Insulating TaNx films were grown by plasma enhanced atomic layer deposition using butylimido tris dimethylamido tantalum and N2+H2 mixed gas as metalorganic source and reactance gas, respectively. Crossbar devices having a Pt/TaNx/Pt stack were fabricated and their electrical properties were examined. The crossbar devices exhibited temperature-dependent nonlinear I (current) - V (voltage) characteristics in the temperature range of 90-300 K. Various electrical conduction mechanisms were adopted to understand the governing electrical conduction mechanism in the device. Among them, the Poole- Frenkel emission model, which uses a bulk-limited conduction mechanism, may successfully fit with the I - V characteristics of the devices with 5- and 18-nm-thick TaNx films. Values of ~0.4 eV of trap energy and ~20 of dielectric constant were extracted from the fitting. These results can be well explained by the amorphous micro-structure and point defects, such as oxygen substitution (ON) and interstitial nitrogen (Ni) in the TaNx films, which were revealed by transmission electron microscopy and UV-Visible spectroscopy. The nonlinear conduction characteristics of TaNx film can make this film useful as a selector device for a crossbar array of a resistive switching random access memory or a synaptic device.