Modern electronics is supported by semiconductor devices, the basic element of its members. A basic understanding of semiconductor physics is required to gain advanced specialized skills such as correctly understanding the operation of semiconductor devices and improving its performance, and designing devices with new electronic functions. This course includes lectures about the basic concepts of semiconductor physics as an introduction to semiconductor engineering.
This course, set as an elementary course among the electrical major courses, is founded on such topics as mathematics, electromagnetism, and quantum physics. The learning process will be to visualize and carefully build basic understandings of electrical conduction, photoreaction, and other topics related to semiconductor physics.
This course will include exercises as appropriate in addition to lectures. Through problem exercises, students will model the essence of the complex phenomena occurring inside semiconductors. Through forming and solving basic equations, they will gain a deep understanding of the logical sequence of the approach and master analysis techniques. Further, they will visualize the obtained numerical values to understand them, resulting in an intuitive understanding based on basic theories.
This course covers the information described below.
First, students will learn, based on quantum mechanics, that energy bands form in solids of atoms joined periodically. Then, from the fact that there is a limit to the density of electrons which can exist in it, they will learn about the concept of density of states. Further, they will apply the approach of thermal statistic distribution to obtain carrier density. From analyzing the motion of electrons in energy bands, students will learn about the concepts of electrons and electron holes, followed by the concepts of doping impurities and of n-type and p-type semiconductors. After understanding the potential distribution of p–n junctions, students will learn the concepts of drift, diffusion, and recombination, which will form a foundation for understanding electrical conduction in solids. Next, after having learned carrier continuity equations which are fundamental to analyzing electrical conduction in semiconductors, students will further their learning through the viewpoints of both analytic and numerical solutions using specific examples of application. Thus, they will gain the basic understanding of the current-voltage characteristics of p–n junctions, essential to understanding semiconductor devices.
The goal of this course is that students will master the basic physical properties of semiconductors, the basis of semiconductor device engineering, by meeting the learning outcomes below steadily one by one.
- Able to list and explain vital crystal structures used often in semiconductor engineering.
- Able to express periodic structure in terms of unit cells and unit structures.
- Able to specify lattice planes using Miller indices.
- Able to explain the differences between metals and semiconductors (insulators) qualitatively based on atomic orbitals and the Pauli exclusion principle.
- Able to analyze the motion of electrons in the step potential and the square-well potential using the Schrödinger equation and able to calculate energy levels and existence probabilities.
- Able to calculate the transmission and reflection of electrons and explain the relationship with electric currents.
- Able to explain the formation of an energy band from the existence conditions of the solution of the Schrödinger equation in the periodic potential.
- Able to explain terms of allowable band, forbidden band, valence band, conduction band, and Brillouin zone.
- Able to explain conductive carriers in conduction bands and valence bands.
- Able to approximate the effective mass of electrons and electron holes based on the energy band.
- Able to calculate the density of states in an isotropic three-dimensional solid.
- Able to calculate the concentration of electrons and electron holes from the distribution law and the density of states, and to explain the temperature dependence of each.
- Able to explain n-type and p-types due to impurity doping and the relationship to majority and minority carriers.
- Able to explain drift current, mobility, diffusion current, and recombination.
- Able to derive carrier continuity equations and solve them under several simple conditions including photoreaction.
- Able to express the form of the potential distribution near the p–n junction boundary under the depletion approximation in a mathematical expression and to explain it in a diagram, and to find the junction capacitance based on the result.
- Able to derive that the current–voltage characteristic of p–n junctions are exponential by solving carrier continuity equations based on the conduction model of diffusion and recombination.
- Able to show the relationship between electron current and hole current at a p–n junction on a band diagram, and to explain its temperature characteristics.
- Able to explain the photoreaction of p–n junctions and to calculate the photoelectric current.
- Able to show a band diagram of a metal–semiconductor junction boundary and explain its current–voltage characteristics.
Corresponding educational goals are:
(1) Specialist skills Fundamental specialist skills
(4) Applied skills (inquisitive thinking and/or problem-finding skills) Organization and analysis
(7) Skills acquiring a wide range of expertise, and expanding it into more advanced and other specialized areas
Band structure of solids, square well potential, electronics states in periodic potential structures, effective mass, density of states of carriers, distribution function, intrinsic carrier concentration, doping, mobility, drift current, diffusion current, carrier recombination, band profile, carrier continuity equation, pn junction, metal-semiconductor junction
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Lectures are provided based on Power-point presentation slides. Quizzes or exercise problems are assigned in the class.
|Course schedule||Required learning|
|Class 1||Crystal structure of solids, unit cell, Miller index||Draw lattice plane of given Miller index. Find Miller index of illustrated lattice plane.|
|Class 2||Origin of energy band structure: from atoms to solids, metal/semiconductor/insulator||Explain the origin of band structure from energy states of the atoms.|
|Class 3||Fundamentals of quantum mechanics: Schrodinger equation, states of a confined electron in one-dimensional square well with infinite potential||Show energy levels and wave functions of a confined electron in an infinite quantum-well.|
|Class 4||Formation of band structure: Bloch's theorem, allowed band, forbidden band, effective mass, concept of electron and hole||Explain the origin of band structure from periodic potential using Bloch's theorem.|
|Class 5||Fundamentals of statistical mechanics: Density of states, Fermi-Dirac's distribution function, Fermi level, intrinsic carrier concentration||Derive intrinsic carrier concentration of semiconductor.|
|Class 6||Control of carrier concentration: impurity doping, p-type, n-type, electron and hole concentration, temperature dependence||Show carrier concentration of n- and p-type semiconductor with impurity doping.|
|Class 7||Fundamentals of electron transport: drift and diffusion, mobility and diffusion constant, resistivity, hole effect, recombination||Explain drift-diffusion model of electron transport. Derive carrier continuity eq.|
|Class 8||Confirmation of the understanding||Confirmation of the understandings and problem solving skills|
|Class 9||Carrier continuity equation||Basic skills of solving carrier continuity equation|
|Class 10||Application of carrier continuity equation: carrier generation and recombination, diffusion and recombination, diffusion length||Intermediate skills of solving carrier continuity equation: diffusion length|
|Class 11||Formation of pn junction: band structure, junction capacitance||Derive and draw band profile of pn junction.|
|Class 12||Current voltage characteristics of pn junction: understanding from carrier continuity equation||Explain current-voltage characteristics of pn junction by solving carrier continuity equation.|
|Class 13||Current voltage characteristics of pn junction: rectification characteristics, electron current and hole current, temperature dependence||Explain rectification characteristics and its temperature dependence of pn junction|
|Class 14||Metal-Semiconductor junction: band profile, principle of electron transport, current-voltage characteristics||Explain metal-semiconductor junction comparing with pn junction|
|Class 15||Application of semiconductors: pn junctions for electron devices and photonic devices||Show some examples of application of pn junction.|
Kiyoshi Takahasi, Youichi Yamada, "Semiconductor engineering (3rd edition)", Morikita publishing
Makoto Konagai, "Semiconductor physics", Baifukan
Quizzes in class: 20%, Midterm exam: 40%, Final exam: 40%
Fundamentals of Electromagnetism 1 (EEE.E201) is desirable (not mandatory).