The solar cell performance parameters extraction usually relies on the dc current–voltage (J-V) measurements. Subsequent fitting with one- or two-diode equations gives information on series resistance (Rs), shunt resistance (Rsh), the saturation currents (J01 and J02) and the corresponding non-ideal factors (n1 and n2) in the quasi-neutral and depletion regions of the cell respectively . These values, however, are not enough or sometimes not very sensitive to actual electrical processes that govern the device's performance. Meaningful information may be gathered by analysing the complex dynamic impedance (Z=Zʹ + iZ′′) response of a solar cell to small oscillating signals in a range of frequencies, often as a function of external stimuli , , , , , , by the impedance spectroscopy (IS) technique. A solar cell's dynamic response is governed by charge accumulation, transport and recombination processes, the width of the space charge layer, and the density of trap centres. Various electrical processes happening in different cell regions, such as diffusion and recombination in the bulk of the absorber material, interfaces, and junctions, may be simply visualized from the IS data when plotted on a complex Zʹ-Z′′ plane, also called the Nyquist plot. One can visually distinguish the series and parallel resistances of a solar cell on the Nyquist plot, while the dc J-V curve needs diode equation fitting or comparison with the corresponding pseudo-J-V curve without the effect of series resistance obtained from a Suns-Voc measurement . The system then could be modelled as an electrical equivalent circuit (EEC) composed of various resistive (R1, R2 …) and capacitive (C1, C2 …) elements arranged in a simple configuration. It is essential that the EEC is based on the device's physical picture and be simple enough so that the data can be interpreted in this context. By studying the behaviour of these electrical elements with variations in external stimuli, the IS helps to understand and improve the performance of the devices, and also in the design of efficient power conditioning circuits in a photovoltaic system.
A parallel arrangement of the R and C (R||C) circuit draws a semi-circular arc on the complex Zʹ-Z′′ plot. In an IS measurement, the cell's response may appear as distinct time constants τi (=RiCi, i=1, 2 …) corresponding to well-resolved arcs, which can be ascribed to the individual electrical processes occurring in different regions of the cell based on the physical insight. EEC constructed of simple electrical elements are helpful for systems having one or more distinct RC time constants. However, in the presence of a time-constant distribution, the above assumption is no longer valid. To explain the complex behaviour of the response from a device having disordered junctions/systems in which traps are distributed in energy and space, advanced elements such as the constant phase element (CPE) can be incorporated into the EEC model , .
In contrast to the conventional diffused-junction silicon solar cells, the impedance response of the a-Si:H/c-Si heterojunction (SHJ) cell can be very sensitive to electronic exchanges with trap levels in the highly disordered a-Si:H layers. SHJ solar cells combine the high efficiency of c-Si wafer technology with the high throughput and low-temperature processing of a-Si:H thin films , . The near-perfect passivation of the silicon surface by a few nanometres thin intrinsic a-Si:H layer is the heart of such high voltage SHJ cells , , . The stack of intrinsic and doped (p- and n-type) a-Si:H layers serve as (hole- and electron-) selective contacts. Such a-Si:H layers present band offsets and discontinuities, aside from a very high density of trap states spread throughout their band gap. Although the layers are very thin, the high density of states distributed over the entire band gap can give contributions to complex optical and electrical responses, and transport and recombination processes are likely to be different from that of the diffused-junction c-Si cell and may not be discerned using the usual J-V analysis. Hence IS is an appropriate technique for characterizing the dynamic response of the SHJ cell.
Earlier work on IS of c-Si solar cells was to resolve different capacitive and resistive elements , , , ,  as well as to explain an anomalous negative capacitance  via modelling with simple EECs. Previously, IS has been adopted for the a-Si:H/c-Si HJ solar cells made on p-type silicon wafers to describe the influence of a buffer i-a-Si:H passivating layer, in which the appearance of distinct high-frequency arc was attributed to the effect of the buffer layer . Aside from this, the recombination processes in SHJ solar cells under illumination have also been described in terms of distinct electron and hole capture times extracted from the IS measurements . The SHJ cells in these reports had Al-alloyed back surface field as hole-selective contact; that is, only the front surface was passivated with i-a-Si:H buffer layer. Also, the influence of time constant distribution was not discussed, and the ac equivalent circuit consisted of two R||C units in a series combination. Previously, EEC with the inclusion of CPE has been used to explain the response of trap states in a-SiC/c-Si heterojunctions , thin film CdTe solar cells , and GaAs-based metal–oxidesemiconductor structures . In this article, we have investigated the impedance response of both-sides passivated, complete (p/i)-a-Si:H/n-Si/(i/n)-a-Si:H front-junction SHJ solar cells having power conversion efficiency within 15–18%. We discuss the type of response from the SHJ cells that leads to the CPE behaviour. Then we pay attention to the impedance behaviour of the SHJ cell under illumination. Finally, specific focus is given to the characteristic bias and illumination intensity dependence of the recombination time constant.
The front-junction SHJ solar cells (shown in Fig. 1) in this study are fabricated from as-cut n-type Si (FZ, 2Ω-cm, 〈100〉,280µm) wafer following due procedure: pre-clean, saw damage removal (SDR), texturing, post-clean, PECVD of passivating i-layer, p-type emitter, and the n-type BSF a-Si:H layers. The cells are defined by an area of 1.7cm×1.7cm ITO (∼80nm) deposited by sputtering, followed by evaporation of the Ag grid on the front. The rear side is fully covered with a stack of ITO and
Results and discussion
A conventional diffused-junction c-Si solar cell may be considered as a standard diode. The static J-V relationship of this diode is sufficiently explained by a standard diode equation governed by the classical Shockley diffusion law, which states that the transport is limited by charge carrier diffusion in the neutral bulk. In this circumstance, the impedance spectrum of the c-Si solar cell mainly consist of a simple semicircle expressed as an equivalent circuit of the resistance RP and
The impedance response of the disordered a-Si:H/c-Si heterojunction has a time-constant distribution, which could be successfully modelled by incorporating a CPE in place of a pure C in the EEC. In comparison with the IS of a standard homojunction c-Si solar cell, in which a CPE is seldom incorporated in its EEC, the necessary requirement of a dispersion parameter to model the IS of the SHJ cell indicates a broad distribution of time constants, that is, a shallow distribution of exponential
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Shahnawaz Alam for helping in the transparent conducting oxide layers preparation. The authors would like to acknowledge the financial support from the Department of Science and Technology (DST), Government of India, under the Water and Clean Energy area of the Technology Mission Division, Grant no. DST/TMD/CERI/RES/2020/48 and DST/ETC/CASE/RES/2023/04. One of the authors (S.M.) would like to thank DST for providing INSPIRE Faculty award, vide sanction order number DST/INSPIRE/04/2017/000821.
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