I am looking to create a SAM layer on a 20 x 20 mm gold surface using EDC and NHS which will link to Igg antibodies. However, I want to know if there is a way of calculating the exact/correct amount of linker solution needed for the surface are?
Well you need to know the "dimensions" of the molecule you want to be used as linker. With this info, you can estimate the surface area covered by one molecule.
Nearly all reactions in this field are performed with a large excess of reagents. By washing your gold surface, all unreacted reagents can be removed easily. Please note that IgG molecules are much larger than the linker molecules and that you do not need to use all linker molecules for the conjugation. In addition, it might be helpful to use an oriented way of antibody conjugation, e.g., by Protein A or G.
Finally, it should be mentioned that you won't end up with an IgG SAM anyway.
https://www.mdpi.com/2409-9279/2/2/35
BTW: Many proteins can be firmly adsorbed on plain gold without any linker. I would try this first.