A new version of scattering theory is suggested for the 1D electron tu
nnelling. The Bardeen formula is generalized. The appropriate correcti
on terms form a rapidly converging series. II is shown that the transm
ission coefficient for an arbitrary 1D barrier can be exactly expresse
d in terms of the solution to the problem of particle reflection from
the barrier sides. The spectral features of the field-emission resonan
ces caused by elastic and inelastic scattering of tunnelling electrons
by the 2D lattice of surface atoms and by isolated adsorbed particles
are considered. The potentialities of the ''intraresonator'' vibratio
nal STM spectroscopy of adsorbates are analyzed. (C) 1997 Elsevier Sci
ence B.V.