Effect of Cation\nCu/Al Ratio and Surface Proximity\non the Electronic Structure and Optical Properties of Cu-Rich Cu<sub>1+<i>x</i></sub>Al<sub>1–<i>x</i></sub>S<sub>2–<i>y</i></su

In this work, we\nemploy density functional theory to\ninvestigate\nthe electronic structure and optical properties of both Cu-rich Cu<sub>1+<i>x</i></sub>Al<sub>1–<i>x</i></sub>S<sub>2–<i>y</i></sub> bulk and quantum dot (QD)\ncrystals. The copper deep acceptor, which substitutes Al (Cu<sub>Al</sub>), is dominant under Cu-rich (Al-poor, S-poor) growth conditions,\nand in QDs, it may form spontaneously. In the presence of copper at\ninterstitial sites, stable acceptor–donor complexes, such as\nCu<sub>Al</sub>–2Cu<sub>i</sub> and Cu<sub>Al</sub>–Cu<sub>i</sub>, can be present, which in turn may be a source of p-type\nconductivity and optical transitions. Cu<sub>Al</sub> reveals a tendency\ntoward the formation of aggregates and Cu acceptor pairing that may\ndecrease empty energy levels. The lowering acceptor states may also\nbe induced by the formation of a large broad band above the valence\nband maximum that stems from the increasing concentration of host\nCu atoms. We find that Cu<sub>Al</sub>, incorporated in the presence\nof high concentrations of copper in the host structure, gives rise\nto photoluminescence (PL) transitions at lower energies, in comparison\nwith PL transitions originating from the impurities in a stochiometric\ncrystal. The effect arises as a result of crystal distortion in the\nvicinity of the dopant: larger distortions occur in higher Cu/Al ratios\nand under the surface proximity in QDs as a result of stronger energy\nrelaxations.