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||band gaps in metals, semiconductors, and insulators, thermal excitation, photoexcitation, the Maxwell-Boltzmann distribution, intrinsic and extrinsic semiconductors, doped materials, compound semiconductors
||Maxwell-Boltzmann distribution, donor level, charge carrier, bias voltage, semiconductor, n-type, p-type, silicon, germanium, carrier mobility, band gap, intrinsic semiconductor, extrinsic semiconductor, dopant, conductivity, photoexcitation, thermal excitation, valence band, conduction band, pair generation, aliovalent, supervalent, electron, hole, James Clerk Maxwell, Ludwig Boltzmann
||silicon (Si), germanium (Ge), phosphorous (P), gallium arsenide (GaAs), gallium phosphide (GaP)
||light-emitting diodes (LEDs) in traffic lights and electronics, CD/DVD optical discs (Blu-Ray), photosensors, point-junction transistors, microchips in computers (Pentium) and cell phones
Before starting this session, you should be familiar with topics from Structure of the Atom (Session 1 through Session 7), including:
- Photon frequency, wavelength, and energy
- Atomic absorption and emission of photons
- The Bohr model of the atom
Some material from this session spills over into the next (Session 15); make sure you've covered it before moving on to the Electronic Materials Self-Assessment page.
Session 19 discusses the behavior and location of dopants in crystal lattices, and Session 24 explains how to control the depth and concentration of dopants via diffusion. The Maxwell-Boltzmann curve describes other processes governed by thermal activity, such as crystal vacancies and defects (Session 19) and chemical reaction kinetics (Session 23).
After completing this session, you should be able to:
- Describe the mechanisms for forming charge carriers in a semiconductor, and how they behave in the presence and absence of an applied voltage.
- Calculate how many charge carriers exist at a given temperature for intrinsic and extrinsic semiconductors, and how much dopant must be added to produce a desired band gap or charge carrier density.
- Sketch the Maxwell-Boltzmann distribution at several different temperatures, and explain how it applies to electrons in semiconductors.
- Explain why donor levels don't form a continuous band structure in doped semiconductors.
Archived Lecture Notes #3 (PDF)
[A&E] 12.6, "Bonding in Metals and Semiconductors."
||Band theory; requirements for metallic behavior; insulators; semiconductors
Lecture Slides (PDF - 2.5MB)
In intrinsic semiconductors, electron-hole charge carrier pairs are promoted to the conduction band by ambient thermal energy, as described by the Maxwell-Boltzmann distribution. Carrier density is also affected by the presence of dopants, which change the width of the band gap and produce excess electrons or holes. Engineering impurities in semiconducting materials allows the production of electronic devices such as photovoltaics, light-emitting diodes, CD/DVD optical discs, and photosensors.
For Further Study
Textbook Study Materials
See the [A&E] companion website from Pearson for PowerPoint outlines of each chapter, plus online quizzes, interactive graphs and 3D molecular animations:
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.)
James Clerk Maxwell
William Shockley, John Bardeen, Walter Brattain – 1956 Nobel Prize in Physics
Other OCW and OER Content
The resources listed below are selected from a wide variety of sites covering semiconductors and their applications. Motivated users are encouraged to search MIT OpenCourseWare and other sites for more advanced material based on their specific interests.
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