k.p theory of quantum dots with smooth alloy profiles

Due to their tunable electronic and optical properties, epitaxial quantum dots have many applications including lasers, solar cells and water splitting. Since most applications require that these electronic and optical properties be carefully tuned, models must capture all essential physics to enable accurate prediction of device functionality. Most quantum dot electronic structure models assume sharp material interfaces, even though epitaxial quantum dots frequently have alloy diffusion, creating diffuse interfaces. We present a Fourier-space k.p method for modelling the electronic structure of wurtzite quantum dots with continuous alloy profiles. We calculate strain and piezoelectric potentials with elastic and dielectric constants that vary smoothly with the alloy profile. Our method calculates single-particle electronic states of either isolated quantum dots or arrays of dots. We demonstrate our methodology on 1D GaN/InGaN quantum dot arrays, representing quantum dots grown in wires. In all cases, the effects of indium diffusion as occurs in molecular beam epitaxy are found to significantly modify the electronic structure of the dots.