A method of making a display device, the method including fabricating a matrix of light-emitting diodes (LEDs), each including electrodes accessible from a back face of the matrix and light-emitting surfaces accessible from a front face of the matrix; securing, onto the back face of the matrix, a stack of layers including at least one semiconducting layer, a gate dielectric layer, and a layer of gate conducting material; and starting from the stack of layers, fabricating an electronic control circuit electrically coupled to the electrodes, including fabricating field-effect transistors (FETs) including active zones and gates, the active zones being formed in the at least one semiconducting layer, and the gates being formed in the gate dielectric layer and in the layer of gate conducting material.