Quantum states and interband optical spectra in spherical GaAs-(Ga,Al)As quantum dots doped with on-centre shallow donor impurities: a real-time wavepacket propagation method

A time-dependent approach for the calculation of eigenenergies, eigenfuncti ons and optical spectra, within the effective-mass and single-hole-band app roximations, of low-dimensional semiconductor systems is presented. Tn this method, energy and optical spectra are obtained by Fourier analysis of a t ime-autocorrelation function constructed from an appropriately chosen propa gated wavepacket. Eigenfunctions are determined by a direct Fourier analysi s of such a propagated wavepacket. The time evolution of the wavefunction i s obtained by numerical integration of the time-dependent Schrodinger equat ion. This approach shares the virtues of the more common numerical methods (accuracy, flexibility and automatic enforcement of boundary conditions) wi th the additional advantage that it can yield an entire eigen or optical sp ectrum in a single calculation. The methodology is applied to the calculati on of all the eigenenergies and eigenfunctions of the conduction band, and the intensities of the transitions from the ground state of the valence ban d to all the states of the conduction band, in spherical GaAs-(Ga,AI)As qua ntum dots with finite confinement and a wide range of radii, without and wi th an on-centre shallow donor impurity.