Computational Microelectronics – serie

This book summarizes the research of more than a decade. Its early motivation dates back to the eighties and to the memorable talks Dr. C. Moglestue (FHG Freiburg) gave on his Monte-Carlo solutions of the Boltzmann transport equation at the NASECODE conferences in Ireland. At that time numerical semiconductor device modeling basically implied the application of the drift-diffusion model. On the one hand, those talks clearly showed the potential of the Monte-Carlo model for an accurate description of many important transport issues that cannot adequately be addressed by the drift-diffusion approximation. On the other hand, they also clearly demonstrated that at that time only very few experts were able to extract useful results from a Monte-Carlo simulator. With this background, Monte-Carlo research activities were started in 1986 at the University of Aachen (RWTH Aachen), Germany. Different to many other Monte-Carlo research groups, the Monte-Carlo research in Aachen took place in an environment of active drift-diffusion and hydrodynamic model development.

Basically all properties of semiconductor devices are influenced by the distribution of point defects in their active areas. This book contains the first comprehensive review of the properties of intrinsic point defects, acceptor and donor impurities, isovalent atoms, chalcogens, and halogens in silicon, as well as of their complexes. Special emphasis is placed on compiling the structures, energetic properties, identified electrical levels and spectroscopic signatures, and the diffusion behavior from experimental and theoretical investigations. In addition, the book discusses the fundamental concepts of silicon and its defects, the electron system, diffusion, thermodynamics, and reaction kinetics which form the scientific basis needed for a thorough understanding of the text. Therefore, the book is able to provide an introduction to newcomers in this field up to a comprehensive reference for experts in process technology, solid-state physics, and simulation of semiconductor processes.

Communication and information systems are subject to rapid and highly so­ phisticated changes. Currently semiconductor heterostructure devices, such as Heterojunction Bipolar Transistors (HBTs) and High Electron Mobility Transis­ tors (HEMTs), are among the fastest and most advanced high-frequency devices. They satisfy the requirements for low power consumption, medium integration, low cost in large quantities, and high-speed operation capabilities in circuits. In the very high-frequency range, cut-off frequencies up to 500 GHz [557] have been reported on the device level. HEMTs and HBTs are very suitable for high­ efficiency power amplifiers at 900 MHz as well as for data rates higher than 100 Gbitfs for long-range communication and thus cover a broad range of appli­ cations. To cope with explosive development costs and the competition of today's semicon­ ductor industry, Technology Computer-Aided Design (TCAD) methodologies are used extensively in development and production. As of 2003, III-V semiconductor HEMT and HBT micrometer and millimeter-wave integrated circuits (MICs and MMICs) are available on six-inch GaAs wafers. SiGe HBT circuits, as part of the CMOS technology on eight-inch wafers, are in volume production. Simulation tools for technology, devices, and circuits reduce expensive technological efforts. This book focuses on the application of simulation software to heterostructure devices with respect to industrial applications. In particular, a detailed discussion of physical modeling for a great variety of materials is presented.

In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe­ maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu­ tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati­ cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts.

The application of the Monte Carlo method to the simulation of semiconductor devices is presented. A review of the physics of transport in semiconductors is given, followed by an introduction to the physics of semiconductor devices. The Monte Carlo algorithm is discussed in great details, and specific applications to the modelling of semiconductor devices are given. A comparison with traditional simulators is also presented.

The SISDEP 93 conference proceedings present outstanding research and development results in the area of numerical process and device simulation. The miniaturization of today's semiconductor devices, the usage of new materials and advanced process steps in the development of new semiconductor technologies suggests the design of new computer programs. This trend towards more complex structures and increasingly sophisticated processes demands advanced simulators, such as fully three-dimensional tools for almost arbitrarily complicated geometries. With the increasing need for better models and improved understanding of physical effects, these proceedings support the simulation community and the process- and device engineers who need reliable numerical simulation tools for characterization, prediction, and development. This book covers the following topics: process simulation and equipment modeling, device modeling and simulation of complex structures, device simulation and parameter extraction for circuit models, integration of process, device and circuit simulation, practical applications of simulation, algorithms and software.

