Simulation of the efficiency dependency of multi-junction photovoltaic cells based on titanium oxide and copper oxide using SCAPS software

1. Introduction

Recent research has turned toward the development of multi-junction structures, which can significantly enhance energy conversion by utilizing a broader spectrum of sunlight and mitigating recombination losses. Multijunction cells, by stacking materials with different band gaps, allow for more efficient photon absorption and better charge separation. Among the materials being investigated for solar cell production, TiO₂ and Cu_xO (cupric oxide – CuO and cuprous oxide – Cu₂O) are widely used due to their features, such as low production cost, low power consumption, ease of synthesis, and high theoretical efficiency [1–4]. Incorporating TiO₂ and Cu_xO in a multijunction configuration could overcome the limitations of single-junction devices, particularly those caused by lattice mismatch and interface defect densities. The development of current thin-film solar cells focuses on new structures that primarily enable reduced production costs and increased cell efficiency. However, implementing all new ideas in the laboratory and evaluating the results is unnecessary and a waste of time. Therefore, it seems reasonable to use tools that allow numerical simulations, enabling the “construction” and optimisation of solar cell performance, followed by physical testing of the most promising solutions. At present, researchers use a range of tools to simulate thin-film solar cells, depending on the problem complexity, application context, and expected outcomes [5–6]. The aim of our paper was to simulate TiO₂/Cu_xO multi-junction solar cells [7–10] and among several most popular simulation programs for such a type of junctions are the following tools: ADEPT [11, 12], AFORS-HET [13, 14], AMPS [15, 16], PC1D [17, 18], SCAPS [19, 20], SILVACO [21, 22], SENTAUROS [23, 24], and SESAME [25, 26]. We decided to use a solar cell capacitance simulator (SCAPS) software, which, despite the limitations and issues described later in this paper, allowed us to perform simulations of the operation of multi-junction photovoltaic structures based on titanium oxide and copper oxides. It should also be emphasised that this software is the most used and cited solution, which ultimately determined our choice. SCAPS is a onedimensional solar cell simulator widely used for modelling the electrical behaviour of heterojunction devices under varied physical and environmental conditions. The study evaluates how junction design, material parameters, and layer thicknesses influence cell efficiency and open-circuit voltage (V_oc). The results described in the literature indicate that optimisation of these parameters, especially at the heterojunction interface, can significantly improve carrier transport and overall device performance. The findings aim to provide design guidelines and highlight the potential of TiO₂/Cu_xO-based systems as sustainable alternatives for next-generation solar cell technologies.

2. Experimental

2.1. Methods

The present study involves a numerical simulation of both single-junction (n-TiO₂/p-CuO) and tandem (n‑TiO₂/ p‑Cu_xO/n-TiO₂/p-Cu_xO) solar cells using the SCAPS software [27–29]. SCAPS (version 3.3.12), along with supplementary scripts dedicated to multi-junction tandem cells, was applied to calculate key photovoltaic parameters from the current–voltage (J – V) characteristics. Among the evaluated parameters, the short-circuit current density (J_sc) and power conversion efficiency (η) under standard test conditions (AM1.5G spectrum, 100 mW/cm², 300 K) were of primary importance.

There are three strategies for studying multi-junction cells, mainly tandem cells, in the SCAPS program [19]. The first is based on calculating generation profiles for the tandem cell and the top and bottom cells. The second one used an additional contact filter containing reflection R’(λ) or transmission T’(λ) for the top and bottom cells. The last strategy considers both the bottom and top cells, as it encompasses all layers of the tandem cell, but during the calculation, some parts of the cell are replaced with an electronically inactive layer.

In our study, we use the first strategy, i.e., calculation of the generation G(λ, x) of electron-hole pairs from the photon flux N(λ, x) penetrating the tandem cell. To obtain the number of pairs G(x) generated in unit volume (cm³) per second for a given spectrum of light, the integration over all wavelengths should be done. The algorithm for this process is implemented in the script provided with SCAPS software. As for other strategies, the calculation is based on splitting the tandem to the top and the bottom cell, but before splitting, the generation profile G_tandem(x) is calculated. Then this profile is split into a top-cell profile G_top(x) and a bottom-cell profile G_bottom(x). These profiles are stored in the files and used for the next steps of the algorithm.

The number of electron-hole pairs generated in the cell is proportional to the number of photons N(λ, x) reaching the depth x in the cell:

where α(λ, x) is the absorption constant. The representative shape of G_tandem(x) for the tandem cell of TiO₂/Cu₂O/ TiO₂/Cu₂O is presented in Fig. 1.

Fig. 1. The generation profile G(x) for a tandem cell of TiO₂/Cu₂O/TiO₂/Cu₂O with a thickness of 0.1/0.4/0.1/1.0 μm, respectively.

