  Recently, it has been investigated how the thermodynamic functions vary when
the surface interactions are taken into account for a nucleon which is confined
in a Woods-Saxon potential well, with a non-relativistic point of view. In this
manuscript, the same problem is handled with a relativistic point of view. More
precisely, the Klein-Gordon equation is solved in presence of mixed
scalar-vector generalized symmetric Woods-Saxon potential energy that is
coupled to momentum and mass. Employing the continuity conditions the bound
state energy spectra of an arbitrarily parameterized well are derived. It is
observed that, when a term representing the surface effect is taken into
account, the character of Helmholtz free energy and entropy versus temperature
are modified in a similar fashion as this inclusion is done in the
non-relativistic regime. Whereas it is found that this inclusion leads to
different characters to internal energy and specific heat functions for
relativistic and non-relativistic regimes.
