9 - High electric field transport

Summary

S = k log Ω.

Carved on the tombstone of Ludwig Boltzmann

Introduction

In Chapter 8 we studied the two-dimensional electron gas (2DEG) and its control with a gate electrode. As we shall see in Chapter 10, the 2DEG is used as the channel of a high-speed FET, the MODFET. We therefore need to develop a picture of horizontal transport in the 2DEG before studying the MODFET. The transport equations developed in this chapter will also be used for the analysis of the heterojunction bipolar transistor (HBT) in Chapter 18

Our analysis of transport in Chapters 4–7 assumed that the electron transport was mostly ballistic, i.e., the mean free path was longer than or comparable to the quantum device length. In this chapter we shall assume instead that the scale upon which the device variation takes place is large compared to the electron mean free path so that no appreciable quantum effects are expected. Indeed, multiple scattering events randomize the phase of the electron so that neglecting quantum interferences is a reasonable approximation in devices of length larger than 1000 Å. As a result a semiclassical analysis that describes the electrons as a gas of classical (known position and momentum) particles in a band (e.g., the conduction band) should be sufficient to study horizontal transport in submicron gate-length FETs (0.1–1 μm).

In this chapter we shall review the existing picture of transport developed for the three-dimensional electron gas (3DEG) based on the Boltzmann equation formalism. We will see, for example, how we can derive the semiclassical transport equations introduced in Chapter 2 for heterostructures.