## 1 Introduction  
In the relentless pursuit of clean and efficient energy sources, solar energy has emerged as a focal point of considerable interest. At the forefront of solar energy production, photovoltaics stands as a pivotal avenue, evolving through distinct generations to enhance their capabilities. The first generation, characterized by crystalline silicon, laid the foundation for solar technology. Building upon this, the second generation introduced amorphous silicon, refining the efficiency and expanding the potential applications of solar cells. The third generation represents a leap forward, incorporating innovative technologies such as nanocrystalline materials, quantum dots, organic compounds, and dye-sensitized solar cells, diversifying the landscape of solar energy capture. Advancing even further, the fourth generation, featuring materials like graphene, exemplifies the cutting edge of solar technology. Graphene, with its exceptional electrical conductivity and flexibility, holds promise for revolutionizing solar cells, paving the way for unprecedented efficiency and versatility in energy production [1, 2]. This dynamic progression across generations underscores the ongoing commitment to harnessing the full potential of solar energy, driving us towards a cleaner and more sustainable energy future [1]. Dye-sensitized solar cells (DSSC) belong to the third generation, comprising an electrode, a counter electrode, an electrolyte, and a dye. In this system, light excites an electron from the dye, initiating a journey through the electrode and the external circuit, ultimately being captured by the counter electrode, thereby regenerating the electrolyte as 3I-/I-3. Electrolyte 3I/I-3 is the electrolyte used, with a specific ratio of three iodine molecules (I3) to one iodide ion (I-) in the redox process. In this process, the iodide regenerates with the electron that goes through the counter electrode in the DSSC. It is important that there is no recombination between the dye/electrolyte to improve efficiency. Dye-sensitized solar cells (DSSCs) differ from other types of solar cells due to their unique design involving three essential processes, light absorption leading to the generation of electric charges, electron transport, and hole transport, all occurring through three distinct materials. This distinctive structure classifies them as highly interfacial devices. To maximize the energy conversion efficiency of DSSCs, it is crucial to improve both the charge transfer and transport rates. This enhancement ensures that a significant proportion of electrons can be extracted for external loads, minimizing the likelihood of electron-hole pair recombination. Notably, given the interdependence of transport and transfer rates, simultaneous optimization of electron transfer rates is imperative for achieving higher-efficiency DSSCs [3, 4]. Commonly, the electrode is composed of oxides such as TiO\({}_{2}\), SnO\({}_{2}\), ZnO, etc. [5]. Zinc oxide (ZnO) stands out as a promising material for DSSC electrodes due to its high electron mobility, wide bandgap of around 3.33 eV (similar to TiO\({}_{2}\)), and transparency in the visible light range, allowing light to penetrate and reach the dye molecules within the DSSC and, hence, facilitate effective light absorption and subsequent generation of electron-hole pairs [6, 7, 8]. The chemical stability of ZnO is critical, as it prevents DSSCs from degrading over time, even when exposed to environmental factors, thereby ensuring their durability and continued functionality [9]. Moreover, the flexibility in the synthesis of ZnO and the control over its morphology are additional factors that contribute to its suitability for DSSC applications. It has been reported that the nanoporous dye-sensitized ZnO films exhibit a remarkable propensity for ultrafast electron injection from the dye to the conduction band of the ZnO particles [10, 11].