Can you be more specific about current carrying requirements? Otherwise minimum thickness is one atomic layer.
Suppose I want to replace ITO in solar cells ... then what should be the thickness?
Problem in single layer of Graphene is that it can not be that much rigid to hold the total assembly.
So what should be the minimum thickness so that it can be rigid and replace the ITO coated Glass
I suggest you still use glass or another substrate for rigidity/support.
Ms Querebillo's comment is very important. As thickness of graphene increases, optical transmission decreases. Current technology can give you a transparent, conductive coating with excellent barrier properties. However, you will need mechanical support (backing layer) from another material.
To replace the ITO with another TCE is a challenge. Broadly speaking, the sheet resistance and transmission are important. ITO does not have a fantastic sheet resistance (10-15 Ohms/square) in films with typical thickness of 100 nm which give transmission of ~90%. Multi layer graphene has been used to replace the ITO in solar cells ( not so sure whether you can still call it graphene then!) but they cannot deliver same performance. Single sheet graphene is indeed not rigid enough to be usable in optoelectronic devices easily. One of the msot successful examples is this paper: DOI: 10.1021/nl501981f
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