Stress analysis for nanomembranes under stamp compression

Many high performance flexible and stretchable electronics are manufactured by transferring inorganic semiconductor nanomembranes from their rigid donor substrates to soft receiving substrates via elastomeric rubber stamps. As nanomembrane thickness reduces to nanometers or subnanometers (e.g., 2D materials), they can be easily ruptured during the stamping process by shear stresses. Through analytical modeling, this paper reveals the membrane stress in the nanomembrane induced by stamp compression as a function of the stamp and nanomembrane property and geometry, as well as the traction-separation relation between the nanomembrane and the donor substrate. While membrane stress in the nanomembrane increases monotonically with the compressive loading applied on the stamp, an abrupt increase appears when nanomembrane-substrate interface starts to fail. While the stamp is assumed to be incompressible material in the main text, more general solutions for compressible stamps are offered in the supplementary material (see Appendix B).