The "breakdown voltage" of a diode is the minimum "reverse" voltage to make the diode conduct in reverse. Some devices also have a "forward breakdown voltage".
Breakdown voltage is a characteristic of an insulator that defines the maximum voltage difference that can be applied across the material before the insulator collapses and conducts. In solid insulating materials, this usually creates a weakened path within the material by creating permanent molecular or physical changes by the sudden current. Within rarefied gases found in certain types of lamps, "breakdown voltage" is also sometimes called the "striking voltage".
The breakdown voltage of a material is not a definite value because it is a form of failure and there is a statistical probability whether the material will fail at a given voltage. When a value is given it is usually the mean breakdown voltage of a large sample. Another term is also withstand voltage where the probability of failure at a given voltage is so low it is considered, when designing insulation, that the material will not fail at this voltage.
Two different breakdown voltage measurements of a material are the AC and impulse breakdown voltages. The AC voltage is the line frequency of the mains. The impulse breakdown voltage is simulating lightning strikes, and usually uses a 1.2 microsecond rise for the wave to reach 90% amplitude then drops back down to 50% amplitude after 50 microseconds.
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