How to calculate the piezoelectric polarization of semi-polar InGaN?
GaN-based light-emitting devices suffer from strong polarization of the InGaN light-emitting layers when grown along the wurtzite c-axis. That is why researchers worldwide work on growing these devices in different, so-called semi-polar crystal directions that promise less polarization. These promises are typically derived from theoretical polarization models. The most cited model was published by Romanov et al. in 2006 (link). It gives analytical formulas for the piezoelectric polarization as function of the angle between growth direction and c-axis. However, when I tried to use this model, I realized that the given formulas do not produce the results plotted in the paper (see figure).
Luckily, two of our NUSOD 2015 authors (link) just published a more general model for InGaN quantum dot polarization (link). They found perfect agreement with Romanov’s model, but only after making several corrections to his equation (18). First, they replaced the second piezoelectric coefficients e33 by e31, which obviously was a typo, because this produced the results plotted in the paper (blue line). Second, they introduced factor 2 in front of all e15 coefficients, as required for the transition from Voigt notation to Cartesian notation. This generated the green line in the figure and full agreement between both models.
Maybe these corrections are already discussed in the literature. If you, Dear Reader, are aware of such a paper, please let me know.