We present a study of the optical properties of GaN/AlN and InGaN/GaN quantum dot (QD) superlattices grown via plasma-assisted molecular-beam epitaxy, as compared to their quantum well (QW) counterparts. The three-dimensional/two-dimensional nature of the structures has been verified using atomic force microscopy and transmission electron microscopy. The QD superlattices present higher internal quantum efficiency as compared to the respective QWs as a result of the three-dimensional carrier localization in the islands. In the QW samples, photoluminescence (PL) measurements point out a certain degree of carrier localization due to structural defects or thickness fluctuations, which is more pronounced in InGaN/GaN QWs due to alloy inhomogeneity. In the case of the QD stacks, carrier localization on potential fluctuations with a spatial extension smaller than the QD size is observed only for the InGaN QD-sample with the highest In content (peak emission around 2.76 eV). These results confirm the efficiency of the QD three-dimensional confinement in circumventing the potential fluctuations related to structural defects or alloy inhomogeneity. PL excitation measurements demonstrate efficient carrier transfer from the wetting layer to the QDs in the GaN/AlN system, even for low QD densities ($10 10 cm À3). In the case of InGaN/GaN QDs, transport losses in the GaN barriers cannot be discarded, but an upper limit to these losses of 15% is deduced from PL measurements as a function of the excitation wavelength.

A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple comprehensive solution that extends the declarative least-fixpoint semantics of Horn Clauses, along with the optimization techniques used in the bottom-up implementation approach adopted by many Datalog systems. We start by identifying a large class of programs of great practical interest in which the use of min or max in recursive rules does not compromise the declarative fixpoint semantics of the programs using those rules. Then, we revisit the monotonic versions of count and sum aggregates proposed in (Mazuran et al. 2013b) and named, respectively, mcount and msum. Since mcount, and also msum on positive numbers, are monotonic in the lattice of set-containment, they preserve the fixpoint semantics of Horn Clauses. However, in many applications of practical interest, their use can lead to inefficiencies, that can be eliminated by combining them with max, whereby mcount and msum become the standard count and sum. Therefore, the semantics and optimization techniques of Datalog are extended to recursive programs with min, max, count and sum, making possible the advanced applications of superior performance and scalability demonstrated by BigDatalog (Shkapsky et al. 2016) and Datalog-MC (Yang et al. 2017). This paper is under consideration for acceptance in TPLP.