Semiconductors' Photoelectrochemistry: A Kinetic and Thermodynamic Analysis in the Light of Equilibrium and Nonequilibrium Models

Kinetic and energetic aspects of the photoinduced transfer of charge at the semiconductor−electrolyte interface are analyzed in the light of the equilibrium, conventional photoelectrochemical model (A) attributable to Gerischer, the irreversible, stochastic model (B) proposed by Williams and Nozik, and the nonequilibrium, irreversible model presented here. On the basis of detailed balance and local microscopic reversibility principles, Gerischer's model presents a complete theoretical framework able to describe the kinetic behavior of a photoelectrochemical cell and adopt the quasi-Fermi level formalism as an approach to nonequilibrium, illumination conditions Although model A considers entropy loss as unavoidable (the entropy increases to a maximum near equilibrium), it is not able to predict the time dependent entropy term which characterizes any irreversible process (nonequilibrium conditions). By contrast, model B considers detailed balance and microscopic reversibility principles to be incompatible with the existence of irreversibility, which constitutes a handicap for describing interfacial charge-transfer rate constants under illumination. Moreover, the stochastic model does not take into account the entropy that must be lost in any photoelectrochemical reaction. To overcome the limitations of models A and B, a new irreversible approach, model C, built up on the basis of nonequilibrium thermodynamics and able to reconcile the irreversible character of photoelectrochemical reactions with the production of entropy, is presented here. Identical kinetic behavior is predicted by equilibrium model A and nonequilibrium model C, since both models compute interfacial charge-transfer rate constant ratios in accord with detailed balance and microscopic reversibility principles. The physical meaning of the nonequilibrium quasi-Fermi energy as well as its thermodynamic implications in concepts like photogenerated free energy and entropy loss in a photoelectrochemical reaction are reexamined in the light of the Gibbs expression. A new energy balance formalism based upon the concepts of photoelectrochemical affinity and entropy production is introduced.