A new hexagonal phase of Si1−xGex alloys have been successfully synthesized through efforts in recent reports. Utilizing the combined first-principle calculations and special quasi-random model, we precisely investigated the structural, electronic, optical, and vibrational properties of hexagonal Si and Ge and disordered hexagonal Si1−xGex random alloys. We found a large negative deviation between the calculated lattice constants within the revised Perdew–Burke–Ernzerhof for solids functional and the linear fitting results. The electronic structures obtained by using the Tran–Blaha modified Becke–Johnson exchange potential confirm that hexagonal Si1−xGex (x > 0.625) alloys present direct bandgaps. Through solving the Bethe–Salpeter equation, the linear optical spectra of hexagonal Si and Ge are demonstrated. We reveal that the peaks of complex dielectric functions are redshifted with the addition of Ge atoms. Also, the real and imaginary parts exhibit strong anisotropy, which makes hexagonal Si1−xGex alloys potentially useful as nonlinear crystals. The transition is allowed in the infrared region for the hexagonal Si1−xGex (x > 0.625) alloys, and the linear optical spectra can be continuously tuned over a wide range of frequency with Ge addition in the infrared region. Furthermore, density-functional perturbation theory calculations were carried out to predict the off-resonance Raman activity. The results suggest that the vibrational modes of the Si–Si bond exhibit a strong dependency on the compositions, which provides a useful way to identify the most probable atomic configurations of hexagonal Si1–xGex alloys in future experiments.

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