We experimentally demonstrate a sigmoidal variation of the composition profile across semiconductor heterointerfaces. The wide range of material systems (III-arsenides, III-antimonides, III-V quaternary compounds, III-nitrides) exhibiting such a profile suggests a universal behavior. We show that sigmoidal profiles emerge from a simple model of cooperative growth mediated by twodimensional island formation, wherein cooperative effects are described by a specific functional dependence of the sticking coefficient on the surface coverage. Experimental results confirm that, except in the very early stages, island growth prevails over nucleation as the mechanism governing the interface development and ultimately determines the sigmoidal shape of the chemical profile in these two-dimensional grown layers. In agreement with our experimental findings, the model also predicts a minimum value of the interfacial width, with the minimum attainable value depending on the chemical identity of the species. A central goal of modern materials physics is the control of interfaces down to the atomic level. In particular, the behavior of layered materials depends on the atomicscale structural roughness and chemical mixing across the interface [1]. Although abrupt interfaces between conventional semiconductors (such as III-V compounds) are fabricated and element profiles across these interfaces are obtained with atomic resolution, the relation between the layer growth processes and the parameters governing the interface formation and evolution is not satisfactorily understood. In this respect, there is an ongoing discussion about how interfaces can be quantitatively described on the basis of a growth model and whether there is a minimum interface width.Recently Hulko et al. [2,3] and have shown empirically that experimental concentration profiles in III-V two-dimensional (2D) heterostructures, e.g. quantum wells (QW) grown by molecular beam epitaxy (MBE), can be accurately reproduced by a sigmoidal function of the formHere, x 0 denotes the nominal mole fraction of one of the species, z is the position across the interface along the growth direction, and L is the parameter quantifying the interface width (L is proportional to the widely reported length W , over which the concentration changes from 10% to 90% of its plateau value). Moreover, the accuracy of the sigmoidal fitting seems to be independent of the experimental technique used to obtain the element distribution [2,5,7] and, more interestingly, of the compound semiconductor. In this letter, we show that a sigmoidal profile emerges from a simple model of cooperative growth with 2D island formation. Furthermore, the use of a generalized sigmoidal expression gives a reliable and systematic quantification of the chemical interface. It sheds light on basic aspects of the early stages of heteroepitaxial growth, and permits to find a correlation between the profile and the interface properties in morphologically perfect epitaxial layers [8], which have been grown in the thermodynam...