Unusual Deformation and Fracture in Gallium Telluride Multilayers

The deformation and fracture mechanism of two-dimensional (2D) materials are still unclear and not thoroughly investigated. Given this, mechanical properties and mechanisms are explored on example of gallium telluride (GaTe), a promising 2D semiconductor with an ultrahigh photoresponsivity and a high flexibility. Hereby, the mechanical properties of both substrate-supported and suspended GaTe multilayers were investigated through Berkovich-tip nanoindentation instead of the commonly used AFM-based nanoindentation method. An unusual concurrence of multiple pop-in and load-drop events in loading curve was observed. Theoretical calculations unveiled this concurrence originating from the interlayer-sliding mediated layers-by-layers fracture mechanism in GaTe multilayers. The van der Waals force dominated interlayer interactions between GaTe and substrates was revealed much stronger than that between GaTe interlayers, resulting in the easy sliding and fracture of multilayers within GaTe. This work introduces new insights into the deformation and fracture of GaTe and other 2D materials in flexible electronics applications.


Materials and samples preparation
The single-crystal bulk GaTe ingot was grown by the modified vertical Bridgeman method, with the help of an accelerated crucible rotation technique to improve the mass and heat transport and smoothen the solid-liquid interface during the crystal growth. High purity powders of gallium (99.99%, Alfa Aesar) and telluride (99.99%, Alfa Aesar) with chemical stoichiometry were mixed in a rocking synthesize furnace and sealed in an evacuated quartz ampoule (<10 -4 torr vacuums). GaTe flakes were mechanically exfoliated onto 300 nm SiO2/Si or PDMS substrates from a single-crystal bulk GaTe wafer cut from the above GaTe ingot.

GaTe multilayers transfer and membrane slits fabrication
To characterize the intrinsic in-plane mechanical properties of both supported and suspended 2D GaTe, free-standing GaTe multilayers were transferred onto SiO2/Si substrates and a series of membrane slits, which were patterned and fabricated onto SiO2/Si substrates via standard CMOS processing, to form supported and suspended samples, respectively (Table S1). After being exfoliated from the bulk using Scotch tape, the GaTe multilayers including tape were attached to a PDMS substrate where thinner GaTe multilayers can be further exfoliated from the tape.
GaTe multilayers on PDMS were characterized using micro-Raman spectroscopy at a laser excitation wavelength of 488 nm; no detectable glue residue on the GaTe multilayers was also confirmed using this method. A similar pick-up dry transfer technique 1-3 was developed to transfer the target GaTe multilayers onto designated membrane slits fabricated on the SiO2/Si substrates. The rectangular geometry of these slits was 3-6 m in width, 20-40 m in length, and these slits were etched through the whole 300-nm-thick SiO2 films which were thermal oxidized onto the surface of Si substrates.

Materials properties characterization
To investigate and understand the mechanical properties of 2D GaTe multilayers, nanoindentation tests were performed using a Hysitron TI 980 Nanoindenter on both supported and suspended GaTe multilayers. A series of indents with different indent depths controlled under the displacement mode were generated using a Berkovich indenter with a 65.3 o tip angle. To explore the morphology evolution and visualize the crack details of the indents that were induced by different forces, high-resolution field-emission SEM (Quanta200 FEG, FEI) images were taken. Detailed sample S4 thickness, indentation depths and the tomography of indents were obtained through AFM (Bruker Dimension Edge) using the tapping mode. Residual stress and its distribution after nanoindentation were characterized through the shifts of Raman modes (measured by Renishaw InVia Raman spectrometer at a laser excitation wavelength of 488 nm, using a 100×0.9NA objective with a spot radius of 0.44±0.02 m), calibrated with the Si Raman line. A reference Raman spectrum of GaTe flakes was measured prior to nanoindentation in the indent area which was later used for the evaluation of residual stress. Raman spectra within the indent region were analyzed for indications of possible phase transformation.   Figure 4 in the main text). Cubic and stishovite crystal structure were adopted for the diamond indenter and the SiO2, respectively. The GaTe structure was obtained from first-principles calculations, in which the bond length dGa-Te and dGa-Ga is 2.70 Å and 2.46 Å, 5 respectively. In MD simulations, 5-layered and 10-layered GaTe nanosheets were considered. The spacing of adjacent GaTe layers is 9.2 Å, S5 while the distance between the lowermost GaTe layer and the SiO2 is 5 Å. These values were obtained after a sufficiently long relaxation achieving a convergence in the simulation. The initial distance between the indenter and the uppermost GaTe layer was set as 10 Å to avoid vdW interactions. During the whole simulation process, both diamond indenter and SiO2 layer were regarded as a rigid body by setting the velocity of their atoms as zero. The force interactions between atoms in monolayer GaTe were described by the Stillinger-Weber potential using parameters from Jiang et al. 6 The C-C interactions in the indenter were described by the adaptive intermolecular reactive empirical bond order potential, 7 while the interactions between atoms in SiO2 were described by the Tersoff potential 8 using parameters from Munetoh et al. 9 The vdW interactions between adjacent GaTe layers (Ga and Te atoms), the indenter and GaTe multilayers (Ga, Te and C atoms), the GaTe multilayers and substrate (Ga, Te, Si and O atoms) were described by the 12-6 Lennard-Jones (LJ) potential. Detailed parameters used in the LJ potential are listed in Table S2. Periodic boundary conditions were applied along in-plane x and y directions, while free boundary condition was used along the z direction. Before loading, the

