As you can understand my knowledge in electronics is limited. I am trying to find throughout the internet a way to find the maximum current I can put through a transistor or diode versus their size. Specifically in the region of nanometers and micrometers in VLSI projects. I can find a lot of info for diodes and transistors for PCBs but no info at all for applications in ICs. Any info (even with a big amount of error plus/minus, just a ballpark is fine) or a table I can find on the internet is also nice. Thank you.
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