Eby G. Friedman

Clock distribution networks in synchronous digital integrated circuits

Clock distribution networks synchronize the flow of data signals among synchronous data paths. The design of these networks can dramatically affect system-wide performance and reliability. A theoretical background of clock skew is provided in order to better understand how clock distribution networks interact with data paths. Minimum and maximum timing constraints are developed from the relative timing between the localized clock skew and the data paths. These constraint relationships are reviewed, and compensating design techniques are discussed. The field of clock distribution network design and analysis can be grouped into a number of subtopics: 1) circuit and layout techniques for structured custom digital integrated circuits; 2) the automated layout and synthesis of clock distribution networks with application to automated placement and routing of gate arrays, standard cells and larger block-oriented circuits; 3) the analysis and modeling of the timing characteristics of clock distribution networks; and 4) the scheduling of the optimal timing characteristics of clock distribution networks based on architectural and functional performance requirements. Each of these areas is described the clock distribution networks of specific industrial circuits are surveyed and future trends are discussed.

Effects of inductance on the propagation delay and repeater insertion in VLSI circuits

A closed-form expression for the propagation delay of a CMOS gate driving a distributed RLC line is introduced that is within 5% of dynamic circuit simulations for a wide range of RLC loads. It is shown that the error in the propagation delay if inductance is neglected and the interconnect is treated as a distributed RC line can be over 35% for current on-chip interconnect. It is also shown that the traditional quadratic dependence of the propagation delay on the length of the interconnect for RC lines approaches a linear dependence as inductance effects increase. On-chip inductance is therefore expected to have a profound effect on traditional high-performance integrated circuit (IC) design methodologies. The closed-form delay model is applied to the problem of repeater insertion in RLC interconnect. Closed-form solutions are presented for inserting repeaters into RLC lines that are highly accurate with respect to numerical solutions. RC models can create errors of up to 30% in the total propagation delay of a repeater system as compared to the optimal delay if inductance is considered. The error between the RC and RLC models increases as the gate parasitic impedances decrease with technology scaling. Thus, the importance of inductance in high-performance very large scale integration (VLSI) design methodologies will increase as technologies scale.

3-D Topologies for Networks-on-Chip

Several interesting topologies emerge by incorporating the third dimension in networks-on-chip (NoC). The speed and power consumption of 3D NoC are compared to that of 2D NoC. Physical constraints, such as the maximum number of planes that can be vertically stacked and the asymmetry between the horizontal and vertical communication channels of the network, are included in speed and power consumption models of these novel 3D structures. An analytic model for the zero-load latency of each network that considers the effects of the topology on the performance of a 3D NoC is developed. Tradeoffs between the number of nodes utilized in the third dimension, which reduces the average number of hops traversed by a packet, and the number of physical planes used to integrate the functional blocks of the network, which decreases the length of the communication channel, is evaluated for both the latency and power consumption of a network. A performance improvement of 40% and 36% and a decrease of 62% and 58% in power consumption is demonstrated for 3D NoC as compared to a traditional 2D NoC topology for a network size of N = 128 and N = 256 nodes, respectively.

On-Chip Optical Interconnect Roadmap: Challenges and Critical Directions

Intrachip optical interconnects (OIs) have the potential to outperform electrical wires and to ultimately solve the communication bottleneck in high-performance integrated circuits. Performance targets and critical directions for ICs progress are yet to be fully explored. In this paper, the International Technology Roadmap for Semiconductors (ITRS) is used as a reference to explore the requirements that silicon-based ICs must satisfy to successfully outperform copper electrical interconnects (IEs). Considering the state-of-the-art devices, these requirements are extended to specific IC components

TEAM: ThrEshold Adaptive Memristor Model

Memristive devices are novel devices, which can be used in applications ranging from memory and logic to neuromorphic systems. A memristive device offers several advantages: nonvolatility, good scalability, effectively no leakage current, and compatibility with CMOS technology, both electrically and in terms of manufacturing. Several models for memristive devices have been developed and are discussed in this paper. Digital applications such as memory and logic require a model that is highly nonlinear, simple for calculations, and sufficiently accurate. In this paper, a new memristive device model is presented-TEAM, ThrEshold Adaptive Memristor model. This model is flexible and can be fit to any practical memristive device. Previously published models are compared in this paper to the proposed TEAM model. It is shown that the proposed model is reasonably accurate and computationally efficient, and is more appropriate for circuit simulation than previously published models.

