Derivation of built-in polarization potentials in nitride-based semiconductor quantum dots

Abstract

We present a simple analytical approach for the calculation of the built-in strain-induced and spontaneous potentials in nitride-based semiconductor quantum dots. We derive the built-in potentials and electric fields in terms of volume or surface integrals. We describe using a number of simplifying assumptions the general properties of piezoelectric and spontaneous fields in GaN / AlN and InN / GaN quantum dots and obtain analytic solutions to the potential along and close to the axis of symmetry in spherical, cylindrical, cuboidal, truncatedcone, and ellipsoidal dots. We show that the potential distribution in a hexagonal quantum dot is well represented by that of an equivalent dot with circular symmetry. We demonstrate that the built-in electric fields in nitride dots can provide a strong additional lateral confinement for carriers localized in the dot. This additional lateral confinement strongly modifies the electronic structure and optical properties of nitride-based quantum dot structures.

Built-in field control in alloyedc-plane III-N quantum dots and wells

“…The calculation of the total built-in potential u in a QD is more complicated because the piezoelectric polarization vector is no longer a constant vector along the [0001] direction within the QD and within the barrier. To calculate the polarization potential in nitride-based QDs we apply a real-space surface integral approach developed by Williams et al 24 This method admits analytical solutions in certain cases and provides an extremely useful insight into the parameters that influence the magnitude and the shape of the polarization potential. In this work, we use the solutions obtained in Ref.…”

“…In this work, we use the solutions obtained in Ref. 24 for a linescan of the potential u QD ðzÞ along the z-direction through the center of a truncated-cone shaped QD. Using the notation of Ref.…”

“…The analytical solution for these integrals, as well as an expression for the material-and strain-dependent coefficients J and K, is given in Ref. 24. Finally, the built-in field E(z) corresponding to the potentials given in Eqs.…”

Built-in field reduction in InGaN/GaN quantum dot molecules

“…Hamiltonian. Strain and polarization fields are calculated using a surface integral method, 19 with a linear interpolation for all parameters except for the spontaneous polarization, where we apply a quadratic interpolation. 20 When modeling the electronic structure of coupled c-plane nitride QDs, the sign of the shear piezoelectric coefficient e 15 becomes important, since it affects the behavior of / p outside a single QD.…”

Elastic interaction energy between a silicon interstitial and a carbon substitutional in a silicon crystal

“…The use of a cube is arbitrary, but the strain field a distance of just one unit cell away from the source of the strain is almost independent of the shape of the source. 19 It is now necessary to estimate the effective misfit strain of a cube of silicon, which contains an extra atom in the form of an interstitial. Misfit strain * for a small volume of material A embedded in material B is defined as…”