In order to carry out fundamental research on novel electronic, optical, and magnetic materials and devices, one has to understand the behaviors of electrons in solids. This course aims at learning wave-like aspect of electrons in crystals, excitation of solids with high- (optical) frequency electromagnetic waves, and resultant optical properties of solids. Energy bands in the most advanced materials, in particular low dimension systems, will also be reviewed.
1. Understand the validity of expressing electron orbital with “waves”
2. Grab physical meaning of energy bands in condensed matters (crystalline solids)
3. Understand the concept of optically induced polarization with “exciton”
4. Understand the concept of quantum size effects
5. Understand the process and time scale of transferring energy from light to solids
Kronig-Penney model, energy bands, exciton, quantum size effects, ultrafast phenomena
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
In the first half part, we review the validity of expressing electron orbital with “waves”. Each student will be asked to carry out numerical calculation using Kronig-Penney model, through which we aim at grabbing the physical meaning of energy bands in condensed matters (crystalline solids). In the second half part, we discuss subjects of excitons, quantum size effects, and ultrafast phenomena using published materials selected by the class lecturer, through which we aim at deepening our knowledge on interaction between light and solids. Group discussions will be introduced depending on the subjects.
|Course schedule||Required learning|
|Class 1||Introduction 1: waves in solids, calculating the Kronig-Penney model I (explanation and home works)||understand the Kronig-Penney model for the implementation of actual calculation|
|Class 2||Introduction 2: Why it is reasonable to use the E-k relation for solids?||Is it possible to select and excite one electron out of N electrons ?|
|Class 3||Calculating the Kronig-Penney model II (results of home works, discussions)||Discuss the relation between band structures and the size of crystal cell|
|Class 4||Energy band structure: why there exist direct and indirect band gaps?||Why pure silicon crystal can not emit light efficiently?|
|Class 5||Optically induced polarization and Excitons||Review hydrogen atom model, and calculations of binding energy and Bohr radius|
|Class 6||Quantum confinement I: modulation of energy bands||derivation of density of states, optical absorption spectrum|
|Class 7||Quantum confinement II: influence on excitons||Why quantum wells, wires, and dots are good?|
|Class 8||Ultrafast phenomenon||How long does it take for electrons to receive energy from light? How long does it take for electrons to lose the absorbed energy?|
We use text prepared by Munekata.
(1) Introduction to Solid State Physics, C. Kittel, 6th or later Eds.
(2) Quantum Physics, Ginsberg
(3) Semiconductor Optics,
With discussions (40 %) and reports (60 %) of subjects disclosed during the class. Values shown in parentheses are just for your reference.
The menu of this class is made on the basis of assumption that students have qualified the class “Fundamentals of light and matters I” or the classes comparable to it, or have qualified classes of elemental solid state physics, or have acquired fundamental knowledge on solid state physics.
The text prepared by HM consists of mixture of materials and articles picked up from advanced textbooks and milestones papers.