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Electronic Materials
Session Overview
| Modules | Electronic Materials |
| 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 |
Prerequisites
Before starting this session, you should be familiar with prior topics from Structure of the Atom (Session 1 through Session 7) and Bonding & Molecules (Session 8 through Session 12), specifically:
- 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
Learning Objectives
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.
Reading
Archived Lecture Notes #3 (PDF)
| Book Chapters | Topics |
|---|---|
| [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 |
Lecture Video
Resources
Lecture Summary
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.
Homework
For Further Study
Supplemental Readings
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.)
People
Felix Bloch – 1952 Nobel Prize in Physics
Other OCW and OER Content
| Content | Provider | Level | Notes |
|---|---|---|---|
| Introduction to Semiconductors | DoITPoMS | Undergraduate | See “Introduction to Energy Bands.” |
| 5.112 Principles of Chemical Science | MIT OpenCourseWare | Undergraduate (first-year) | Start - 8:15 in Lecture 34: Bonding in Metals and Semiconductors |
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 |
Prerequisites
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.
Reading
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
Resources
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.
Homework
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.)
People
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.
| 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) |
This self-assessment page completes the Electronic Materials module, and covers material from the following sessions.
- Session 13: Band Theory of Solids
- Session 14: Semiconductors
- Session 15: Introduction to Crystallography (first part)
On this page are a simple weekly quiz and solutions; relevant exam problems and solutions from the 2009 class; help session videos that review selected solutions to the exam problems; and supplemental exam problems and solutions for further study.
Weekly Quiz and Solutions
This short quiz is given approximately once for every three lecture sessions. You should work through the quiz problems in preparation for the exam problems.
Exam Problems and Solutions
These exam problems are intended for you to demonstrate your personal mastery of the material, and should be done alone, closed-book, with just a calculator, the two permitted reference tables (periodic table, physical constants), and one 8 1/2" x 11" aid sheet of your own creation.
After you’ve taken the exam, watch the help session videos below for insights into how to approach some of the exam problems.
Exam Help Session Videos
In these video, a 3.091 teaching assistant reviews one of the exam problems, demonstrating their approach to the solution, and noting some common mistakes made by students.
Supplemental Exam Problems and Solutions
These additional exam problems from prior years’ classes are offered for further study.
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