Ternary alloy semiconductor of germanium-silicon-tin (GeSiSn) has attracted for electronic and optoelectronic applications, because this group-IV alloy material provides energy band engineering independent on the lattice constant like group III-V compound semiconductors [1]. In addition, GeSiSn/Ge(Sn) heterostructure realizes type-I energy band alignment with a sufficiently large band offset at both conduction and valence band edges with no or very small lattice mismatching [2,3], and that is preferable for effective carrier confinement for light emitting devices and high mobility transistors. On the other hand, there are still challenges for crystal growth with strain and band engineering of group-IV ternary alloy semiconductor thin films. GeSn is one of promising candidates for optoelectronic applications since it realizes direct transition group-IV semiconductor. GeSn with an in-plane lattice constant larger than Ge is better to enhance the emission efficiency, as the conduction band edge of the gamma-valley lowers than that of the L-valley with large lattice constant and/or in-plane tensile strain. Thus, a buffer layer such as GeSiSn with a lattice constant sufficiently larger than Ge is required to obtain direct transition GeSn thin films, and lattice-constant engineering technology of buffer and GeSn layers should be developed with well-controlled strain relaxation technique. Recently, we explored effective strain engineering technique of GeSiSn ternary alloy epitaxial layers on Ge and Si substrate to obtain much larger in-plane lattice constant. We investigated the effect of low-temperature growth of Ge buffer layer on the strain relaxation of GeSiSn layer [4,5]. Also, we examined the ion implantation technique into substrate to enhance the strain relaxation of GeSiSn epitaxial layers grown on Ge substrate [6]. We can achieve GeSiSn epitaxial layers with the enhancement of strain relaxation and the lattice constant larger than Ge, although the crystalline quality of these epitaxial layers should be still improved. We previously reported that the strain direction as compressive and tensile ones is significantly influence of GeSiSn epitaxial layers [7]. The control of strain structure and its relaxation process is keys to obtain high crystalline quality of GeSiSn and GeSn heteroepitaxial layers for improving the electronic and optoelectronic properties of group-IV heterostructures. References [1] S. Zaima, O. Nakatsuka, N. Taoka, M. Kuorsawa, W. Takeuchi, and M. Sakashita, Sci. Technol. Adv. Mater. 16, 043502 (22pages) (2015). [2] T. Yamaha, S. Shibayama, T. Asano, K. Kato, M. Sakashita, W. Takeuchi, O. Nakatsuka, and S. Zaima, Appl. Phys. Lett. 108, 061909 (5 pages) (2016). [3] M. Fukuda, K. Watanabe, M. Sakashita, M. Kurosawa, O. Nakatsuka, and S. Zaima, Semicond. Sci. Technol. 32, 104008 (2017). [4] M. Fukuda, T. Yamaha, T. Asano, S. Fujinami, Y. Shimura, M. Kurosawa, O. Nakatsuka, and S. Zaima, Mater. Sci. Semicond. Proc. 70, 156 (2017). [5] M. Fukuda, D. Rainko, M. Sakashita, M. Kurosawa, D. Buca, O. Nakatsuka, and S. Zaima, Semicond. Sci. Technol. 33 (12), 124018 (8 pages) (2018). [6] M. Fukuda, D. Rainko, M. Sakashita, M. Kurosawa, D. Buca, O. Nakatsuka, and S. Zaima, Jpn. J. Appl. Phys. 58, SIIB23 (2019). [7] T. Asano, T. Terashima, T. Yamaha, M. Kurosawa, W. Takeuchi, N. Taoka, O. Nakatsuka, and S. Zaima, Solid State Electronics 110, pp. 49-53 (2015).