  We have studied the structure and free energy landscape of a semi-flexible
lattice-polymer in the presence of a surface. At low temperatures coexistence
of two-dimensional integer-folded crystals is observed. As the temperature is
increased there is a transition from these crystalline configurations to a
disordered coil adsorbed onto the surface. The polymer then gradually develops
three-dimensional character at higher temperatures. We compute the free energy
as a function of increasing crystallinity and compare with the free energy
profiles assumed by the Lauritizen-Hoffman surface nucleation theory of polymer
crystallization. Our free energy profiles exhibit a `sawtooth' structure
associated with the successive formation of chain folds. However, in the early
stages of crystallization our profiles significantly deviate from those assumed
by surface nucleation theory because the initial nucleus is not a single stem
but two incomplete stems connected by a fold. This finding has significant
implications for the theoretical description of polymer crystallization.
