Theory of the quantum confinement effect on excitons in quantum dots of indirect-gap materials

The quantum confinement effect on excitons in quantum dots of indirect-gap materials is investigated and a mechanism that induces an indirect-to-direct conversion of the character of the optical transition is clarified. The exciton transition energy and the exciton binding energy are calculated and found to be in good agreement with experimental results on Si and Ge nanostructures. The large exciton binding energy in Si and Ge quantum dots suggests that the photoluminescence from these nanostructures is of excitonic origin even at room temperature. The estimated radiative lifetime of excitons is strongly size dependent and varies from nanosecond to millisecond corresponding to the diameter from \ensuremath{\sim}10 to \ensuremath{\sim}30 \AA{}. These theoretical results suggest strongly the importance of the quantum confinement effect in the luminescence processes of porous Si.