Modeling and Design Techniques for 3-D ICs under Process, Voltage, and Temperature Variations

Three-dimensional (3-D) integration is a promising solution to further enhance the density and performance of modern integrated circuits (ICs). In 3-D ICs, multiple dies (tiers or planes) are vertically stacked. These dies can be designed and fabricated separately. In addition, these dies can be fabricated in different technologies. The effect of different sources of variations on 3-D circuits, consequently, differ from 2-D ICs. As technology scales, these variations significantly affect the performance of circuits. Therefore, it is increasingly important to accurately and efficiently model different sources of variations in 3-D ICs. The process, voltage, and temperature variations in 3-D ICs are investigated in this dissertation. Related modeling and design techniques are proposed to design a robust 3-D IC. Process variations in 3-D ICs are first analyzed. The effect of process variations on synchronization and 3-D clock distribution networks, is carefully studied. A novel statistical model is proposed to describe the timing variation in 3-D clock distribution networks caused by process variations. Based on this model, different topologies of 3-D clock distribution networks are compared in terms of skew variation. A set of guidelines is proposed to design 3-D clock distribution networks with low clock uncertainty. Voltage variations are described by power supply noise. Power supply noise in 3-D ICs is investigated considering different characteristics of potential 3-D power grids in this thesis. A new algorithm is developed to fast analyze the steady-state IR-drop in 3-D power grids. The first droop of power supply noise, also called resonant supply noise, is usually the deepest voltage drop in power distribution networks. The effect of resonant supply noise on 3-D clock distribution networks is investigated. The combined effect of process variations and power supply noise is modeled by skitter consisting of both skew and jitter. A novel statistical model of skitter is proposed. Based on this proposed model and simulation results, a set of guidelines has been proposed to mitigate the negative effect of process and voltage variations on 3-D clock distribution networks. Thermal issues in 3-D ICs are considered by carefully modeling thermal through silicon vias (TTSVs) in this dissertation. TTSVs are vertical vias which do not carry signals, dedicated to facilitate the propagation of heat to reduce the temperature of 3-D ICs. Two analytic models are proposed to describe the heat transfer in 3-D circuits related to TTSVs herein, providing proper closed-form expressions for the thermal resistance of the TTSVs. The effect of different physical and geometric parameters of TTSVs on the temperature of 3-D ICs is analyzed. The proposed models can be used to fast and accurately estimate the temperature to avoid the overuse of TTSVs occupying a large portion of area. A set of models and design techniques is proposed in this dissertation to describe and mitigate the deleterious effects of process, voltage, and temperature variations in 3-D ICs. Due to the continuous shrink in the feature size of transistors, the large number of devices within one circuit, and the high operating frequency, the effect of these variations on the performance of 3-D ICs becomes increasingly significant. Accurately and efficiently estimating and controlling these variations are, consequently, critical tasks for the design of 3-D ICs.