MD simulations conducted in this work
GaTe multilayer system was relaxed at 1K in the NVT ensemble (constant atom number, volume and temperature) for 100 ps to obtain an equilibrium structure with a stable energy. After sufficient relaxation, the indenter moves down at a velocity of 0.05 Å/ps during the loading process until achieving the specified displacement or load; then, the indenter moves backwards to the initial position with the same velocity.
Note that the force obtained was calculated as the total force on the centroid of the indenter. Table S2. Lennard-Jones (LJ) potential parameters for the nanoindentation MD simulations. Arithmetic mix rule is employed to model the LJ potential between different elements.
Atom-Atom C-C [10] Ga-Ga [11] Te-Te [12] Si-Si [13] O-O [10]   Type-III, which with almost the same layer thickness (see Table 1, only one layer   Figure S2(a) and (b), respectively. In sample-4, three almost symmetric pile-ups around the pyramidal imprint were observed accompanied by three similar cracks with lengths of ~1.5m. In sample-5, the pile-ups are more pronounced but there is no obvious formation of cracks. It should also be noted that only in sample-5, some weak 'darker' fractural features of materials as those in Figure  3-4 were observed. The mapping area has a step resolution of 0.5m for all samples. The stress is calculated from the Raman shifts to the reference spectrum based on the stress-sensitive out-of-plane Ag mode (210cm -1 ) using an experimentally obtained stress coefficient of 2.59cm -1 /GPa. The black line is along one of the axis of the pyramidal indent area and the black dots are selected for Raman spectra comparison (see Figure S6). Figure S4(b, d) shows an average residual stress of about 0.18±0.12GPa (tensile) and 0.20±0.13GPa (tensile) was created in sample-4 and sample-5 after the nanoindentation, respectively (the error bar represents the homogeneity of stress distribution). It is also shown that fracture tends to result in larger tensile residue stress in the indent area, while compressive stress tends to form around the indent to balance the tensile stress generated on the indent. A larger inhomogeneous stress was formed around the edges of the indent imprint in sample-5 (see Figure S4d), similar to the condition of 300 nm depth indent sample (sample-3, see Figure 2i in the main text) which has the same thickness; this is mainly due to asymmetric or un-sharp crack S10 prolongations formed with the indent fracture thus resulting in an asymmetric stress accumulation. Figure S5. Micro-Raman spectrum evolution along the black line and selected points (as marked in Figure 2 in the main text) after: (a) 80 nm depth indentation (sample-1, corresponding to Figure 2g in the main text), and (b) 250 nm (sample-2, corresponding to Figure 2h in the main text); inset is the detailed Raman spectrum comparison between the indent-center and non-indent area. No significant amorphous-like broadened peaks appeared in the Raman spectrum, while the new peaks around 90 and 99cm -1 observed in the near-indent-center region (as shown in insets) which are similar to those features discussed in the main text, likely the consequence from a local amorphization like structure transformations. Figure S6. Micro-Raman spectrum evolution along the black line and selected points marked in Figure S4 for (a) sample-4, and (b) sample-5. Inset in (b) is the detailed Raman spectra comparison of the near-center region and the non-indent region; no significant materials changes happened, while an amorphous like Raman spectrum similar to that of Figure 3 and Figure S5b appeared, indicating a local amorphization like structure transformation was similarly induced. Figure S7. AFM profile measurements on the nanoindentation pit of the 300nm depth (sample-3) indentation sample, with the indent depth, pile up depth and sink in depth labeled, respectively. An indent depth of ~235.5nm was left after the nanoindentation although a 300nm displacement was loaded, and a maximum pile-up of ~274.2nm was resulted while the opposite crack corner presented a slight sink-in depth of ~6.8nm. From the AFM topography, by plotting the depth profile across the indent region, a permanent concave imprint of ~50nm in depth was left after the nanoindentation, as illustrated by the AFM curve in the inset of Figure S8a and the AFM phase images in Figure S8b, indicating a permanent plastic or unrecoverable deformation. Notably, the asymmetric depth profile may be due to the indentation position not at the center of the rectangular slits (located at ~4.5m/6m position of the slits). No observable difference can be seen in the Raman spectra, implying an unchanged sample quality even after nanoindentation of an available maximum depth (250nm in this work). S14 Figure S9. Details of the generated fractures and interlayer sliding along the in-plane x-direction at various depth of loading and unloading process for (a) '10L, no defects' samples and (b) '10L, defects' samples obtained in MD simulations.