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 energy bands will be formed in a periodic potential of solids, which is the basis for carrier transport in metals and semiconductors.
This course also covers band theories of solids based on nearly-free-electron approach with a periodic perturbation potential and more precise tight binding theory. The concepts of Brillouin zone, Bloch theorem, empty lattice approximation, and chemical bonds in solids are introduced as a basis for the band theories. Then, students will gain an understanding of the nearly-free-electron approach using the perturbation theory and the tight binding theory of solid. In particular, students lean the calculation methodology of the band structures of diamond and zinc-blend semiconductors.
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.
Also, through the course, the students will be able to
3. understand the generation of band structures in a periodic lattice potential and the nearly-free-electron model of solids using the perturbation theory.
4. comprehend the concept and methodology of the tight binding theory.
5. understand the band structures of diamond and zinc-blend semiconductors.
Quantum mechanics, Perturbation theory, Solid state physics, periodic potential, Energy band, Bloch's wave, Band structure
✔ 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 | Free electron model of solids | 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 I | Chemical bonds, Fundamentals of tight binding theory |
Class 14 | Tight binding theory II | Tight binding theory of 2-dimensional lattices |
Class 15 | Band structures of semiconductors | Tight binding theory of diamond and zinc-blend semiconductors, and the band structures of semiconductors |
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.