Plane-wave implementation of the real-space k⋅pk⋅p formalism and continuum elasticity theory

In this work we demonstrate how second-order continuum elasticity theory and an eight-band k⋅pk⋅p model can be implemented in an existing density functional theory (DFT) plane-wave code. The plane-wave formulation of these two formalisms allows for an accurate and efficient description of elastic and electronic properties of semiconductor nanostructures such as quantum dots, wires, and films. Gradient operators that are computationally expensive in a real-space formulation can be calculated much more efficiently in reciprocal space. The accuracy can be directly controlled by the plane-wave cutoff. Furthermore, minimization schemes typically available in plane-wave DFT codes can be applied straightforwardly with only a few modifications to a plane-wave formulation of these continuum models. As an example, the elastic and electronic properties of a III-nitride quantum dot system are calculated.