Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

Two sets of diffusion-reaction numerical simulations using a finite difference method(FDM) were conducted to investigate fast impurity diffusion via interstitial sites invacancy-rich materials such as Cu(In,Ga)Se2 (CIGS) andCu2ZnSn(S, Se)4 (CZTSSe or CZTS) via thedissociative diffusion mechanism where the interstitial diffuserultimately reacts with a vacancy to produce a substitutional. The first set of simulationsextends the standard interstitial-limited dissociative diffusion theoryto vacancy-rich material conditions where vacancies are annihilatedin large amounts, introducing non-equilibrium vacancy concentrationprofiles. The second simulation set explores the vacancy-limited dissociativediffusion where impurity incorporation increases the equilibriumvacancyconcentration. In addition to diffusion profiles of varying concentrationsand shapes that were obtained in all simulations, some of the profiles can be fittedwith the constant- and limited-source solutions of Fick’s second law despite thenon-equilibrium condition induced by the interstitial-vacancy reaction. The first setof simulations reveals that the dissociative diffusioncoefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. Inthe second set of numerical simulations, impurity-induced changes in thevacancyconcentration lead to distinctive diffusion profile shapes. The simulationresults are also compared with published data of impurity diffusion inCIGS. According to the characteristicproperties ofdiffusion profiles from the two set of simulations, experimentaldetection of the dissociative diffusion mechanism in vacancy-richmaterialsmay be possible