I am trying to fit this kind of data plot. So far I came with a mix of 2 stretched exponential and one linear (Fitting1.jpg). But it's not that, as it cannot take the long convex curvature at the right of the plot (Fitting2.jpg). Also when I take the same set of function, it does not match other curves from the same experimental setup. This curve represents the current in function of time after starting the illumination of a solar cell. I am expecting super dispersive transport dictated by a complex netword of traps. Please let me know if you already saw such shape. Thank you.
I have seen similar shapes in kinetics of solid state reactions, when reaction mechanism changes. The latter part of the curve corresponds to diffusion-controlled process (it is not linear but curved). See Vyazovkin and Wight 1998 article " Isothermal and nonisothermal reaction kinetics in solids: in search of ways toward consensus". Generally, isothermal reaction curves show similar profiles for diffusion-controlled processes. That model might fit this process based on the characteristics of the system.
Dr. Blagojevic, thank you for your suggestion. I understood that the diffusion process concerns more atoms, ions or molecules for solid phase change. It might be relevant to my problem by supposing that the drop in the current would be cause by time and light dependence on the solid structure. I will dig further.
Dr. Liebel, thank you for your reply. You came with a similar conclusion to mine. Most of the work I refer to use the stretched exponential instead of sum of exponential. The stretch factor, beta, characterize the distribution of functions.
While diffusion does usually apply to atoms and ions, electrons can be viewed as diffusing through a material, especially if it is some kind of hopping conductivity. Dispersive electron transport dictated by a complex network of traps should look similar to transport of a molecule through a material dominated by adsorption sites (which is where diffusion becomes dominant process). Therefore, similar mathematical description could apply.
Yes I have dispersive transport in my solid. It is just hard with such data to know if the trend is dictated by the carrier generation or recombination or both. It would then be related to a slow generation mechanism (negative stretched exponential) which competes with an even slower recombination process (positive stretched exponential). The maximum current is normally reached after 3-5 minutes, it's pretty long I believe. I am looking lately into the concepts of photodarkening, photo-induced defect creation and photo-induced volume expansion.
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