A transfer matrix model of a luminescent down-shifter (LDS) layer, consisting of silicon nanocrystals (Si-NCs) embedded in a silicon oxide matrix, on a silicon solar cells is presented. To enhance the efficiency of the silicon solar cell, we propose using a SiO2/Si-NCs double layer stack, as an anti-reflection-coating (ARC) and as a LDS material. The optical characteristics of this stack have been simulated and optimized as a front surface coating. The cell performances have been simulated by means of a two-dimensional device simulator and compared with the performances of a reference silicon solar cell. We found a 6% relative enhancement of the energy conversion efficiency with respect to the reference cell. We demonstrate that this enhancement results from the lower reflectance and from the down-shifter effect of the Si-NCs activated coating stack.