While there is typically a very small current when a diode is reverse biased it is typically ignored. There is a voltage where the device breaks down and conducts but in general purpose diodes this is not desirable as it destroys the diode. A zener diode is a type of diode where this reverse breakdown is often desirable as part of the design. A lot of people think of a zener diode as an ordinatry diode that is able to survive breakdown. So in an ordinary diode as long as the voltage does not exceed the reverse breakdown spec, miniscule current will flow in reverse no matter how much current the supply is able to source.
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Here is one of the first hits google provided me. Looks to be some learning material here:
https://learn.sparkfun.com/tutorials/diodes/real-diode-characteristics
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Something of interest, I recall helping out in a design of a product that needed a very very high impedance to ground in one part of the circuit, yet not a complete open circuit. At times there could be enough leakage on the circuit board to satisfy this but it was certainly no guarantee. Resistors in the megohm range that we needed were next to impossible to obtain. The solution was to use a diode. It had just enough guaranteed leakage resistance to satisfy our needs.