Solid-phase reactions limited by an energy barrier

The reactions of formation and decay of defect-impurity complexes in solids are investigated theoretically on the basis of the generalized Liouville equation in phase space. The use of this equation (instead of the diffusion equation ordinarily used) yields an expression for the total rate constants of the reaction of complex formation which correctly takes into account both factors limiting the reaction rate in the general case: the diffusional mobility of the constituents and the energy barrier of the reaction. A comparison is made with the Waite theory, which is based on the diffusion equation and takes into account the presence of an energy barrier for the reaction by means of a radiation boundary condition on a reaction sphere. It is shown that the Waite method of taking the energy barrier into account leads to a systematic and substantial underestimate of the barrier-limited part of the total rate constant of the reaction. The possibility of generalizing the theory developed in this paper to the case of reactions which can involve not only atoms and defects but also the charge carriers in semiconductors (electrons and holes) is discussed. Zh. Tekh. Fiz. 67, 33–38 (November 1997)