The thicknesses of the individual layers were selected based on insights from previous research [4, 9], while the material properties used in the simulations were obtained from our previous work concerning SCAPS simulations [30]. The specific parameters for TiO₂ and Cu_xO layers used in the simulations are summarised in Table 1.

Table 1.

Parameters of TiO₂, and Cu_xO layers [13].

Material properties	n-TiO2	p-CuO	p-Cu2O
Bandgap (eV)	3.2	1.51	2.2
Electron affinity (eV)	4.2	4.07	3.2
Relative dielectric permittivity	10.0	18.1	7.11
CB effective density of states(1/cm3)	2 · 1017	2.2 · 1019	2 · 1017
VB effective density of states(1/cm3)	6 · 1017	5.5 · 1020	1.1 · 1019
Electron mobility (cm2/Vs)	100	100	200
Hole mobility (cm2/Vs)	250	0.1	80
Shallow uniform donor densityND(1/cm3)	1017	0	0
Shallow uniform acceptor density NA (1/cm3)	0	1016	1018

2.2. Problem setup

One of the simulated structures of the single and the tandem TiO₂/Cu_xO heterojunction solar cells is illustrated in Fig. 2.

Simulations were performed for different junction designs, layer thicknesses, and optical filters applied to contacts. Among many attempts to obtain the best efficiency, we have applied the SCAPS defined optical filter “95% mirror” (and set it as transmission) for the front contact and “80% mirror” (reflection) for the back contact. For a single junction cell, efficiency increases with increas-

(a) (b)

Fig. 2. (a) Single n-TiO₂/p-CuO and (b) tandem n‑TiO₂/p‑Cu₂O/ n-TiO₂/p-CuO heterostructure used in numerical simulations.

ing thickness of p-type layers (Cu₂O or CuO). In Table 2, the parameters for the following “single” cells are presented: n-TiO₂/p-CuO–0.1/2 μm and n-TiO₂/p-Cu₂O–0.1/2 μm.

The configuration for tandem cells is presented in Fig. 2 (b). The calculation procedure for the double layers was carried out according to the following scheme: 1) determining the thickness of the individual layers in tandem, 2) running a script prepared on the basis of the script provided with the SCAPS programme (“test tandem split generation.script”), and 3) changing the thickness of individual layers in order to achieve the best efficiency and repeating the calculation. Only the p-type layers, i.e., Cu₂O and CuO, were changed, because, as our previous simulations showed, they have the greatest influence on the final efficiency of individual cells [30]. Due to the shape of the curve G(x) (see Fig. 1), it was expected that the thickness of the first copper oxide layer (when viewed from the front contact side) should be as thin as possible so that a sufficient number of electron-hole pairs would be generated in the second junction.

To achieve the best efficiencies for tandem cells, a calculation was performed for different thicknesses of the first layer (#1) of copper oxide, taking the thickness of the second layer (#2) of copper as a parameter. The result of the calculations based on the script are graphs showing the individual parameters of the tandem cell, such as: number of electron-hole pairs generated G(x), efficiency of the cell as a function of the R_back parameter (%), i.e., reflection from the rear contact, current J_sc(R_back), V_oc(R_back), FF(R_back). Figure 4 shows the efficiency obtained for the selected R_back = 80%. The explanation of this behaviour of the performance dependence on the thickness of the layers can be based on the dependence G(x), i.e., the number of electron-hole pairs generated as a function of the distance x from the front contact of the tandem cell. The thinner layer #1, the more light reaches the second (counting from the front contact) junction and thus generates a greater number of electron-hole pairs there. However, excessive reduction in the thickness of layer #1 causes the first junction to malfunction. The thickness of the second layer #2 of copper oxide has no such significant impact on the performance of the entire cell as the thickness of the layer #1.

3. Results and discussion

The main parameters of the structures obtained from the simulations are summarised in Table 2. Furthermore, Figure 3 presents the J(V) relation for n-TiO₂/p-Cu₂O and n-TiO₂/p-CuO structures. The best parameters for the single heterojunction were obtained for the TiO₂/CuO structure and we expected even better results for a double heterojunction with TiO₂ and CuO layers. Unfortunately, we were unable to obtain results for the tandem structure of n-TiO₂/p-CuO/n-TiO₂/p-CuO, so we have decided to perform calculations for a double p-type Cu₂O layer and mixed p-type Cu₂O/CuO layers. The best parameters were obtained for the TiO₂/Cu₂O/TiO₂/CuO structure, but the results were worse than in the case of both single structures: TiO₂/Cu₂O, as well as TiO₂/CuO.

Table 2.

J–V characteristics of a single-junction n-TiO₂/p-Cu_xO and a different tandem n-TiO₂/p-Cu_xO/n-TiO₂/p-Cu_xO solar cells (25 °C).

