  Using a microscopic model of lattice vibrations in the STO(001) substrate, an
additional 50 mev longitudinal optical (LO) interface mode is identified. The
soft mode propagating mainly in the first TiO2 layer ("O chains") has stronger
electron - phonon coupling to electron gas in FeSe than a well known 100 mev
hard mode. The coupling constant, critical temperature, replica band are
calculated. Although there exists a forward in the electron - phonon scattering
peak, it is clearly not as sharp as assumed in recent theories (delta function
- like). The satellite is broad and its peak appears at frequency much higher
than the phonon frequency consistent with observations. Possible relation of
the transverse counterpart of the surface LO soft mode with known phonons is
discussed.