The book contains a comprehensive review of the physics, modelling and simulation of electron transport at interfaces in semiconductor devices. Particular emphasis is put on the consistent derivation of interface or boundary conditions for semiconductor device simulation. It combines a review of existing interface charge transport models with original developments. A unified representation of charge transport at semiconductor interfaces is introduced. Models for the most important interfaces are derived, classified within the unique modelling framework, and discussed in the context of device simulation. Discretization methods for numerical solution techniques are presented.

Device simulation has two main purposes: to understand and depict the physical processes in the interior of a device, and to make reliable predictions of the behavior of an anticipated new device generation. Towards these goals the quality of the physical models is decisive. The introductory chapter of this book contains a critical review on models for silicon device simulators, which rely on moments of the Boltzmann equation. With reference to fundamental experimental and theoretical work an extensive collection of widely used models is discussed in terms of physical accuracy and application results. This review shows that the quality and efficiency of the phys­ ical models, which have been developed for the purpose of numerical simulation over the last three decades, is sufficient for many applications. Nevertheless, the basic understanding of the microscopic processes, as well as the uniqueness and accuracy of the models are still unsatisfactory. Hence, the following chapters of the book deal with the derivation of physics-based models from a microscopic level, also using new approaches of "taylored quantum-mechanics". Each model is compared with experimental data and applied to a number of simulation exam­ ples. The problems when starting from "first principles" and making the models suitable for a device simulator will also be demonstrated. We will show that demands for rapid computation and numerical robustness require a compromise between physical soundness and analytical simplicity, and that the attainable accuracy is limited by the complexity of the problems.

In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe­ maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu­ tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati­ cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts.

Strain is used to boost performance of MOSFETs. Modeling of strain effects on transport is an important task of modern simulation tools required for device design. The book covers all relevant modeling approaches used to describe strain in silicon. The subband structure in stressed semiconductor films is investigated in devices using analytical k.p and numerical pseudopotential methods. A rigorous overview of transport modeling in strained devices is given.

The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. Efficient methods for building the Schrödinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented.

The book covers all aspects from the expansion of the Boltzmann transport equation with harmonic functions to application to devices, where transport in the bulk and in inversion layers is considered. The important aspects of stabilization and band structure mapping are discussed in detail. This is done not only for the full band structure of the 3D k-space, but also for the warped band structure of the quasi 2D hole gas. Efficient methods for building the Schrödinger equation for arbitrary surface or strain directions, gridding of the 2D k-space and solving it together with the other two equations are presented.

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time.In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies and scattering self-energies, are examined and efficient methods for their evaluation are explained. Finally, the application of these methods to study novel electronic devices such as nanotubes, graphene, Si-nanowires and low-dimensional thermoelectric devices and photodetectors are discussed.

Strain is used to boost performance of MOSFETs. Modeling of strain effects on transport is an important task of modern simulation tools required for device design. The book covers all relevant modeling approaches used to describe strain in silicon. The subband structure in stressed semiconductor films is investigated in devices using analytical k.p and numerical pseudopotential methods. A rigorous overview of transport modeling in strained devices is given.

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time.In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies and scattering self-energies, are examined and efficient methods for their evaluation are explained. Finally, the application of these methods to study novel electronic devices such as nanotubes, graphene, Si-nanowires and low-dimensional thermoelectric devices and photodetectors are discussed.

Communication and information systems are subject to rapid and highly so­ phisticated changes. Currently semiconductor heterostructure devices, such as Heterojunction Bipolar Transistors (HBTs) and High Electron Mobility Transis­ tors (HEMTs), are among the fastest and most advanced high-frequency devices. They satisfy the requirements for low power consumption, medium integration, low cost in large quantities, and high-speed operation capabilities in circuits. In the very high-frequency range, cut-off frequencies up to 500 GHz [557] have been reported on the device level. HEMTs and HBTs are very suitable for high­ efficiency power amplifiers at 900 MHz as well as for data rates higher than 100 Gbitfs for long-range communication and thus cover a broad range of appli­ cations. To cope with explosive development costs and the competition of today's semicon­ ductor industry, Technology Computer-Aided Design (TCAD) methodologies are used extensively in development and production. As of 2003, III-V semiconductor HEMT and HBT micrometer and millimeter-wave integrated circuits (MICs and MMICs) are available on six-inch GaAs wafers. SiGe HBT circuits, as part of the CMOS technology on eight-inch wafers, are in volume production. Simulation tools for technology, devices, and circuits reduce expensive technological efforts. This book focuses on the application of simulation software to heterostructure devices with respect to industrial applications. In particular, a detailed discussion of physical modeling for a great variety of materials is presented.

