A 1N5819 is a 40V 1A Schottky diode.
Any Schottky diode with a similar rating will be acceptable (see below)
BUT in fact a 1N5817 or equivalent would be slightly superior here. The difference is small but there is no point in throwing away efficiency for no resultant benefit. The 1N5817 has a SLIGHTLY lower forward voltage drop when conducting so cause very slightly less losses overall. You may get a percent or two extra efficiency by using it.
1N5817 - 20 V 450 mV drop at 1A
1N5818 - 30 V 550 mV drop at 1A
1N5819 - 40 V 600 mV drop at 1A
For 5V output (5 + .450) / (5 + .6) = 0.973
ie notionally at 1A you need to make about 2% more voltage at thesame current with the higher voltage diode.
1N5817, 1N5818, 1N5819 data sheet
The output voltage is 5V so a diode of 10V and above rating will be notionally OK for D3.
A 20V rating will be very safe.
Looking through tables and checking forward voltage drops would allow you to select a Schottky diode that was best suited, but most of similar ratings will be OK.
1N5819 is axial leaded through hole mount - but you could easily solder an SMD part on the board bottom if one had especially good specs. One does, if you can get it - see below.
You don't say where you are and that affects availability somewhat, but using memory & digikey as a guide:
Generic SMD: SS12 = 20V, SS14 = 40V
ST STPS1L20MF 1A 20V 430 mV at 1A
Microsemi LSM115JE3/TR13 15V 1A 220 mV at 1A !!!!!!!!!!
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