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LM2765: LM2765 diode

Part Number: LM2765

We want to insert a cheap and small as possible diode.

why a MBR0520LT1 is not sufficient enough and you suggest a 1N817?

You are talking on power on and if we are looking on current: the MBR0520LT1 

If we calculate the current we get a current: 
I = dU/dt * C = 10V/0,2ms (our slope) * 3µF (worst case) = 0,15A

The diode should be able to carry it:

Non-Repetitive Peak Surge Current
(Surge Applied at Rated Load Conditions Halfwave, Single Phase, 60 Hz)
IFSM 5.5 A

To load the capacitor we need << 1ms.

If we are looking on forward voltage at a current of 0,15V the difference is small: 

0,22V versus  0,28V @25°C