Carlo Jacoboni - Böcker

The majority of the chapters in this volume represent a series of lectures. that were given at a workshop on quantum transport in ultrasmall electron devices, held at San Miniato, Italy, in March 1987. These have, of course, been extended and updated during the period that has elapsed since the workshop was held, and have been supplemented with additional chapters devoted to the tunneling process in semiconductor quantum-well structures. The aim of this work is to review and present the current understanding in nonequilibrium quantum transport appropriate to semiconductors. Gen­ erally, the field of interest can be categorized as that appropriate to inhomogeneous transport in strong applied fields. These fields are most likely to be strongly varying in both space and time. Most of the literature on quantum transport in semiconductors (or in metallic systems, for that matter) is restricted to the equilibrium approach, in which spectral densities are maintained as semiclassical energy­ conserving delta functions, or perhaps incorporating some form of collision broadening through a Lorentzian shape, and the distribution functions are kept in the equilibrium Fermi-Dirac form. The most familiar field of nonequilibrium transport, at least for the semiconductor world, is that of hot carriers in semiconductors.

The technological means now exists for approaching the fundamentallimiting scales of solid state electronics in which a single carrier can, in principle, represent a single bit in an information flow. In this light, the prospect of chemically, or biologically, engineered molccular-scale structures which might support information processing functions has enticed workers for many years. The one common factor in all suggested molecular switches, ranging from the experimentally feasible proton-tunneling structure, to natural systems such as the micro-tubule, is that each proposed structure deals with individual information carrying entities. Whereas this future molecular electronics faces enormous technical challenges, the same Iimit is already appearing in existing semiconducting quantum wires and small tunneling structures, both superconducting and normal meta! devices, in which the motion of a single eh arge through the tunneling barrier can produce a sufficient voltage change to cut-off further tunneling current. We may compare the above situation with today's Si microelectronics, where each bit is encoded as a very !arge number, not necessarily fixed, of electrons within acharge pulse. The associated reservoirs and sinks of charge carriers may be profitably tapped and manipulated to proviele macro-currents which can be readily amplified or curtailed. On the other band, modern semiconductor ULSI has progressed by adopting a linear scaling principle to the down-sizing of individual semiconductor devices.

The operation of semiconductor devices depends upon the use of electrical potential barriers (such as gate depletion) in controlling the carrier densities (electrons and holes) and their transport. Although a successful device design is quite complicated and involves many aspects, the device engineering is mostly to devise a "best" device design by defIning optimal device structures and manipulating impurity profIles to obtain optimal control of the carrier flow through the device. This becomes increasingly diffIcult as the device scale becomes smaller and smaller. Since the introduction of integrated circuits, the number of individual transistors on a single chip has doubled approximately every three years. As the number of devices has grown, the critical dimension of the smallest feature, such as a gate length (which is related to the transport length defIning the channel), has consequently declined. The reduction of this design rule proceeds approximately by a factor of 1. 4 each generation, which means we will be using 0. 1-0. 15 ). lm rules for the 4 Gb chips a decade from now. If we continue this extrapolation, current technology will require 30 nm design rules, and a cell 3 2 size < 10 nm , for a 1Tb memory chip by the year 2020. New problems keep hindering the high-performance requirement. Well-known, but older, problems include hot carrier effects, short-channel effects, etc. A potential problem, which illustrates the need for quantum transport, is caused by impurity fluctuations.

The operation of semiconductor devices depends upon the use of electrical potential barriers (such as gate depletion) in controlling the carrier densities (electrons and holes) and their transport. Although a successful device design is quite complicated and involves many aspects, the device engineering is mostly to devise a "best" device design by defIning optimal device structures and manipulating impurity profIles to obtain optimal control of the carrier flow through the device. This becomes increasingly diffIcult as the device scale becomes smaller and smaller. Since the introduction of integrated circuits, the number of individual transistors on a single chip has doubled approximately every three years. As the number of devices has grown, the critical dimension of the smallest feature, such as a gate length (which is related to the transport length defIning the channel), has consequently declined. The reduction of this design rule proceeds approximately by a factor of 1. 4 each generation, which means we will be using 0. 1-0. 15 ). lm rules for the 4 Gb chips a decade from now. If we continue this extrapolation, current technology will require 30 nm design rules, and a cell 3 2 size < 10 nm , for a 1Tb memory chip by the year 2020. New problems keep hindering the high-performance requirement. Well-known, but older, problems include hot carrier effects, short-channel effects, etc. A potential problem, which illustrates the need for quantum transport, is caused by impurity fluctuations.

The technological means now exists for approaching the fundamentallimiting scales of solid state electronics in which a single carrier can, in principle, represent a single bit in an information flow. In this light, the prospect of chemically, or biologically, engineered molccular-scale structures which might support information processing functions has enticed workers for many years. The one common factor in all suggested molecular switches, ranging from the experimentally feasible proton-tunneling structure, to natural systems such as the micro-tubule, is that each proposed structure deals with individual information carrying entities. Whereas this future molecular electronics faces enormous technical challenges, the same Iimit is already appearing in existing semiconducting quantum wires and small tunneling structures, both superconducting and normal meta! devices, in which the motion of a single eh arge through the tunneling barrier can produce a sufficient voltage change to cut-off further tunneling current. We may compare the above situation with today's Si microelectronics, where each bit is encoded as a very !arge number, not necessarily fixed, of electrons within acharge pulse. The associated reservoirs and sinks of charge carriers may be profitably tapped and manipulated to proviele macro-currents which can be readily amplified or curtailed. On the other band, modern semiconductor ULSI has progressed by adopting a linear scaling principle to the down-sizing of individual semiconductor devices.

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.

This book originated out of a desire to provide students with an instrument which might lead them from knowledge of elementary classical and quantum physics to moderntheoreticaltechniques for the analysisof electrontransport in semiconductors.

This book originated out of a desire to provide students with an instrument which might lead them from knowledge of elementary classical and quantum physics to moderntheoreticaltechniques for the analysisof electrontransport in semiconductors. The book is basically a textbook for students of physics, material science, and electronics. Rather than a monograph on detailed advanced research in a speci?c area, it intends to introduce the reader to the fascinating ?eld of electron dynamics in semiconductors, a ?eld that, through its applications to electronics, greatly contributed to the transformationof all our lives in the second half of the twentieth century, and continues to provide surprises and new challenges. The ?eld is so extensive that it has been necessary to leave aside many subjects, while others could be dealt with only in terms of their basic principles. The book is divided into ?ve major parts. Part I moves from a survey of the fundamentals of classical and quantum physics to a brief review of basic semiconductor physics. Its purpose is to establish a common platform of language and symbols, and to make the entire treatment, as far as pos- ble, self-contained. Parts II and III, respectively, develop transport theory in bulk semiconductors in semiclassical and quantum frames. Part IV is devoted to semiconductor structures, including devices and mesoscopic coherent s- tems. Finally, Part V develops the basic theoretical tools of transport theory within the modern nonequilibrium Green-function formulation, starting from an introduction to second-quantization formalism.