Phase Transitions in Amorphous Germanium under Non-Hydrostatic Compression

Abstract

As the pioneer semiconductor in transistor, germanium (Ge) has been widely applied in information technology for over half a century. Although many phase transitions in Ge have been reported, the complicated phenomena of the phase structures in amorphous Ge under extreme conditions are still not fully investigated. Here, we report the different routes of phase transition in amorphous Ge under different compression conditions utilizing diamond anvil cell (DAC) combined with synchrotron-based X-ray diffraction (XRD) and Raman spectroscopy techniques. Upon non-hydrostatic compression of amorphous Ge, we observed that shear stress facilitates a reversible pressure-induced phase transformation, in contrast to the pressure-quenchable structure under a hydrostatic compression. These findings afford better understanding of the structural behaviors of Ge under extreme conditions, which contributes to more potential applications in the semiconductor field.

1. Introduction

Ge is an essential element in the semiconductor industry, and has attracted numerous experimental and theoretical investigations. The common phase of Ge at ambient conditions is a diamond-cubic structure (two atoms per unit cell), but many more crystalline structures have been presented by applying high pressure. A transformation to the β-Sn structure (tetragonal) occurs at around 11 GPa [1]. At pressures above 12 GPa, a new dense phase with a tetragonal structure (12 atoms per unit cell) appears in ordinary cubic Ge [2]. Another denser phase called ST12 with a space group of $P{4}_3{2}_{1}2(D_4^8$) was discovered by Kasper and Richards [3]. An intermediate orthorhombic phase (space group Imma) forms at ~75 GPa [4]. Under higher pressures, a simple hexagonal phase emerges at 80–90 GPa [5,6,7], then transforms to a Cmca phase and finally changes to an hcp structure at 160–180 GPa [6]. Some metastable crystalline phases have also been studied via indentation approach [3,8]. However, their decompression process does not follow the reversible phase sequence observed under compression. Specific decompression phases have been revealed to strongly rely on the rate of decompression. The metastable ST12 structure [2,9,10], BC8 structure [11,12], and R8 ($R\overline{3}$) structure [12,13] occur at different decompression rates. In addition, hydrostaticity may explain their different phase selection [14].

Studies on amorphous Ge (a-Ge) have also focused on the structural transformations from amorphous to crystalline or another amorphous phase. For example, heated a-Ge changes to a diamond structure, but it transforms into a β-Sn structure under compression [15]. Freund et al. revealed that a-Ge remains in the amorphous phase up to 8.9 GPa [16]. Through X-ray absorption spectroscopy (XAS) measurements, a phase transition from amorphous-to-amorphous at 8 GPa was examined by Principi et al. [17]. A size effect on the phase stability also exists in Ge, which can be used to inhibit the transition to β-Sn structure [18,19]. The superconducting transition temperature (T_c) of the high-density metallic amorphous phase in Ge under high pressure is found to be higher than the β-Sn structured crystalline phase [20]. In general, investigations about high pressure structure of compressed a-Ge were carried out under the hydrostatic conditions. Moreover, there were also some studies on the phase transformation in a-Ge using indentation approaches [3,8,21,22,23], but the non-hydrostatic pressure induced by indenter cannot be achieved as high as the pressure generated in DAC.

In this paper, we compared the phase evolution of amorphous Ge under hydrostatic and non-hydrostatic pressures, respectively, using DAC combined with synchrotron-based XRD and Raman spectroscopy techniques. We found that a-Ge transforms into a β-Sn structure above ~11 GPa under hydrostatic condition, then changes to the ST12 phase upon decompression. The resultant ST12 phase is quenchable to ambient pressure, which is consistent with previous studies [2,9,10]. In contrast, the non-hydrostatic process induced a reversible amorphous-to-amorphous transformation of a-Ge. The origin of this difference will be discussed in terms of the shear stress/strain on the phase transition of amorphous Ge.

