The stringent requirements of power noise on complex multi-domain power delivery networks (PDN), and the complicated relationship between signal integrity and power integrity (PI) have led to an ever challenging PI sign-off process. A lumped PDN model is widely used, where the power network is treated as a two-port network with the impedances extracted by an electromagnetic solver. A distributed model of the power network is however preferred during a PI sign-off flow, providing a more accurate circuit model for time domain simulations. Hundreds or even thousands of ports need to be properly evaluated during the PDN extraction process, which can be computationally expensive and error prone. A Python tool is described here to enable a fast and configurable process for distributed port assignment during the PDN extraction process. An enhanced automation flow, integrated with the Python tool, has also been developed to support early power network exploration. In one case study, a 360X speedup in the port assignment process is achieved while revealing a high risk power network within the package. The proposed automation flow is versatile and highly adaptive for different power network topologies.

The conventional power network design process requires iterative modifications to the existing power network to eliminate hot spots and to converge to target impedance parameters. At later stages in the IC design process, this procedure may require significant time and human resources due to the limited flexibility to accommodate necessary changes. Power delivery exploration during early stages of the design process may bring considerable savings to the system development effort. The number of iterations may be greatly reduced by choosing the initial parameters sufficiently close to the optimum. This paper presents a power delivery exploration framework based on constrained global optimization. The power network parameters are estimated at early stages of the development process, while considering both electrical and nonelectrical factors, such as area and cost. A Laplace transform-based circuit simulator is described that is well suited for optimization purposes due to the high computational efficiency when a large number of iterations is required. The proposed framework has been applied to the distribution of voltage domains in a large scale complex integrated system, while minimizing the cost of the decoupling capacitor placement. The optimal number of voltage rails are determined, demonstrating an approximately 40% lower on-chip area than alternative solutions.

Over the past decades, aggressive voltage scaling combined with increased power demands has placed stringent requirements on on-chip power quality. Unwanted voltage fluctuations and droops may cause a variety of issues, ranging from glitch power to device malfunction. If revealed at the later stages of the design process, mitigation techniques may become unbearably costly in both time and money. A framework for exploratory power delivery optimization is described to enhance the power delivery network during early stages of the design process in accordance with design specifications. The power delivery design process is converted into a constrained minimization problem, consisting of design metrics combined into objective and constraint functions. The framework supports the optimization of the power network characteristics while considering external, non-electrical design specifications, such as cost and area, providing a comprehensive network analysis capability. In one case study, a 15% reduction in decoupling capacitor placement along with a 38.6% reduction in power consumption is achieved while satisfying performance and power quality constraints.

This work proposes reliability aware through silicon via (TSV) planning for the 3D stacked silicon integrated circuits (ICs). The 3D power distribution network is modeled and extracted in frequency domain which includes the impact of skin effect. The worst case power noise of the 3D power delivery networks (PDN) with local TSV failures resulting from fabrication process or circuit operation is identified in both frequency and time domain. From the experimental results, it is observed that a single TSV failure could increase the maximum voltage variation up to 70% which should be considered in nanoscale ICs. The parameters of the 3D PDN are designed such that the power distribution is reliable under local TSV failures. The spatial distribution of the power noise, reliability and block out area is analyzed to enhance the reliability of the 3D PDN under local TSV failure.

Reliable design of power distribution network for stacked integrated circuits introduces new challenges i.e., substrate coupling among through silicon vias (TSVs) and tiers grid in addition to reliability issues such as electromigration and thermo-mechanical stress, compared to conventional system on chip (SoC). In this paper a comprehensive modeling of the TSV and stacked power grid with frequency dependent parasitic is proposed. The analytical model considers the impact of the substrate coupling between the TSVs and layers grid. A frequency domain based analysis flow is introduced to incorporate frequency dependent parasitics. The design of a reliable power distribution network is formulated as an optimization problem to minimize power noise under reliability and electro-migration constraints. Experimental results demonstrate the efficacy of the problem formulation and solution technique.

