Transistors and Diodes maximum current per size
The limiting quantity is not current but power dissipation. 
Therefore you should ask for power dissipation (not current) per size (i.e. chip area), a quantity with unit W/cm². 

You can get the ballpark number if you look at high performance mircoprocessors.
I don't know exact up to date exact numbers but it is, quite impressing, in the same range as power densities of heating plates used for cooking:
ca. 10 W/cm²