomposition approach, integrated systems can be divided into separate subdomains. Individual subdomains can be discretized independently based on its detailed feature size and formulated using the finite element method with associated boundary conditions. The coupling between domains is captured using Lagrange multipliers. For large multiscale 3-D problems, the cascadic multigrid method combined with the subspace confined preconditioned conjugate gradient method is used to accelerate the convergence of the solution with hierarchical meshing grids. Several examples are simulated and the results validate the accuracy and efficiency of the electrical-thermal cosimulation using nonconformal domain decomposition.

DC IR drop solver for large scale 3D power delivery networks

In this paper, DC IR drop simulation of 3D power delivery network (PDN) based on finite volume method with nonuniform grid is presented. Location-dependent resistivity is taken into account in the finite volume formulation which enables simulation of power delivery network with inhomogeneous resistivity. The generated system equation Yx = b is solved using the conjugate gradient (CG) method with a diagonal pre-conditioner. One large scale 3D integration example is simulated, and the results show that by employing the diagonal pre-conditioner and using the symmetric property of the impedance matrix Y, the conjugate gradient method based DC IR drop solver can solve large 3D DC IR drop problem with more than 10 million unknowns with 3 GB memory.

3D transient thermal solver using non-conformal domain decomposition approach

3D integration becomes promising to be able to continue the system integration trend due to short TSV interconnection used for stacked dies. This paper proposes an efficient transient thermal modeling method using non-conformal domain decomposition approach for 3D stacked ICs and systems. To alleviate the problem arising from the feature scale difference between stacked dies as well as package and PCB, the 3D system is divided into many subdomains. Each subdomain (die, package or PCB) can be meshed independently using different gridding based on its feature size and therefore the required meshing cells are greatly reduced compared to conventional method such as finite element or finite volume method. The heat flow continuity between subdomains is captured using the introduced interface basis functions. In addition, the proposed compact micro-fluidic model based on finite volume method is proved to be compatible with the finite element model for solid medium based on introduced forced convection boundary and energy conservation. The experimental results show the proposed method offers up to 5x unknown reduction and 91x speed-up compared to conventional finite element method.