Comment on "Simulation of current–voltage curves for inverted planar structure perovskite solar cells using equivalent circuit model with inductance"

In a recent letter, Cojocaru et al.¹⁾ proposed an equivalent circuit containing an inductor for a perovskite solar cell with small hysteresis. Cojocaru et al. argued that the inductance originates from the equivalent circuit model of a Schottky diode mentioned in Ref. 2. However, the inductance of a Schottky diode is not an intrinsic physical property of the Schottky junction, but an extrinsic property of a packaged diode, i.e., the inductance of the package.^2,3) Since we cannot expect that a packaged Schottky diode is embedded in a perovskite solar cell, the physical meaning of the equivalent circuit is questionable. It is worth noting that the inductance of any packaged diode must be considered in high-frequency circuits, while it can be ignored in low-frequency circuits such as those used in the current–voltage characterization of a solar cell.

Cojocaru et al. also estimated the value of the inductance to be as high as 50 or 500 mH. Obviously, the high inductance is essential to reproduce the hysteresis under the scan speed assumed in Ref. 1. Unlike the commercial inductor shown in Fig. 4 of Ref. 1, neither winding nor a magnetic core is installed in a perovskite solar cell. Therefore, the inductance of a flat perovskite solar cell must be similar to that of a flat conductor. The inductance L (nH) of a flat rectangular conductor of length l, width w, and thickness t in centimeters is given by⁴⁾

$$\begin{equation} L=2.0\times l\times\left[\ln\left(\frac{2.0\times l}{w+t}\right)+0.5+0.2235\left(\frac{w+t}{l}\right)\right]. \end{equation} \tag{ 1 }$$

Since the circuit parameters (other than the diodes) as well as the inductor in the model shown in Fig. 2 of Ref. 1 seem to be normalized by unit area, we may assume l = w = 1 cm and t = 10 µm. The inductance is then calculated to be approximately 3 nH. This may be considered as the package inductance of the solar cell. Typical commercial Schottky diodes have similar package inductance values.^2,3) Although the inductance is raised if we use materials with high magnetic permeability and multiple windings of the wire, it is hard to expect an inductance as high as 50 or 500 mH in a device with such a small footprint as well as a low height.

Modern electronic circuit simulators are quite user-friendly and one can construct circuit models that generate plausible current–voltage curves with the desired hysteresis by manipulating them for a while. However, if a key circuit parameter in the model does not meet basic physical criteria, such as those based on electromagnetism, the model cannot be validated and probably does not provide a better understanding of the phenomenon under study.