A one-dimensional growth model where particles are adsorbed with probability P _A and desorbed with probability P _D = exp (-nE/k _B T), where n is the number of nearest-neighbors (NN), E is the NN interaction energy, k _B is the Boltzmann constant and T is the temperature, is presented and studied by means of numerical simulations. It is shown that, at a given temperature, there is a critical adsorption probability [Formula: see text], such as the model displays a roughening/wetting transition between a smooth and a rough interface for [Formula: see text] and [Formula: see text], respectively. The former phase is bounded to the substratum while the later propagates at constant velocity away from the substratum. The roughening phase diagram, i.e. a critical curve [Formula: see text] versus T, is evaluated and discussed.