Which is the device which will consume that current and at what voltage range?
The diode connected in reverse will not act as costant current regulator. It is not made for that purpose. Leakage current is an undesired phenomenon depend upon tepmerature and material properties. If i ask you, are you making a noise generator t hen that would be true. Diode reverse leakage is used to input an amplifier to generate noise.
See noise geneator schmatics.
Zener diodes make more noise so they are used . And see why metal oxide resistors are made and used instead of carbon resistors.
Reverse leakage current - Wikipedia, the free encyclopedia