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I know, that in a reversed biased connection the reverse saturation current flowing is negligible but before the depletion layer is widened to its maximum capacity. It seems the current flowing through the circuit would have a great magnitude (depending on the power source). Is there any name given to that current?

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    $\begingroup$ It derives directly from the depletion capacitance, so consider it from that perspective. $\endgroup$
    – Jon Custer
    Mar 17 '20 at 23:03
  • $\begingroup$ Your answer a bit unclear . would be really helpful if you elaborate . $\endgroup$ Mar 17 '20 at 23:05
  • $\begingroup$ Well, you need to move a certain amount of charge to induce a change to the voltage across the depletion region. The actual current will depend on that capacitance and the resistance across the rest of the semiconductor to the contacts. $\endgroup$
    – Jon Custer
    Mar 18 '20 at 0:20
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As stated in the comments, the depletion layer acts like the insulating dielectric layer in a capacitor. The effect is much like charging a capacitor through a resistor (the rest of the diode), except that as the layer widens the capacitance falls. The current has no special name.

This variation in capacitance with applied reverse DC bias voltage is exploited in diodes optimised for the effect and known as varicap diodes. They are typically used for tuning solid-state analog RF circuits.

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