Diode and transistor have reverse breakdown voltage. Are these devices permanently destroyed under such voltage? Also, do these devices have breakdown voltage when AC voltage is applied? How much AC voltage and frequency these can tolerate, say $1V$ at $50$ Hz, $1V$ at $1$ MHz?
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For the most part - yes, the device is damaged if the crystal or other materials have suffered electrical breakdown. Breakdown is the same process that creates lightning - when the voltage is so high that a previously insulating material suddenly becomes conductive, often violently transmitting a large electrical current, which generates heat and damage.
If this happens in a semiconductor crystal, the breakdown damaged area is often an short-circuit, and the heat generated may melt the contact metals in small areas.
The exception is devices that are designed to operate in breakdown mode, such as Zener Diodes and Avalanche Photodetectors, which utilize the properties of controlled breakdown to give them particular electrical properties.
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