Properties of electrons in solids are the basis of all the electronic materials and electron devices. This course provides fundamental treatment to understand the electron's behaviors in solids based on the solid state physics.
Beginning with a brief review of fundamental quantum mechanics, some perturbation theories will be lectured to understand electron states in various potentials where the analytical solution of Schrodinger equation is hard to be obtained.
In order to treat electrons in solids, the electrons should be regarded as waves. We will see that carrier electrons can be treated as waves which propagate in the solids, and which cause scattering and diffraction. Furthermore, it is recognized that an energy band will be formed if a periodic perturbation potential is applied to nearly free electron model, which is the basis to treat carrier electrons in metals and semiconductors.
More precise band calculations based on the Bloch’s theorem and tight binding approximation will be lectured in order to understand more specific band structure of the important crystals, such as diamond zinc-blend crystals. Precise discussion about electron states in k-space in the band structures will be given to understand the electron properties in such crystals
Furthermore, the relationship between band structures and space symmetries will be lectured to apply space group theory to calculations and understanding of the band structures.
1. Understanding of fundamental quantum mechanics and some perturbation theories for various potentials where the analytical solution is hard to be obtained.
2. Treatment to regard carrier electrons as propagating waves, which cause scattering and diffraction.
3. Energy band will be formed if a periodic perturbation potential is applied to a nearly free electron model.
4. Precise band calculations based on the Bloch’s theorem and a tight binding approximation method.
5. Band structures of diamond and zinc-blend structures.
6. Precise discussion about electron states in k-space of the band structures.
7. Understanding of a relationship between the band structure and the space symmetry.
Quantum mechanics, Perturbation theory, Solid state physics, periodic potential, Energy band, Bloch's wave, Band structure, Symmetry and group theory
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Exercises are carried out after every lecture in the class to help students understand.
Course schedule | Required learning | |
---|---|---|
Class 1 | Review of quantum mechanics I | Basis of quantum mechanics, Schrodinger equation, properties of wave functions, operator, steady states, degenerate and non-degenerated states |
Class 2 | Review of quantum mechanics II | Hermitian operator, Completeness of wave functions, vector representation of state, matrix representation of operators, Dirac notation, orthogonalization and unitary transformation. |
Class 3 | Time-independent perturbation theory - Non degenerated system- | Time-independent perturbation theory for non-degenerated system. |
Class 4 | Time-independent perturbation theory and matrix elements | Time-independent perturbation theory and relationship with matrix elements, Stark effect, etc. |
Class 5 | Time-independent perturbation theory - Degenerated system- | Time-independent perturbation theory for degenerated system. |
Class 6 | Time-dependent perturbation theory | Time-dependent perturbation theory for non-degenerated system. Transition of states and selection rule. |
Class 7 | Absorption and emission of light using time dependent perturbation theory | Absorption and emission of light using time dependent perturbation theory. Transition probability, golden rule, |
Class 8 | Basis of waves in solid -propagation, scattering and diffraction- | Basis to treat particles as waves in solid -propagation, scattering and diffraction- |
Class 9 | 固体の自由電子モデル | Hamiltonian for single electron approximation, Quantum well model of solids, Free electron model with periodic boundary condition |
Class 10 | Nearly free electron model of solids | Lattice potential and energy gap generation, Nearly free electron model based on perturbation theory |
Class 11 | Bravais lattice, Reciprocal lattice, and Brillouin zone | Bravais lattice and translation vector, Reciprocal lattice, Brillouin zone |
Class 12 | Bloch theorem and Empty lattice band | Bloch theorem, Reduced zone, Empty lattice approximation |
Class 13 | Tight binding theory | Chemical bonds, Tight binding theory |
Class 14 | Band structures of semiconductors | Calculation of band structures of diamond and zinc-blend semiconductors, and chemical trend of the band structures |
Class 15 | Symmetry and band structures | Irreducible representation and character tables, Understanding band structures from the point of view of symmetry |
Course materials will be provided from OCW-i
Course materials will be provided from OCW-i
C.Kittel : "Introduction to Solid State Physics," John Wiley & Sons, Inc.
H.Ibach and H.Lute : "Solid-State Physics," Springer-Verlag
W.A.Harrison: "Electronic structure and the properties of solids: The Physics of the Chemical Bond ", Dover Publications.
Evaluation will be based on the exercises done in classes (40%) and a term-end examination (60%).
Knowledge of fundamentals on quantum mechanics.