Basically all properties of semiconductor devices are influenced by the distribution of point defects in their active areas. This book contains the first comprehensive review of the properties of intrinsic point defects, acceptor and donor impurities, isovalent atoms, chalcogens, and halogens in silicon, as well as of their complexes. Special emphasis is placed on compiling the structures, energetic properties, identified electrical levels and spectroscopic signatures, and the diffusion behavior from experimental and theoretical investigations. In addition, the book discusses the fundamental concepts of silicon and its defects, the electron system, diffusion, thermodynamics, and reaction kinetics which form the scientific basis needed for a thorough understanding of the text. Therefore, the book is able to provide an introduction to newcomers in this field up to a comprehensive reference for experts in process technology, solid-state physics, and simulation of semiconductor processes.

This book summarizes the research of more than a decade. Its early motivation dates back to the eighties and to the memorable talks Dr. C. Moglestue (FHG Freiburg) gave on his Monte-Carlo solutions of the Boltzmann transport equation at the NASECODE conferences in Ireland. At that time numerical semiconductor device modeling basically implied the application of the drift-diffusion model. On the one hand, those talks clearly showed the potential of the Monte-Carlo model for an accurate description of many important transport issues that cannot adequately be addressed by the drift-diffusion approximation. On the other hand, they also clearly demonstrated that at that time only very few experts were able to extract useful results from a Monte-Carlo simulator. With this background, Monte-Carlo research activities were started in 1986 at the University of Aachen (RWTH Aachen), Germany. Different to many other Monte-Carlo research groups, the Monte-Carlo research in Aachen took place in an environment of active drift-diffusion and hydrodynamic model development.

Computer-aided-design (CAD) of semiconductor microtransducers is relatively new in contrast to their counterparts in the integrated circuit world. Integrated silicon microtransducers are realized using microfabrication techniques similar to those for standard integrated circuits (ICs). Unlike IC devices, however, microtransducers must interact with their environment, so their numerical simulation is considerably more complex. While the design of ICs aims at suppressing "parasitic” effects, microtransducers thrive on optimizing the one or the other such effect. The challenging quest for physical models and simulation tools enabling microtransducer CAD is the topic of this book. The book is intended as a text for graduate students in Electrical Engineering and Physics and as a reference for CAD engineers in the microsystems industry.

Device simulation has two main purposes: to understand and depict the physical processes in the interior of a device, and to make reliable predictions of the behavior of an anticipated new device generation. Towards these goals the quality of the physical models is decisive. The introductory chapter of this book contains a critical review on models for silicon device simulators, which rely on moments of the Boltzmann equation. With reference to fundamental experimental and theoretical work an extensive collection of widely used models is discussed in terms of physical accuracy and application results. This review shows that the quality and efficiency of the phys­ ical models, which have been developed for the purpose of numerical simulation over the last three decades, is sufficient for many applications. Nevertheless, the basic understanding of the microscopic processes, as well as the uniqueness and accuracy of the models are still unsatisfactory. Hence, the following chapters of the book deal with the derivation of physics-based models from a microscopic level, also using new approaches of "taylored quantum-mechanics". Each model is compared with experimental data and applied to a number of simulation exam­ ples. The problems when starting from "first principles" and making the models suitable for a device simulator will also be demonstrated. We will show that demands for rapid computation and numerical robustness require a compromise between physical soundness and analytical simplicity, and that the attainable accuracy is limited by the complexity of the problems.