Results	TiO2/Cu2O	TiO2/CuO	TiO2/Cu2O/ TiO2/Cu2O	TiO2/Cu2O/ TiO2/CuO
Open-circuit voltage, Voc (V)	1.8398	0.8386	8	2.1465
Short-circuit current, Jsc (mA/cm2)	8.5645	26.1522	1.84	5.2895
Fill Factor, FF (%)	65.95	84.96	20	49.39
Efficiency, η (%)	10.39	18.63	3.3	5.61

From the carrier generation profile G(x) shown in Fig. 1, a significant decrease in the number of generated carriers can be observed across the entire thickness of TiO₂ layers #1 and #2. However, the SCAPS numerical procedure fails to converge for TiO₂ layers with a thickness of 0.05 µ m, corresponding to half of the thickness used in the single-junction configuration. Moreover, reduced carrier generation in the interconnection region results in a substantial increase in the tandem device series resistance, thereby decreasing the short-circuit current (J_sc). It is important to emphasise that the used methodology provides a detailed and physically realistic description of recombination processes, bulk and interfacial defects, as well as charge-carrier transport within each sub-cell, and is therefore well suited for material comparison and the analysis of design trends in tandem device architectures. However, it does not represent a fully self-consistent model of a series-connected tandem device, as it does not explicitly account for the interconnection layers or the recombination junction, nor does it enforce a global current–voltage coupling between the sub-cells. Consequently, the results obtained within this framework should be interpreted as qualitative and comparative rather than as a direct prediction of the absolute electrical characteristics of the complete tandem device.

(a) (b)

Fig. 3. Current density vs. voltage: (a) n-TiO₂/p-Cu₂O structure, (b) n-TiO₂/p-CuO structure.

Figure 4 shows the efficiency of a tandem cell of TiO₂/Cu₂O/TiO₂/Cu₂O. The horizontal axis shows the thickness of the first (when viewed from the front contact side) layer of Cu₂O and the thickness of the second layer of Cu₂O is marked with different colours. The grey colour indicates cases where it is not possible to determine the performance. The thicknesses of both titanium oxide layers were 0.1 μm. The data were matched using a function of the form y = Ae[–Bx] with two parameters: A and B. From Fig. 4, it can be seen that the highest efficiency was achieved for the following thicknesses of copper oxide layers: layer #1: 0.4 μm, layer #2: 1 μm (parameters of tandem are in Table 2). Analysing the graph, we can also see that the efficiency of the tandem cell increases with increasing thickness of the layer #2 and with decreasing thickness of the layer #1. However, once a certain minimum thickness of the layer #1 is exceeded, it is no longer possible to obtain a solution using the method implemented in the script (probably due to numerical problems).

Fig. 4. Efficiency dependence of the TiO₂/Cu₂O/TiO₂/Cu₂O multi-junction on the thickness of Cu₂O layer #1 for various thicknesses of Cu₂O layer #2.

4. Conclusions

TiO₂/Cu_xO photovoltaic cells, due to their structure and the availability of materials, are widely studied worldwide, including by our team. Thanks to buffer layers or annealing, we achieved progressively higher cell efficiency in our previous experiments. To further improve our structures, we used the SCAPS program to simulate both single and tandem TiO₂/Cu_xO structures. Due to the structure and physical processes in the layers, we expected to achieve improvements in the parameters of tandem structures compared to single ones. However, it turned out that the best efficiency was obtained for the n-TiO₂/p-CuO single structure (18.63%), while the best result for the n-TiO₂/pCu2O/n-TiO₂/p-CuO tandem structure was only 5.61%. Unfortunately, it was not possible to perform simulations of tandem n-TiO₂/p-CuO/n-TiO₂/p-CuO cells due to an emerging discrepancy in the numerical calculations.

In contrast, the numerical procedure for the TiO₂/Cu₂O/ TiO₂/Cu₂O tandem returns an unexpected value of V_oc ~ 8 V and an FF of 20% (Table 2), whereas the parameters extracted and calculated directly from the corresponding simulated J – V curve are: J_sc = 1.8 mA/cm², V_oc = 3 V, FF = 56%, and efficiency η = 3.08%.

Difficulties in simulating the properties of tandem systems of photovoltaic cells are also indicated in the SCAPS user manual, where one can find information about the frequent occurrence of convergence in the simulation of more than one number of p-n junctions.

The simulation results obtained in this study differ from those reported in the literature, where multilayer structures typically exhibit an increase in solar cell efficiency. One of the possible explanations of this result are optical losses in the first junction, what is confirmed by reduction of electron-hole pairs generated in the second cell of the tandem. In addition, the applied methodology limitations do not give back a fully self-consistent model of a seriesconnected tandem device, as it neither explicitly accounts for the interconnection layers nor enforces a global current–voltage coupling between the sub-cells. Therefore, due to the limitations of the SCAPS simulation model, the authors will verify the results both theoretically, by using additional simulation tools and experimentally, by fabricating analogous photovoltaic structures via the magnetron sputtering method.

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