Electronic properties of zinc oxide quantum dot: Insights from first-principles calculations using density functional theory

We present ab initio calculations of the electronic, spin-orbit coupling (SOC), and quantum-harmonic vibrational properties of a strongly confined piezoelectric ZnO quantum dot (QD). Our model system is a stoichiometric Zn14O28 cluster (42 atoms) whose local coordination mimics the interior of larger 5–10 nm ZnO nanocrystals, placing it firmly in the strong-confinement regime. Using PBE-based density functional theory (DFT) in Quantum ESPRESSO with non-collinear SOC and fully relativistic pseudopotentials, we quantify the confinement-induced bandgap widening relative to bulk, analyze the projected density of states, and construct a momentum-resolved spectral function A(k, E) by projecting discrete QD states onto bulk-like plane waves along a pseudo-high-symmetry path. This k-projected representation reveals SOC-induced band splittings and Rashba-type spin textures at the conduction-band edge while preserving time-reversal symmetry in the non-magnetic system. Within DFT+U and density-functional perturbation theory, we further examine how confinement and broken symmetry distort the piezoelectric response and phonon spectrum. We re-normalize the piezoelectric tensor with respect to an effective dot volume appropriate for a finite cluster and find an enhanced, anisotropic response compared to bulk ZnO, rather than the unphysically large values obtained with the full supercell volume. The harmonic phonon spectrum exhibits confinement-induced shifts and soft modes that point to reduced lattice thermal transport, but it also includes residual imaginary branches, so we restrict our use of these data to qualitative trends in vibrational and thermodynamic behavior rather than quantitative thermal-conductivity predictions. Taken together, these results provide a microscopic picture of how strong quantum confinement in ZnO QDs reshapes band edges, SOC-driven spin textures, and electromechanical response, and they outline a consistent first-principles framework for connecting finite-cluster calculations to experimentally relevant nanocrystals.