Process for adaptation between two crystallized semiconductor materials, and semiconductor device

The invention relates to a process for growing, on a substrate of a first material (5), a layer of a second material (7) whose crystalline unit cell parameters do not match those of the first material. In order to avoid curvature of the substrate due to the stress caused by the mismatch between the unit cell parameters of the two materials (5, 7), the substrate is first subjected to a calculated stress by introducing into its crystal structure deforming domains (6) which induce a stress opposite to that imposed subsequently by the growth of the layer of second material. Depending on the linear coefficients of expansion of the two materials, the layer is grown epitaxially either on the face of the substrate stressed by the deforming domains or on its opposite face. Application to GaAs/Si semiconductor devices.