There are some reports publishing VRH transport of metal oxide electro-ceramics at high temperature which is greater than 300 K. While VRH is usually applied at low temperature to describe hopping conduction in the semiconductors and/or amophous glassy materials. In addition, Mott himself proposed this model to be applicable in the low temperature range. Is it possible for the metal oxide materials to exhibit electrical conduction by variable range hopping at high temperatures? If yes, what could be the reason?
Variable range hopping is a particular case of tunnel current where electrons transit form defects to defect or particles to particles in an inhomogeneous material.
Like all the tunnel current mechanisms, hopping is affected by the temperature: The probability for an electron to transit depends on the height of the tunnel barrier it faces. At high temperature the electron has a lot of thermic energy and the potential barrier it faces appears lower. As a result the the current density increases.
However if the temperature becomes too high the thermic energy of the electron can overcome the potential barrier. In this case the conduction mechanism is no longer based on tunneling but on thermionic emission. This phenomenon is described by the Poole-Frenkel equation.
In theory the transition temperature between Hopping and Poole-Frenkel depends on the depth of the electron traps. This depth can be tricky to measure in practice but if you take an oxide/metal particles composite as an example you should be able to observe hopping at high temperature by using a high electron work function metal encompassed in a low electronic affinity oxide (the high of the barrier is the difference between those two values in first approximation).
A high density of traps should also favorize hopping over Poole-Frenkel as it increase the barrier transparency while keeping the barrier height identical (in first approximation, if the Schottky effect is neglected).
In one sentence you may see VRH at high temperature for materials with deep traps and high trap density.
You may be interested by the reference below if you want to dig into the different conduction mechanisms (or chapter 2 of my thesis if you speak french...).
Chiu, F. C. (2014). A review on conduction mechanisms in dielectric films. Advances in Materials Science and Engineering, 2014. https://doi.org/10.1155/2014/578168
Article A Review on Conduction Mechanisms in Dielectric Films
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