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.

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    \$\begingroup\$ If you're using a transistor in a VLSI layout, then the manufacturing process document will have all you need. It depends on current density, heatsinking, geometry, lots of things that will make any ballpark estimate completely useless. \$\endgroup\$ – Neil_UK Sep 27 '19 at 9:39
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    \$\begingroup\$ And to add to that: it also depends on expected lifetime (consumer devices are less strict than automotive for example), temperature range (when hot, devices cannot support as much current). A ballpark value I often see is around 1mA / 1 um width. That still doesn't tell you much as devices can be folded up and then reach much higher values. \$\endgroup\$ – Bimpelrekkie Sep 27 '19 at 9:46
  • \$\begingroup\$ The doping, and thus the inherent non-depletion-region ohmic behavior, will set the voltage drop at high currents, and thus set the local HEAT GENERATION, which as Bimpelrekkie explains will affect the allowed current and lifetime. The use of metallization to remove heat, to spread heat, is a design task and choice, also. However the silicon is about as good a heat path as the aluminum. Chat with your process-development people about benefits of any copper layers. \$\endgroup\$ – analogsystemsrf Sep 27 '19 at 11:12

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


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