Si-rich oxide/SiO2 multilayer films with different N2O flow rates have been deposited by plasma enhanced chemical vapor deposition technique, and Si quantum dot (Si-QD)/SiO2 multilayer films are obtained by 1100 °C annealing. Steady photoluminescence (PL) spectra show that the main optical emission mechanism changes from quantum confinement effect of Si-QDs to interface defect states with increasing the flow rate of N2O. Curve fittings of time-resolved PL spectra show that two log-normal decay time distribution bands are obtained, and both the most frequent life-times decrease with increasing the flow rate of N2O, while increase with the red shift of detecting wavelength. Analyses indicate that defect states density and size distribution of Si-QDs strongly influence the PL decay properties.

Maximal accretive realizations and bound-preserving self-adjoint extensions are two fundamental problems in applications of semi-bounded operator theory to differential equations. On the basis of using differential operator theory in direct sum spaces and Phillips theory for maximal accretive extensions of accretive operators, a complete characterization of the set of maximal accretive boundary conditions for Sturm–Liouville differential operators is presented. As an application, all possible forms of bound-preserving self-adjoint extensions of regular Sturm–Liouville operators are also characterized via various explicit boundary conditions. The methodology can also be applied to dealing with general classes of semi-bounded symmetric differential operators.