Noel Menezes

Repeater scaling and its impact on CAD

We study scaling in the context of typical block-level wiring distributions, and identify its impact on the design process. In particular, we study the implications of exponentially increasing repeater and clocked repeater counts on the algorithms and methodologies used for physical synthesis and full-chip assembly, showing that mere capacity scaling of current algorithms and methodologies is insufficient to handle the new challenges. Finally, we suggest a few approaches to tackle these challenges by constructing a case for abstract fabrics.

Performance computation for precharacterized CMOS gates with RC loads

For efficiency, the performance of digital CMOS gates is often expressed in terms of empirical models. Both delay and short-circuit power dissipation are sometimes characterized as a function of load capacitance and input signal transition time. However, gate loads can no longer be modeled by purely capacitive loads for high performance CMOS due to the RC metal interconnect effects. This paper presents a methodology for interfacing empirical gate models to reduced order RC interconnect models in terms of a nonlinear iteration procedure. The delay and power are calculated with errors on the same order as those for the original empirical equations. Moreover, a linear equivalent gate model is generated which accurately captures the delays at the interconnect fan-out nodes.

A Gate-Delay Model for High-Speed CMOS Circuits

As signal speeds increase and gate delays decrease for high-performance digital integrated circuits, the gate delay modeling problem becomes increasingly more difficult. With scaling, increasing interconnect resistances and decreasing gate-output impedances make it more difficult to empirically characterize gate-delay models. Moreover, the single-input-switching assumption for the empirical models is incompatible with the inevitable simultaneous switching for today.s high-speed logic paths. In this paper a new empirical gate delay model is proposed. Instead of building the empirical equations in terms of capacitance loading and input-signal transition time, the models are generated in terms of parameters which combine the benefits of empirically derived k-factor models and switch-resistor models to efficiently: 1) handle capacitance shielding due to metal interconnect resistance, 2) model the RC interconnect delay, and 3)provide tighter bounds for simultaneous switching.

Skew And Delay Optimization For Reliable Buffered Clock Trees

Recenily, seveml design auiomaiion approaches for delay and skew minimization of clock nets have been proposed. These approaches are based upon varying the widths and lengths of the clock tree wires io minimize skew and sometimes delay. Most of these iechniques do noi consider the clock iree power dissipation, occupied area, or the reliabiliiy of ihe resvlts with regard to the ineviiable process variations. In this paper, concurreni buffer insertion and global wire width adjusimenis are used to reliably reduce both delay and power from that obtained for a reliable buflerless soluiion. Moreover, in spite of ihe belief ihai ihe mismaich in bufler delays can resuli in significant clock skew, our resulis show ihai buflers can actually reduce the process dependent skew for a reliable design.

Statistical static timing analysis: how simple can we get?

With an increasing trend in the variation of the primary parameters affecting circuit performance, the need for statistical static timing analysis (SSTA) has been firmly established in the last few years. While it is generally accepted that a timing analysis tool should handle parameter variations, the benefits of advanced SSTA algorithms are still questioned by the designer community because of their significant impact on complexity of STA flows. In this paper, we present convincing evidence that a path-based SSTA approach implemented as a post-processing step captures the effect of parameter variations on circuit performance fairly accurately. On a microprocessor block implemented in 90nm technology, the error in estimating the standard deviation of the timing margin at the inputs of sequential elements is at most 0.066 FO4 delays, which translates in to only 0.31% of worst case path delay.

Reliable Non-Zero Skew Clock Trees Using Wire Width Optimization

Recognizing that routing constraints and process variations make non-zero skew inevitable, this paper describes a novel methodology for constructing reliable low-skew clock trees. The algorithm efficiently calculates clock-tree delay sensitivities to achieve a target delay and a target skew. Moreover, the sensitivities also show that wires should be widened as opposed to lengthened to reduce skew since the former improves reliability while the latter reduces it. This paper introduces the concept of designing reliable clock nets with process-insensitive skew.

A sequential quadratic programming approach to concurrent gate and wire sizing

With an ever-increasing portion of the delay in high-speed CMOS chips attributable to the interconnect, interconnect-circuit design automation continues to grow in importance. By transforming the gate and multilayer wire sizing problem into a convex programming problem for the Elmore delay approximation, we demonstrate the efficacy of a sequential quadratic programming (SQP) solution method. For cases where accuracy greater than that provided by the Elmore delay approximation is required, we apply SQP to the gate and wire sizing problem with more accurate delay models. Since efficient calculation of sensitivities is of paramount importance during SQP, we describe an approach for efficient computation of the RC circuit delay sensitivities.

A multi-port current source model for multiple-input switching effects in CMOS library cells

The problem of multiple-input switching (MIS) has been mostly ignored by the timing CAD community. Not modeling MIS for timing can result in as much as 100% error in stage delay and slew calculation. The impact is especially severe on stages immediately after a bank of flops, where the inputs have a high probability of arriving simultaneously. Other problems such as modeling of interconnect loads, complex (nonlinear/nonmonotonic) input waveforms, power-droop impact on cell delay, nonlinear input capacitances, delay variations due to cross-capacitance, etc. are also known sources of error. In this paper, we introduce the multi-port current source model (MCSM). MCSM can efficiently handle an arbitrary number of simultaneously switching inputs, including single-input switching (SIS). Moreover, MCSM is comprehensive in that other modeling problems associated with delay and noise computation are elegantly covered. We demonstrate the applicability of MCSM on a large 65 nm industrial test-case. For cells experiencing MIS, the model yields delay and slew-rate errors within plusmn5% for 88.3% and 93.0% of the cases, respectively. We also present data that show that MCSM is an effective receiver model which captures active loading effects without incurring significant additional error. MCSM makes combined cell-level timing, noise, and power analysis a possibility

The scaling challenge: can correct-by-construction design help?

We present the results of scaling studies in the context of typical block-level wiring distributions, and study the impact of the identified trends on the post-RTL design process. In particular, we look at the implications of exponentially increasing repeater and clocked repeater counts on the algorithms and methodologies used for logic synthesis, technology mapping, layout, and full-chip assembly, and identify several new research problems relevant to future designs. Next, we introduce the basic principles of correct-by-construction (CbC) design. We look at some techniques for post-RTL design meeting CbC philosophy, and then construct a case for flexible, abstract fabrics. Finally, we suggest CbC approaches to tackle the new synthesis and layout challenges identified in this paper.

Noise-aware repeater insertion and wire-sizing for on-chip interconnect using hierarchical moment-matching

Recently, several algorithms for interconnect optimization via repeater insertion and wire sizing have appeared based on the Elmore delay model. Using the Devgan noise metric a noise-aware repeater insertion technique has also been proposed recently. Recognizing the conservatism of these delay and noise models, we propose a moment-matching based technique to interconnect optimization that allows for much higher accuracy while preserving the hierarchical nature of Elmore-delay-based techniques. We also present a novel approach to noise computation that accurately captures the effect of several attackers in linear time with respect to the number of attackers and wire segments. Our practical experiments with industrial nets indicate that the corresponding reduction in error afforded by these more accurate models justifies this increase in runtime for aggressive designs which is our targeted domain. Our algorithm yields delay and noise estimates within 5% of circuit simulation results.