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Zener Diodes are used in the "REVERSE" bias mode, i.e. the anode connects to the negative supply, and from its I-V characteristics curve above, we can see that the Zener diode has a region in its reverse bias characteristics of almost a constant voltage regardless of the current flowing through the diode. This voltage across the diode (it's Zener Voltage, Vz) remains nearly constant even with large changes in current through the diode caused by variations in the supply voltage or load. This ability to control itself can be used to great effect to regulate or stabilise a voltage source against supply or load variations. The diode will continue to regulate until the diode current falls below the minimum Iz value in the reverse breakdown region.
Zener diode Characteristics Lecture Video: