A method for manufacturing the active plate of a flat matrix display screen, in which each cell comprises an electrode plate connected by a transistor to a first conductive line, comprising the steps of providing an outgrowth coated with an insulator of each first conductive line at the level of each cell; etching or making porous an end portion of each outgrowth; laterally growing, for example, by a VLS method, a PIP or NIN semiconductor structure in each end portion which has been etched or made porous; and establishing a contact at the free end of the semiconductor structure and forming a gate at the level of the median portion of the semiconductor structure.