Impact of second-order piezoelectricity on electronic and optical properties of $c$-plane In$_{x}$Ga$_{1-x}$N quantum dots: Consequences for long wavelength emitters

Abstract: In this work we present a detailed analysis of the second-order piezoelectric effect in $c$-plane In${x}$Ga${1-x}$N/GaN quantum dots and its consequences for electronic and optical properties of these systems. Special attention is paid to the impact of increasing In content $x$ on the results. We find that in general the second-order piezoelectric effect leads to an increase of the electrostatic built-in field. Furthermore, our results show that for an In content $\geq$30\% this increase in the built-in field has a significant effect on the emission wavelength and the radiative lifetimes. For instance, at 40\% In, the radiative lifetime is more than doubled when taking second-order piezoelectricity into account. Overall our calculations reveal that when designing and describing the electronic and optical properties of $c$-plane In${x}$Ga${1-x}$N/GaN quantum dot based light emitters with high In contents, second-order piezoelectric effects cannot be neglected.