  Using a thermodynamical approach, we calculate the deformation of a spherical
elastic particle placed on a rigid substrate, under zero external load, and
including an ingredient of importance in soft matter: the interfacial tension
of the cap. In a first part, we limit the study to small deformation. In
contrast with previous works, we obtain an expression for the energy that
precisely contains the JKR and Young-Dupr\'e asymptotic regimes, and which
establishes a continuous bridge between them. In a second part, we consider the
large deformation case, which is relevant for future comparison with numerical
simulations and experiments on very soft materials. Using a fruitful analogy
with fracture mechanics, we derive the exact energy of the problem and thus
obtain the equilibrium state for any given choice of physical parameters.
