14. Semiconductors

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Session Overview

Modules Electronic Materials
Concepts band gaps in metals, semiconductors, and insulators, thermal excitation, photoexcitation, the Maxwell-Boltzmann distribution, intrinsic and extrinsic semiconductors, doped materials, compound semiconductors
Keywords 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
Chemical Substances silicon (Si), germanium (Ge), phosphorous (P), gallium arsenide (GaAs), gallium phosphide (GaP)
Applications 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

Looking Ahead

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).

Learning Objectives

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)

Book Chapters Topics
[Saylor] 12.6, "Bonding in Metals and Semiconductors." Band theory; requirements for metallic behavior; insulators; semiconductors

Lecture Video

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Lecture Slides (PDF - 2.5MB)

Lecture Summary

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.


Problems (PDF)

Solutions (PDF)

For Further Study

Supplemental Readings

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

Ludwig Boltzmann

William Shockley, John Bardeen, Walter Brattain1956 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.

Content Provider Level Notes
Semiconductor Concepts HyperPhysics High School  
Introduction to Semiconductors DoITPoMS Undergraduate  
PV CDROM PVEducation.org Undergraduate Focuses on photovoltaic design and manufacturing; Module 3: PN Junction covers semiconductor basics.
Introduction to Semiconductors, Doped Semiconductors Connexions Undergraduate  
5.112 Principles of Chemical Science MIT OpenCourseWare Undergraduate (first-year)

Lecture 14: Distribution of Molecular Energies (Maxwell-Boltzmann statistics)

Start - 8:15 in Lecture 34: Bonding in Metals and Semiconductors (semiconductors)

6.012 Microelectronic Devices and Circuits MIT OpenCourseWare Undergraduate Other semesters of this course are available: Spring 2009, Fall 2009
6.152J/3.155J Micro/Nano Processing Technology MIT OpenCourseWare Undergraduate (elective)  


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