On the effect of periodic Mg distribution in $GaN:δ-Mg$

$p$-type doping of group-III nitrides represents a well recognized crucial challenge in the realization of optical and magneto-optical devices based on wide band gap semiconductors. The insertion of Mg in a $δ$-doping fashion into a GaN matrix is expected to be very promising for the enhanced incorporation of acceptors. The authors present a comprehensive study of the $GaN:δ-Mg$ material system, starting from the optimization of the metal organic chemical vapor deposition process monitored in situ via spectroscopic ellipsometry and reflectometry and giving then evidence of the periodic distribution of the Mg ions through high-resolution secondary ion mass spectroscopy measurements. Furthermore, the effect of the acceptor distribution in the layers on the optical and transport properties is highlighted.