Hot Carriers in Semiconductor Nanostructures

Physics and Applications

Jagdeep Shah

• Verlag: Academic Press
• Jahr: 2012
• ISBN:
  9780080925707
• Thema: Naturwissenschaften
• Thema: Quantentheorie

Nonequilibrium hot charge carriers play a crucial role in the physics and technology of semiconductor nanostructure devices. This book, one of the first on the topic, discusses fundamental aspects of hot carriers in quasi-two-dimensional systems and the impact of these carriers on semiconductor devices. The work will provide scientists and device engineers with an authoritative review of the most exciting recent developments in this rapidly moving field. It should be read by all those who wish to learn the fundamentals of contemporary ultra-small, ultra-fast semiconductor devices.

• Topics covered include
• Reduced dimensionality and quantum wells
• Carrier-phonon interactions and hot phonons
• Femtosecond optical studies of hot carrier
• Ballistic transport
• Submicron and resonant tunneling devices

Part I

Overview

I.1

Overview

Jagdeep Shah AT&T Bell Laboratories Holmdel, New Jersey

1. Introduction 3

2. Fundamental Aspects of Quasi-2D Systems 5

2.1. Electron-Phonon Interaction in Quasi-2D Systems 6

2.2. Many-Body Effects 7

2.3. Hot-Phonon Effects 7

2.4. Scattering Processes Specific to Quasi-2D Systems 8

2.5. Tunneling Times 8

2.6. Quantum Transport 8

3. Monte Carlo Simulations 9

3.1. Monte Carlo Simulations of Ultrafast Optical Studies 9

3.2. Monte Carlo Simulations of Submicron Devices 10

4. Optical Studies of Hot Carriers in Semiconductor Nanostructures 10

4.1. Ultrafast Luminescence Studies of Carrier Relaxation and Tunneling 10

4.2. Femtosecond Pump-and-Probe Transmission Studies 11

4.3. Ultrafast Pump-and-Probe Raman Scattering Studies 11

4.4. Electron–Hole Scattering 12

5. Transport Studies and Devices 12

5.1. Ballistic Transport in Nanostructures 12

5.2. Resonant Tunneling Hot-electron Transistors 13

5.3. Resonant Tunneling Diodes 13

6. Summary 13

References 14

1 INTRODUCTION

In thermal equilibrium, all elementary excitations in a semiconductor (e.g., electrons, holes, phonons) can be characterized by a temperature that is the same as the lattice temperature. Under the influence of an external perturbation such as an electric field or optical excitation, the distribution functions of these elementary excitations deviate from those in thermal equilibrium. In general, the nonequilibrium distribution functions are nonthermal (i.e. cannot be characterized by a temperature). But, under special conditions, they can be characterized by a temperature that may be different for each elementary excitation and different from the lattice temperature. The term “hot carriers” is often used to describe both these nonequilibrium situations.

Investigation of hot-carrier effects plays a central role in modern semiconductor science. Properties of hot carriers are determined by various interactions between carriers and other elementary excitations in the semiconductor. Therefore, investigations of hot-carrier properties provide information about scattering processes that are of fundamental interest in the physics of semiconductors. Furthermore, these processes determine high-field transport phenomena in semiconductors and thus form the basis of many ultrafast electronic and optoelectronic devices. The field of hot carriers in semiconductors thus provides a link between fundamental semiconductor physics and high-speed devices.

Although some theoretical work on high-field transport in semiconductors dates from 1930s, experimental investigations started in 1951 with the high-field experiments of Ryder and Shockley (the early work is referenced by Conwell [1]). These and other investigations that followed in the next quarter of a century concentrated on bulk semiconductors and semiconductor devices, and provided quantitative understanding of many phenomena and new insights into the high-field transport processes in semiconductors. This work is extensively covered in excellent books by Conwell [1], Nag [2,3], and Reggiani [4]. The topic has also been the subject of NATO Advanced Study Institutes [5,6].

