Edinburgh Research Explorer Dense SixGe1-x (0 <x <1) Materials Landscape Using Extreme Conditions and Precession Electron Diffraction

High pressure and temperature experiments on Ge and Si mixtures to 17 GPa and 1500 K allow us to obtain extended Ge-Si solid solutions with cubic ( 3 Ia ) and tetragonal ( P 4 3 2 1 2) crystal symmetries at ambient pressure. The cubic modification can be obtained with up to 77 atomic percent Ge, and the tetragonal modification for Ge concentrations above that. Together with Hume-Rothery criteria, melting point convergence is employed here as a favoured attribute for solid solution formation. These compositionally tunable alloys are of growing interest for advanced transport and optoelectronic applications. Furthermore, the work illustrates the significance of employing precession electron diffraction for mapping new materials landscapes resulting from tailored high pressure and temperature syntheses.


Introduction
While cubic diamond-structured silicon is the single most important material in the semiconductor industry, it has an indirect band gap 1 and a fixed lattice constant, constraining it from efficient light emitting applications including most prominently photovoltaics and laser devices. This constraint remains present for its associated cubic diamond-structured pure germanium 1 and silicon-germanium alloy 2 counterparts because they also retain fundamental indirect band-gaps. There is a strong drive however to extend the functionality of (Si, Ge)-based technology from microelectronics into optoelectronics. This has led to investigation of a number of avenues, all based on processing of cubic diamond-structured (Si, Ge), to address this constraint. 3,4 These avenues include doping silicon with erbium to serve as a lasing centre 5 , etching silicon with hydrogen fluoride to create pores resulting in luminescence due to quantum confinement effects 6 , inducing tensile strain coupled with n-type doping in germanium to access direct-gap emission in the indirect gap material 7 and hybrid approaches 8 interfacing silicon with other light emitting chemical compounds.
Our approach is different. Rather than process the existing cubic diamond structure that does not intrinsically exhibit targeted properties, transform it instead to a different crystal symmetry that does.
That is, develop a new Si 1-x Ge x materials landscape by exploring synthesis of new structures which intrinsically contain tunable properties including fundamental direct band-gaps. To evaluate optimal pressure and temperature regions for novel solid solution formation, we examine the phase relations of the two endmembers, Si and Ge. 9,10 Si and Ge are both semiconductors with the cubic diamond structure up to about 10 and 12 GPa respectively. 11 Hence synthesis within this pressure regime will only allow us to obtain the known cubic diamond structured semiconducting SiGe equilibrium modification. 12 Above about 12 GPa however, the endmembers are both metallic, having transformed to the β-Sn modification. 11,13 Ge retains this modification up to 75  to metallic GeII (β-Sn structure (I4 1 /amd)) above 9 GPa. This structure is retained to 45 GPa.
Semiconducting SiI (cubic diamond structure m Fd 3 ) transforms to metallic SiII (β-Sn structure (I4 1 /amd)) above 11 GPa. Above 13 GPa, this phase transforms to an orthorhombic (Imma) modification, to a hexagonal modification (P 6 /mmm) above 15 GPa, another orthorhombic phase (Cmca) above 38 GPa, and a further hexagonal modification (P6 3 /mmc) above 42 GPa. This is not to say that at higher pressures synthesis of SiGe is not merited. While, the crystal structures are indeed no longer the same, the atomic radii ratios are still within about 6% of each other and the electronic properties remain compatible (Figures 1, 2). Furthermore, the melting points are virtually identical at 17 GPa which serves as an additional barrier against segregation ( Figure 3). Contrastingly 29 , at ambient pressure, despite the four criteria for solid solution being formally fulfilled, the more than 500 K melting point difference between Si and Ge, leads in actuality, to profound segregation effects.
