The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Electronic Properties of Non-Circular Quantum Dots

Esa Räsänen

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium K at Helsinki University of Technology (Espoo, Finland) on the 28th of May, 2004, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7101-X)   [965 KB]
Dissertation is also available in print (ISBN 951-22-7100-1)

Abstract

Quantum dots are nanoscale electronic objects, typically fabricated using two-dimensional semiconductor heterostructures or three-dimensional atomic clusters. In addition to promising technological applications, quantum dots represent excellent sources of interesting many-electron quantum physics.

This thesis deals with the theoretical modeling of two-dimensional quantum dots consisting of less than twenty electrons. The aim is to clarify how the geometry of the confining potential affects the ground-state structure of the system with and without the presence of an external magnetic field. The question is of a great importance in understanding and predicting the basic electronic properties of actual quantum-dot devices.

The calculations are based on the density-functional theory applied within a real-space multigrid approach, which is shown to be a powerful method for the systems considered in this thesis. The accuracy of the method is, however, highly dependent on the local spin-density approximation used. Hence, different parametrizations for the exchange-correlation energy are compared. Furthermore, the problem of the density-functional theory as a mean-field approach using a single-configuration wave function is analyzed in this thesis.

Quantum dots of various shapes are investigated, beginning with polygonal systems to determine the critical densities for the Wigner crystallization. Rectangular dots are shown to be particularly sensitive to the geometry, but a qualitative agreement is obtained with the experimental addition energy spectra. The lack of circular symmetry does not prevent the maximum-density-droplet formation when an external magnetic field is applied, and the high-field limit may be characterized by remarkably regular state oscillations. The symmetry can also be distorted by an external impurity, for which a realistic model is obtained with a comparison to experimental data. Presumably, some of the rich variety of phenomena identified in this thesis for non-circular quantum dots will have a realization in the future nanoelectronics.

This thesis consists of an overview and of the following 7 publications:

  1. Räsänen E., Saarikoski H., Puska M. J. and Nieminen R. M., 2003. Wigner molecules in polygonal quantum dots: a density-functional study. Physical Review B 67, pages 035326 : 1-7.
  2. Räsänen E., Saarikoski H., Stavrou V. N., Harju A., Puska M. J. and Nieminen R. M., 2003. Electronic structure of rectangular quantum dots. Physical Review B 67, pages 235307 : 1-8. © 2003 American Physical Society. By permission.
  3. Saarikoski H., Räsänen E., Siljamäki S., Harju A., Puska M. J. and Nieminen R. M., 2003. Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories. Physical Review B 67, pages 205327 : 1-5. © 2003 American Physical Society. By permission.
  4. Harju A., Räsänen E., Saarikoski H., Puska M. J., Nieminen R. M. and Niemelä K., 2004. Broken symmetry in density-functional theory: analysis and cure. Physical Review B 69, pages 153101 : 1-4. © 2004 American Physical Society. By permission.
  5. Räsänen E., Puska M. J. and Nieminen R. M., 2004. Maximum-density-droplet formation in hard-wall quantum dots. Physica E 22, pages 490-493.
  6. Räsänen E., Harju A., Puska M. J. and Nieminen R. M., 2004. Rectangular quantum dots in high magnetic fields. Physical Review B 69, pages 165309 : 1-5. © 2004 American Physical Society. By permission.
  7. Räsänen E., Könemann J., Haug R. J., Puska M. J. and Nieminen R. M., Impurity effects in quantum dots: towards quantitative modeling. Physical Review B, submitted for publication. © 2004 by authors and © 2004 American Physical Society. By permission.

Keywords: quantum dot, density-functional theory, hard-wall confinement, Wigner crystallization, maximum-density droplet

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© 2004 Helsinki University of Technology

Last update 2011-05-26