Two-terminal switching devices characterized by high on/off current ratios and by high breakdown voltage are provided. These devices can be employed as switches in the driving circuits of active matrix displays, e.g., in electrophoretic, rotating element and liquid crystal displays. The switching devices include two electrodes, and a layer of a broad band semiconducting material residing between the electrodes. According to one example, the cathode comprises a metal having a low work function, the anode comprises an organic material having a p+ or p++ type of conductivity, and the broad band semiconductor comprises a metal oxide. The work function difference between the cathode and the anode material is preferably at least about 0.6 eV. The on/off current ratios of at least 10,000 over a voltage range of about 15 V can be achieved. The devices can be formed, if desired, on flexible polymeric substrates having low melting points.