The direction of the field changed considerably in 1970s and 1980s because of several developments. The quasi-two-dimensional nature of carriers in the conducting channels in Si mosfets brought into play new physical phenomena [7]. The mid 1970s brought the first high-quality quantum-well heterostructures, consisting of thin layers of semiconductors with different bandgaps and grown using the techniques of molecular-beam epitaxy (for a recent review, see, for example, Madhukar in [8]). Semiconductor nanostructures have led to many exciting developments in the physics of semiconductors [8–10]. Furthermore, the ability to grow and fabricate semiconductor structures on nanometer scales has led to the development of many new devices, such as modulation-doped field-effect transistors and resonant tunneling diodes. Nonequilibrium transport of carriers is a common thread in these ultrasmall, ultrafast devices operating at high electric fields. Ballistic transport in nanonstructures provided another focal point of interest. These developments have led to considerable interest in the investigation of hot-carrier effects in semiconductor nanostructures.

An important milestone in the field of hot carriers in semiconductors was the demonstration in late 1960s that optical excitation can create hot carriers and optical spectroscopy can provide information about the distribution function of hot carriers. Although transport measurements provide considerable information about various scattering processes in semiconductors, they are averaged over the carrier distribution functions. In contrast, optical techniques, by providing the best means of determining the carrier distribution functions, allow one to investigate the microscopic scattering processes. Another development that has significantly altered the course of this field is the recent availability of ultrafast lasers with pulsewidths as short as 6 fs (for a recent review of the field of ultrafast lasers and their applications to physics, chemistry and biology, see [11]). These lasers allowed the investigation of the time evolution of the carrier distribution functions on ultrashort time scales. Since different scattering processes occur on different time scales, it became possible to isolate various scattering processes by appropriate choices of time windows.

The availability of high-speed computers has made it possible to carry out ensemble Monte Carlo simulations of submicron devices and ultrafast carrier relaxation in semiconductors. Detailed comparison of these simulations with the device performance or with experimental observations of carrier relaxations obtained with ultrafast lasers has provided valuable new information.

Finally, the ability to grow nanostructures has led to interesting new transport phenomena such as ballistic transport of electrons and led to devices based on nonequilibrium transport through such nanostructures. Examples of the devices are resonant tunneling diodes, resonant tunneling hot-electron transistors and modulation-doped field-effect transistors.

As one can see from this brief historical survey, the field of hot carriers in semiconductors and their nanostructures has been a dynamic field with many important developments in the past decade. The purpose of this book is to review the most exciting of these developments in the four areas discussed above. The book is divided into four parts, with several chapters in each part. Part II deals with the fundamental aspects of hot-carrier physics in quasi-2D systems. Part III deals with Monte Carlo simulations of ultrafast optical experiments in quasi-2D systems and of submicron devices. Part IV discusses optical studies of hot carriers in quasi-2D systems, and Part V deals with ballistic transport, resonant tunneling transistors and diodes. In the remainder of this chapter, I will present an overview of these developments.

2 FUNDAMENTAL ASPECTS OF QUASI-2D SYSTEMS

Hot-carrier effects are determined by many different scattering processes, such as carrier–carrier scattering, carrier–phonon scattering, intervalley scattering, and intersubband scattering. An understanding of these processes is essential for an understanding of hot-carrier phenomena and devices. These fundamental processes are reviewed in Part II.

2.1 Electron–Phonon Interaction in Quasi-2D Systems

Electronic states in a quantum confined system are different from those in a bulk semiconductor. The conduction and valence bands break up into various subbands as a result of confinement. The wavefunctions of the confined states penetrate into the barrier for finite barrier heights but vanish at the boundary for infinitely high barriers. For thick barriers, each well in a multiple quantum-well structure can be treated as independent of the other wells. With decreasing barrier thickness, the wavefunctions in the adjacent wells overlap with each other and lead to the phenomenon of minibands, with some interesting transport consequences [12]. These modifications of the electronic states in quasi-2D systems are well known and have been discussed in many reviews (see, for example, Weisbuch in [8]). A brief discussion is given by Ridley in Chapter II.1.

While the electrons are simple, the holes in quasi-2D systems are extremely complicated. The valence bands in bulk III–V semiconductors are nonparabolic and anisotropic. Inclusion of quantization effects leads to very complicated band structure for the heavy- and light-hole valence subbands. It is only very recently that it has become possible to map out the dispersion relations of the valence bands in quantum wells experimentally. Detailed understanding of hot-hole phenomena will clearly require a better understanding of these complicated bands.

For this reason, most of the work on carrier–phonon interactions in quasi-2D systems deals with electron–phonon interactions. This is reviewed in detail by Ridley in Chapter II.1. Early work in this field considered confined carrier states but bulk phonon modes. Howeve...