Introduction

In the previous chapter, we laid the foundation for quantitative understanding of the performance of heterojunction bipolar transistors (HBTs) with a particular emphasis on fT and fmax. In particular, the connection of these quantities to microscopic physics such as carrier transport was described, as was their connection to higher-level parametric descriptions of the transistor, as embodied in an equivalent circuit.

In this chapter, we will discuss the practical constraints imposed by real material systems, epitaxial growth techniques and fabrication processes. The effect of these constraints on fT and fmax will be studied using the results of Chapter 18. The overall goal of the chapter is to develop physical insight into three areas: (i) the key elements which distinguish material technologies that are suitable for HBTs, and the relationship between the choice of material system and device performance; (ii) the interplay of process development issues and device performance; (iii) other factors than transport, doping behavior, and device geometry (such as reliability) that further constrain device performance. In particular, we will cover the history and evolution of material systems, from AlGaAs/GaAs to InP/GaAsSb, which have been used for HBTs, and we will describe a representative fabrication sequence. Armed with this background knowledge, we will apply some of the theoretical results of Chapter 18 to a state-of-the-art production HBT, and examine the prospects for improving its performance. We will also look at some examples of other problems that arise when a device is scaled and operated for maximum fT and fmax.

High-speed heterostructure devices is a textbook on modern high-speed semiconductor devices intended for both graduate students and practising engineers. This book is concerned with the physics and processes involved in the devices’ operation as well as some of the most recent techniques for modeling and simulating these devices. Emphasis is placed on the heterostructure devices of the immediate future: namely the MODFET, HBT and RTD. The principle of operation of other devices such as the Bloch oscillator, RITD, Gunn diode, quantum cascade laser and SOI and LD MOSFETs is also introduced.

This text was initially developed for a graduate course taught at The Ohio State University and comes with a complete set of homework problems. MATLAB programs are also available for supporting the lecture material. They can be used to regenerate a number of the pictures in the book and to assist the reader with some of the homework assignments.

This book should also prove useful to researchers and engineers, as it presents research material which is disseminated throughout the research literature and has never before been presented together in a book.

This text starts with two chapters reviewing the semiclassical theory of heterostructure devices. Five chapters are dedicated to presenting a realistic picture of heterostructures, introducing quantum devices and developing practical tools for analyzing quantum transport in these devices in the presence of scattering, and at high frequencies. One chapter is focused on the Boltzmann equation and its application to the derivation of moment equations for high-field transport.

Introduction

In Chapter 8 we studied the charge control of the 2DEG (two-dimensional electron gas). In Chapter 9 we studied high-field transport models applicable to horizontal transport in the 2DEG. The motivation for these studies was the application of the 2DEG as the channel of a field-effect transistor (FET). The resulting FET is referred under the various names of MODFET (modulation doped FET (University of Illinois, USA)), HEMT (high electron mobility FET (Japan)), TEGFET (two-dimensional electron gas FET (France)), and SDHT (segregation doping heterojunction transistor (Bell Lab., USA)) depending on the different laboratories which simultaneously developed it. The AlAs–InGaAs–InP lattice-matched MODFET [2] which provides power gain at millimeter frequencies (fmax = 405 GHz) is presently with the HBT one of the fastest semiconductor transistors. The microwave characteristic of the MODFET will be discussed in Chapters 11, 12, 13, 15 and 16.

We compare in Figure 10.1 the layout of an AlGaAs–GaAs MODFET (c) with that of that of a silicon MOSFET (a) and a GaAs MESFET (b). Although the layout of the MODFET is similar to that of the MESFET, its normal principle of operation (control of a 2DEG with a gate voltage) is similar to that of the MOSFET. Other semiconductors can be used to fabricate MODFETs (see [1] for a review). A semiconductor with a bandgap much wider than that of AlGaAs can also be used to simulate an insulator.

Introduction

Modern technology has made possible the growth of thin crystalline epitaxial layers of different semiconductors. These epitaxial layers can be as small as a few lattice parameters. For small heterostructures (100 Å or less) a quantum treatment of heterostructures becomes necessary. In this chapter we will attempt to build a quantum picture of heterostructures. Note that the conventional quantum picture of a semiconductor crystal cannot be applied to rapidly varying semiconductor heterostructures since crystals are defined as periodic structures extending up to infinity. New theoretical techniques are thus required to describe these ‘spatially-varying crystals’.

