Charge distributions in KTa₁₋xNbxO₃ optical beam deflectors formed by voltage application

Controlling the space charge distributions in a crystal is indispensable for controlling a KTa₁₋xNbxO₃(KTN) optical beam deflector. The space charge is built up by applying a voltage and injecting electrons into the KTN crystal. Although a homogeneous distribution is preferable, we observed experimentally that the injected electrons concentrated in the vicinity of the cathode and for some samples the concentration was much lower around the anode. We investigated the electron dynamics theoretically and found that such inhomogeneity was caused by a freezing effect where the motion was very slow considering the duration of the practical voltage application. The depth of the space charge spread or the electron penetration depth from the cathode was proportional to the applied voltage and the permittivity, and inversely proportional to the density of traps or localized states that bind electrons. We believe that the trap density was too large for the samples with inhomogeneous charge distributions.