We investigated a semiconductor heterostructure based on InGaAsP multi quantum wells using optical and electrical characterizations in the scope of hot carrier solar cell device. The potential of the investigated quantum well structure to overpass the Schockley Queisser limit is discussed. Population density, temperature and quasi-Fermi level splitting of photogenerated carriers are investigated by fitting the full luminescence spectra using generalized Planck's law. A proper optical study is realized thanks to a detailed description of the absorption of excitons and free carriers in the quantum well. Optical measurements are compared to electrical measurements where the open circuit voltage electrically measured is higher than the minimum absorption threshold. To probe the hot carrier effect in such measurements we look at the changes in thermodynamic properties of carriers in the quantum well and in the barriers when changing the excitation power and the electrical bias.