Resistive metal/β-Ga₂O₃/metal structures with different interelectrode distances and electrode topologies were investigated. The oxide films were deposited by radio-frequency magnetron sputtering of a Ga₂O₃ (99.999%) target onto an unheated sapphire c-plane substrate (0001) in an Ar/O₂ gas mixture. The films are sensitive to ultraviolet radiation with wavelength λ = 254. Structures with interdigital electrode topology have pronounced persistent conductivity. It is shown that the magnitude of responsivity, response time τ_r, and recovery time τ_d are determined by the concentration of free holes p involved in recombination processes. For the first time, it is proposed to consider hole trapping both by surface states N_ts at the metal/Ga₂O₃ interface and by traps in the bulk of the film.