  In this paper, we consider a microscopic semilinear elliptic equation posed
in periodically perforated domains and associated with the Fourier-type
condition on internal micro-surfaces. The first contribution of this work is
the construction of a reliable linearization scheme that allows us, by a
suitable choice of scaling arguments and stabilization constants, to prove the
weak solvability of the microscopic model. Asymptotic behaviors of the
microscopic solution with respect to the microscale parameter are thoroughly
investigated in the second theme, based upon several cases of scaling. In
particular, the variable scaling illuminates the trivial and non-trivial limits
at the macroscale, confirmed by certain rates of convergence. Relying on
classical results for homogenization of multiscale elliptic problems, we design
a modified two-scale asymptotic expansion to derive the corresponding
macroscopic equation, when the scaling choices are compatible. Moreover, we
prove the high-order corrector estimates for the homogenization limit in the
energy space $H^1$, using a large amount of energy-like estimates. A numerical
example is provided to corroborate the asymptotic analysis.
