Device Modelling of Perovskite Solar Cells using Small Perturbation Methods

Abstract

Perovskite solar cells (PSCs) have shown large power conversion efficiencies in the laboratory, comparable to Silicon-based solar cells, in a very short time since their inception. However, a major impediment to their commercialization is their low stability in ambient environmental conditions and low tolerance to humidity. This instability is deeply connected to the mixed ionic-electronic conduction in PSCs, which is manifested in the hysteresis observed in current-voltage curves of the PSC, which depends strongly on external parameters of measurement. Therefore, this thesis aims to develop a holistic electrical model of PSCs using kinetic information to understand recombination, charge accumulation and transport of electronic carriers and ions. Existing models in the literature model the PSC similar to an organic solar cell, with a net electric field through the absorber that is the difference between the workfunctions (WF) of the two selective contacts. This electric field is modulated by the ions and determines the open circuit voltage (V_oc) via the built-in voltage (V_bi), therefore being mainly a charge collection model. However, this model cannot account for several types of hysteresis observed and also the giant capacitance that scales exponentially with voltage and light intensity, far larger than a purely ionic Helmholtz capacitance. Based on existing observations of an extremely slow decay of the V_oc and a persistent photovoltage, combined with huge charge densities visualised at the electron selective contact (ESL)/perovskite interface, a kinetic model based on the formation of an accumulation of both electronic and ionic carriers at the ESL/perovskite interface at large forward bias is proposed. This recombination based model connects the internal and external voltage of the PSC via the slow movement of the ions, which reproduces several of the hysteretic trends and their dependence on external parameters of voltage, scan speed and light intensity. The model is then extended to include surface recombination between the accumulated holes and electrons in the ESL, which depends strongly on the properties of the compact TiO2 layer. The interplay between charge accumulation and surface recombination explains the unique V_oc hysteresis observed in triple layer mesoscopic PSCs. The validity of the model depends largely on the nature and quality of transport in the PSC, which is then investigated by a two-pronged approach. The first method involves investigating the dependence of the ESL WF on the obtained V_oc for high efficiency PSCs. A WF variation of over 1 eV yielded very similar V_oc values and almost identical j_sc values, indicating that the V_bi does not control the V_oc and that transport in the PSC is predominantly diffusive, with potential drops likely being absorbed completely at the interfaces. After establishing that recombination is the dominant mechanism controlling the performance of the PSC, Impedance Spectroscopy (IS) was used to identify the internal separation of potential (ie alternate recombination pathways) in the PSC. Due to the large disparity in results in IS that depends on materials and methods, including the general lack of information obtained in the case of PSCs, Intensity Modulated Photocurrent Spectroscopy (IMPS) measurements were also carried out. From existing knowledge about the IS equivalent circuit (EC) and the large low frequency (LF) capacitance observed, a basic theory of IMPS for PSCs was developed to interpret the IMPS spectra, with an internal separation of photovoltage across resistances in the EC yielding a unique reduction in the external quantum efficiency (EQE) at low frequencies between 10 Hz – 10 mHz. This effect was also directly measured from the standard method of measuring the EQE using the differential spectral response method, where chopper frequencies between 10-500 Hz yield a variation as large as 10% in the measured EQE at short circuit (SC) conditions. In addition, the nature of the elements of the EC forming the time constants in either quadrant in an IMPS Q-plane plot is clarified through detailed derivations and simulations. Finally, IMPS and IS measurements were carried out at OC conditions to develop the underlying EC using information and parameter matching from both small perturbation techniques. This allows for the observation of an extra capacitance from IMPS measurements that is invisible in IS measurements due to the different elements forming time constants in either technique. This capacitance is two orders smaller than the giant LF capacitance, whose charging resistance is critical at controlling the net device resistance at standard voltage scan rates for measuring the PSC performance. The developed EC reproduces both the IS and IMPS response of PSCs, taking a large stride forward in creating a robust EC for the PSC that is generally subject to large variation in response based on materials and design.