This book represents a comprehensive text devoted to charge transport at semiconductor interfaces and its consideration in device simulation by interface and boundary conditions. It contains a broad review of the physics, modelling and simulation of electron transport at interfaces in semiconductor devices. Particular emphasis is put on the consistent deriva­ tion of interface or boundary conditions for semiconductor device simula­ tion. The book is of interest with respect to a wide range of electronic engineering activities, as process design, device design, process character­ ization, research in microelectronics, or device simulator development. It is also useful for students and lecturers in courses of electronic engineering, and it supplements the library of technically oriented solid-state physicists. The deepest roots of this book date back to the mid-seventies. Being a student of electrical engineering, who was exposed for the first time to the material of semiconductor device electronics, I was puzzled by noticing that much emphasis was put on a thorough introduction and understand­ ing of the basic semiconductor equations, while the boundary conditions for these equations received very much less attention. Until today on many occasions one could get the impression that boundary conditions are unimportant accessories; they do not stand on their own besides the bulk transport equations, although it is clear that they are of course a necessary complement of these.

The application of the Monte Carlo method to the simulation of semiconductor devices is presented. A review of the physics of transport in semiconductors is given, followed by an introduction to the physics of semiconductor devices. The Monte Carlo algorithm is discussed in great details, and specific applications to the modelling of semiconductor devices are given. A comparison with traditional simulators is also presented.

During the first decade following the invention of the transistor, progress in semiconductor device technology advanced rapidly due to an effective synergy of technological discoveries and physical understanding. Through physical reasoning, a feeling for the right assumption and the correct interpretation of experimental findings, a small group of pioneers conceived the major analytic design equations, which are currently to be found in numerous textbooks. Naturally with the growth of specific applications, the description of some characteristic properties became more complicated. For instance, in inte­ grated circuits this was due in part to the use of a wider bias range, the addition of inherent parasitic elements and the occurrence of multi­ dimensional effects in smaller devices. Since powerful computing aids became available at the same time, complicated situations in complex configurations could be analyzed by useful numerical techniques. Despite the resulting progress in device optimization, the above approach fails to provide a required compact set of device design and process control rules and a compact circuit model for the analysis of large-scale electronic designs. This book therefore takes up the original thread to some extent. Taking into account new physical effects and introducing useful but correct simplifying assumptions, the previous concepts of analytic device models have been extended to describe the characteristics of modern integrated circuit devices. This has been made possible by making extensive use of exact numerical results to gain insight into complicated situations of transistor operation.

To be perfect does not mean that there is nothing to add, but rather there is nothing to take away Antoine de Saint-Exupery The drift-diffusion approximation has served for more than two decades as the cornerstone for the numerical simulation of semiconductor devices. However, the tremendous speed in the development of the semiconductor industry demands numerical simulation tools that are efficient and provide reliable results. This makes the development of a simulation tool an interdisciplinary task in which physics, numerical algorithms, and device technology merge. For the sake of an efficient code there are trade-offs between the different influencing factors. The numerical performance of a program that is highly flexible in device types and the geometries it covers certainly cannot compare with a program that is optimized for one type of device only. Very often the device is sufficiently described by a two­ dimensional geometry. This is the case in a MOSFET, for example, if the gate length is small compared with the gate width. In these cases the geometry reduces to the specification of a two-dimensional device. Here again the simplest geometries, which are planar or at least rectangular surfaces, will give the most efficient numerical codes. The device engineer has to decide whether this reduced description of the real device is still suitable for his purposes.

Metal Oxide Semiconductor (MOS) transistors are the basic building block ofMOS integrated circuits (I C). Very Large Scale Integrated (VLSI) circuits using MOS technology have emerged as the dominant technology in the semiconductor industry. Over the past decade, the complexity of MOS IC's has increased at an astonishing rate. This is realized mainly through the reduction of MOS transistor dimensions in addition to the improvements in processing. Today VLSI circuits with over 3 million transistors on a chip, with effective or electrical channel lengths of 0. 5 microns, are in volume production. Designing such complex chips is virtually impossible without simulation tools which help to predict circuit behavior before actual circuits are fabricated. However, the utility of simulators as a tool for the design and analysis of circuits depends on the adequacy of the device models used in the simulator. This problem is further aggravated by the technology trend towards smaller and smaller device dimensions which increases the complexity of the models. There is extensive literature available on modeling these short channel devices. However, there is a lot of confusion too. Often it is not clear what model to use and which model parameter values are important and how to determine them. After working over 15 years in the field of semiconductor device modeling, I have felt the need for a book which can fill the gap between the theory and the practice of MOS transistor modeling. This book is an attempt in that direction.