| Summary: | Two sets of diffusion-reaction numerical simulations using a finite difference method
(FDM) were conducted to investigate fast impurity diffusion via interstitial sites in
vacancy-rich materials such as Cu(In,Ga)Se2 (CIGS) and
Cu2ZnSn(S, Se)4 (CZTSSe or CZTS) via the
dissociative diffusion mechanism where the interstitial diffuser
ultimately reacts with a vacancy to produce a substitutional. The first set of simulations
extends the standard interstitial-limited dissociative diffusion theory
to vacancy-rich material conditions where vacancies are annihilated
in large amounts, introducing non-equilibrium vacancy concentration
profiles. The second simulation set explores the vacancy-limited dissociative
diffusion where impurity incorporation increases the equilibrium
vacancy
concentration. In addition to diffusion profiles of varying concentrations
and shapes that were obtained in all simulations, some of the profiles can be fitted
with the constant- and limited-source solutions of Fick’s second law despite the
non-equilibrium condition induced by the interstitial-vacancy reaction. The first set
of simulations reveals that the dissociative diffusion
coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In
the second set of numerical simulations, impurity-induced changes in the
vacancy
concentration lead to distinctive diffusion profile shapes. The simulation
results are also compared with published data of impurity diffusion in
CIGS. According to the characteristic
properties of
diffusion profiles from the two set of simulations, experimental
detection of the dissociative diffusion mechanism in vacancy-rich
materials
may be possible.
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