Book contents
- Frontmatter
- Contents
- Preface
- List of constants, conversions, and prefixes
- Part I Setting the scene
- Part II Small systems
- Part III Energy and the first law
- Part IV States and the second law
- Part V Constraints
- Part VI Classical statistics
- Part VII Quantum statistics
- 19 Introduction to quantum statistics
- 20 Quantum gases
- 21 Blackbody radiation
- 22 The thermal properties of solids
- 23 The electrical properties of materials
- 24 Low temperatures and degenerate systems
- Appendices
- Further reading
- Problem solutions
- Index
23 - The electrical properties of materials
from Part VII - Quantum statistics
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- List of constants, conversions, and prefixes
- Part I Setting the scene
- Part II Small systems
- Part III Energy and the first law
- Part IV States and the second law
- Part V Constraints
- Part VI Classical statistics
- Part VII Quantum statistics
- 19 Introduction to quantum statistics
- 20 Quantum gases
- 21 Blackbody radiation
- 22 The thermal properties of solids
- 23 The electrical properties of materials
- 24 Low temperatures and degenerate systems
- Appendices
- Further reading
- Problem solutions
- Index
Summary
In this chapter, we use quantum statistics to help us understand the distinctive electrical properties of conductors, semiconductors, and insulators. We have previously learned that although the occupation number has the same form for all systems, the spectrum of accessible states varies from one to the next. For this reason, we begin this chapter with a brief and simplified overview of band structure.
Band structure
The splitting of levels
As atoms are brought close together, the overlapping of their electron clouds allows electrons to move from one atom to another. These interactions with their neighbors cause shifts in the allowed electron energies. What were initially states of identical energies in isolated identical atoms turn into “bands” of very closely spaced states for the shared electrons in groups of atoms.
Band widths and structure
In general, the outer states of higher energy experience greater overlap, which usually results in greater splitting and wider bands (Figure 23.1). Within any band, the density of states usually is largest near the middle and falls off near the edges (Figure 23.2). Electrons preferentially fill the lowest energy states, so at low temperatures the lower bands are full and the higher bands are empty.
The highest completely filled band in the T → 0 limit is called the “valence band.” Because it is full, there are no empty states into which these valence electrons can move. (Although pairs could trade places, they are identical particles, so it is the same as staying put.)
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- Information
- An Introduction to Thermodynamics and Statistical Mechanics , pp. 477 - 503Publisher: Cambridge University PressPrint publication year: 2007