  In a recent experiment the superconducting gap of a single unit cell thick
FeSe film on SrTiO$_3$ substrate is observed by scanning tunneling spectroscopy
and angle-resolved photoemission spectroscopy. The value of the superconducting
gap is much larger than that of the bulk FeSe under ambient pressure. In this
paper we study the effects of screening due to the ferroelectric phonons on
Cooper pairing. We conclude it can significantly enhance the energy scale of
Cooper pairing and even change the pairing symmetry. Our results also raise
some concerns on whether phonons can be completely ignored for bulk iron-based
superconductors.
