Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 FOUNDATIONS
- 2 ELECTRONS AND PHONONS IN CRYSTALS
- 3 HETEROSTRUCTURES
- 4 QUANTUM WELLS AND LOW-DIMENSIONAL SYSTEMS
- 5 TUNNELLING TRANSPORT
- 6 ELECTRIC AND MAGNETIC FIELDS
- 7 APPROXIMATE METHODS
- 8 SCATTERING RATES: THE GOLDEN RULE
- 9 THE TWO-DIMENSIONAL ELECTRON GAS
- 10 OPTICAL PROPERTIES OF QUANTUM WELLS
- A1 TABLE OF PHYSICAL CONSTANTS
- A2 PROPERTIES OF IMPORTANT SEMICONDUCTORS
- A3 PROPERTIES OF GaAs–AlAs ALLOYS AT ROOM TEMPERATURE
- A4 HERMITE'S EQUATION: HARMONIC OSCILLATOR
- A5 AIRY FUNCTIONS: TRIANGULAR WELL
- A6 KRAMERS–KRONIG RELATIONS AND RESPONSE FUNCTIONS
- Bibliography
- Index
Introduction
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Introduction
- 1 FOUNDATIONS
- 2 ELECTRONS AND PHONONS IN CRYSTALS
- 3 HETEROSTRUCTURES
- 4 QUANTUM WELLS AND LOW-DIMENSIONAL SYSTEMS
- 5 TUNNELLING TRANSPORT
- 6 ELECTRIC AND MAGNETIC FIELDS
- 7 APPROXIMATE METHODS
- 8 SCATTERING RATES: THE GOLDEN RULE
- 9 THE TWO-DIMENSIONAL ELECTRON GAS
- 10 OPTICAL PROPERTIES OF QUANTUM WELLS
- A1 TABLE OF PHYSICAL CONSTANTS
- A2 PROPERTIES OF IMPORTANT SEMICONDUCTORS
- A3 PROPERTIES OF GaAs–AlAs ALLOYS AT ROOM TEMPERATURE
- A4 HERMITE'S EQUATION: HARMONIC OSCILLATOR
- A5 AIRY FUNCTIONS: TRIANGULAR WELL
- A6 KRAMERS–KRONIG RELATIONS AND RESPONSE FUNCTIONS
- Bibliography
- Index
Summary
Low-dimensional systems have revolutionized semiconductor physics. They rely on the technology of heterostructures, where the composition of a semiconductor can be changed on the scale of a nanometre. For example, a sandwich of GaAs between two layers of AlxGa1−xAs acts like an elementary quantum well. The energy levels are widely separated if the well is narrow, and all electrons may be trapped in the lowest level. Motion parallel to the layers is not affected, however, so the electrons remain free in those directions. The result is a two-dimensional electron gas, and holes can be trapped in the same way.
Optical measurements provide direct evidence for the low-dimensional behaviour of electrons and holes in a quantum well. The density of states changes from a smooth parabola in three dimensions to a staircase in a two-dimensional system. This is seen clearly in optical absorption, and the step at the bottom of the density of states enhances the optical properties. This is put to practical use in quantum-well lasers, whose threshold current is lower than that of a three-dimensional device.
Further assistance from technology is needed to harness low-dimensional systems for transport. Electrons and holes must be introduced by doping, but the carriers leave charged impurities behind, which limit their mean free path. The solution to this problem is modulation doping, where carriers are removed in space from the impurities that have provided them.
- Type
- Chapter
- Information
- The Physics of Low-dimensional SemiconductorsAn Introduction, pp. xv - xviiiPublisher: Cambridge University PressPrint publication year: 1997