Quantum Phenomena in Nano Systems (Nano3)

Course content

The aim of the course is to give students an introduction to experimental nanoelectronics and thus an understanding of quantum phenomena and electron transport in nanosystems. The course integrates theory and experiment and is aimed specifically at students in Nanoscience (bachelor).

Based on the previous course in quantum mechanics, the necessary theoretical background in solid state physics is provided. Particular emphasis is placed on the free electron model and band structure. The free electron model applied to mesoscopic systems is reviewed and in particular derived from the transmission formalism that is central to the understanding of quantum phenomena and electron transport in nanosystems. Some important topics are also quantized conductivity, Hall effect, Coulomb blockade, single electron transistors (quantum dots) and their application to quantum computation, as well as materials (eg semiconductors and carbon nanotubes). Calculation-based exercises illustrate the theory.


Experimental part: A number of laboratory exercises of 2-4 hours duration are performed. In some cases, provided data may replace an experimental exercise. The exercises can, for example, deal with:


A) Production of a nanoscale device: The use of a cleanroom for the production of microcircuits by photolithography.

B) The samples produced can form the basis for measurements at liquid helium temperature (4.2 K), where the charge carrier concentration is determined by two different methods: Hall effect and Shubnikov-de Haas oscillations.

C) Measurement of quantized conductivity in a 1-dimensional conductor.

D) Electrical measurements of single electron transport through a so-called quantum island. The component will be made of a carbon nanotube or semiconductor nanowire. The exercises are documented with reports, which form the basis for the oral examination.

E) Introduction to electrical measurements, instruments, circuits and data collection.


(not all exercises from the above list will necessarily be completed)


BSc Programme in Nanoscience

Learning outcome


  • explain why electrical measurements in nanosystems may be different from everyday (macroscopic) electrical components
  • explain the band structure of solids, including the difference between metals, semiconductors and insulators
  • explain how the dimensionality of nanoscale devices can affect their electrical properties
  • use simple test setups for measuring nanodevices
  • know the low-temperature techniques for measuring nanodevices
  • demonstrate theoretical understanding of selected quantum phenomena within electron transport in nanosystems
  • perform simple, illustrative calculations for quantitative description of these phenomena
  • describe the manufacture of selected electrical nanodevices
  • describe and justify the performance of the experiments performed
  • apply the theory to experimental data, including interpretation of the results obtained in the exercises
  • reproduce (qualitatively) graphs that reproduce typical experimental data, as well as describe trends and characteristics in the graphs
  • relate and/or differentiate between the quantum phenomena treated in the course and the exercises and to be able to explain differences / similarities between experimental measurements and ideal theoretical phenomena
  • formulate a correct and comprehensible report for each of the experiments performed, including selecting and presenting the most relevant information within the scope of the report.



After the course, the goal is for students to have knowledge of the manufacture of nanoscale devices and typical electrical measurement techniques, as well as to be able to explain the basic theory of the quantum mechanical properties of nanodevices and the observed phenomena.



The course gives the student competence to be able to acquire further knowledge within the subject, e.g. by following advanced courses in quantum physics.

Through the experimental part of the course, the student is trained in performing experiments, interpreting and presenting data, as well as shedding light on the differences/similarities between theory and practice for the phenomena.

Lectures, exercises and laboratory experiments.

Materials and notes are prepared by the teachers. The course website provides information regarding distribution and sale of this.

The student is expected to have taken basic courses in physics and mathematics, corresponding to the physics and mathematics courses in the first year of the bachelor's program in nanoscience.

Peer feedback (Students give each other feedback)
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Written assignment, laboratory reports during course
Type of assessment details
Oral test, 20 min, 2/3 of course grade
Laboratory reports, 1/3 of course grade

The reports of the laboratory exercises are the starting point for a presentation at the oral examination.
In the oral test, the theoretical material of the course is also examined.
There is no preparation time, but students have two minutes to gather their thoughts and write/draw on the board before they present the topic that they have randomly drawn.

One-third of the course grade comes from the two best laboratory reports submitted by the student.
Only certain aids allowed

Students may bring 1 A4 sheet of notes to the oral exam

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal assessors
Criteria for exam assessment

See learning outcomes.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 20
  • Preparation
  • 147,5
  • Theory exercises
  • 20
  • Practical exercises
  • 18
  • Exam
  • 0,5
  • English
  • 206,0


Course number
7,5 ECTS
Programme level

1 block

Block 3
No restrictions/no limitation
The number of seats may be reduced in the late registration period
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Ferdinand Kuemmeth   (8-707a6a72726a796d4573676e33707a336970)
  • Anasua Chatterjee   (17-6f7c6f81836f3c71766f828273807873734e7c70773c79833c7279)
Saved on the 28-02-2022

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