Modeling and optimization of interconnects and package for signal and power integrity

As the technology scales down, interconnects do not scale as well as devices do. Today, interconnects have become the bottleneck of the performance of high speed systems. In this dissertation, we study efficient models and optimization methodologies for the signal integrity of interconnects and power integrity of packages considering inductance. We first propose a decoupling model, which decouples multiple coupled transmission lines into uncoupled lines, each with an independent driver and an independent receiver. The model is accurate for interconnects with frequency independent parasitics and homogeneous dielectric, and is extended with good accuracy for frequency dependent parasitics and inhomogeneous dielectrics. Combining the decoupling model and a closed-form solution to a single transmission line, we obtain time domain waveform accurately and efficiently. We further study the worst coupling noise between RLCK interconnects with non-linear drivers and receivers. Considering timing windows, we determine switching patterns and switching times of multiple aggressors to generate the worst-case crosstalk noise (WCN) for a quiet or a noisy victim. We propose a new SS+AS algorithm. On average the SS+AS algorithm only underestimates WCN by 3%.; Beyond traditional interconnects, we study the signal integrity of multi-channel interconnects. We derive a closed-form model for signal-to-noise ratio (SNR) considering ports and branches and propose efficient figures of merit (FOMs) for signal distortion. Experiments show that the SNR model is accurate compared to SPICE simulation and the signal distortion FOMs are effective. Using the proposed models, we automatically synthesize coplanar waveguides for radio-frequency interconnects with capacitive couplers. We minimize the total interconnect area under the constraints of SNR and signal distortion. Compared to the published manual designs, the synthesized solutions can reduce up to 80% area.; We further study the decoupling capacitor optimization problem for the power integrity of packages. We develop an incremental noise computation method based on FFT over incremental impedance matrix evaluation, and then use the simulated annealing algorithm to minimize the total cost of decoupling capacitors under the constraints of a noise bound. Compared to the existing impedance based approaches, our algorithm reduces the decoupling capacitor cost by 3x and is also more than 10x faster.