A display may have an array of pixels formed from organic light-emitting diodes and thin-film transistor circuitry. A planarization layer may be interposed between the thin-film transistor circuitry and the organic light-emitting diodes. To protect the organic light-emitting diodes from photoactive compounds that may be outgassed from the planarization layer, an inorganic barrier layer may be interposed between the planarization layer and the organic light-emitting diodes. The inorganic barrier layer may be formed on top of and/or below a pixel definition layer that defines light-emitting zones for the organic light-emitting diodes. In another suitable arrangement, the inorganic barrier layer may itself define light-emitting zones and may be used in place of a polymer-based pixel definition layer. The inorganic barrier layer may include trenches in which the emissive material of the light-emitting diodes is formed.