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how to design diode current in BandGap?

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Generally, 3uA is OK. If the pnp bipolar is used, the main point is making the bipolar working in the region that its beta is constant when your current changes.
 

How low current can be used for the diode current in BG?
 

Also remember that the dVbe/dT is a function of current. Any changes in the current will effect the temperature of the bandgap.

Added after 44 seconds:

Any changes in the current will effect the temperature coefficent of the bandgap.
 

First, you need to decide which PNP you use (5X5, 10X10).
These two PNPs are usually used.

Second, you simulation IV curve based diode connection (base and collector are connect to ground). Find the flat region.

Usually, few uA to few 10uA are Ok.
 

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