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
4 - QUANTUM WELLS AND LOW-DIMENSIONAL SYSTEMS
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
Real electrons are three-dimensional but can be made to behave as though they are only free to move in fewer dimensions. This can be achieved by trapping them in a narrow potential well that restricts their motion in one dimension to discrete energy levels. If the separation between these energy levels is large enough, the electrons will appear to be frozen into the ground state and no motion will be possible in this dimension. The result is a two-dimensional electron gas (2DEG). The same effect can be achieved with a two-dimensional potential well, which leaves the electrons free to move in one dimension only – a quantum wire.
In the first part of this chapter we shall study some simple one-dimensional potential wells used to trap electrons. The infinitely deep square well cannot be made in practice, but its simplicity makes it a frequently used model. A well of finite depth provides a much better description of a real quantum well. Parabolic wells can be grown by changing the composition of the semiconductor continuously, but this potential proves to be most relevant for the study of magnetic fields. The final example is a triangular well, which can be used as a rough description of the two-dimensional electron gas formed at a doped heterojunction. Next we shall see how these potential wells make electrons behave as though they are two-dimensional.
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- The Physics of Low-dimensional SemiconductorsAn Introduction, pp. 118 - 149Publisher: Cambridge University PressPrint publication year: 1997