(untitled) (International Journal of Mathematics and Physics, 2026)
ZnO nanowires have attracted considerable attention due to their wide band gap, high chemical stability, and pronounced quantumscale effects, making them promising components for optoelectronic and sensor devices. The electronic states of such nanostructures strongly depend on the properties of the substrate, especially in heterostructures containing porous materials. In this work, the formation of quantum levels and the electronic properties of ZnO nanowires in two systems ZnO/ZnSe(bulk) and ZnO/porousZnSe/ZnSe with porosity ranging from 20% to 80% were theoretically investigated. The base nanowire model, with a radius of 25 nm and a height of 500 nm, describes the structure as a cylindrical infinite potential well, while the influence of porous ZnSe is incorporated through porositydependent barrier parameters: dielectric constant, and electron affinity. Analytical solutions of the Schrödinger equation obtained using Bessel functions, together with numerical simulations in Matlab, revealed strong radial quantum confinement: the radial quantization energy significantly exceeds the longitudinal one for the first levels, and the groundstate energy is about 0.0015eV. To quantitatively analyze the effect of substrate porosity, a finite cylindrical potential well model is employed, in which the barrier heightV0(P)=χZnO−χeff(P) explicitly depends on porosity through the dielectric constant and electron affinity of porous ZnSe, calculated using the Bruggeman effective medium equation and the Penn relation, respectively. Numerical simulations performed for nanowire radii in the range 5−20 nm showed that increasing ZnSe porosity leads to systematic upward shifts of the ground-state energy, with absolute changes reaching up to 3−4 meV for nanowires with radius R < 10 nm. The obtained results confirm that porous ZnSe is an effective tool for tuning the electronic states of ZnO nanowires and open up opportunities for optimizing UV photodetectors and photovoltaic converters by controlling substrate porosity. Keywords: ZnO nanowires, porous ZnSe, quantum confinement, electronic states, optoelectronic applications.