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

Learn the basic properties and designs of modern VLSI devices, as well as the factors affecting performance, with this thoroughly updated second edition. The first edition has been widely adopted as a standard textbook in microelectronics in many major US universities and worldwide. The internationally-renowned authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices. Equations and parameters provided are checked continuously against the reality of silicon data, making the book equally useful in practical transistor design and in the classroom. Every chapter has been updated to include the latest developments, such as MOSFET scale length theory, high-field transport model, and SiGe-base bipolar devices.

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Fundamentals of Modern VLSI Devices

Random-matrix theories in quantum physics : common concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

Due to the unprecedented growth in wireless applications over the past decade, development of low-cost solutions for RF and microwave communication systems has become of great importance. This practical new book is the first comprehensive treatment of lumped elements, which are playing a critical role in the development of the circuits that make these cost-effective systems possible. The books offers you an in-depth understanding of the different types of RF and microwave circuit elements, including inductors, capacitors, resistors, transformers, via holes, airbridges, and crossovers. Supported with over 220 equations and more than 200 illustrations, it covers the practical aspects of each element in exceptional detail. No other single volume treats this subject matter in such depth. From materials, fabrication, and analyses - to design, modeling, and physical, electrical, and thermal applications, this unique resource offers you complete coverage of the critical topics you need understand for your work in the field. Offering the most comprehensive, up-to-date body of knowledge on lumped elements, the book is an indispensable professional reference and serves as an excellent text for senior undergraduate and graduate-level courses in RF and microwave circuit design.

Lumped Elements for RF and Microwave Circuits

This review of design principles for implementation of a spiral inductor in a silicon integrated circuit fabrication process summarizes prior art in this field. In addition, a fast and physics-based inductor model is exploited to put the results contributed by many different groups in various technologies and achieved over the past eight years into perspective. Inductors are compared not only by their maximum quality factors (Q/sub max/), but also by taking the frequency at Q/sub max/, the inductance value (L), the self-resonance frequency (f/sub SR/), and the coil area into account. It is further explained that the spiral coil structure on a lossy silicon substrate can operate in three different modes, depending at first order on the silicon doping concentration. Ranging from high to low substrate resistivity, inductor-mode, resonator-mode, and eddy-current regimes are defined by characteristic changes of Q/sub max/, L, and f/sub SR/. The advantages and disadvantages of patterned or blanket resistive ground shields between the inductor coil and substrate and the effect of a substrate contact on the inductor are also addressed in this paper. Exploring optimum inductor designs under various constraints leverages the speed of the model. Finally, in view of the continuously increasing operating frequencies in advancing to new generations of RF systems, the range of feasible inductance values for given quality factors are predicted on the basis of optimum technological features.

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On the design of RF spiral inductors on silicon

The effect of substrate RF losses on the characteristics of silicon-based integrated transformers is studied experimentally by using a substrate transfer technique. The maximum available gain is used to evaluate the quality of transformers similarly to that of active devices. The silicon substrate has a pronounced effect on the quality factor and mutual resistive coupling factor of the primary and secondary coils, thereby degrading the maximum available gain of the transformer. A highly structured patterned ground shield is shown to improve the maximum available gain of a transformer at high frequencies, while at low frequencies, it has little effect on the maximum available gain and even degrades the quality factors of the transformer coils. It is shown that the low-frequency degradation of the coil quality factors relates to local eddy currents in the patterned metal shield.

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Substrate effects in monolithic RF transformers on silicon

Surface passivation of high-resistivity silicon (HRS) by amorphous silicon thin-film deposition is demonstrated as a novel technique for establishing HRS as a microwave substrate. Metal-oxide-silicon (MOS) capacitor measurements are used to characterize the silicon surface properties. An increase of the quality factor (Q) of a 10-nH spiral inductor by 40% to Q=15 and a 6.5-dB lower attenuation of a coplanar waveguide (CPW) at 17 GHz indicate the beneficial effect of the surface passivation for radio frequency (RF) and microwave applications. Regarding CPW attenuation, a nonpassivated 3000-/spl Omega//spl middot/cm substrate is equivalent to a 70-/spl Omega//spl middot/cm passivated substrate. Surface-passivated HRS, having minimum losses, a high permittivity, and a high thermal conductivity, qualifies as a close-to-ideal radio frequency and microwave substrate.

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Surface-passivated high-resistivity silicon substrates for RFICs

We demonstrate that graphene ribbons can be modeled as circuit elements, which have dual capacitive-inductive nature. In the subwavelength regime, the surface current density on a single graphene ribbon subject to an incident p-polarized plane wave is derived analytically and then it is extended to coplanar arrays of graphene ribbons by applying perturbation theory. It is demonstrated that even isolated graphene ribbons have capacitive properties and the interaction between them in an array only changes the capacitance. Finally, we propose an accurate circuit model for the ribbon array by applying appropriate boundary conditions.

Analytical Modeling of Graphene Ribbons as Optical Circuit Elements

We demonstrate, for the first time to our knowledge, a passive, electrically tunable integrated radio frequency (RF) inductor based on a planar solenoid with a thin-film ferromagnetic(FM) (NiFe) core. Variation of inductance is achieved by leading an additional dc current through the same device, thereby changing the effective permeability of the FM core. Tuning ranges (relative variations in inductance) of 85%, 35%, and 20% are achieved at 0.1, 1, and 2 GHz, respectively, for inductances in the range of 1 to 150 nH.

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Behzad Rejaei

Papers

On the design of RF spiral inductors on silicon

Substrate effects in monolithic RF transformers on silicon

Surface-passivated high-resistivity silicon substrates for RFICs

Analytical Modeling of Graphene Ribbons as Optical Circuit Elements

Integrated tunable magnetic RF inductor