From Astrophysics to Perovskites: Why Saha Physics Cannot Describe the Exciton to Free Electron–Hole Pairs Statistics in Semiconductors

The Saha equation has long served as the standard model for describing thermodynamic equilibrium between neutral atoms and their ionized counterparts in astrophysical plasmas. Over the past decade, this formalism has been increasingly adopted to describe the equilibrium between excitonic and free electron–hole (e–h) populations in semiconductors, especially halide perovskites. Here, we argue that this application is fundamentally limited. The Saha equation has been developed for systems in thermodynamic equilibrium, while a photoexcited semiconductor is out of equilibrium. Moreover, in all semiconductors, strong many-body interactions, density-dependent Coulomb screening, and band gap renormalization invalidate the key Saha assumption of a fixed exciton binding energy. As a result, Saha-based phase diagrams fail to capture the Mott transition, the density-driven transition from an excitonic gas to a plasma of free electron–hole pairs, and to describe semiconductor laser operation. We hope that our considerations help the perovskite community correctly describe the electronic population in their works.