Electrochemical charging
of nanocrystal films opens up new possibilities
for designing quantum dot-based device structures, but a solid theoretical
framework of this process and its limitations is lacking. In this
work, drift-diffusion simulations are employed to model the charging
of nanocrystal films and gain insight into the electrochemical doping
process. Through steady state simulations it is shown that the Fermi
level and doping density in the nanocrystal film depend on the concentration
of the electrolyte in addition to the value of the applied potential.
Time-resolved simulations reveal that charging is often limited by
transport of electrolyte ions. However, ion transport in the film
is dominated by drift, rather than diffusion, and the concentration
profile of ions differs substantially from concentration profiles
of diffusing redox species at flat electrodes. Classical electrochemical
theory cannot be used to model this type of mass transport limited
behavior in films of nanocrystals, so a new model is developed. We
show that the Randles–Ševčík equation,
which is derived for electrochemical species diffusing in solution,
but is often applied to films as well, results in a significant underestimation
of the diffusion coefficients of the charge compensating electrolyte
ions.