A distributed on-chip decoupling capacitor network is proposed in this paper. A system of distributed on-chip decoupling capacitors is shown to provide an efficient solution for providing the required on-chip decoupling capacitance under existing technology constraints. In a system of distributed on-chip decoupling capacitors, each capacitor is sized based on the parasitic impedance of the power distribution grid. Various tradeoffs in a system of distributed on-chip decoupling capacitors are also discussed. Related simulation results for typical values of on-chip parasitic resistance are also presented. The worst case error is 0.003% as compared to SPICE.

On-chip power distribution grids with multiple supply voltages are discussed in this paper. Two types of interdigitated and paired power distribution grids with multiple supply voltages and multiple grounds are presented. Analytic models are also developed to estimate the loop inductance in four types of proposed power delivery schemes. Two proposed schemes, fully and pseudo-interdigitated power delivery, reduce power supply voltage drops as compared to conventional interdigitated power distribution systems with dual supplies and a single ground by, on average, 15.3% and 0.3%, respectively. The performance of the proposed on-chip power distribution grids is compared to a reference power distribution grid with a single supply and a single ground. The voltage drop in fully interdigitated and fully paired power distribution grids with multiple supplies and multiple grounds is reduced, on average, by 2.7% and 2.3%, respectively, as compared to the voltage drop of an interdigitated power distribution grid with a single supply and a single ground. The proposed power distribution grids are a better alternative to a single supply voltage and a single ground power distribution system. On-chip resonances in power distribution grids with decoupling capacitors are intuitively explained in this paper, and circuit design implications are provided. It is also noted that fully interdigitated and fully paired power distribution grids with multiple supply voltages and multiple grounds are recommended to decouple power supply voltages.

Decoupling capacitors are widely used to reduce power supply noise. On-chip decoupling capacitors have traditionally been allocated into the white space available on a die or placed inside the rows in standard cell circuit blocks. The efficacy of on-chip decoupling capacitors depends upon the impedance of the power/ground lines connecting the capacitors to the current loads and power supplies. A design methodology for placing on-chip decoupling capacitors is presented in this paper. A maximum effective radius is shown to exist for each on-chip decoupling capacitor. Beyond this effective distance, a decoupling capacitor is ineffective. Depending upon the parasitic impedance of the power distribution system, the maximum voltage drop seen at the current load is caused either by the first droop (determined by the rise time) or by the second droop (determined by the transition time). Two criteria to estimate the minimum required on-chip decoupling capacitance are developed based on the critical parasitic impedance. In order to provide the required charge drawn by the load, the decoupling capacitor has to be charged before the next switching cycle. For an on-chip decoupling capacitor to be effective, both effective radii criteria should be simultaneously satisfied.

Decoupling capacitors are widely used to reduce power supply noise. On-chip decoupling capacitors have traditionally been allocated into the white space available on the die based on an unsystematic or ad hoc approach. In this way, large decoupling capacitors are often placed at a significant distance from the current load, compromising the signal integrity of the system. This issue of power delivery cannot be alleviated by simply increasing the size of the on-chip decoupling capacitors. To be effective, the on-chip decoupling capacitors should be placed physically close to the current loads. The area occupied by the on-chip decoupling capacitor, however, is directly proportional to the magnitude of the capacitor. The minimum impedance between the on-chip decoupling capacitor and the current load is therefore fundamentally affected by the magnitude of the capacitor. A distributed on-chip decoupling capacitor network is proposed in this paper. A system of distributed on-chip decoupling capacitors is shown to provide an efficient solution for providing the required on-chip decoupling capacitance under existing technology constraints. In a system of distributed on-chip decoupling capacitors, each capacitor is sized based on the parasitic impedance of the power distribution grid. Various tradeoffs in a system of distributed on-chip decoupling capacitors are also discussed. Related simulation results for typical values of on-chip parasitic resistance are also presented. An analytic solution is shown to provide accurate distributed system. The worst case error is 0.003% as compared to SPICE. Techniques presented in this paper are applicable not only for current technologies, but also provide an efficient placement of the on-chip decoupling capacitors in future technology generations.