This makes extended homogeneous solid solution formation, extremely difficult, 30 especially on the germanium-rich side, due to the larger segregation coefficients for germanium-rich compositions. 31,32 The impetus for synthesis, and promise of obtaining technologically important, tunable novel solid solutions is reinforced by a host of recent experiments and calculations on preparation, stability and optoelectronic properties of Si and Ge phases. [33][34][35][36][37][38][39][40][41][42] Pure Ge obtained at ambient pressure from above 10-12 GPa is tetragonal (P4 3 2 1 2) 43 and calculated to exhibit a direct-band gap. 44 Figure 2. Ge-Si atomic radii ratio (% difference) pressure dependence from ambient to 38 GPa. Points a through e reveal respectively the ratios between GeI ( m Fd 3 ) and SiI, GeII (I4 1 /amd) and SiI ( m Fd 3 ) , GeII and SiII (I4 1 /amd), GeII and SiXI (Imma) and GeII and SiV (P 6 /mmm). 19,[21][22][23][24][25] The dashed line depicts the Hume-Rothery tolerance atomic radius ratio boundary below which solid solution formation is favored. Hence a Ge-rich tetragonal GeSi solid solution should exhibit a tunable direct band-gap. 45 Furthermore, Si with the P4 3 2 1 2 tetragonal modification could upon doping exhibit a higher superconducting temperature than those of the other Si-modifications. 46 While Si does not form this tetragonal phase, targeted solid solution with Ge, which does, could then lead to a bulk Si-based tetragonal phase with elevated superconducting T c upon doping. Additionally, pure Si obtained at ambient conditions from above 12-13 GPa is cubic ( 3 Ia ) and is a semi-metal. 43 stage allowed us to record multiple zone-axes patterns from single crystals. The CM30 is also equipped with a Nanomegas "Spinning Star" precession system and a Noran EDX detector for local chemical analysis. The camera length for TEM was calibrated using pure silicon. Semi-quantitative chemical analysis was carried out without standards for the determination of the Cliff-Lorimer factors and without measurement of local thin foil thickness. Precession electron diffraction (PED) measurements were performed in microdiffraction mode, i.e. with a nearly parallel incident beam focused on the specimen with a spot size in the range of 10 to 50 nm. The precession semi-angle of 2° was set to record PED patterns. The maximum precession angle of about 3° was systematically used in order to further identify the kinematically forbidden reflections. [56][57][58] PED performed at a high precession semi-angle of ≥ 2° in particular, significantly reduces the overall dynamical effects involved in an electron diffraction pattern, which in turn allows for a drastically improved measurement of kinematical intensities of diffracted reflections from the single crystallites. This facilitates differentiation even between closely related diffraction patterns and concomitant accurate crystallographic indexing of the new phases. [56][57][58][59][60][61][62][63] Supporting angle dispersive X-ray diffraction measurements were performed at the ID11 beamline of the European Synchrotron Radiation Facility. A monochromatic X-ray beam (λ = 0.31849 Å) was focused to 10 µm x 7 µm using a tunable X-ray focusing apparatus (transfocator) containing twenty beryllium lenses and 254 aluminium lenses. 64  degree rotation applied, the spatial resolution with a small beam spot sufficed, in avoiding copper diffraction peaks. Use of the TEM grid, means that one can formally examine the same sample as was examined with TEM, which is particularly important for obtaining multifaceted complementary structural, chemical and morphological information, particularly from precious material. The zone-axis electron diffraction patterns were interpreted using the software "Electron Diffraction" version 7.01 by considering the kinematical approximation. 65 Note that in all the simulated zone-axis diffraction patterns shown hereafter an empty circle represents a kinematically forbidden reflection and the size of a filled circle is proportional to the intensity of the diffracted reflection. The X-ray diffraction patterns were circularly integrated using Fit2D 66 and the one-dimensional patterns were fitted and indexed using the Topas 3.0 software. 67 The chemical signatures taken from the samples at ID11 in-parallel with the diffraction, was performed using the program PyMCA. 68  Ge-Si experimental zone-axis PED pattern (Figure 5a) is compared with its corresponding simulated 3 Ia (Figure 5b) and its site ordered 3 Pa symmetry analogue (Figure 5c), revealing that our Ia space group measured without and with precession and a (b) simulated [111] zone-axis pattern.

