Higher-order nonlinear electromechanical effects in wurtzite GaN/AlN quantum dots

Abstract

As we demonstrated earlier, conventional mathematical models based on linear approximations may be inadequate in the analysis of properties of low-dimensional nanostructures and band structure calculations. In this work, a general three-dimensional axisymmetric coupled electromechanical model accounting for lattice mismatch, spontaneous polarization and higher-order nonlinear electrostriction effects has been applied to analyze properties of GaN/AlN quantum dots coupled with wetting layer. The generalized model that accounts for five independent electrostriction coefficients has been solved numerically via a finite-element implementation. The results, exemplified for truncated conical GaN/AlN quantum dots, demonstrate that the effect of nonlinear electrostriction in GaN/AlN nanoheterostructure quantum dots could be significant. In particular, the influence of nonlinear electromechanical effects on optoelectronic properties is highlighted by the results on band structure calculations based on a multiband effective mass theory.

On the entanglement of electrostriction and non-linear piezoelectricity in non-centrosymmetric materials

“…We may underline that in this field, incomplete formula for the M lmi tensor have been used up to now. 6,34,35 An extended and self-contained thermodynamical model of third-order electro-elastic coupling is used with symmetry analyses and DFT calculations to evaluate properly the various linear and non-linear coefficients. It is shown that in noncentrosymmetric materials, electrostrictive and non-linear piezoelectric phenomena are strongly coupled, except for materials crystallizing in a cubic lattice associated to point group 432.…”

Composition dependence of elastic constants in wurtzite AlGaInN alloys

“…However, there are serious indications that deviations from this simple rule should be expected in the a) Electronic mail: m.lopuszynski@icm.edu.pl case of elastic properties, 4-7 similarly to, e.g., nonlinear dependence on composition predicted for piezoelectric properties 8 . Since subtle nonlinear effects in elasticity and electrostriction proved to be significant when modeling nitride devices, [9][10][11] also the accurate composition dependence of c ij can be of interest, for correct and accurate description of nanostructures. In the present study, we give a detailed overview of influence of composition on c ij in random wurtzite Al x Ga y In 1−x−y N. The work is based on our previous calculations for cubic phases.…”

Controlling susceptibilities of quantum dots influenced by electromechanical effects

“…As it shown in [31] such influence can be quite important in a number of practically situations. The authors of [31] were the first to use a general three-dimensional axisymmetric coupled electromechanical model accounting for lattice mismatch, spontaneous polarization and higher-order nonlinear electrostriction effects in the application to the analysis of properties of quantum dots coupled with wetting layer. Notwithstanding that their generalized model that accounted for five independent electrostriction coefficients was efficiently solved numerically via a finite-element-method (FEM) implementation.…”

“…Notwithstanding that their generalized model that accounted for five independent electrostriction coefficients was efficiently solved numerically via a finite-element-method (FEM) implementation. The model (1)- (13) implemented here also via the FEM strategy can be extended to account for higher order nonlinear electromechanical effects in a way similar to [31]. Such effects are known to influence optoelectronic properties in bandstructure calculations based on a multiband effective mass theory.…”