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 nano systems. The course integrates theorical concepts and experiment and is aimed specifically at students in Nanoscience (bachelor). Following up on their previous course in quantum mechanics, basic theoretical background in solid state physics is discussed, namely the free electron model and band structure. From the perspective of a physicist, we introduce different materials (e.g. semiconductors, metals, insulators) and introduce the phenomenon of Coulomb blockade at low temperatures and its role in single-electron tunneling transistors. We discuss the emergence of quasi two-dimensional electron gases in semiconducting heterostructures and how they are manufactured and characterized in a Hall bar geometry (carrier density, carrier mobility), before discussing the integer quantum Hall effect that arises under application of a strong perpendicular magnetic field.


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


A) Production of a nanoscale device: The use of a cleanroom for the production of microcircuits by photolithography is exemplified by the etching of a semiconductor Hall bar.

B) Low-temperature measurements of Coulomb blockade and single-electron transport.

C) Low-temperature measurements of a Hall bar, where the charge carrier concentration is determined by two different methods: Hall effect and Shubnikov-de Haas oscillations (4 K, up to 2 Tesla). The onset of the integer quantum Hall effect is discussed by comparison with data obtained at even lower temperatures and even larger magnetic fields.


The exercises are documented with reports, which form the basis for the oral examination.


BSc Programme in Nanoscience

Learning outcome


  • explain the band structure of solids, including the difference between metals, semiconductors and insulators
  • explain why electrical measurements in nano systems may be different from everyday (macroscopic) electrical components
  • describe the manufacture of selected electrical nanodevices
  • demonstrate theoretical understanding of selected quantum phenomena within electron transport in nano systems
  • perform simple, illustrative calculations for quantitative description of these phenomena
  • 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
  • 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, students will have basic knowledge of the manufacture and physical properties of selected nanoscale devices, and are able to explain the basic quantum mechanical concepts that are behind 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 or condensed matter physics.

Through the experimental part of the course, the student is trained in, gathering, interpreting and presenting data (both in written and oral form), as well as shedding light on the differences/similarities between theory and practice for the phenomena.

In class, we will discuss online lectures and reading material that the students engage with before each lecture. In laboratory exercises, groups of students will together enter the cleanroom or perform low-temperature measurements, assisted by teachers or TAs. Students prepare for lectures, lab exercises, and lab report independently (usually in small groups).

The course website will provide information regarding reading materials and recorded lectures.

The student is expected to have taken basic courses in physics, mathematics, specifically quantum mechanics and calculus.

Peer feedback (Students give each other feedback)

Oral discussion of student work in class.

Written feedback on lab report(s).

Peer feedback on student presentations (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 (no preparation), 20 min, 2/3 of course grade
Laboratory reports, 1/3 of course grade

The oral exam covers the content of the laboratory exercises and the theoretical material covered in the course.
Exam registration requirements

The student must participate in all laboratory experiments and submit at least two laboratory reports as a prerequisite for going to the oral exam.

Only certain aids allowed

One A4 sheet with key words, as discussed in class.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal assessors

Same as exam.

Experimental participation requirements cannot be disregarded. Students who do not meet the requirement must follow the course again.

If the student has participated, but has not received approved lab reports, new lab reports can be handed in no later than 3 weeks before the re-examination.

Criteria for exam assessment

See learning outcomes.

Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 165,5
  • Practical exercises
  • 20
  • Exercises
  • 20
  • 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 Coordinator
  • Saulius Vaitiekenas   (7-7d6b7f76737f7d4a786c7338757f386e75)

Saulius Vaitiekenas
Ferdinand Kuemmeth

Saved on the 05-10-2023

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