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Why zener breakdown voltage decreases with increase in temperature?

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Because during avalanche breakdown, with the increase in temperature the amplitude of vibration of crystal atoms increases so the probability of collision of the carriers with crystal atoms increases, and there is loss of energy of the carriers and applied reverse voltage should be increased to make up the loss of energy to start avalanche process. But during zener breakdown, with the increase in temperature, the energy of valence electrons increases and it becomes easier for these electrons to escape from covalent bonds hence, zener breakdown voltage decreases with an increase in temperature.

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