2. Experiments

The amorphous Ge samples were fabricated by a magnetron sputtering system. We conducted in situ high-pressure synchrotron XRD measurements at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory, Berkeley, CA, USA and the Advanced Photon Source (APS), Argonne National Laboratory, Chicago, IL, USA) utilizing DACs. At room temperature, the amorphous Ge specimens were non-hydrostatically compressed to ~33 GPa and hydrostatically compressed to ~18 GPa, respectively. Uniaxial compression is employed by a diamond anvil cell. The powder sample was loaded into a laser-drilled stainless-steel gasket hole with a diameter size of ~100 μm and sandwiched between the two opposite anvils and the gasket. The culet sizes of the diamond anvils were 300 μm. No pressure-transmitting-medium (PTM) was used within the DAC chamber to detect the shear effect and obtain a non-hydrostatic environment. Under hydrostatic conditions, ethanol was used as a PTM. A micro-sized ruby ball was utilized as the pressure standard according to its fluorescence R₁–R₂ line shift [24].

The in situ high-pressure angle-dispersive XRD measurements of non-hydrostatic compression were performed at the beamline 12.2.2 of ALS, where the synchrotron monochromatic X-ray beam was focused to ~30 × 30 μm² with a wavelength of 0.4959 Å. The X-ray diffraction patterns were collected at pressure intervals of several GPa by a two-dimension image plate Mar345 detector with a resolution of 100 μm/pixel. Cerium dioxide (CeO₂) powder was employed to calibrate the distance between the sample and the detector. The hydrostatic experiment was performed at the beamline 16-BM-D of APS with a similar setup (except that the X-ray beam size was ~4 × 4 μm² and the X-ray wavelength was 0.3100 Å). For further structural investigations, we also performed high-pressure Raman spectrum measurements (with a laser wavelength of 532 nm) without a PTM to track the phase changes.

3. Results and Discussion

The original phase is predominantly amorphous, which is clearly evidenced by the very broad diffraction rings and the minority crystalline phase detectable in the XRD patterns (Figure 1). The XRD patterns of amorphous Ge under hydrostatic pressures are shown in Figure 2. The bumps at low pressure represent the amorphous information. The weak peak at ~5.3 degrees below 8.6 GPa can be indexed to the (111) plane of the face-centered-cubic (fcc) structure. Above 8.6 GPa, the fcc phase disappears and three clear peaks (a, b, and c) emerge on further compression to ~11.3 GPa, which can be well-fitted to the β-Sn phase of Ge [1]. As the pressure increases, these peaks shift to higher Bragg angles due to the shrinkage of the lattice constants. During decompression, the β-Sn phase vanishes, and new peaks emerge (d, e, f, and g), which can be indexed with the ST12 structure (a representative Le Bail fitting is shown in Figure 3). Thus, the β-Sn phase is pressure-unquenchable. After decompressing to ambient pressure, the ST12 structure of Ge can be retained. Therefore, under hydrostatic condition, the amorphous Ge first transforms to the β-Sn phase by compression, and is then pressure-quenched to the ST12 phase. Previous works suggested that a slow decompression rate facilitates the ST12 structure [2,25]. In particular, the bulk-sized ST12-Ge (~2 mm in diameter and length) was synthesized after slow decompression from 14 GPa by a multi anvil press [10].

During hydrostatic compression/decompression, the shear stresses are relatively negligible. To better understand the influence of the non-hydrostatic pressure environment (shear stress) on the phase transition of amorphous Ge, we carried out a contrasting experiment under similar conditions but with no PTM. The transmission electron microscope (TEM) characterization of the raw amorphous Ge can be seen in Figure 4. The pressure dependent evolution of the diffraction patterns is shown in Figure 5. There are no sharp peaks and the XRD pattern is dominated by two broad peaks (bumps) in the original sample at ambient pressure, indicating the amorphous structure. With increasing pressure, these bumps shift to higher Bragg angles. From 12.9 to 17.8 GPa, the broad peaks undergo an abrupt change, which can be correlated to the pressure-induced low-density-amorphous (LDA) to high-density-amorphous (HDA) phase transformation [1]. The phase transformation way is obviously different from that in hydrostatic compression. The structure of Ge remains amorphous up to 12.9 GPa, which is unlike previous studies under hydrostatic compressions [16,17]. The higher critical transition pressure in this work may come from the shear stress provided by non-hydrostatic compression. When decompressing to around 5 GPa, this HDA phase disappears, while the original amorphous phase was recovered. Therefore, this LDA-HDA transition is reversible under non-hydrostatic compression.

