We analyze single-electron tunneling from the bound state above the su
rface of liquid helium. For strong enough magnetic fields parallel to
the surface, the tunneling must be accompanied by ripplon scattering.
The effective width of the tunneling barrier strongly and nonmonotonic
ally depends on the momentum transferred to ripplons. The escape rate
is affected by Landau quantization of the states behind the barrier. T
he results obtained here also apply to electrons on other cryogenic su
bstrates. [S0163-1829(98)50444-4].