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Electrons in Low Dimensional Systems

Module PH2284

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2021

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022WS 2021/2SS 2021

Basic Information

PH2284 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Responsible coordinator of the module PH2284 in the version of SS 2021 was Francesco Allegretti.

Content, Learning Outcome and Preconditions


(1) Free and confined electrons in solids. (2) Electrons in a periodic potential: band theory of solids and dimensionality. Semiconductor materials, graphene and carbon nanotubes. (3) Two-dimensional electron gas. Quantum wells, quantum wires, quantum dots. (4) Surface electronic states, surface confinement, density of states vs. dimensionality. (5) Nanostructures and 2-D materials: from top-down control to bottom-up assembly. (6) Some important experimental techniques (scanning tunneling microscopy and spectroscopy, angle-resolved photoelectron spectroscopy, two-photon photoemission, inverse photoemission etc.) (7) Tunneling and tunnel junctions. (8) Coulomb blockade and single electron transistors. (9) Classical and semiclassical transport, ballistic transport, quantum resistance. (10) Quantum Hall effect and topological states.

Learning Outcome

After successful completion of the module the students are able to: (1) understand the physical laws governing the behaviour of electrons in solids and the influence of the reduced dimensionality; (2) understand the role of nanoscale phenomena and electron confinement in determining the electronic properties and physical behaviour of nanostructures; (3) evaluate the potential for exploitation of confinement effects in devices and applications.


No preconditions in addition to the requirements for the Master’s program in Physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Electrons in Low Dimensional Systems Allegretti, F. Fri, 11:00–13:00, PH II 227
UE 2 Exercise to Electrons in Low Dimensional Systems Allegretti, F. dates in groups eLearning

Learning and Teaching Methods

The module consists of a lecture and exercise classes. In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise classes the learning content is deepened and practised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.


  • Lecture: beamer presentation with slides, board work.
  • Tutorials with board work, discussion and problem solving to stimulate the active participation of the students.
  • Self-evaluation by means of multiple-choice tests.
  • Visits to on-campus laboratories.


Beamer presentation with slides, blackboard, lecture notes, exercise sheets. Lab visit. Execution of multiple choice tests in the Moodle platform.


Recommended textbook: George W. Hanson, Fundamentals of Nanoelectronics, Pearson/Prentice Hall (2007).

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Describe the energy levels and band structure of a quantum well.
  • How can one perform surface band mapping by means of angle-resolved photoelectron spectroscopy?
  • What is the Coulomb blockade?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Exam Repetition

The exam may be repeated at the end of the semester.

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