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 (Fig. S1(a)); while the BTS matrix has large grains with layered structure on the micron scale (Fig. S1(b)). Appropriately, on the fracture surface of the composite specimens (f=0.5 wt.%, for instance) (Fig. S1(c)) one can find out some nanoparticles with size of 50-200nm, corresponding to which there is a shortage of element Bi(Te)/Se and a rich of Ga/As, as shown by element mapping of EDX (Fig. S1(d)). Hence these particles on the fracture surface can be ascribed toGaAs inclusions.