|Concepts||properties of metals and insulators, band theory of solids (Drude; Bloch; Heitler and London), band gaps in metals, semiconductors, and insulators|
|Keywords||metallic bonding, free electron gas, band gap, electrical conductivity, Bloch wave, photoexcitation, charge carrier, metal, insulator, semiconductor, thermal conductivity, valence band, conduction band, antibonding orbital, bonding orbital, carrier mobility, absorption edge, thermal excitation, electron, hole, current, Paul Drude, Felix Bloch, Walter Heitler, Fritz London|
|Chemical Substances||copper (Cu), beryllium (Be), diamond (C), silicon (Si), germanium (Ge), tin (Sn), lead (Pb)|
|Applications||photovoltaics, photosensors, light-emitting diodes (LEDs), temperature sensors|
- Electron orbital filling order, energy levels, and the Schrödinger equation
- Linear combination and hybridization of orbitals
- Electromagnetic radiation, particularly the visible spectrum, and how to convert between wavelength, frequency, and energy
After completing this session, you should be able to:
- Describe the "free electron gas" model and its shortcomings in explaining the physical properties of metals.
- Derive the band structure of a solid, starting from the orbital diagrams of individual atoms.
- Calculate the absorption edge, carrier density, and electrical conductivity of a material, and predict how incident photons of given energies or wavelengths will interact with a material.
- Explain how electronic structure and bonding affects the thermal conductivity, electrical conductivity, optical behavior, and other bulk properties of solids.
- Classify materials as metals, insulators, or semiconductors, and sketch a schematic band diagram for each one, with key features labeled.
- Describe what happens during photoexcitation and thermal excitation.
|[Saylor] 12.5, "Correlation Between Bonding and the Properties of Solids."||Ionic solids; molecular solids; covalent solids; metallic solids|
|[Saylor] 12.6, "Bonding in Metals and Semiconductors."||Band theory; requirements for metallic behavior; insulators; semiconductors|
|[JS] 2.4, "The Metallic Bond."||Metallic bonding; delocalized electrons; electronegativity|
|[JS] 15.1, "Charge Carriers and Conduction."||Holes and electrons; Ohm's Law; resistivity/conductivity; carrier mobility and drift velocity|
|[JS] 15.2, "Energy Levels and Energy Bands."||Pauli exclusion, Hund's rule, and orbital filling; energy bands and gaps; the Fermi function; thermal promotion; metals, insulators, and semiconductors|
Prof. Ron Ballinger (homepage) gives today's lecture, explaining how the behavior of electrons in aggregate solids determines their electrical and thermal conductivities, optical absorption, and other physical properties. He derives the valence and conduction band structures for electrons in metals (e.g. Cu, Be) using LCAO-MO, and then extends this approach to insulators (e.g. C) and semiconductors (e.g. Si, Ge), which exhibit band gaps. Electrons are promoted across the band gap by photoexcitation or thermal excitation, leaving holes behind. Controlling the population and flow of charge carriers is the fundamental principle underlying modern semiconductor engineering.
For Further Study
Bloch, Felix. "Über die Quantenmechanik der Elektronen in Kristallgittern." Zeitschrift für Physik A: Hadrons and Nuclei 52 (1928): 555-600. (Note: this article is in German.)
Heitler, Walter, and Fritz London. "Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik." Zeitschrift für Physik A: Hadrons and Nuclei 44 (1927): 455-472. (Note: this article is in German.)