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## Course Summary

The proposed course may be considered as an introduction to physics of low dimensional quantum confined heterostructures, that are the structures where the carrier motion is restricted in one or more directions at the distances of the order of de Broglie wavelength. It leads to a considerable transformation of the electronic spectrum of such systems resulting in many new fundamental properties. The development of the technology allowing to change the composition of semiconductor at a scale of nanometers revolutionized semiconductor physics and the number of publications concerning the physics of low dimensional structures as well as to their numerous applications reveals a fast and steady growth over the last few decades. The investigation of various aspects of physical properties of low dimensional systems is today a dominating field of modern semiconductor physics. So understanding of basic concepts of physics of low dimensional structures is quite necessary to anybody specialized in solid state physics as well as in solid state electronics.

Meanwhile there seems to be a broad gap in the literature between textbooks on quantum mechanics and those on classical solid state and semiconductor physics, and very few books and lecture courses devoted to low dimensional semiconductor structures are available for Russian students especially published in Russian. One of the task of this course is to some extent to fill the gap and to give some fundamental background of low dimensional physics which should be acquired not only by students who intend to study the physical properties of quantized systems but also by those who are specialized in various applications of low dimensional structures. The number of fundamental topics relevant to the general understanding of the field is quite large and we concentrated main attention to the electronic properties of quantum confined heterostructures, transport and optical transitions in low dimensional electronic systems, and to the difference between the electronic properties of low dimensional structures and those of bulk semiconductors. Some applications utilizing the most fascinating properties of such systems will be considered as well.

The course is pitched at the level of magister students and beginning postgraduate students. It is assumed that students are familiar with main concepts of quantum mechanics and solid state physics.

## Course Format

Hours of lecture | Hours of discussion | Hours of independent study | Hours total |
---|---|---|---|

34 | 17 | 45 | 96 |

**Please note** that students are expected to study outside of class for three hours for every hour in class.

## Course Content

The plan is to work through the following topics:

- Quantum confinement and charge carrier spectrum transformation in low dimensional structures. Calculation techniques for electronic spectra determination in quantum confined structures. Envelope function method. Effective mass approximation in envelope function formalism. Spectra of confined electronic states in multi-valley semiconductors. The possibility of electronic states engineering in heterostructures.
- Transport phenomena in heteropstructures. Electron scattering in low dimensional structures and carrier mobility. Inter- and intrasubband scattering. Ballistic transport and quantum conductance in quantum wires.
- Resonant tunneling transport in superlattices and multiple quantum well structures. Minibands. Various regimes of resonant tunneling transport – sequential resonant tunneling, miniband transport, Wannier-Stark states hopping conductivity. Bloch oscillations. Nonlinear vertical transport and electric field domains in in superlattices and multiple quantum well structures.
- Shallow impurity states spectra in quantum wells.
- Optical properties of heterostructures. Interband and intersubband absorption. Excitons and excitonic luminescence. Exciton binding energy in low dimensional structures. Excitonic luminescence of quantum dots. Optical gain on intersubband transitions.
- Transport phenomena in superlattices and multiple quantum well structures in a magnetic field. Electron spectrum in quantum well in quantizing magnetic field. Magnetoresistance in different regimes of tunneling. Integer and fractional quantum Hall effect.
- Mesoscopic systems in low dimensional structures. Single electron effects. Coulomb blockade.
- Applications of resonant tunneling transport phenomena in micri- and nanoelectronics. Semiconductor intersubband emission lasers – quantum cascade lasers. Quantum well photodetectors. Resonant tunneling diode. Resonant tunneling transistors.

## Textbooks

Primary textbooks:

- Dr John H. Davies.
The Physics of Low-dimensional Semiconductors: An Introduction. Cambridge University Press, December 1997.

Additional textbooks:

- Gerald Bastard. Wave Mechanics Applied to Semiconductor Heterostructures. Wiley-Interscience, Les Ulis Cedex, France : New York, N.Y, 1 edition edition, January 1991.
- Claude Weisbuch and Borge Vinter. Quantum Semiconductor Structures: Fundamentals and Applications. Academic Press, Boston, 1 edition edition, May 1991.

## Grading

Class participation | 10% |

Homework assignments | 20% |

Midterm exam | 20% |

Final exam | 50% |