The hysteresis index (HI) measures the magnitude and type of the J-V hysteresis in perovskite solar cells.
We define a new hysteresis index as:
are the values of the integral power output in reverse and forward directions, respectively, and
This HI definition basically says: divide the "area" (integrated power output) between forward and reverse scans by the sum of "areas" below forward and reverse J-V characteristics.
It is valid if the forward and reverse characteristics do not cross!
A generalization of the HI definition for mixed hyteresis is indicated in
Solar Energy 173, 976 (2018)
Advantages of the new hysteresis index:
HI is an integral measure reflecting the difference between the forward and reverse scans in (0,Voc) scan range.
By construction, HI is properly scaled, -1 < HI < 1;
The hysteresis type is identified: positive values correspond to normal hysteresis, negative values indicate inverted hysteresis.
The choice of denominator in the HI definition ensures a balanced evaluation of both normal and inverted hysteresis.
(*)
Previous definitions of HI's:
Definitions based on the difference between the currents in forward and reverse scans at given bias (e.g. 0.8Voc, 0.6Voc, Voc/2).
Definitions based on the ratio between maximum power output of the two scans.
Definitions based on integral power output of the two scans.
Ignored aspects in previous definitions of HI's:
Changing the bias for evaluating HI leads to different HI's; comparing different samples may depend on the chosen bias.
Evaluating HI at a given bias point reflects only a local property of the J-V characteristics, unlike the proposed integral measure.
In the case of mixed hysteresis (i.e. there is a crossing point between the forward and reverse characteristics), the hysteresis type may change depending on the chosen bias point.
Only one of the currents is typically considered in the denominator definition of HI's; this may lead to an unbalanced evaluation of normal and inverted hysteresis.
(*)
G. A. Nemnes, Cristina Besleaga, A. G. Tomulescu, Alexandra Palici, L. Pintilie, A. Manolescu and Ioana Pintilie,
"How measurement protocols influence the dynamic J-V characteristics of perovskite solar cells: theory and experiment", Solar Energy 173, 976 (2018) arXiv:1803.00285
