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Despite of great progress in development of third-generation PV cells (a non-univocal class including various materials: dye sensitized, multi-junction cells, quantum dots, perovskites etc), about 95% of the total PV market is still represented by crystalline silicon solar cells, which have rather low efficiency in the conventional configuration. Thus, a conceptually simpler and cheaper approach to exceed the theoretical efficiency limit of silicon cells is the addition of the special quantum cutting layer to these cells. It allows to fully exploit highly mature technologies of photovoltaics, and it theoretically can raise the solar cells efficiency from 31 to 37%. However, such result can be reached only after development of the proper quantum cutting material(s). We have demonstrated that Yb doped Scheelite like molybdate single crystals are promising quantum cutting materials. These crystals efficiently absorb UV Solar quanta and emit the sufficiently increased number of the secondary quanta near 1 micron, which are then absorbed by silicon cell with production of increased number of electron-hole pairs. In our contribution we present the growth of a several series of the crystals of Scheelite family, having various host compositions (CaMoO4, NaGd(MoO4)2, NaLa(MoO4)2, NaGd(1-x)Yx(MoO4)2, NaYMoWO8), doped with different concentrations of Yb, as well as crystallochemical and spectroscopic characterization of these crytals.