The name 'Stokes shift' as applied to molecules, implies vibronic coupling (yes, related to Raman process).

In QDs, however, the mechanism for Stokes shift is completely different. It is named Stokes shift only to maintain the visual analogy to organic emitters (emission vs. absorption).

The vibronic coupling was estimated to be much smaller in QD than in molecules, insufficient to explain the observed shift between absorption and emission. The exciton finestructure always containing dark (triplet) states which are lower in energy than bright (singlet) states can be the origin of Stokes shift. Another strong contributor is the polydispersity of QD ensemble.

When a solid undergoes an electronic transition, it typically changes the vibrational state. This leads to the concept of vibronic (i.e., vibrational-electronic) transitions. Electronic transitions can be provoked by various energy providing mechanisms. But, the interaction of the electronic states of the atoms in a solid with the vibrational lattice modes, usually called electron-phonon coupling causes as a consequence of the vibrational energy consumption, a redshift of the photoluminescence (PL) peak with respect to the fundamental transition. In general, the degradation of the optical energy is called Stokes shift.

Anyway, you can consult with these books for exact details:

1. M. Fox, Optical Properties of Solids, 2nd ed. (Oxford University, 2010).

2. J. I. Pankove, Optical Processes in Semiconductors (Dover, 1971).

Thank you, Puspendu! So, as I understand, this phenomena is similar with laser dye or laser crystals like Ti: Sapphire.I am more familar with laser materials. But I do see lots of  papers discussing it, for example, dark state, surface trapping state, defect, and so on. And it seems no definate answers now and this shift are strongly relates to QD size, temperature, and even excitation light intensity.   

Yes, interaction with phonons - is one of possible reason.

The occurrence of Stokes shift could also indicate on a complicated mechanism of excitation energy transfer from a light-absorbing system to luminescence centres.

The name 'Stokes shift' as applied to molecules, implies vibronic coupling (yes, related to Raman process).

In QDs, however, the mechanism for Stokes shift is completely different. It is named Stokes shift only to maintain the visual analogy to organic emitters (emission vs. absorption).

The vibronic coupling was estimated to be much smaller in QD than in molecules, insufficient to explain the observed shift between absorption and emission. The exciton finestructure always containing dark (triplet) states which are lower in energy than bright (singlet) states can be the origin of Stokes shift. Another strong contributor is the polydispersity of QD ensemble.