Fig. 3: Theoretical modeling and experimental measurements of the 3D capacitive sensor.

a Schematic illustration of the deformation configuration for the 3D capacitive sensor under the out-of-plane compressive force loading. b Electrical response of a 3D capacitive sensor at different levels of compressive displacement (U). The right panel shows the approximate linear correlation for relatively small compressive displacements (<99 μm). c Response of a 3D capacitive sensor under the compressive loading applied by AFM (0.05 V for each increment voltage). The incremental force of adjacent steps is 33.77 nN. d Sensitivity of Z-direction displacement as a function of the initial gap (d₀). The right panel shows the measurement system. e Variation of the output signal of a sample without external loads during 100,000 s. f Cyclic testing of the 3D capacitive sensor for 50 cycles. The initial gap between the upper and lower electrodes is tuned in sequence (from ~200 to ~85 to ~54 μm) in an adjustment cycle.