Silicon Photonics: Fundamentals and Devices

6.9 Tensile-Strained Ge Layers

It was pointed out in Section 2.8 that the band gaps for the Γ valley and L valley in Ge differ by only about 140 meV. The application of tensile strain to Ge alters these two valleys at different rates, and at about 2% tensile strain Ge becomes a direct-gap material. The tensile strain can be applied by growing Ge on GeSn; however, the result may not be a type I heterostructure, and therefore the barrier layer is a ternary alloy GeSiSn.

The calculated results presented in Figures 2.15, 2.16 and 2.17 give clear evidence of indirect-to-direct crossover.

So far, there is no experimental evidence for these conclusions. However, some theoretical calculations have appeared in the literature about the values of gain coefficient using the direct nature of the band gap.

The work by Liu et al.68 considers both tensile strain and heavy doping in the n-Ge layer. The needed tensile strain makes the direct band gap 0.5 eV, which does not emit a 1550 nm. Instead, the authors considered less strain so that the band gap difference is about 115 meV and the presence of heavy doping and injection moves the electronic quasi-Fermi level to touch the Γ valley. The gain occurs due to stimulated emission from the Γ valley to higher lying LH band. The authors used the measured direct-gap absorption data for tensile-strained n-Ge and fitted it by using the expression

(6.17)

where A is the fitting parameter and other symbols are self-explanatory.

The gain is calculated from ...