PED
zone-axis diffraction patterns of the Ge-Si crystallites obtained with P4 3 2 1 2 symmetry (Figures 7a, c) together with their simulated diffraction patterns (Figures 7b, d) revealing the excellent match with the  The only other highly crystalline symmetry detected from a few crystallites after release from 12 GPa, was the ambient pressure cubic diamond symmetry likely because this pressure may be close to the transition pressure between SiGe cubic diamond and the β-Sn modification. [70][71][72][73][74][75] Disordered structures with hexagonal symmetry, likely with varying polytypic characteristics, for a range of Ge-Si compositions were however also detected here from all pressures. These were more prevalent as the Ge content increased. Indeed their enhanced presence in the reaction product matrix for Ge-richer compositions has hindered us so far from obtaining an accompanying X-ray diffraction pattern of Ge-Si with P4 3 2 1 2 symmetry and will be the focus of a further report. Angle dispersive X-ray diffraction measurements on the other hand, from binary 3 Ia Si-richer compositions were obtained. An X-ray diffraction pattern from a sample extracted from a pellet which has a bulk 20:80 Ge:Si composition, based on chemical analysis using scanning electron microscopy, is shown in Figure 10.

Discussion
We provide here an explanation for the composition-structure relationship measured and why in particular the binary Ge-Si cubic 3 Ia phase is obtained for a larger range of Ge-Si compositions than the P4 3 2 1 2 phase is. With respect to compression of Ge and Si (Figure 1), differences upon release from 17 GPa are that, GeII transforms to P4 3 2 1 2 below about 9 GPa and is retained at 1 atm, and SiII transforms to an 3 R phase below about 9 GPa, before 3 Ia is obtained below 2 GPa and retained at 1 atm. 10,43 The Si 3 Ia and Ge P4 3 2 1 2 phases are stable indefinitely at ambient conditions. are respectively ρ = 2.998 g/cm 3 and ρ = 3.938 g/cm 3 . 12 These crystal structures, rather than the cubic diamond structure, are obtained, because they are kinetically accessible from denser phases upon release. 76 Indeed, even intermediate heating experiments on Si 3 Ia result in a hexagonal (P6 3 mc 2H) rather than the diamond phase because the bond reconstruction required for the latter is too severe. 43,47 The internal energies of the P4 3  Another reason that the 3 Ia symmetry may be compositionally more favoured, even for same group members, is because of an energetic cost to having same element nearest neighbours. 10,69 While group IV binaries with P4 3 2 1 2 79 and 3 Ia symmetries ( Figure 5) both adopt structures without long range siteordering, only the 3 Ia symmetry has an equivalent site-ordered 3 Pa description 80 which allows nearest neighbours to be of the second element. P4 3 2 1 2 does not have this option, because unlike 3 Ia , it contains rings with odd numbers of atoms. 10,69,81 Hence local level site ordering 10 to alleviate any residual strain is only favored for the 3 Ia symmetry. These considerations provide an explanation for why, within this newly established SiGe materials landscape, the 3 Ia symmetry spans a wider range of compositions than the P4 3 2 1 2 symmetry does.

Conclusions
The combination of high pressures and temperatures has allowed us to form a materials landscape for Ge x Si 1-x 0<x<1 containing tetragonal P4 3 2 1 2 and cubic 3 Ia symmetries, with projected electronic character ranging from semiconducting to semi-metallic, of optoelectronic, transport and thermoelectric interest. 39,46 Further, Ge-Si alloying, in addition to providing tunability of properties can also contribute to greater structural stability. For example, Ge alloys with tetragonal symmetry exhibit enhanced cycling performance as battery anodes. 40 The work here also includes the first participation of Si in a P4 3

Table of contents synopsis
Pressure gently tunes to radically transforms matter, making it formidable in developing targeted materials and materials landscapes. Crystals may initially be small and sparsely populated within complex agglomerates. X-ray and electron diffraction offer complementing angular and spatial resolution. Precession improves electron diffraction intensities, strengthening single-crystal assignment.
We develop a dense SiGe landscape by heating Si and Ge at pressures where they undergo phase transitions, transform to metals and their melting points converge. Distinctive precession electron diffraction patterns are shown above.