  We apply the fermion functional renormalization group method to determine the
pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a
five band model with pure repulsive interactions, we find an electronic-driven
superconducting pairing instability. For the doping and interaction parameters
we have examined, extended s-wave, whose order parameter takes on opposite sign
on the electron and hole pockets, is always the most favorable pairing
symmetry. The pairing mechanism is the inter Fermi surface Josephson scattering
generated by the antiferromagnetic correlation.
