Influence of non-hydrostatic pressure on phase transformations in germanium.

Abstract

Semiconducting materials are critical for modern electronic developments, with silicon and germanium being the two most commonly used. Germanium is modified to create many key technologies in modern society. Many of the important properties of germanium are derived from its diamond cubic crystal structure (dc-Ge). On compression to 10 GPa, dc-Ge phase transforms to a metallic $\beta$-Sn-Ge phase. When unloaded new metastable phases with technologically useful properties are formed: r8-Ge, bc8-Ge, hd-Ge, or st12-Ge. The resultant phase is determined by many factors including temperature, presence of shear stresses, and loading rate. While the presence of shear is known to alter the phase transformation pathway of Ge on unloading, little work has been done to examine how large shear forces influence loading behaviour. In this work, the effect of shear is investigated using various pressure media in standard diamond anvil cell compression, and rotation diamond anvil cell to induce large shear during compression. \emph{In situ} Raman spectroscopy and X-ray diffraction are performed during compression and decompression to determine the phase of Ge. Compression of dc-Ge in hydrostatic pressure media such as neon (Ne), potassium chloride (KCl) and sodium chloride (NaCl) resulted in an interesting difference in $\beta$-Sn-Ge transformation pressures. The purely hydrostatic Ne conditions result in dc-Ge transforming into $\beta$-Sn-Ge at 13 GPa, while the less hydrostatic KCl and NaCl transformed at the expected \textapprox10 GPa. It is suggested that only a small amount of shear is required to initiate phase transformation at 10 GPa. However, very hydrostatic compression in Ne requires higher pressure before the phase transformation will occur, due to the lack of these shear stresses. Non-hydrostatic loading conditions were investigated, with bridging of the anvils during initial compression resulting in formation of $\beta$-Sn-Ge and st12-Ge at pressures as low as 1 GPa in multiple locations across the sample. The local pressures were also investigated by measuring the pressure across an entire sample during a third non-hydrostatic compression. Active rotation of one anvil during non-hydrostatic compression resulted in the formation of $\beta$-Sn-Ge at pressures below 4 GPa. Interestingly, decompression from this pressure resulted in $\beta$-Sn-Ge forming back into dc-Ge. Demonstrating that high shear can alter the transformation pathway such that no metastable phases are formed. This work discusses the mechanisms and energetics of the observed transformations. High plastic strain inducing defects is discussed as a viable mechanism for the low pressure dc-Ge to $\beta$-Sn-Ge phase transformation. Further, the energetics of the new model presented are used to explain dc-Ge formation in a-Ge nanoindentation works from literature. The model presented suggests that $\beta$-Sn-Ge is possible to form at pressures as low as 2 GPa using plastic strain. However, $\beta$-Sn-Ge formed this way will not phase transform into a metastable Ge phase unless pressure is increased above a threshold of \textapprox8 GPa. Instead, $\beta$-Sn-Ge will phase transform back to dc-Ge. This has implications for large scale formation of metastable Ge phases. Indicating that high shear alone is unable to significantly lower the energy requirement to obtain metastable Ge phases.