Steady-State and Transient Response Analysis of DSSC Based on Electron Diffusion Coefficient and Chemical Capacitance

Abstract

<p>A study of the transition from transitory state to steady state in DSSCs based on natural dyes is presented; cochineal was used as dye and <italic>Li</italic>⁺, <italic>Na</italic>⁺, and <italic>K</italic>⁺ were the ions added to the electrolyte. The photocurrent profiles were obtained as a function of time. Several DSSCs were prepared with different cations and their role and the transitory-to-steady transition was determined. A novel hybrid charge carrier source model based on the Heaviside function <italic>H</italic>(<italic>t</italic>) and the Lambert-Beer law, was developed and applied to analysis of the transient response of the output photocurrent. Additionally, the maximum effective light absorption coefficient <italic>α</italic> and the electronic extraction rate <italic>κ</italic> for each ion were determined: <italic>α</italic><italic>_Li</italic>_⁺, <italic>_Na</italic>_⁺, <italic>_K</italic>_⁺ = (0.486, 0.00085, 0.1126) cm⁻¹, and also the electronic extraction rate <inline-formula><mml:math id="m1" display="inline"><mml:semantics id="sm1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>κ</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mi>x</mml:mi><mml:mi>t</mml:mi><mml:mo>.</mml:mo></mml:mrow><mml:mrow><mml:mi>L</mml:mi><mml:msup><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msubsup></mml:mrow></mml:semantics></mml:math></inline-formula>, <italic>Na</italic>⁺, <italic>K</italic>⁺ = (1410, 19.07, 19.69) cm s⁻¹. The impedance model using Fick<italic>’</italic>s second law was developed for carrier recombination to characterize the photocurrent.</p>