  We generalize to N2LO Skyrme functionals the semi-classical approach of
Grammaticos and Voros in order to calculate the Extended Thomas Fermi
expressions of the new densities and currents appearing at the N2LO level.
Within a one dimensional symmetric semi infinite nuclear matter model and using
a simple Fermi-like density profile, we obtain an easy-to-use formula for the
surface energy including the contributions of the central, density-dependent
and spin-orbit terms up to $\hbar^2$. Such a formula can be easily used as a
first attempt to constrain the surface properties of new N2LO Skyrme
parametrizations. The N2LO parametrization tested in this paper is shown to
exhibit a shift (compared to a full Hartree-Fock calculation) which is
quantitatively similar to the one obtained with the traditional Skyrme
parametrizations.
