Nanoscale membranes have emerged as a new class of vertical nanostructures that enable the integration of horizontal networks of III-V nanowires on a chip. In order to generalize this method to the whole family of III-Vs, progress in the understanding of the membrane formation by selective area epitaxy in oxide slits is needed, in particular for different slit orientations. Here, it is demonstrated that the shape is primarily driven by the growth kinetics rather than determined by surface energy minimization as commonly occurs for faceted nanostructures. To this end, a phase-field model simulating the shape evolution during growth is devised, in agreement with the experimental findings for any slit orientations, even when the vertical membranes turn into multi-faceted fins. This makes possible to reverse-engineer the facet-dependent incorporation times, which were so far unknown, even for common low-index facets. The compelling reproduction of the experimental morphologies demonstrates the reliability of the growth model and offers a general method to determine microscopic kinetic parameters governing out-of-equilibrium three-dimensional growth.

Strain engineering in Sn-rich group IV semiconductors is a key enabling factor to exploit the direct band gap at mid-infrared wavelengths. Here, we investigate the effect of strain on the growth of GeSn alloys in a Ge/GeSn core/shell nanowire geometry. Incorporation of Sn content in the 10-20 at.% range is achieved with Ge core diameters ranging from 50nm to 100nm. While the smaller cores lead to the formation of a regular and homogeneous GeSn shell, larger cores lead to the formation of multi-faceted sidewalls and broadened segregation domains, inducing the nucleation of defects. This behavior is rationalized in terms of the different residual strain, as obtained by realistic finite element method simulations. The extended analysis of the strain relaxation as a function of core and shell sizes, in comparison with the conventional planar geometry, provides a deeper understanding of the role of strain in the epitaxy of metastable GeSn semiconductors.Strained semiconductor heterostructures provide a rich playground for investigating the epitaxy of lattice-mismatched materials. 1 In the last decades SiGe alloys grown with a graded composition on Si were extensively studied to relieve strain by nucleating misfit dislocations in the buffer layers. [2][3][4] Recently, direct band gap and metastable GeSn alloys gained tremendous interest as a 2 platform for Si-compatible photonics operating at mid-infrared wavelengths. [5][6][7][8][9] In unstrained GeSn the direct band gap is achieved at Sn contents higher than 10at.%, hence well above the ~1at.% equilibrium solubility of Sn in Ge. The incorporation of Sn is highly sensitive to the inplane strain that the GeSn layer experiences during growth. 10,11 Due to the large lattice mismatch between Ge and α-Sn (>10%), the growth of GeSn layers has been developed on high-quality Gevirtual substrates (Ge-VS) on Si. 12,13 Partial strain relaxation can induce a compositional grading in GeSn, 8,14-16 eventually leading to segregation and precipitation of Sn, compromising material quality. [17][18][19] In GeSn layers grown on Ge-VS, the compressive strain is reduced in a multi-layer buffered heterostructure grown with different Sn contents by controlling the growth temperature 20,21 and precursors flows. 22 The high amount of strain induces nucleation of dislocations in the low (7-11at.%) Sn content buffer layers, 11,23 and the resulting uniform (plastic) strain relaxation enhances the Sn incorporation above 16at.% in the GeSn layers grown on top. 8,11,14,19 One-dimensional nanowires(NWs) provide additional degrees of freedom in tuning the effect of strain in the growth of lattice-mismatch heterostructures 24,25 when using a core/shell NW geometry. 26 The shell displays an increasing strain relaxation with thickness provided by the free surfaces at the sidewalls, while the elastic compliance of the NW core allows for enhanced strain relaxation in the shell, accommodating the lattice mismatch of the system and avoiding bending. 26,27 Recent studies on Ge/GeSn core/shell NWs 15,16,28,29...

We address the role of non-uniform composition, as measured by energy-dispersive x-ray spectroscopy, in the elastic properties of core/shell nanowires for the Ge/GeSn system. In particular, by finite element method simulations and transmission electron diffraction measurements, we estimate the residual misfit strain when a radial gradient in Sn and a Ge segregation at the nanowire facet edges are present. An elastic stiffening of the structure with respect to the uniform one is concluded, particularly for the axial strain component. More importantly, refined predictions linking the strain and the Sn percentage at the nanowire facets enable us to quantitatively determine the maximum compressive strain value allowing for additional Sn incorporation into a GeSn alloy. The progressive incorporation with increasing shell thickness, under constant growth conditions, is specifically induced by the nanowire configuration, where a larger elastic relaxation of the misfit strain takes place.

Nanowires have emerged as a promising platform for the development of novel and high-quality heterostructures at large lattice misfit, inaccessible in a thin film configuration. However, despite core-shell nanowires allowing a very efficient elastic release of the misfit strain, the growth of highly uniform arrays of nanowire heterostructures still represents a challenge, for example due to a strain-induced bending morphology. Here we investigate the bending of wurtzite GaP/In Ga P core-shell nanowires using transmission electron microscopy and energy dispersive x-ray spectroscopy, both in terms of geometric and compositional asymmetry with respect to the longitudinal axis. We compare the experimental data with finite element method simulations in three dimensions, showing that both asymmetries are responsible for the actual bending. Such findings are valid for all lattice-mismatched core-shell nanowire heterostructures based on ternary alloys. Our work provides a quantitative understanding of the bending effect in general while also suggesting a strategy to minimise it.

The faceting of a growing crystal is theoretically investigated by a continuum model including the incorporation kinetics of adatoms. This allows us for predictions beyond a simple Wulff analysis which typically refers to faceted morphologies in terms of the equilibrium crystal shape for crystals with an anisotropic surface-energy, or to steady-state kinetic shape when the crystals grow with orientation-dependent velocities. A phase-field approach is implemented in order to account simultaneously for these contributions in two-and three dimensions reproducing realistic kinetic pathways for the morphological evolution of crystal surfaces during growth. After a systematic characterization of the faceting determined by orientation-dependent incorporation times, several different crystal morphologies are found by tuning the relative weights of thermodynamic and kinetic driving forces. Applications to realistic systems are finally reported showing the versatility of the proposed approach and demonstrating the key role played by the incorporation dynamics in out-of-equilibrium growth processes.