# FYS3410 - Condensed matter physics

## Course description

## Schedule, syllabus and examination date

**Choose semester**

## Course content

- Periodic structures, understanding of diffraction experiment and reciprocal lattice
- Imperfections in crystals: diffusion, point defects, dislocations
- Crystal vibrations: phonon heat capacity and thermal conductivity
- Free electron Fermi gas: density of states, Fermi level, and electrical conductivity
- Electrons in periodic potential: energy bands theory classification of metals, semiconductors and insulators
- Semiconductors: band gap, effective masses, charge carrier distributions, doping, pn-junctions
- Metals: Fermi surfaces, temperature dependence of electrical conductivity

## Learning outcome

Students receive an introduction to the field providing basic knowledge but also serving as a briefing on current issues within the field of condensed matter physics and materials science as the basis for selection of a master thesis program.

Students are expected to demonstrate understanding of periodic potential manifestations in solids and should be able to describe basic phenomena, x-ray diffraction, dispersion, density of states and energy band concept, in crystals using classical or quantized laws or approximations. With this we mean:

- reciprocal lattice vectors to be calculated for typical high symmetrical crystals and the relationship between Miller indices (hkl) and the distance between the lattice plains is to be understood.
- Laue equation to be derived and the meaning of the Ewald construction, as well as Brillouin zones can be explained.
- equilibrium concentration of point defects (e.g. vacancies) shall be calculated as a function of temperature and pressure.
- diffusion phenomena to be explained on the atomic level.
- dispersion for a linear lattice containing one and two atoms per primitive basis to be derived and the meaning of optical and acoustic phonons to be explained - especially at the origin and near the first Brillouin zone boundary.
- phonon density of states to be derived in the 1- and 3-dimensional cases.
- lattice contribution to heat capacity should be calculated using the Debye and Einstein approximations.
- temperature dependence of thermal conductivity should be explained.
- Fermi-Dirac distribution could be derived.
- density of states and heat capacity for the Fermi electron gas will be derived in the 1- and 3-dimensional cases and concepts of Fermi level and Fermi surface to be explained.
- temperature dependence of electrical conductivity should be explained in terms of the Fermi electron gas theory.
- energy band structure should be explained in terms of the periodic potential and illustrated by using Kronig-Penny model.
- band structure in the empty lattice approximation, zero potential, to be visualized in the first Brillouin zone in a simple cubic crystal.
- approaching band structure in the nearly free electron model, specifically near Brillouin zone boundaries, so that the origin for the band gap is understood.
- classification into metals, semiconductors and insulators anchored in the energy band structure.
- effective mass can be introduced and the meaning of the effective mass values near Brillouin zone boundaries should be explained.
- carrier charge distributions as a function of temperature in intrinsic and doped semiconductors to be calculated.
- hole and electron profiles through a pn-junction and its rectification properties should be explained.
- reduced, periodic and expanded zone schemes to be explained.
- construction of Fermi surfaces to be explained.

## Admission

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

## Prerequisites

### Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

One of these:

- Mathematics R1
- Mathematics (S1+S2)

And and in addition one of these:

- Mathematics (R1+R2)
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies. Read more about special admission requirements (in Norwegian).

### Recommended previous knowledge

Knowledge corresponding to the following courses at the University of Oslo: FYS-MEK1110 - Mechanics, FYS1120 - Electromagnetism, FYS2130 - Waves and oscillations, FYS2140 - Quantum physics and FYS2160 - Thermodynamics and statistical physics.

## Overlapping courses

10 credits overlap against FYS230.

## Teaching

The course contains 3-4 hours of lectures and 2 hours of group work every week. Compulsory problems will be included.

## Examination

Written midterm-exam (medio March) (3 hours) with approx. 40 % weight. Final oral exam (primo June) with approx. 60% weight..

### Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

### Explanations and appeals

### Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.