Fig. 4.

Characterisations of out of plane piezoelectricity of 2D GaPO₄. a AFM topography of a unit cell thick GaPO₄ nanosheet. b–f Vertical piezoresponse amplitude profiles at different AC driving voltages. The insets represent the statistical distribution of the piezoresponse amplitude variations of GaPO₄ film (white colour) and the substrate (grey colour). g Average piezoresponse amplitude as a function of the applied AC voltage extracted from the statistical distributions of the amplitude variations of GaPO₄ and the substrate. Error bars signify the standard deviations which are introduced to indicate uncertainty of the measurements. h Value of d^eff₃₃ for GaPO₄ films with different thicknesses. The bulk value for d₃₃ is extracted from ref.⁴⁹. Error bars signify the deviations of slope of piezoelectric amplitude for the driving bias voltage (AC) for experimental d^eff₃₃. DFT simulations of 2D GaPO₄ nanosheets of higher thicknesses are not reported due to difficulties with accuracy and energy convergence