1：Experimental Design and Method Selection:

The study combines temperature-variant nanoindentation with atomic force microscope (AFM) for biaxial deformation and first-principles density functional theory (DFT) calculations to analyze elastic properties and fracture behaviors. The nonlinear-membrane model is used to fit force-indentation depth curves, and equivalent modulus is calculated for anisotropic materials.

2：Sample Selection and Data Sources:

MoTe2 thin flakes were prepared by mechanical exfoliation from bulk crystals onto SiO2/Si substrates with pre-patterned circular holes. Samples included 2H, 1T’, and Td phases, with Td obtained by cooling 1T’ samples below 250 K. Data from nanoindentation, Raman spectroscopy, SHG, and TEM were used.

3：List of Experimental Equipment and Materials:

AFM (Bruker Multimode 8), TEM (FEI Tecnai G2 F20), SEM (Jeol 7000), Raman spectrometer (Horiba HR800), cooling stage (Multimode cooler), high-purity Mo foil (99.95%, Alfa Aesar), Te ingot (99.99%, Alfa Aesar), TeCl4 powder (99%, Aladdin), UV photolithography and dry etching for substrate preparation.

4：95%, Alfa Aesar), Te ingot (99%, Alfa Aesar), TeCl4 powder (99%, Aladdin), UV photolithography and dry etching for substrate preparation. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Samples were scanned in tapping-mode AFM to stabilize, then indented at the center of suspended membranes. Force and indentation depth were recorded, with multiple indentations per membrane before fracture. Temperature was varied for phase transitions. SHG and Raman measurements were conducted to determine lattice orientations and phase characteristics.

5：Data Analysis Methods:

Force-indentation depth curves were fitted using equations for elastic modulus and breaking strength. DFT calculations used VASP code with PAW potentials and vdW-DF correction for energy and strain analysis. Statistical analysis included Gaussian fitting for modulus distributions.