The microstructures of as-prepared GaAs powders, fracture surface of BTS matrix and the fracture surface of a typical composite sample with f=0.5 were further investigated by using field emission scanning electron microscopy (FE-SEM). FE-SEM observations show that the most of the GaAs particles of as-prepared GaAs powders are of the sizes in sub-micrometers (Figure S1(a)); while the BTS matrix has large grains with layered structure on the micron scale (Figure S1(b)). On the fracture surface of the composite specimens (f=0.5 wt.%, for instance) (Figure S1(c)) one can find out some nanoparticles with size of 50-200nm, and it can be seen from Figure S1(d) that there are some white spots at the grain boundaries. By careful inspection with energy dispersive X-ray spectroscopy (EDX), one finds that there is a shortage of element Bi(Te)/Se and a rich of Ga/As in the areas with white spots, as shown in Figure S1(e), indicating that the white spots are actually GaAs grains, in agreement with XRD measurements. Present results indicate that nanophase GaAs are successfully incorporated into the BiTeSe matrix.