Figures of merit to characterize the importance of on-chip inductance

A closed-form solution for the output signal of a CMOS inverter driving an RLC transmission line is presented. This solution is based on the alpha power law for deep submicrometer technologies. Two figures of merit are presented that are useful for determining if a section of interconnect should be modeled as either an RLC or an RC impedance. The damping factor of a lumped RLC circuit is shown to be a useful criterion. The second useful figure of merit considered in this paper is the ratio of the rise time of the input signal at the driver of an interconnect line to the time of flight of the signals across the line. AS/X circuit simulations of an RLC transmission line and a five section RC II circuit based on a 0.25-/spl mu/m IBM CMOS technology are used to quantify and determine the relative accuracy of an RC model. One primary result of this paper is evidence demonstrating that a range for the length of the interconnect exists for which inductance effects are prominent. Furthermore, it is shown that under certain conditions, inductance effects are negligible despite the length of the section of interconnect.

Equivalent Elmore delay for RLC trees

Closed-form solutions for the 50% delay, rise time, overshoots, and settling time of signals in an RLC tree are presented. These solutions have the same accuracy characteristics of the Elmore delay for RC trees and preserves the simplicity and recursive characteristics of the Elmore delay. Specifically, the complexity of calculating the time domain responses at all the nodes of an RLC tree is linearly proportional to the number of branches in the tree and the solutions are always stable. The closed-form expressions introduced here consider all damping conditions of an RLC circuit including the underdamped response, which is not considered by the Elmore delay due to the nonmonotone nature of the response. The continuous analytical nature of the solutions makes these expressions suitable for design methodologies and optimization techniques. Also, the solutions have significantly improved accuracy as compared to the Elmore delay for an overdamped response. The solutions introduced here for RLC trees can be practically used for the same purposes that the Elmore delay is used for RC trees.

Closed-Form Expressions of 3-D Via Resistance, Inductance, and Capacitance

Closed-form expressions of the resistance, capacitance, and inductance for interplane 3-D vias are presented in this paper. The closed-form expressions account for the 3-D via length, diameter, dielectric thickness, and spacing to ground. A 3-D numerical simulation is used to extract electromagnetic solutions of the resistance, capacitance, and inductance for comparison with the closed-form expressions, revealing good agreement between simulation and the physical models. The maximum error for the resistance, capacitance, and inductance is less than 8%.

Memristor-Based Material Implication (IMPLY) Logic: Design Principles and Methodologies

Memristors are novel devices, useful as memory at all hierarchies. These devices can also behave as logic circuits. In this paper, the IMPLY logic gate, a memristor-based logic circuit, is described. In this memristive logic family, each memristor is used as an input, output, computational logic element, and latch in different stages of the computing process. The logical state is determined by the resistance of the memristor. This logic family can be integrated within a memristor-based crossbar, commonly used for memory. In this paper, a methodology for designing this logic family is proposed. The design methodology is based on a general design flow, suitable for all deterministic memristive logic families, and includes some additional design constraints to support the IMPLY logic family. An IMPLY 8-bit full adder based on this design methodology is presented as a case study.

Predictions of CMOS compatible on-chip optical interconnect

Interconnect has become a primary bottleneck in integrated circuit design. As CMOS technology is scaled, it will become increasingly difficult for conventional copper interconnect to satisfy the design requirements of delay, power, bandwidth, and noise. On-chip optical interconnect has been considered as a potential substitute for electrical interconnect in the past two decades. In this paper, predictions of the performance of CMOS compatible optical devices are made based on current state-of-art optical technologies. Electrical and optical interconnects are compared for various design criteria based on these predictions. The critical dimensions beyond which optical interconnect becomes advantageous over electrical interconnect are shown to be approximately one tenth of the chip edge length at the 22 nm technology node.