Dynamic compact thermal modeling of package-on-package by thermal resistor-capacitor ladder

Package-on-package (PoP) has become a popular package for high performance SoC in mobile world in recent years as it occupies less area on printed circuit board by stacking DRAM on top of the package of SoC. However, this 3D package makes the thermal coupling effect between SoC and DRAM more prominent. Hence, a sophisticated thermal analysis including transient behavior would be beneficial to avoid unexpected performance suffering from throttling and maximize the power budgeting for SoC and DRAM.Transient thermal analysis conducted with commercial computational fluid dynamics (CFD) tool was time-consuming and laborious especially when the analysis scope ranged from PoP to full handheld device. For this reason, the dynamic compact thermal model (DCTM) would be the preferred methodology. In this work, the generic DCTM of PoP was proposed and developed based on a simplified grounded resistor-capacitor network as known as Cauer RC ladder. The particle swarm optimization algorithm was adopted to extract relevant parameters of RC ladder model. Comparing with the majority of conventional approach which used 2-rung or 3rung RC ladder model for package level thermal modeling, a RC model with 6-rung ladder was utilized in order to comprehend the thermal characteristic from package to full system level which was targeting to describe the thermal behavior of SoC inside a handheld device. Once the adequate number of rungs for Cauer RC ladder was identified from the single-heat-source cases, the next step was to extend its coverage to the multiple-heat-sources analysis for PoP which has both self-heating effect of two packages and thermal coupling effect between top and bottom packages. The thermal coupling effect was modeled by the thermal crosstalk and two individual RC ladders were used for the self-heating and thermal coupling effect respectively. After that, the principle of superposition was applied to combine the results and complete a full dynamic compact thermal modeling for PoP. Under the same boundary condition with CFD model, the proposed DCTM was demonstrated to be power-waveform independent and was applicable for diverse power profiles of PoP from various user scenarios and thermal throttling with satisfying accuracy.