  In 1980 Binnig et al. reported tunneling measurements on Nb-doped SrTiO3, and
interpreted their results as indicating two-band superconductivity in the bulk
of SrTiO3. However: (1) Effective masses determined from tunneling results in
the normal state by Sroubek in 1969 and 1970 are much smaller than those
determined by most other methods. The much smaller masses were attributed to
properties of a surface layer by the present author in 1971; (2) The only other
reports of two-band superconductivity in bulk SrTiO3 can be used to infer much
smaller values of band separations than found by Binnig et al.. In this paper
we give an alternative explanation of the results of Binnig et al. in terms of
superconductivity in a surface layer. We obtain fair fits to the band gaps
versus Fermi energy for the two bands in three samples where two surface
subbands are occupied and to the temperature dependence of the gaps in one
crystal, using a model with three adjustable interaction parameters, an
adjustable energy for the phonons which dominate the pairing, and an adjustable
ratio for the mean-field Tc to the actual Tc. We show results for a combined
fit to the low-temoerature band gaps and to the T-dependence in one crystal.
The phonon energy which gives the best fit is 21 meV. This is probably an
appropriate average over the three longitudinal polar modes and acoustic modes
in the material. A large value of about two is found for the ratio T_(cmf}/Tc,
and we conjecture that this arises because a band with a small Fermi energy not
seen in the tunneling results plays a part in increasing T_{cmf}/Tc.
