Temperature dependence of the step free energy

We have derived an expression for the step free energy that includes the usual thermally induced step meandering term and a vibrational entropy term related to the step edge atoms, The latter term results from the reduced local coordination of the step atoms with respect to the terrace atoms and was introduced recently by Frenken and Stoltze as well as by Bonzel and Emundts. Additionally, we have added third and fourth terms that deal with the vibrational entropy contribution of the thermally generated step and kink atoms. At elevated temperatures the two latter vibrational entropy terms are of the same order of magnitude. Incorporation of these vibrational entropy terms results in a faster decrease of the step free energy with increasing temperature than anticipated previously. This enhanced temperature dependence of the stop free energy results in a lower thermal roughening temperature of the facet.