There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

We introduce the notion of a Physical Random Function (PUF). We argue that a complex integrated circuit can be viewed as a silicon PUF and describe a technique to identify and authenticate individual integrated circuits (ICs).We describe several possible circuit realizations of different PUFs. These circuits have been implemented in commodity Field Programmable Gate Arrays (FPGAs). We present experiments which indicate that reliable authentication of individual FPGAs can be performed even in the presence of significant environmental variations.We describe how secure smart cards can be built, and also briefly describe how PUFs can be applied to licensing and certification applications.

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Silicon physical random functions

The semiconductor industry will soon abandon its pursuit of Moore's law. Now things could get a lot more interesting.

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The chips are down for Moore's law.

In this paper, recent progress of phase change memory (PCM) is reviewed. The electrical and thermal properties of phase change materials are surveyed with a focus on the scalability of the materials and their impact on device design. Innovations in the device structure, memory cell selector, and strategies for achieving multibit operation and 3-D, multilayer high-density memory arrays are described. The scaling properties of PCM are illustrated with recent experimental results using special device test structures and novel material synthesis. Factors affecting the reliability of PCM are discussed.

Phase Change Memory

This paper describes an algorithm for generating provably passive reduced-order N-port models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reduced-order macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed.

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PRIMA: passive reduced-order interconnect macromodeling algorithm

While advances in semiconductor technologies have pushed achievable scale and performance to phenomenal limits for ICs, nanoscale physical realities dictate IC production based on what we can afford. We believe that IC design and manufacturing can be made more affordable, and reliable, by removing some design and implementation flexibility and enforcing new forms of design regularity. This paper discusses some of the trade-offs to consider for determination of how much regularity a particular IC or application can afford. A Via Patterned Gate Array is proposed as one such example that trades performance for cost by way of new forms of design regularity.

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Exploring regular fabrics to optimize the performance-cost trade-off

Implementing logic blocks in an integrated circuit in terms of repeating or regular geometry patterns (Palusinski et al., 2001 and Strojwas, 2003) can provide significant advantages in terms of manufacturability and design cost (Pileggi et al., 2003). Various forms of gate and logic arrays have been recently proposed that can offer such pattern regularity to reduce design risk and costs. In this paper, we propose a full-mask-set design methodology which provides the same physical design coherence as a configurable array, but with area and other design benefits comparable to standard cell ASICs. This methodology is based on a set of simple logic primitives that are mapped to a set of logic bricks that are defined by a restrictive set of RET (resolution enhancement technique)-friendly geometry patterns. We propose a design methodology to explore trade-offs between the number of bricks and associated level of configurability versus the required silicon area. Results are shown to compare a design implemented with a small number of regular bricks to an implementation based on a full standard cell library in a 90nm CMOS technology.

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Design methodology for IC manufacturability based on regular logic-bricks

In this work we investigate the architecture of a Via Patterned Gate Array (VPGA) [1], focusing primarily on: 1) the optimal lookup table (LUT) size; and 2) a comparison the crossbar and switch block routing architectures. Unlike FPGAs, the routing architectures in a VPGA do not dominate the total area of the circuit. Therefore our results suggest that using smaller LUTs results in a much faster and smaller design. In the routing architecture comparison, our results also show that the switch block architecture is inferior to the crossbar architecture in terms of area utilization. As the number of routing tracks grows, the switch block architecture begins to dominate the total area of the design as in the case of the FPGAs.

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An architectural exploration of via patterned gate arrays

In the past, complying with design rules was sufficient to ensure acceptable yields for a design. However, for sub 100nm designs, this approach tends to create patterns which cannot be reliably printed for a given optical setup, thus leading to hot-spots and systematic yield failures. The recent challenges faced by both the design and process communities call for a paradigm shift whereby circuits are constructed from a small set of lithography friendly patterns which have previously been extensively characterized and ensured to print reliably. In this paper, we describe the use of a regular design fabric for defining the underlying silicon geometries of the circuit. While the direct application of this methodology to the current ASIC design flow would result in unnecessary area and performance overhead, we overcome these penalties via a unique design flow that ensures shape-level regularity by reducing the number of required logic functions as much as possible as part of the top-down design flow. It will be shown that with a small set of Boolean functions and careful selection of lithography friendly patterns, we not only mitigate but essentially eliminate such penalties. Additionally, we discuss the benefits of using extremely regular designs constructed from a limited set of lithography friendly patterns not only to improve manufacturability but also to relax the pessimistic constraints defined by design rules. Specifically we introduce the basis for the use of "pushed-rules" for logic design as is commonly done for SRAM designs. This in turn facilitates a common OPC methodology for logic and SRAM. Moreover, by taking advantage of this newfound manufacturability and predictability of regular circuits, we will show that the performance of logic built upon regular fabrics can surpass that of seemingly more arbitrarily constructed logic.

Larry Pileggi

Papers

PRIMA: passive reduced-order interconnect macromodeling algorithm

Exploring regular fabrics to optimize the performance-cost trade-off

Design methodology for IC manufacturability based on regular logic-bricks

An architectural exploration of via patterned gate arrays

Maximization of layout printability/manufacturability by extreme layout regularity