Pressure, as an effective approach, is usually utilized to adjust and control the performance of materials. The pressure dependent phase stability of material is commonly detected by hydrostatic compression [26,27], i.e., using a PTM to maintain the isotropic pressure in the sample chamber. However, materials may undergo different phase transitions, depending on the pressure environment [28,29]. Under non-hydrostatic compression, a pressure gradient exists in the samples, resulting in large shear stress. Caspersen et al. presented a multiscale model to simulate the pressure-driven martensitic phase transformation (from bcc to hcp), revealing the significant effect of shear on this transition [30]. Therefore, new potential phases and novel properties may be discovered by non-hydrostatic compression. In this study, the observation of different pathways of phase transition in amorphous Ge under different pressure environments mainly results from whether the shear stress in the sample was large or not. The pressure difference from the center to the edge of the sample chamber can be as large as ~10 GPa under external pressure up to 30 GPa without a PTM [31]. Therefore, the large pressure gradient inside the sample chamber induces sufficient shear stress to actuate different structural behaviors from those during hydrostatic compression.

Besides the high-pressure XRD measurements, high-pressure Raman spectrum measurements, with a fixed time of 10 s and three time exposures, were performed using an inVia Renishaw Raman spectrometer system with a 20× magnification objective. A laser wavelength of 532 nm and a grating of 2400 lines·mm⁻¹ provided a spectral resolution better than 1 cm⁻¹. A laser power inferior to 10 mW was used to avoid sample heating. All the vibrational modes of the a-Ge covalent bond may have Raman activity due to the absence of lattice symmetry. The bond length and bond angle between one a-Ge atom and its four nearest atoms are usually different, resulting in the wide distribution of the density of vibrational state and asymmetrical Raman peaks (Figure 6). A peak at ~280 cm⁻¹ is observed at low pressure, which corresponds to the transverse optic phonon mode (TO mode) [32]. This TO mode shifts to a higher wavenumber upon compression with the peak broadening and peak weakening, indicating that the average bond length shrinks and bond strength increases. The low-pressure Raman peak disappears above 14.1 GPa where a broader peak occurs, illustrating an LDA-had phase transition here (which corresponds to the XRD results in Figure 5). The Raman peak of HDA phase also shifts to higher wavenumber under further compression to 30 GPa. Under decompression, the Raman peak of HDA phase appears red shift and its strength weakens until 4.5 GPa, then the TO mode of LDA phase appears again, which means the original amorphous phase comes back and shows a hysteretic nature. No β-Sn phase forms under non-compression. This observed LDA-HDA phase transition by Raman spectra supports the XRD results (Figure 5).

To better understand the process of phase transition of a-Ge, we plotted the pressure-dependent Raman shift and Full Width at Half Maximum (FWHM). Figure 7 shows that the TO mode of LDA phase changes into another Raman mode at 14.1 GPa, with a formation of an HDA phase. The wavenumber of HDA phase decreases, meaning the average bond length is longer than that in LDA phase, i.e., the average distance (the center atom to its all nearest atoms) between a-Ge atoms increases. The average vibration energy is reduced because of increasing atomic distance, which is consistent with the previous XAS experiments [1]. Upon decompression, this HDA phase can be retained to 4.5 GPa, which is much lower than the transition pressure under compression process. The HDA phase of Ge is relatively stable under lower pressure, but cannot be quenched to the ambient pressure. The hysteresis curve of LDA-HDA Raman shift presents the typical characteristics of the first order phase transition, i.e., significant volume and density mutations. The Raman shift of high pressure recovered structure is comparable to the original value within the acceptable range of error, reflecting the same structure. The value of the FWHM is relevant to the monochromatic degree of vibrational frequency, and reflects the disorder degree of amorphous sample. The decreasing FWHM represents the increasing crystalline ordering. Under increasing pressure, an obvious turning point of FWHM curve occurs in amorphous Ge at ~14.1 GPa, indicating a relatively enhanced ordered structure is formed, i.e., the disorder degree of a-Ge is decreasing. Raman shift and FWHM have the same changing trend. Both the XRD and Raman spectra results confirmed that amorphous Ge undergoes a reversible pressure-induced LDA-HDA phase transformation under non-hydrostatic compression.

