Giving 0.1 V to diode will result in decrease of depletion width. So if i give 0.1 V for long time, will the depletion width be reduced to zero, i.e. will diode conduct?
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1No, it wont conduct – karthik Jay Jul 15 '17 at 09:56
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2You do get a small, constant current: the forward leakage. – pjc50 Jul 15 '17 at 10:07
4 Answers
If you partially prop open a door with wedge, will that door become more ajar over time? Without other forces acting on the door, no it won't; it will remain partially ajar as originally set by the wedge.
It's the same for the depletion width; it will remain as set by the applied voltage.

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A diode will conduct at 0.1v, just not very much. It will conduct at 10mV, and not only that, the current at +10mV is not much different to the current at -10mV.
It does this instantly, there is no long term change in depletion region width.
The current at those low voltages is so little that most people don't consider it to be conducting until the current rises to 'sensible' levels, like uA to mA. At these currents, silicon diodes do need around 0.7v.
For instance, look at this answer . Measurements of a 1N4148 diode shows it has a slope resistance of about 30Mohms over the +/- 10mV range. A schottky BAT42 conducted more current, being equivalent to 1Mohm over a similar range. A diode sold as a 'low leakage' type, the BAS116, was not measurable by me, much more than 20Gohms over the same range.

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will diode conduct?
it will always conduct, no matter how small the voltage is. Just the level of conduction is quite small.

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