lagrangian formalism - Energy-momentum tensor of the Dirac field

I'm trying to compute the energy momentum tensor for the dirac field $$\mathcal{L}=\bar\psi(i\gamma_\mu\partial^\mu-m)\psi $$$$T^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\psi)}\partial^\nu\psi-\eta^{\mu\nu}\mathcal{L}$$ and I'm not clear on how to treat the term in $\eta^{\mu\nu}\mathcal{L}$: the first term gives $i\bar\psi\gamma^\mu\partial^\nu\psi$ which is the tensor given by Peskin-Schroeder but I don't get how to compute the term in $\eta$