Raman-strain relations in highly strained Ge: Uniaxial ⟨100⟩, ⟨110⟩ and biaxial (001) stress

The application of high values of strain to Ge considerably improves its light emission properties and can even turn it into a direct band gap semiconductor. Raman spectroscopy is routinely used for strain measurements. Typical Raman-strain relationships that are used for Ge were defined up to ∼1% strain using phonon deformation potential theory. In this work, we have studied this relationship at higher strain levels by calculating and measuring the Raman spectral shift-strain relations in several different strain configurations. Since differences were shown between the usual phonon deformation potential theory and ab-initio calculations, we highlight the need for experimental calibrations. We have then measured the strain in highly strained Ge micro-bridges and micro-crosses using Raman spectroscopy performed in tandem with synchrotron based micro-diffraction. High values of strain are reported, which enable the calibration of the Raman-strain relations up to 1.8% of in plane strain for the (001) biaxial stress, 4.8% strain along ⟨100⟩, and 3.8% strain along ⟨110⟩. For Ge micro-bridges, oriented along ⟨100⟩, the nonlinearity of the Raman shift-strain relation is confirmed. For the ⟨110⟩ orientation, we have shown that an unexpected non-linearity in the Raman-strain relationship has also to be taken into account for high stress induction. This work demonstrates an unprecedented level of strain measurement for the ⟨110⟩ uniaxial stress and gives a better understanding of the Raman-strain relations in Ge.