Effects of electrostatic force on piezoelectric materials under high electric field: Impact on GaN-based nanoscale structures

The determination of the electromechanical properties of materials for a parallel-plate capacitor structure is affected by the electrostatic force between their electrodes. The corrections resulting from this electric-field-induced stress are usually assumed to be linked to the quadratic dependence of the strain on the electric field (electrostriction). Here we show by calculations based on thermodynamic grounds for this simple structure that the effect of the electrostatic force on piezoelectric materials can lead to both quadratic and linear corrections through the combination of the piezoelectric coupling and spontaneous polarization. The case of GaN-based capacitor nanoscale structures is presented taking into account the boundary conditions imposed as well as the effect of geometry. The results in this example point to corrections in the piezoelectric and electrostrictive coefficients higher than 0.3 pm V^-1 and 2.6×10^-22 m² V^-2, respectively.