Abstract
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.
Highlights
A class of non-stoichiometric optoelectronic materials such as copper indium gallium selenide (Cu(In,Ga)Se2 or CIGS) and copper zinc tin sulfide/selenide (Cu2ZnSn(S, Se)[4] or CZTSSe) have become a significant topic of research and development as photovoltaic materials due their attractive properties compared to traditional silicon-based photovoltaic materials
The CVini model shows that rapid foreign interstitial diffusion with a changeover to foreign substitutionals via vacancy annihilation in vacancy-rich materials can lead to diffusion profiles fitted with the standard constant- and limited-source solutions of the Fick’s second law despite an induced non-equilibrium vacancy concentration
Assuming full validity of the CVini model, dissociative diffusion mechanism in vacancy-rich materials may have three experimental indicators: 1) Gaussian-like diffusion profiles are obtained despite a constant diffuser source; 2) fitting the experimental diffusion profile with the limited-source equation (Eq (14)) results in the limited-source profile slightly overestimating the experimental profile near the surface; 3) for CSeq/CVeq ratios 1, increasing the initial vacancy concentration CVini decreases the measured diffusion coefficient of the diffusion profile
Summary
A class of non-stoichiometric optoelectronic materials such as copper indium gallium selenide (Cu(In,Ga)Se2 or CIGS) and copper zinc tin sulfide/selenide (Cu2ZnSn(S, Se)[4] or CZTSSe) have become a significant topic of research and development as photovoltaic materials due their attractive properties compared to traditional silicon-based photovoltaic materials. Such attractive properties include higher optical absorption coefficients – resulting in reduced material utilization and cost – as well as earth-abundant, non-toxic elements inherent to CZTS. Two cases are studied where 1) the impurity interstitial diffusion is sufficiently rapid that vacancies are practically immobile, and 2) impurity interstitial diffusion becomes exceedingly fast that the concentration of impurity atoms in interstitial sites are maintained at the equilibrium value everywhere at all times, leading to the case where vacancy diffusion is the slowest process
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