Hierarchical Decoupling Capacitor Optimization for Power Distribution Network of 2.5D ICs with Co-Analysis of Frequency and Time Domains Based on Deep Reinforcement Learning

With the growing need for higher memory bandwidth and computation density, 2.5D design, which involves integrating multiple chiplets onto an interposer, emerges as a promising solution. However, this integration introduces significant challenges due to increasing data rates and a large number of I/Os, necessitating advanced optimization of the power distribution networks (PDNs) both on-chip and on-interposer to mitigate the small signal noise and simultaneous switching noise (SSN). Traditional PDN optimization strategies in 2.5D systems primarily focus on reducing impedance by integrating decoupling capacitors (decaps) to lessen small signal noises. Unfortunately, relying solely on frequency-domain analysis has been proven inadequate for addressing coupled SSN, as indicated by our experimental results. In this work, we introduce a novel two-phase optimization flow using deep reinforcement learning to tackle both the on-chip small signal noise and SSN. Initially, we optimize the impedance in the frequency domain to maintain the small signal noise within acceptable limits while avoiding over-design. Subsequently, in the time domain, we refine the PDN to minimize the voltage violation integral (VVI), a more accurate measure of SSN severity. To the best of our knowledge, this is the first dual-domain optimization strategy that simultaneously addresses both the small signal noise and SSN propagation through strategic decap placement in on-chip and on-interposer PDNs, offering a significant step forward in the design of robust PDNs for 2.5D integrated systems.