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Statistical physics examines the collective properties of large ensembles of particles, and is a powerful theoretical tool with important applications across many different scientific disciplines. This book provides a detailed introduction to classical and quantum statistical physics, including links to topics at the frontiers of current research. The first part of the book introduces classical ensembles, provides an extensive review of quantum mechanics, and explains how their combination leads directly to the theory of Bose and Fermi gases. This allows a detailed analysis of the quantum properties of matter, and introduces the exotic features of vacuum fluctuations. The second part discusses more advanced topics such as the two-dimensional Ising model and quantum spin chains. This modern text is ideal for advanced undergraduate and graduate students interested in the role of statistical physics in current research. 140 homework problems reinforce key concepts and further develop readers' understanding of the subject.
The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.
Discover a rigorous treatment of aerogels processing and techniques for characterization with this easy-to-use reference. Presents the basics of aerogel synthesis and gelation to open porous nanostructures, and the processing of wet gels like ambient and supercritical drying leading to aerogels. Describes their essential properties with their measurement techniques and theoretical models used to analyse relations to their nanostructure. Linking the fundamentals and with practical applications, this is a useful toolkit for advanced undergraduates, and graduate students doing research in material and polymer science, physical chemistry, and chemical and environmental engineering.
Chapter 7 deals with fully-depleted SOI and double-gate MOSFETs. A general, asymmetric double-gate model is applied to long channel SOI MOSFETs. For symmetric double-gate MOSFETs – the generic form of FinFETs, an analytic potential model is described that covers all regions of operation continuously. The scale length model first introduced in Chapter 6 for bulk MOSFETs is modified for short-channel DG MOSFETs. Nanowire MOSFET models, both long and short channel, are also discussed. The last section examines the scaling limits of DG and nanowire MOSFETs based on quantum mechanical considerations.
This chapter begins by reviewing MOSFET scaling – the guiding principle for achieving density, speed, and power improvements in VLSI evolution. The implications of the non-scaling factors, specifically, thermal voltage and silicon bandgap, on the path of CMOS evolution are discussed. The rest of the chapter deals with the key factors that govern the switching performance and power dissipation of basic digital CMOS circuits. After a brief description of static CMOS logic gates, their layout, and noise margin, Section 8.3 considers the parasitic resistances and capacitances that may adversely affect the delay of a CMOS circuit. These include source and drain series resistance, junction capacitance, overlap capacitance, gate resistance, and interconnect capacitance and resistance. In Section 8.4, a delay equation is formulated and applied to study the sensitivity of CMOS delay to a variety of device and circuit parameters such as wire loading, device width and length, gate oxide thickness, power-supply voltage, threshold voltage, parasitic components, and substrate sensitivity in stacked circuits. The last section addresses the performance factors of MOSFETs in RF circuits, in particular, the unity-current-gain frequency and unity-power-gain frequency.
Chapter 2 covers the appropriate level of basic device physics to make the book self-contained, and to prepare the reader with the necessary background on device operation and material physics to follow the discussion in the rest of the book. Starting with the energy bands in silicon, Chapter 2 introduces the basic concepts of Fermi level, carrier concentration, drift and diffusion current transport, and Poisson’s equation. Also addressed in this chapter are generation and recombination, minority carrier lifetime, and current continuity equation.
Chapter 10 covers the basic design of a bipolar transistor. The design of the individual device regions, namely the emitter, the base, and the collector, are discussed separately. Since the detailed characteristics of a bipolar transistor depend on its operating point, the focus of this chapter is on optimizing the device design according to its intended operating condition and environment, and on the tradeoffs that must be made in the optimization process. The physics and characteristics of SiGe-base bipolar transistors are discussed in depth. The design of symmetric lateral bipolar transistors on SOI is also covered, including the development of analytical models for the device parameters, base and collector currents, and the transit times.
Chapter 5 describes the basic characteristics of MOSFET devices, using n-channel MOSFET as an example for most of the discussions. It deals with the more elementary long-channel MOSFETs, with sections on the charge sheet model, regional I–V models, and subthreshold current characteristics. A recently developed non-GCA model gives insights to the saturation region behavior while clarifying the misleading term of “pinch-off” in most standard textbooks. In the section on channel mobility, the strain effects, both biaxial and uniaxial, on electron and hole mobilities are discussed. The last section addresses the body effect, temperature effect, and quantum effect on the long-channel threshold voltage.
In Chapter 12, the basic operational and device design principles of commonly used memory devices are discussed. The memory devices covered include CMOS SRAM, DRAM, bipolar SRAM, and several commonly used in nonvolatile memories. Typical read, write, and erase operations of the various memory arrays are explained. The issue of noise margin in scaled CMOS SRAM cells is discussed. A brief discussion of more recent developments of NAND flash technologies, including multi-bit per cell, 3D NAND, and wear leveling is given.
The basic components of a bipolar transistor are described in Chapter 9. Both vertical bipolar transistors, including SiGe-base transistors, and symmetric lateral bipolar transistors on SOI are covered. The discussion focuses on the vertical n–p–n transistors, since they are the most commonly used. The difference between n–p–n vertical transistors and symmetric lateral n–p–n transistors are pointed out where appropriate. The basic operation of a bipolar transistor is described in terms of two p–n diodes connected back to back. The basic theory of a p–n diode is modified and applied to derive the current equations for a bipolar transistor. From these current equations, other important device parameters and phenomena, such as current gain, Early voltage, base widening, and diffusion capacitance, are examined. The basic equivalent-circuit models relating the device parameters to circuit parameters are developed. These equivalent-circuit models form the starting point for discussing the performance of a bipolar transistor in circuit applications.
This chapter deals with the more complex short-channel MOSFETs. Most circuits are built with short-channel devices because of their higher current and lower capacitance. Among the main topics are short-channel effects, scale length model, velocity saturation, and non-local transport. A ballistic MOSFET model is described on the current limit of a MOSFET. Next considered are the major device design issues in a CMOS technology: choice of threshold voltage based on the off-current requirement and on-current performance, power supply voltage, design of nonuniform channel doping, and discrete dopant effects on threshold voltage. The last section discusses high-field effects in a short-channel MOSFET.
Chapter 3 covers the basic physics and operation of p−n junctions and Schottky diodes as well as metal−silicon contacts in general. p−n junctions are basic building blocks of bipolar transistors and key components of MOSFETs. Basic knowledge of their characteristics is a prerequisite to further understand the operation of bipolar devices and for designing MOSFETs. And basic knowledge of Schottky diodes is a prerequisite to understand metal−silicon contacts in general and for designing ohmic contacts with low contact resistance. The chapter ends with a discussion of high-field effects in reverse-biased diodes.
The major factors governing the performance of bipolar transistors in circuit applications are discussed in Chapter 11. Several of the commonly used figures of merit, namely, cutoff frequency, maximum oscillation frequency, and logic gate delay, are examined, and how a bipolar transistor can be optimized for a given figure of merit is discussed. Sections are devoted to examining the important delay components of a logic gate, and how these components can be minimized. The scaling properties of vertical bipolar transistors for high-speed digital logic circuits are discussed. A discussion of the optimization of bipolar transistors for RF and analog circuit applications is given. The chapter concludes with a discussion of the design tradeoff and optimization of symmetric lateral bipolar transistors for RF and analog circuit applications. Finally, several unique opportunities offered by symmetric lateral bipolar transistors, some of them beyond the capability of CMOS, are discussed.