  Metal-Nb$_{2}$O$_{5-x}$-metal memdiodes exhibiting rectification, hysteresis,
and capacitance are demonstrated for applications in neuromorphic circuitry.
These devices do not require any post-fabrication treatments such as filament
creation by electroforming that would impede circuit scalability. Instead these
devices operate due to Poole-Frenkel defect controlled transport where the high
defect density is inherent to the Nb$_{2}$O$_{5-x}$ deposition rather than
post-fabrication treatments. Temperature dependent measurements reveal that the
dominant trap energy is 0.22 eV suggesting it results from the oxygen
deficiencies in the amorphous Nb$_{2}$O$_{5-x}$. Rectification occurs due to a
transition from thermionic emission to tunneling current and is present even in
thick devices (> 100 nm) due to charge trapping which controls the tunneling
distance. The turn-on voltage is linearly proportional to the Schottky barrier
height and, in contrast to traditional metal-insulator-metal diodes, is
logarithmically proportional to the device thickness. Hysteresis in the I-V
curve occurs due to the current limited filling of traps.
