  We report first-principles calculations of electron-phonon coupling in
bilayer graphene and the corresponding contribution to carrier scattering. At
the phonon $\Gamma$ point, electrons with energies less than 200 meV are
scattered predominantly by LA$^\prime$ and TA$^\prime$ modes while
higher-energy electron scattering is dominated by optical phonon modes. Based
on a two-temperature model, heat transfer from electrons with an initial
temperature of 2000 K to the lattice (phonons) with an initial temperature of
300 K is computed, and in the overall relaxation process, most of this energy
scatters into K-point phonon optical modes due to their strong coupling with
electrons and their high energies. A Drude model is used to calculate
photoconductivity for bilayer graphene with different doping levels. Good
agreement with prior experimental trends for both the real and imaginary
components of photoconductivity confirms the model's applicability. The effects
of doping levels and electron-phonon scattering on photoconductiviy are
analyzed. We also extract acoustic and optical deformation potentials from
average scattering rates obtained from density functional theory (DFT)
calculations and compare associated photoconductivity calculations with DFT
results. The comparison indicates that momentum-dependent electron-phonon
scattering potentials are required to provide accurate predictions.
