PATH-INTEGRAL STUDY OF EXCITONS AND BIEXCITONS IN SEMICONDUCTOR QUANTUM DOTS

Computational path integral methods have been used to study the excitonic properties of an effective mass quantum dot model. The results are compared to those of variational calculations. The variational method, using a free particle basis, accurately gives the ground and low lying excited state properties for small radii dots where the kinetic energy dominates over the Coulomb interaction. The path integral approach, which is not restricted to small radii dots, gives a thermal average over states. One thermal effect noted for this model is an inversion of the surface charge layer with temperature due to the competition between thermal and Coulomb energies. At high temperature, where Coulomb effects are secondary, the thermal deBroglie wavelength sets the scale for the density variation near a surface and thus the heavier holes approach the surface more closely than the electrons. As the temperature is lowered the now more important Coulomb binding causes the holes to be cushioned away from the surface by the electron cloud. This inversion temperature decreases as the dot radius increases. Both calculations predict increasing biexciton binding energy with decreasing dot size.