A nano-chemist is aware about that the conductivity of material varies with grain size and grain size in turn depends on the method of synthesis.So one can go through a suitable synthetic methodology to obtain particle size as small as possible for good electrical conductivity. Besides, we can use semiconducting ZnO with conducting polymers like polyaniline, graphene, polypyrolle etc to form composites with better electrical properties.
You can dope ZnO with suitable amounts of dopants. I had doped with Al, Ru, Cd and Cu in either 0.5 %, 1 % or 3 %. Please go through my papers on ZnO and SnO2. Some of my papers on ZnO are -
1. Structural and optical properties of pure and Al doped ZnO nanocrystals
2. Structural, electrical and optical studies on Ruthenium doped ZnO pellets for device applications
3. Influence of Cu doping on the structural, electrical and optical properties of ZnO
As mentioned before by Dr. Arindam Ghosh, You can improve the electrical conductivity of the Zinc oxide nano particle by its doping by a metal element (whether transition or not) like Cu, Al, Cd, ... etc.
First of all, it depends which technique had been employed to fabricate ZnO nano particles. Secondly, Annealing at 200-400 C would also be beneficial in this regard. Finally, Hall effect measurement is more appropriate to find the resistivity and Conductivity.