Our quantum picture will be based upon an envelope model. An envelope model focuses on calculating the relative distribution of the wave-function from atomic cell to atomic cell rather than on the detailed distribution of the electron wave-function in each atomic cell.

The particular envelope picture we shall use is the so-called generalized Wannier picture. The generalized Wannier picture is capable of handling both the concept of band structure and the concept of its variation in space in a rigorous fashion. This model will therefore permit us to understand the impact of the interface upon the band structure in a heterojunction.

Other envelope pictures have been developed such as the Ben Daniel Duke Hamiltonian (effective-mass model [10], see also [11]), the k · p envelope model ([11]), and the tight-binding model ([8]).

Introduction

Modern growth technologies have made possible the growth of new semiconductor devices with unprecedented control on the atomic level. In this chapter we shall briefly introduce the molecular beam epitaxy (MBE) growth technique and discuss its application to the growth of materials (alloys, pseudomorphic, modulation doped) for new device structures. The chapter will conclude with a review of the cubic crystal structure and its reciprocal lattice, as these concepts are used extensively in Chapters 2 and 3.

MBE technology

One of the most versatile growth techniques available for research is the MBE. In this growth technique a semiconductor substrate is placed in a high-vacuum chamber (see Figure 1.1). Different components such as Ga, Al, As, In, P, and Si are heated in separate closed cylindrical cells. These components escape through an opening in the cylindrical cell and form a molecular beam. These beams are directed toward the substrate. A shutter positioned in front of each cell is used to select the desired molecular beams. By selecting a low temperature for the substrate growth and a slow growth rate (a few micrometers per hour), it is possible to grow high-quality crystals, while making abrupt changes in doping and crystal composition.

This growth technique can be used to grow semiconductor alloys such as AlxGa1–xAs, InxGa1–xAs, InxAl1–xAs, and Si1–xGex, where x, the mole fraction, specifies the composition of the alloy.

Pervasive role of phonons in modern solid-state devices

As illustrated throughout this book, phonon effects are pervasive in modern solidstate devices. As is illustrated by the many examples for Chapters 7–10, the importance of these effects is usually at least as great for dimensionally confined structures as for bulk structures. Indeed, in Chapter 7 the effects of dimensional confinement were seen to be important even for biological structures! In this case, a cylindrical shell immersed in a fluid (Sirenko et al., 1996b) was used to model the vibrational behavior of microtubules (MTs) immersed in water. In addition, the examples of Chapters 7 and 9 illustrate that the elastic continuum model provides an accurate description of acoustic phonons in dimensionally confined structures of many geometries including thin films, nanowires with rectangular and circular cross sections, and a variety of dot-like structures. These structures will inevitably be pervasive as elements of nanoscale structures mimicking the well known and larger microelectromechanical structures. Indeed, Cleland and Roukes (1996) reported a technique for fabricating nanometer-scale mechanical structures from bulk, single-crystal Si substrates. As another example of acoustic phonon effects in dimensionally confined structures, it was recently predicted theoretically that Cerenkov-like effects lead to the generation of high-frequency confined acoustic phonons in quantum wells (Komirenko et al., 2000b); see Section 10.6.

In Chapter 8, values of carrier–optical-phonon scattering rates calculated for a variety of dimensionally confined semiconductor structures were found to exceed 1013 s–1.

Phonon effects: fundamental limits on carrier mobilities and dynamical processes

The importance of phonons and their interactions in bulk materials is well known to those working in the fields of solid-state physics, solid-state electronics, optoelectronics, heat transport, quantum electronics, and superconductivity.

As an example, carrier mobilities and dynamical processes in polar semiconductors, such as gallium arsenide, are in many cases determined by the interaction of longitudinal optical (LO) phonons with charge carriers. Consider carrier transport in gallium arsenide. For gallium arsenide crystals with low densities of impurities and defects, steady state electron velocities in the presence of an external electric field are determined predominantly by the rate at which the electrons emit LO phonons. More specifically, an electron in such a polar semiconductor will accelerate in response to the external electric field until the electron's energy is large enough for the electron to emit an LO phonon. When the electron's energy reaches the threshold for LO phonon emission – 36 meV in the case of gallium arsenide – there is a significant probability that it will emit an LO phonon as a result of its interaction with LO phonons. Of course, the electron will continue to gain energy from the electric field.

