The present invention provides a method for the continuous production of semiconductor ribbons by growth from a linear molten zone. The creation of the molten zone is achieved by application of an electric current, direct or alternating, parallel to the surface of the ribbon and perpendicular to the direction of growth, and intense enough to melt the said material, preferably using electrodes of the said material. The molten zone is fed by transference of the material, in the liquid state, from one or more reservoirs, where melting of the feedstock occurs. Preferably, the said electrodes and the said reservoir(s) are only constituted by the said material, thus avoiding contamination by foreign materials. The present invention is applicable, for example, in the industry of silicon ribbons production for photovoltaic application.