Physical phenomena such as energy quantization have to-date been overlooked in solution-processed inorganic semiconducting layers, owing to heterogeneity in layer thickness uniformity unlike some of their vacuum-deposited counterparts. Recent reports of the growth of uniform, ultrathin (<5 nm) metal-oxide semiconductors from solution, however, have potentially opened the door to such phenomena manifesting themselves. Here, a theoretical framework is developed for energy quantization in inorganic semiconductor layers with appreciable surface roughness, as compared to the mean layer thickness, and present experimental evidence of the existence of quantized energy states in spin-cast layers of zinc oxide (ZnO). As-grown ZnO layers are found to be remarkably continuous and uniform with controllable thicknesses in the range 2-24 nm and exhibit a characteristic widening of the energy bandgap with reducing thickness in agreement with theoretical predictions. Using sequentially spin-cast layers of ZnO as the bulk semiconductor and quantum well materials, and gallium oxide or organic self-assembled monolayers as the barrier materials, two terminal electronic devices are demonstrated, the current-voltage characteristics of which resemble closely those of double-barrier resonant-tunneling diodes. As-fabricated all-oxide/hybrid devices exhibit a characteristic negative-differential conductance region with peak-to-valley ratios in the range 2-7.