Course syllabus for Solid state physics

Course in quantum physics

Solid state physics is an obvious part in the education in physics. The course is required for many later courses in the field.

The course provides an overview of the physical properties of solids, experimental methods used to explore them and how properties are explained on the basis of theoretical models at a microscopic level.

Initially it is described how the atoms are arranged in crystalline substances and how the order can be determined by diffraction of incident radiation (x-rays, electrons, neutrons) or via direct imaging methods. In the description of diffraction the reciprocal lattice is introduced, as an essential concept for the understanding of many of the properties of crystalline substances.

The following section describes vibrational waves and thermal properties derived from these. Then defects in the atomic arrangements are treated and their impact on various properties.

The course continues to discuss electronic properties (conductivity, optical reflectivity, plasma oscillations, Landau levels, the Hall voltage), starting first from the free electron model  and thereafter, starting from a description of an electron in a periodic potential (energy gap, operating in the field, optical excitations, effective mass, holes). An important application is to intrinsic and doped semiconductors.

The course has the following content that is also practised:

- Mathematically describe and define a unit cell, a primitive unit cell and the Wigner-Seitz cell in different crystal structures.

- Define planes in crystal structures and their corresponding Miller indices.

- Determine and calculate lattice parameters of crystal structures, and also describe how they can be determined, by diffraction.

- Explain the principle difference between x-ray, neutron, and electron diffraction.

- Calculate the reciprocal lattice of a crystal.

- Calculate the structure factor for different types of structures.

- Describe Brillouin zones.

- Calculate the vibrational modes in crystals in the simple spring-ball model. Describe how quantised vibrations (phonons) contribute to the heat capacity. Be able to explain the difference between the acoustic and optical phonons.

- Describe and calculate the basic aspects of the free electron gas as given by the Fermi-Dirac distribution of a particle in a box or with periodic boundary conditions.

- Explain the concepts Fermi sphere, Fermi surface, Fermi wave vector, Fermi energy, Fermi temperature.

- Calculate the density of states depending on energy spectra and dimensionality.

- Describe the effect of electromagnetic fields through the Drude model for the complex conductivity. How this is related to the DC conductivity, reflectivity, refractive index, and plasma oscillations. Be able to give a simple explanation for the color of different metals.

- Describe the basic difference between metals and semiconductors / insulators using the band structure.

- Explain the meaning of the Bloch theorem for electrons in a periodic potential, and the term crystal momentum.

- Derive the band structure in a weak periodic potential from the empty lattice model, and using the tight-binding model for simple lattices.

- Describe and use the equation of motion of a Bloch electron and how this is related to the concept of effective mass.

- Describe the basic physics of a semiconductor, with direct or indirect band gap, intrinsic or doped. Conduction and valence band, and the description of the electrons in the valence band in terms of holes. Effective mass of bands, mobility concept, as well as the exponential temperature dependence of conductivity.

- Explain how to calculate the chemical potential and the electron / hole density for intrinsic or doped semiconductor.

- Describe the Hall effect and how this is related to the type of charge carriers.

- Describe how the Fermi surface is related to the band structure, and qualitatively derive the Fermi surface of a weak periodic potential.

The course includes lectures, exercises, four compulsory lab sessions, OpenTA tasks, a "dugga" and a written exam.

The lectures highlight the most important aspects of solid state physics and include examples of how the knowledge is applied in different contexts. The exercises provide further examples.

The four compulsory lab sessions provide practical experience of analytical methods for determining material structure and properties.

The Open TA tasks support the work with continuous learning during the course, and the "dugga" provides a check about halfway through the course.

The excercises of the "dugga" are representative of those of the part the final written exam covering the first half of the course.

P. Hofmann, Solid State Physics, An introduction. 3rd edition (Wiley-VCH, 2022)

Further reading: C Kittel: "Introduction to Solid State Physics", 8th (John Wiley and Sons, 2005)

The course ends with a written exam, consisting of numerical problems and descriptive tasks. The course includes a voluntary "dugga" and OpenTA tasks that give bonus points for the exam. The course also contains four compulsory lab sessions.

The laboratories and the written exam are compulsory parts of the course. The final grade is determined by total points (the sum of points on the exam and bonus points from the Open TA tasks and the "dugga").

The exam gives a maximum of 100 points. A total of 50 points up to 70 gives grade 3, 70 and up to 85 points gives grade 4 and 85 points and more gives grade 5.

Bonus on the written exam from the "dugga" is 40% of the points on the "dugga", i.e. a maximum of 20 bonus points. The course has 6 OpenTA tasks that can give a maximum of 6 bonus points on the exam.