Elastic and piezoelectric field around a quantum dot with interface effect

Piezoelectric field is closely related to the elastic field, so it is important for the calculation of piezoelectric field to include the size-dependent interface effect for the interface in nanostructures. This work adopts the semi-coupled model to find the elastic and piezoelectric field for weakly electromechanical coupled materials (GaAs) with the consideration of interface effect. Close-form solutions are derived and numerical results are also provided to show that the piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the quantum dot. Especially, it is demonstrated that the piezoelectric potentials with different interface elasticity parameters are distinct compared with the classical solution near the interface. When the interface elasticity parameter is positive, the interface effect weakens the piezoelectric effect in the material by decreasing the value of the piezoelectric potential and vice versa. The piezoelectric potential concentration ratio calculated by this work with the consideration of interface elasticity is close to 10% different from the classical solution. Such amount of difference is appreciable in the design and fabrication of nanostructures and the effect due to interface elasticity should not be neglected.