Location of Repository

Efficient Calculation of Electron States in Self-Assembled Quantum Dots: Application to Auger Relaxation

By Darren Chaney, Mervyn Roy and P.A. Maksym


This is the author's final draft of the paper published as: Quantum Dots: Fundamentals, Applications, and Frontiers: Proceedings of the NATO Advanced Research Workshop on Quantum Dots: Fundamentals, Applications and Frontiers Crete, Greece, 20-24 July 2003 / edited by Bruce A. Joyce, Pantelis C. Kelires, Anton G. Naumovets, Dimitri D. Vvedensky, pp. 239-255. The final version is available from http://www.springerlink.com/content/k56545x7806611m4/. Doi: 10.1007/1-4020-3315-X_16An efficient method for calculation of self-assembled dot states within the effective mass approximation is described and its application to the calculation of Auger relaxation rates is detailed. The method is based on expansion of the dot states in a harmonic oscillator basis whose parameters are optimised to improve the convergence rate. This results in at least an order of magnitude reduction in the number of basis states required to represent electron states accurately compared to the conventional plane wave approach. Auger relaxation rates are calculated for harmonic oscillator model states and exact states for various pyramidal models. The dipole approximation, previously used to calculate Auger rates, is found to be inaccurate by a factor of around 2–3. The harmonic oscillator states do not reproduce the rates for the more realistic pyramidal models very well and even within the set of pyramidal models variations in the dot shape and size can change the rates by up to an order of magnitude. Typical Auger relaxation rates are on a picosecond timescale but the actual value is strongly dependent on the density of electrons outside the dot

Publisher: Springer
Year: 2005
DOI identifier: 10.1007/1-4020-3315-X_16
OAI identifier: oai:lra.le.ac.uk:2381/7588

Suggested articles



  1. (2003). An efficient method for calculating electronic states in self-assembled quantum dots," submitted to Phys. doi
  2. (1997). Auger carrier relaxation in self-assembled quantum dots by collisions with two-dimensional carriers," doi
  3. (1999). Carrier energy relaxation by means of Auger processes in InAs/InGaAs self-assembled quantum dots," doi
  4. (1998). Composition of InAs quantum dots on GaAs(001): Direct evidence for (In,Ga)As alloying," doi
  5. (2001). Detection of efficient carrier capture in ultrathin InAs/GaAs layers using a degenerate pump-probe technique," doi
  6. (2002). Determination of the shape and indium distribution of lowgrowth-rate InAs quantum dots by cross-sectional scanning tunnelling microscopy," doi
  7. (1999). Electronic and optical properties of strained quantum dots modelled by 8-band theory," doi
  8. (1996). Electronic structure of InAs/GaAs selfassembled quantum dots," doi
  9. (2001). Epitaxially self-assembled quantum dots," doi
  10. (1995). InAs/GaAs pyramidal quantum dots - strain distribution, optical phonons, and electronic-structure," doi
  11. (2000). Inverted electron-hole alignment in InAs-GaAs self-assembled quantum dots," doi
  12. (2000). Nonuniform composition profile in In Ga As alloy quantum dots," doi
  13. (1998). Self-consistent calculation of the electronic structure and electron-electron interaction in self-assembled InAsGaAs quantum dot structures," doi
  14. (2003). The effect of self-assembled quantum dot geometry on Auger relaxation rate,"
  15. (1999). The influence of inter-diffusion on electron states in quantum dots," doi
  16. (2000). Theoretical analysis of electron-hole alignment in InAs-GaAs quantum dots," doi
  17. (1992). Thermodynamic study of molecular-beam epitaxial-growth of InGaAs/GaAs strained layer superlattices," doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.