Transition from Capacitive to Inductive Hysteresis: A Neuron-Style Model to Correlate I–V Curves to Impedances of Metal Halide Perovskites

Abstract

Metal halide perovskite (MHP) devices often show different types of hysteresis in separate voltage domains. At low voltage, the impedance response is capacitive, and the cell gives regular hysteresis. At high voltage, the hysteresis is inverted, corresponding to an inductive response that causes a negative capacitance feature. We calculate the hysteresis current due to a chemical inductor model, and we show that the current is inversely proportional to the voltage scan rate. We formulate a general dynamical model for the solar cell response in the style of neuronal models for the action potential, based on a few differential equations. The model allows us to track the transition from capacitive to inductive properties, both by impedance spectroscopy and current−voltage measurements at different voltage sweep rates. We obtain a correlation of the time constants for the capacitor and the inductor. We interpret the origin of the low-frequency features in terms of ion-controlled surface recombination. This explains the strong correlation of the low-frequency capacitance and inductor, as both originate from the same mechanism. The methodology derived in this paper provides great control over the dynamic properties of metal halide perovskite solar cells, even in cases in which there are qualitative changes of the solar cell current−voltage response over a broad voltage range.

Correlation between hysteresis dynamics and inductance in hybrid perovskite solar cells: studying the dependency on ETL/perovskite interfaces

“…An early round of studies attributed this feature to accumulation of electronic charge at the interfaces. 19,20 A subset of lower frequency capacitance is called inductance (otherwise known as negative capacitance) [21][22][23][24] which appears as a hook or a loop in the Nyquist plot representation of EIS measurements and is believed to be detrimental to PSC performance. 25 Inductance has been interpreted in various ways in the literature such as the emptying rate of an intermediate state 19 and interfacial charge transfer resistance.…”

Electrical Charge Coupling Dominates the Hysteresis Effect of Halide Perovskite Devices

“…The problem is that many interpretations are based on apparently different models. A connection has been established between the type of hysteresis and the dominant features in the equivalent circuit of impedance spectroscopy. , This is also a matter of general interest since the inductive hysteresis turns out to be related to the famous negative capacitance widely observed across different disciplines . It is suggested that a stabilized negative capacitance holds the key for future generations of low consumption microelectronics. , …”

Radiative Recombination Processes in Halide Perovskites Observed by Light Emission Voltage Modulated Spectroscopy

“…The contact impedance contains a surface capacitance C 1 , a resistance R 1 , and a chemical inductor structure [ 60 ] composed of the resistance R a and inductor L a . [ 59,61 ] Therefore, the contact impedance is: $$\[{Z_{\rm{c}}} = {\left( {i{C_1}\omega \; + \;\frac{1}{{{R_1}}} + \frac{1}{{{R_{\rm{a}}}\left( {1 + i\omega /{\omega _{\rm{a}}}} \right)}}} \right)^{ - 1}}\]$$where ω a is the characteristic frequency of the contact chemical inductor. The bulk impedance is: $$\[{Z_{\rm{b}}} = {\left( {{C_\mu }i\omega + \frac{1}{{{R_{{\rm{nr}}}}}} + \frac{1}{{{Z_{{\rm{rad}}}}}}} \right)^{\; - 1}}\]$$and the radiative impedance has the expression: $$\[{Z_{{\rm{rad}}}} = {R_{{\rm{rad}}}}\left( {1 + {\tau _{\rm{d}}}i\omega } \right)\]$$…”

“…The contact impedance contains a surface capacitance C 1 , a resistance R 1 , and a chemical inductor structure [60] composed of the resistance R a and inductor L a . [59,61] Therefore, the contact impedance is:…”

“…We now develop a model for the interpretation of the S spectra in LEVS measurements, in combination with IS spectra that can be measured as a complementary information. The model is based on well-understood features that have been amply investigated in the methods of IS, [29,59] to which we add the equivalent circuit part associated with radiative recombination that is not observed in the electrical impedance measurements. [30] A list of the elements used is presented in Table 1.…”