Engineering Large In-Plane Tensile Strains in Ge Microdisks, Microrings and Racetrack Optical Cavities
Authors: Millar Ross , Gallacher Kevin , Frigerio Jacopo , Ballabio Andrea , Bashir Aneeqa , MacLaren Ian , Isella Giovanni , Paul Douglas J 
Published: February 2020

Despite the fact that Ge is an indirect bandgap material, lasing has been made achievable due to the proximity of the direct band to the indirect in energy . Since the demonstrations of both optically [1] and electrically [2] pumped Ge lasers, there has been significant interest in techniques to lower the high lasing thresholds, which are due to the large carrier concentration required to fill the L valley before carriers can populate the direct band. Tensile strain has been shown to decrease the 𝚪 energy at a greater rate than the L, which leads to a transition to direct-bandgap [3], and would therefore allow a significant reduction in carrier injection for equivalent population inversion, while also reducing the free carrier absorption. This transition has generally been expected to occur between 1.6 and 2 % biaxial strain. In this work, high stress silicon nitride layers are used to transfer in-plane biaxial tensile strains > 2 % in Ge microcavities.
A range of highly strained Ge on Si microcavities have been demonstrated, including Ge microdisks, microrings, and racetracks of varying undercut and diameter. The Ge layers are dry etched, before Tetramethylammonium hydroxide (TMAH) is used to wet etch the Si to provide an undercut. TMAH anisotropically etches Si, and leads to an undercutting profile which depends on the orientation of the waveguide segment, and therefore allows for the partially free standing structures to be engineered, in turn enabling high stress transfer from the silicon nitride stressors. It was found that Ge on Si racetrack structure can be fully undercut in straight sections, leaving supporting posts at the curved segments where the waveguide is aligned to <110> directions. The highest strained cavities demonstrated in this work are 4 µm diameter, highly undercut microdisks structures, which show in-plane biaxial tensile strains of ~ 2.3 % at the top surface, as measured by Raman spectroscopy. Photoluminescence up to 2.4 µm in wavelength is consistent with these strain levels. Equivalent structures with no undercut demonstrate biaxial strains as high as ~ 1 %, which would be suitable candidates for electrically injected devices.
Finite element models (FEM) of the Ge disks are calibrated using the in-plane strain measured from Raman, and the disk curvature measured by transmission electron microscopy (TEM), allowing for an insight into the strain distribution within the disk, which is experimentally inaccessible by the techniques used here. It is found that while most of the top plane is biaxially strained, there is a radial uniaxial stress component around the disk edge, which induces εxy shear strains. This type of shear strain removes the glide reflection plane, and splits the L valleys. The L valleys that decrease in energy serve to counteract the effect of the biaxial strain, and reduces the carrier concentration at the 𝚪, which would be detrimental for optical gain. The finite element model suggests that these regions of shear strain near the disk edge are predominantly between 0.3 and 0.5%. With 2 % biaxial strain, a 0.4% εxy shear strain results in a ~ 57 % reduction in carrier concentration at the 𝚪. This work highlights that the optical overlap of the mode with shear strained regions has to be considered when calculating optical gain.
Ge racetrack structures have the advantage that waveguide segments can be aligned to the correct crystallographic direction (<100>) to ensure that no εxyshear strains occur. However, reduced in-plane strains to ~ 1.2 % at the top surface suggest that disk structures are still preferable where high levels of strain are required. GeSn material systems have been recently shown to be direct bandgap [4], but still suffer from a lack of carriers at the 𝚪 band at room temperature, which could also be improved with moderate tensile strain. In such material systems, these racetrack geometries may be preferable. For instance, they can be engineered in such a way that they are undercut, but there is a Si post directly underneath the region where the optical mode will be supported. This allows the potential for electrical injection, and heat syncing, unlike in disks structures where the mode is supported away from the Si post.
[1] J. Liu et al, Opt. Lett. 35, 679–81 (2010).
[2] R. E. Camacho-Aguilera et al, Opt. Express 20, 11316–20 (2012).
[3] D.J.Paul, Elec.Lett.45,582–584(2009).
[4] S. Wirths, R. Geiger, et al, Nat. Photonics 9, 88–92 (2015).

Figure 1