They also found that non-hysteretic samples (inverted structures) have not such capacitance increase at low frequency and furthermore identified non-capacitive hysteretic currents possibly related with reversible reactivity. In that formulation the curve was proposed to follow the law
 
J = Joper + Jcap + Jnoncap,                                                               (4)
where Joper is the operation current, typically described by equation 2, and Jnoncap can be assimilated to a step-like behavior
photocurrent, that the hysteretic behavior in timescales of seconds to minutes is most likely due to ions, which accumulate at the interfaces of the electrodes and screen the applied field independent of illumination. This was supported by conductance measurements by Beilsten-Edmands et al. [173] that specifically rejected the ferroelectric effect idea. Extra theoretical agreement was provided by van Reenen et al. [174] who achieve hysteresis in his modeled J V characteristics by including both ion migration and electronic charge traps, serving as recombination centers in a numerical drift-diffusion model. Also Richardson et al. [175] used simulations to join electrons, holes and defect mediated ion motion and obtain hysteretic J V patterns with the inclusion of the preconditioning procedures. 
B. Chen et al. [176] reunited several evidences to explain that J V curve hysteresis should be due to two main processes: (i) capacitive effects associated with electrode polarization that provides a slow transient non-steady-state photocurrent and (ii) modification of interfacial barriers induced by ion migration that can modulate charge-collection efficiency so that it causes a pseudo-steady-state photocurrent, which changes according to previous voltage conditioning. As they point out, both phenomena are strongly influenced by ions accumulating at outer interfaces, but their electrical and photovoltaic effects are different: while the time scale for decay of capacitive current is on the order of seconds, the slow redistribution of mobile ions requires several minutes.
Finally, in the recent work by Bisquert and co-workers [160] a model was formulated based on the accumulation of surface electronic charge at forward bias that is released on voltage sweeping, causing extra current over the normal response. The charge shows a retarded dynamics due to the slow relaxation of the accompanying ionic charge, that produces variable shapes depending on scan rate or poling value and time. The equation of work for this surface polarization model is a particular case of equation 4 and can be written as
 
Jnoncap = JncM
r1 + exp
q(V V01
 
 
−   mkBT
,                                  (5)
J = Joper + Cacc
dVs                                                                                                  (6)
dt
that attains JncM for positive potentials V > V0. The characteristic voltage V0 establishes the current onset and
where the accumulation capacitance Cacc is specified as a function of the surface polarization voltage Vs:
is related to a reaction potential.