Band structure and optical properties of pseudomorphic Ge1−x−ySixSny on Ge

Ge is an indirect band gap material. The band structure of Ge is a strong function of strain and alloy composition, and a transition from an indirect to a direct band gap has been observed for y~6-10% for relaxed Ge
_{1_y}
Sn
_y
indicating the possibility of widespread applications of Ge-based photonic devices. The pseudomorphic nature of the Ge-based alloy layer on a substrate is important to keep dislocation densities low at the interface to improve the performance of the device. Band gap engineering of Ge by controlling strain and alloying with Si and Sn has attracted great interest since Ge
_1-x-y
Si
_x
Sn
_y
ternary alloy with two compositional degrees of freedom allows decoupling of the lattice constant and electronic structures. Hence the knowledge of the compositional and strain dependence of the Ge
_1-x-y
Si
_x
Sn
_y
band structure is critical for the design of photonic devices with the desired interband transition energies.