Fig. 2: Working mechanism of contact-dominated localized electric-displacement-field-enhanced pressure sensors.

a Schematics of the cross-sectional view of the contact-dominated pressure sensors without and with applied pressure. Red dashed box corresponding to the part represented by the schematic diagrams in (e). b Normalized capacitance (C/C_min, with C_min being the minimum value of the capacitance) with respect to the dielectric constant and thickness in the initial state (i.e., no pressure applied), left, and under pressure with A^cont/A_base ≈ 0.08, right, obtained by analytical models. c Equivalent stress and strain distributions in regular and hierarchical microstructures under different pressures according to FEM simulations. Schematics and equivalent circuit diagrams for the only metal deposition design (d) and our hybrid electrode design (e) at the contact area when cracks occur. Corresponding electric potential distributions from FEM simulations for the only metal deposition design (f) and our hybrid electrode design (g). h Numerical results based on FEM simulations of the normalized capacitance for the only metal deposition design (\({C}_{{{{\rm{all}}}}}^{{{{\rm{metal}}}}}/{C}_{{{{\rm{origin}}}}}\)) and our hybrid electrode design (\({C}_{{{{\rm{all}}}}}^{{{{\rm{hybrid}}}}}/{C}_{{{{\rm{origin}}}}}\)) with respect to the crack width and crack numbers. The cracks are assumed to be uniformly distributed within the contact electrode. Source data are provided as a Source Data file.