Phase transitions under non-hydrostatic pressure have been extensively investigated using radial DAC XRD techniques [33,34]. Orientation variant selection is reported to reveal the mechanism of the cubic-to-orthorhombic martensitic transformation of Mn₂O₃, which is attributed to structural distortions under shear stress imposed by non-hydrostatic compression [33]. Another martensitic mechanism for the zircon-scheelite transformation in zircon-type gadolinium vanadate (GdVO₄) was also studied by the texturing analysis, including the deformation texture and phase transition texture caused by non-hydrostatic pressure [34]. These significant observations help us to better understand the rheology in geoscience and the displacive phase transformation. Coppari et al. [1] found that the transition pressure of LDA-HDA is 7.9 GPa, and the β-Sn phase is formed above 10.6 GPa with the disorder degree (${\sigma }^2$) increasing. However, we observed that no β-Sn phase is formed, and the transition pressure of LDA-HDA is ~14.1 GPa under non-hydrostatic compression. The main discrepancies come from non-hydrostatic degree (no PTM > NaCl PTM), i.e., giant shear stresses induce that the HDA phase is formed under higher pressure and remains at ~30 GPa.

Many mechanical, transport, and electromagnetic properties of materials are associated with a structure change [35,36,37,38]. Shear stresses and shear strains play essential roles in certain phase transition, especially in the displacive phase change, such as amorphous Ge in this study. Under non-hydrostatic pressure, the structure is easily distorted, after which atomic displacement is induced. The phase transition responds more sensitively to the non-hydrostatic pressure, which provides both pressure and shear stress/strain simultaneously. When covalent bonds in the LDA phase of a-Ge are shortened to a certain value by compression, they have to start to transform into metal bonds and increase the coordination number [1], but other regions may still maintain a covalent bond structure due to the pressure gradient in the sample chamber. However, with more and more metal bonds forming, atoms are easier to move and rearrange under pressure to reduce energy and disorder, and finally, the system reaches an amorphous phase with relatively stable energy, which is the metastable phase of HDA. With the pressure further increasing, the HDA phase gradually becomes orderly and changes into crystalline β-Sn structure after reaching a certain degree of order (such as V-side in Coppari’s experiment). However, the giant shear stress under our experiment greatly hinders the ordering of the HDA phase, resulting in no β-Sn structure forming.

The findings of different structural transition routes in amorphous Ge under non-hydrostatic pressure also enrich the potential applications of Ge. Interestingly, DAC without a PTM is an effective approach to generate ultrahigh shear stress [31,38]. It should be emphasized that non-hydrostatic compression can be applied to explore more structural stability and might obtain the surprising phenomena.

4. Conclusions

In summary, we observed a new pressure-induced LDA-HDA phase transition in Ge under a non-hydrostatic pressure environment by high-pressure XRD and Raman spectrum techniques, in contrast to the known a-Ge-to-β-Sn-Ge structural change under hydrostatic compression in previous work. Large shear stress (strain) induced by non-hydrostatic compression provides the driven force to form this metastable HDA phase. More attention should be paid to the shear stress, which is instructive and meaningful to many other physical properties, such as superconductivity. Our findings extend the phase behaviors in Ge under extreme conditions and contribute to the potential applications of Ge in electronic industries, such as memory materials. Some metastable transition phases with excellent properties are hopeful to exist in wider conditions, even quenched to environmental conditions by taking advantages of shear, such as highly pure h-diamond (a metastable phase in carbon)