Thanks for your reply! Your answer makes the term "flexibility" more clear to me. I think I am more interested in the effects of bending moment on thin films. It's clear that some materials are more prone to brittle fracture than others, so what makes the difference? Is it related to the chemical bonding types and electronic orbital types (eg., s orbital, sp3 orbital). If it's difficult to answer in a few words, can you name some materials, books or papers, that can shed light on my questions? Thank you again!"Flexibility" is ambiguous because it might mean how much force (if you're pushing down on a cantilever) or torque (if you're applying a bending moment) is required to obtain a certain deflection. We quantify this value by the stiffness or elastic modulus (e.g., the Young's elastic modulus). Alternatively, "flexibility" might mean the strength of a film, i.e., how much bending stress it can accommodate before it fails.
Very generally, for ceramics and metals, both stiffness and ideal strength scale with bonding strength. So does melting temperature, so a more refractory compound is usually also stiffer. A complication, however, is that the strength can be much lower than expected in brittle materials, including the material examples you give, when surface imperfections exist. The stiffness of a material is near-universal; the strength depends much more on the deposition method and surface morphology.
A look at the literature suggests that Si and IGZO have similar Young's moduli, between 100 and 200 GPa.
Another factor is that if a thinner layer of material A can do the same job as a thicker layer of material B, the first device can be made more flexible (because the bending stress scales with the distance from the neutral axis) for reasons that aren't even connected to material properties.
Thank you very much for the reply and materials! You're so helpful! I studied thin film transistors(TFTs) on rigid substrate for 2 years or so, now I turn to the study of TFT on flexible substrate, but my knowledge on the mechanical properties of thin films is so limited, so I'm eager to learn more. Thanks!Briefly, a material is brittle when a crack can propagate through it without interruption, somewhat paradoxically because the bonds are too strong. If the bonds were not as strong or directional, the stress concentrations that exist near the crack tip might cause local deformation to blunt the tip and ease the stresses. This is what happens in ductile metals: their bonds are nondirectional and not as strong as ionic bonds, and their crystalline atomic arrangement allows lines of atoms to slide past each other. If you strike a chunk of metal with a hammer, you'll introduce untold numbers of dislocations (line defects) to accommodate the blow, mediate the deformation, and store some of the impact energy. In brittle ionic solids, however, the strong and directional bonds won't allow this type of local plasticity at the crack tip to occur, and the only alternative is for the bonds at the very tip of the atom-sharp stress concentration to simply separate, inducing complete fracture that propagates completely through the material.
This brittle/ductile dichotomy can be quantified somewhat using the fracture toughness: higher values generally correspond to greater ductility. Metals generally have a fracture toughness of 10s of MPa-m1/2, ceramics around 1-5 MPa-m1/2.
So from this background, can you assume that a stronger bond will always correspond to a more brittle microfabricated film? Unfortunately, probably not. The preparation method, previous conditions, microstructure, surface roughness, geometry, surrounding materials, and exact stoichiometry, for example, can be expected to introduce substantial variation in experimentally measured values. An expert on the mechanics of microfabricated films is Robert Ritchie (my advisor's advisor's advisor!). In this presentation, he gives the fracture toughness of single crystal silicon as likely lying somewhere between 1-20 MPa-m1/2. More information for your reading pleasure https://sem.org/wp-content/uploads/2015/12/sem.org-SEM-X-Int-Cong-s015p04-Fracture-Toughness-Polycrystalline-Silicon-Tetrahedral-Amorphous.pdf, here, and https://www.researchgate.net/publication/274334439_Wafer-Level_Strength_and_Fracture_Toughness_Testing_of_Surface-Micromachined_MEMS_Devices [Broken]. You'd probably also get a lot out of Freund and Suresh's Thin Film Materials. Suresh was Ritchie's student.
Anyway, I'm not sure we can predict precise fracture toughness values or ductile-to-brittleness ranking simply from orbital information. I suspect that the bonding type can give broad information but that a fabricated prototype would be necessary to confirm. This is in contrast to stiffness, the other aspect of "flexibility", which is thoroughly understood and can be predicted accurately by knowing the material's composition and almost nothing else. This is because elastic deformation involves only very slight bond stretching rather than the large stretching and failure that are unavoidable when discussing strength and toughness.