Calculation of aluminum circuit board trace required thickness/size

A. I am 100 % positive that you can find data on the load capacity of aluminum in the TT Library.
1. Pure aluminum or alloy? it makes a big difference
2. Load capability of any metal is dependent on the temperature rise that you can live with. You did not state!
3. Just how do you plan on depositing the aluminum?

A. I assume you are designing a circuit! Your concern needs to be current density and not length. Your spec of 3.5 A is a very high current to be carried by a 0.4 mm Al strip. If you don't use enough thickness, you will experience "electromigration". Check some literature on that subject. A lot has been studied and published in the context of ICs and hybrids.

Having suggested that, there are some rules of thumb in the design. Determine the thickness based on the current density not to exceed 1 megamp per cm sq. or less. Then some (50% to 100%) safety factor for coating defects. As a good start, I would consider 10E5 density and find cross section, then determine thickness based on density of Al. Thicker the coating, better off you will be. Then worry about process economics.

A. In the macro world we use about 600 Amps per square inch of cross section as a good safe rating for aluminum. That probably has very little to do with the answer you need for your micro device, but there it is for reference :-)