I think there can be much debate about your statement: 'carbon is considered as a semiconductor material'
There are a number of (allotropic) forms of carbon. Typically, carbon is an insulator with a very low conductivity. Diamond is a wide-band gap semiconductor. Charcoal and graphite can act as conductors.
I attach a paper where the Tauc plot has been used for diamond.
Dear Huda M.H, Researchers use Tauc plot to measure the bandgap of carbon-based nanomaterial. If you find, you can get lots of research articles on Graphene oxide or any other carbon-based nanomaterials where the Tauc plot has been used to measure the bandgap. I have attached a link below as an example.
Article Single step synthesis of reduced graphene oxide/SnO2 nanocom...