Decoupling capacitors are widely used to reduce power supply noise. On-chip decoupling capacitors have traditionally been allocated into the available white space on a die. The efficacy of on-chip decoupling capacitors depends upon the impedance of the power/ground lines connecting the capacitors to the current loads and power supplies. A maximum effective radius exists for each on-chip decoupling capacitor. Beyond this effective distance, a decoupling capacitor is completely ineffective. Two effective radii determined by the target impedance (during discharge) and charge time are presented in this paper. Depending upon the parasitic impedance of the power distribution system, the maximum voltage drop as seen at the current load is achieved either at the first droop or at the end of the switching activity (the second droop). Two criteria to estimate the minimum required on-chip decoupling capacitance are developed based on the critical parasitic impedance. To be effective, the decoupling capacitor has to be fully charged before the next switching event. A design space is described that characterizes the tolerable parasitic resistances and inductances, while restoring the charge on the decoupling capacitor within a target charge time. An overall design methodology for placing on-chip decoupling capacitors is presented in this paper. It is shown that for an on-chip decoupling capacitor to be effective, both effective radii criteria should be simultaneously satisfied.

On-die capacitances interact with the inductance and resistance of the power distribution network to supply electrical charge. A distributed model is generally required to analyze and design a power distribution network to maintain acceptable levels of supply voltage noise. An approximation method is proposed in this paper for modeling the power distribution system in the frequency domain, defining an effective decoupling capacitance and an effective decoupling radius around each switching element, both of which are frequency dependent. At high frequencies, the supply of decoupling charge is highly localized, and the effective decoupling capacitance is determined primarily by the power grid inductance. Design considerations and guidelines are presented for determining the appropriate density of on-die decoupling capacitances and required power grid parameters, depending upon the density and the frequency characteristics of the switching activity of the circuit

Multiple power supply voltages are often used in modern high-performance ICs, such as microprocessors, to decrease power consumption without affecting circuit speed. To maintain the impedance of a power distribution system below a specified level, multiple decoupling capacitors are placed at different levels of the power grid hierarchy. The system of decoupling capacitors used in power distribution systems with multiple power supplies is described in this paper. The noise at one power supply can propagate to the other power supply, causing power and signal integrity problems in the overall system. With the introduction of a second power supply, therefore, the interaction between the two power distribution networks should be considered. The dependence of the impedance and magnitude of the voltage transfer function on the parameters of the power distribution system is investigated. An antiresonance phenomenon is intuitively explained in this paper. It is shown that the magnitude of the voltage transfer function is strongly dependent on the parasitic inductance of the decoupling capacitors, decreasing with smaller inductance. Design techniques to cancel and shift antiresonant spikes out of range of the operating frequencies are presented. It is also shown that it is highly desirable to maintain the effective series inductance of the decoupling capacitors as low as possible to decrease the overshoots of the response of the dual-voltage power distribution system over a wide range of operating frequencies. A criterion for an overshoot-free voltage response is presented in this paper. It is noted that the frequency range of the overshoot-free voltage response can be traded off with the magnitude of the response.

Multiple supply voltages are often utilized to decrease power dissipation in high performance integrated circuits. On-chip power distribution grids with multiple supply voltages are discussed in this paper. A power distribution grid with multiple supply voltages and multiple grounds is presented. The proposed power delivery scheme reduces power supply voltage drops as compared to conventional power distribution systems with dual supplies and a single ground by 17% on average (20% maximum). For an example power grid with decoupling capacitors placed between the power supply and ground, the proposed grid with multiple supply and multiple ground exhibits, respectively, 13% and 18% average performance improvement. The proposed power distribution grid can be an alternative to a single supply voltage and single ground power distribution system.