In the steady state, the processes of electron energy loss by LO phonon emission and electron energy gain from the electric field will come into balance and the electron will propagate through the semiconductor with a velocity known as the saturation velocity.

This book describes a major aspect of the effort to understand nanostructures, namely the study of phonons and phonon-mediated effects in structures with nanoscale dimensional confinement in one or more spatial dimensions. The necessity for and the timing of this book stem from the enormous advances made in the field of nanoscience during the last few decades.

Indeed, nanoscience continues to advance at a dramatic pace and is making revolutionary contributions in diverse fields, including electronics, optoelectronics, quantum electronics, materials science, chemistry, and biology. The technologies needed to fabricate nanoscale structures and devices are advancing rapidly. These technologies have made possible the design and study of a vast array of novel devices, structures and systems confined dimensionally on the scale of 10 nanometers or less in one or more dimensions. Moreover, nanotechnology is continuing to mature rapidly and will, no doubt, lead to further revolutionary breakthroughs like those exemplified by quantum-dot semiconductor lasers operating at room temperature, intersubband multiple quantum-well semiconductor lasers, quantumwire semiconductor lasers, double-barrier quantum-well diodes operating in the terahertz frequency range, single-electron transistors, single-electron metal-oxide-semiconductor memories operating at room temperature, transistors based on carbon nanotubes, and semiconductor nanocrystals used for fluorescent biological labels, just to name a few!

The seminal works of Esaki and Tsu (1970) and others on the semiconductor superlattice stimulated a vast international research effort to understand the fabrication and electronic properties of superlattices, quantum wells, quantum wires, and quantum dots.

Phonon effects in intersubband lasers

The effects of dimensional confinement on optical phonons, phonon-assisted electron intersubband transition rates (Teng et al., 1998), and gain (Kisin et al., 1997) have been evaluated in a series of studies on semiconductor lasers. Many of the novel semiconductor lasers – such as the tunneling injection laser and the quantum cascade laser – contain quantum wells with confinement dimensions of about 50 Å or less. An example of such a semiconductor laser structure is given in Figure 10.1. In this laser, the conduction band is engineered so that the upper and lower energy levels are E3 and E2 respectively, with a third level, E1, such that phonon-assisted tunneling from level E2 to level E1 is promoted. The IF optical phonons are of special importance in such heterostructures. Two properties of the IF optical phonons account for their special significance (Stroscio, 1996) in narrow-well semiconductor lasers: (a) in narrow wells the interface phonons have appreciable interaction potentials throughout the quantum well since, as was demonstrated in Chapter 7, the interface optical phonons have potentials near the heterointerfaces of the form ce–q|z|e–iq·ρ, where, for example, q has values of very roughly 0.02 Å–1 for a typical intrasubband transition in GaAs; and (b) the energies associated with phonon-assisted processes in these heterostructures can be substantially different from those in semiconductor lasers without significant dimensional confinement, since the interface phonons may have frequencies ωq which are significantly different from those of the other phonons in the quantum well.

Basic properties of phonons in würtzite structure

The GaA1N-based semiconductor structures are of great interest in the electronics and optoelectronics communities because they possess large electronic bandgaps suitable for fabricating semiconductor lasers with wavelengths in the blue and ultraviolet as well as electronic devices designed to work at elevated operating temperatures. These III-V nitrides occur in both zincblende and würtzite structures. In this chapter, the würtzite structures will be considered rather than the zincblende structures, since the treatment of the phonons in these würtzite structures is more complicated than for the zincblendes. Throughout the remainder of this book, phonon effects in nanostructures will be considered for both the zincblendes and würtzites. This chapter focuses on the basic properties of phonons in bulk würtzite structures as a foundation for subsequent discussions on phonons in würtzite nanostructures.

The crystalline structure of a würtzite material is depicted in Figure 3.1. As in the zincblendes, the bonding is tetrahedral. The würtzite structure may be generated from the zincblende structure by rotating adjacent tetrahedra about their common bonding axis by an angle of 60 degrees with respect to each other. As illustrated in Figure 3.1, würtzite structures have four atoms per unit cell.

The total number of normal vibrational modes for a unit cell with s atoms in the basis is 3s. As for cubic materials, in the long-wavelength limit there are three acoustic modes, one longitudinal and two transverse. Thus, the total number of optical modes in the long-wavelength limit is 3s – 3.