Introduction

Previous chapters in this book have described in detail how low-dimensional structures affect the optical properties of semiconductor materials. It should therefore be no surprise to readers to find that the main applications of low-dimensional materials have been in optical devices which emit light – particularly the semiconductor laser. The semiconductor laser, even without the use of low-dimensional structures, has become the most common form of laser and new operating wavelengths; new characteristics and new applications appear at an amazing rate. This chapter could not hope to provide a comprehensive review of all these developments. Specialist texts (Agrawal, 1986; Zory, 1993; Coldren and Corzine, 1995) will do that far more effectively. Instead we hope to introduce some of the key concepts, presented in the context of developments in semiconductor physics, which will lead the reader to the more advanced texts. Consequently, many of the sources quoted are review papers and not the original texts.

Many of the advances in low-dimensional semiconductors have been motivated by the fascinating new range of physical phenomena which arise when electrons and holes are confined in very small dimensional structures (Bastard, 1988; Schmitt-Rink et al., 1989; Weisbuch and Vinter, 1991). Advances in semiconductor lasers have driven this fascination, but there has also been a clear focus for the development. The most important of these, to date, has been the need to develop very high-performance semiconductor lasers for optical-fibre-based communication systems (Koch and Koren, 1990).

The operation of semiconductor devices is controlled by how electrons and holes respond to applied, built-in, and scattering potentials. Electrical engineers are used to treating transport phenomenologically – carriers drift in electric fields and diffuse in concentration gradients. For much of the past 40 years during which semiconductor technology advanced from point-contact transistors to megabit memories, drift–diffusion equations have served as the backbone of device analysis. As devices continue to decrease in size and increase in sophistication, however, this simple picture of carrier transport is beginning to lose validity. Device engineers now need a clear understanding of the physics of carrier transport in a variety of semiconductors as well as an understanding of the nature of transport in modern, small devices. The focus of this book is on carrier transport fundamentals beginning at the microscopic level and progressing to the macroscopic effects relevant to devices. The reader should acquire an understanding of the general features of low- and high-field transport in common semiconductors as well as of the characteristics of transport in small devices. He or she should learn how to evaluate scattering rates and mobilities from the semiconductor's material properties and should understand the various approaches commonly used to analyze and simulate devices.

The book is directed at electrical engineering graduate students or practicing device engineers who typically possess a mature understanding of semiconductor fundamentals and devices but only an acquaintance with the basics of quantum mechanics and solid-state physics.

The first edition of this book was written in a period when the drift–diffusion-based description of semiconductor devices was beginning to lose validity and many kinds of interesting transport effects (e.g. velocity overshoot, ballistic transport, real-space transfer, etc.) and their implications for devices were being explored. Since that time, semiconductor devices have continued to shrink in size, so that engineers and device researchers now face these issues daily. When the first edition was written, quantum transport in mesoscopic structures was also an active research field, with many uncertainties being debated. In the intervening years, this field has matured; the general principles are now understood and are becoming relevant to semiconductor technologists as devices continue their relentless march to microscopic dimensions.

The goals of the second edition are much like those of the first. The book is an attempt to help students with little formal training in quantum mechanics or solid state physics (i.e., the typical graduate of an undergraduate electrical engineering program) understand the fundamental concepts of carrier transport in semiconductors. Writing the second edition was an opportunity to update and clarify material in the first edition and to treat new topics. The most significant change in the second edition is the addition of Chapter 9 on transport in mesoscopic structures, a topic that device engineers now deal with.

Two classes of graduate students worked through early versions of this text and helped me to clarify the presentation and reduce the number of typos and errors.

In Chapter 3 we introduced the Boltzmann Transport Equation (BTE) as an alternative to calculating the position and momentum versus time for each carrier within a device. The BTE is usually very difficult to solve; it is much easier to simulate the trajectories of individual carriers as they move through a device under the influence of electric fields and random scattering forces. Since each path is determined by choosing random numbers (properly distributed to reflect the probabilities of the various scattering events) the technique is a game of chance which has become known as Monte Carlo simulation. If the number of simulated trajectories is large enough, the average results are a good approximation to the average behavior of the carriers within a real device. In many cases, Monte Carlo simulation is the most accurate technique available for simulating transport in devices; it is frequently the standard against which the validity of simpler approaches is gauged.

Much of our understanding of high-field transport in bulk semiconductors and in devices has been obtained through Monte Carlo simulation, so it is important to understand the basics of the method. Because it directly mimics the physics, an understanding of the technique is also useful for the insight it affords. This chapter's emphasis is on the underlying principles of the Monte Carlo technique and on how the results of a Monte Carlo simulation are interpreted.

Carrier transport in semiconductor devices is complicated by the rapid spatial and temporal variations that often occur. For large devices, the low- and high-field transport theory developed in previous chapters is directly applicable. Such devices can be analyzed by drift–diffusion equations with field-dependent mobilities and diffusion coefficients. Transport in small devices, however, differs qualitatively from that in bulk semiconductors because the carrier distribution function is no longer determined by the local electric field. Since transport is nonlocal in both space and time, conventional drift–diffusion equations do not apply, but new possibilities for enhancing device performance arise.

In this chapter, we explain why the drift–diffusion equation loses validity for small devices and describe some important features of carrier transport in the presence of rapidly varying fields. The objective is to gain an intuitive understanding of carrier transport in modern devices such as small bipolar and field-effect transitors. To identify the kinds of transport problems that need to be addressed, we begin by describing a generic transistor. We then examine carrier transport under several specific situations that occur in modern devices and explain why the drift–diffusion equation often loses validity. Finally, we briefly examine device simulation to indicate how the transport equations are formulated for numerical solution, so that nonlocal transport can be simulated for realistic devices.

A simple, conceptual model for a transistor consists of a carrier injector, a carrier collector, and a control region that meters the flow of carriers out of the source (Fig. 8.1).