The effect of plasmonic nanoparticles and the thickness of anode interface layer on the efficiency enhancement of organic solar cells

In this work, the effect of gold (Au) nanoparticles (NPs) position on the optical parameters of organic solar cells (OSCs) has been investigated. The position of NPs inside the anode interface layer (AIL) and the active layer has been changed and the role of NPs position in light transmission, power absorption, short-circuit current density (Jsc), and maximum generation rate has been studied. I have also used silver (Ag) nanoparticles inside the middle part of the anode interface layer and have investigated the optical parameters and have compared the transmission and power absorption spectrum with Au NPs. Moreover, the role of AIL thickness in optical parameters has been studied. I use the finite-difference time-domain (FDTD) method for all simulations. This study can be useful for new perspectives and light management in organic solar cells.


Introduction
Photovoltaic technologies are the best solution for climate change and to use of renewable and sustainable energy. For these reasons, extensive efforts have been concentrated on developing new generations of this technology such as Organic solar cells, Quantum dot solar cells, Perovskite solar cells [1][2][3][4][5], etc. Organic solar cells are cheaper than current silicon-based technology and the process of manufacturing them is easier than silicon-based solar cells. They also have salient features such as lightweight, flexibility, and tunable transparency [6,7], etc even though, they have low power conversion efficiency.
Recent OSCs have over 10% power conversion efficiency (PCE) based on single-junction devices. Singlejunction terrestrial OSCs have reached an efficiency of 11.2 ± 0.3 under the global spectrum (1000 w/m * 2) at 25°C [8]. On the other hand, tandem OSCs have achieved 10.6% PCE under standard test conditions [9]. These days, theoretical studies have shown that PCEs of tandem, OSCs can achieve 15%-20% by optimizing the active layer properties and device architectures [10,11].
One of the promising ways to increase the efficiency enhancement of solar cells is plasmonic nanoparticles [12][13][14]. For example, in the previous work, We investigated the effect of plasmonic nanoparticles on the efficiency enhancement of thin-film silicon solar cells [15]. We found that using metallic nanoparticles improves the efficiency of silicon-based solar cells because NPs create highly concentrated near-field, increasing pathlength due to far-field scattering and waveguide coupling [11].
In previous studies, we worked on the optical properties of nanomaterials [16][17][18]. In this work, I have studied the effect of plasmonic nanoparticles on OSCs. I have used Poly (3,4-ethylenedioxy thiophene): poly (styrene sulfonate) (PEDOT: PSS) as an anode interface layer (AIL) and Poly (3-hexylthiophene) (P3HT) and [6,6]-Phenyl-C61-butyric acid methyl ester (PCBM) (P3HT: PCBM) as an active layer. The position of nanoparticles in these layers has been changed and the optical parameters have been investigated. I have also optimized AIL thicknesses and study the effect of variation of thickness on optical parameters.

Method and formalism
In this article, I use the finite-difference time-domain (FDTD) method based on solving Maxwell"s equations for our simulation. I investigate the effect of plasmonic nanoparticles on the efficiency of typical OSC with a photoactive layer of bilayer planar heterojunction which is sandwiched between two electrodes.
The sunlight ranging wavelength is from 300 to 750 nm. In this study, two kinds of nanoparticles Ag and Au are used because these nanoparticles have localized surface plasmon resonance (LSPR) in this sunlight ranging wavelength, and LSPR can improve the efficiency of OSCs [19]. The radius of these NPs is 30nm and the complex index (n,k) of Ag and Au were fitted from reference [20].
In this structure, Al; a metal with low work function (WF), with dimensions: X = 2, Y = 2, Z = 0.5 μm have been used as a cathode which has been taken from reference [21] and zinc oxide (ZnO) is as a cathode interface layer (CIL) with a thickness 0.07 μm and acts as an electron transfer layer (ETL). Zinc oxide (ZnO) is an inorganic n-type semiconductor that is one of the best materials for metal oxide cathode interface layer because it has low cost, easy synthesis, non-toxic properties [22], etc and this material was fitted from reference [23].
Poly (3,4-ethylenedioxy thiophene): poly (styrene sulfonate)(PEDOT: PSS) is used as an anode interface layer to modify the ITO electrode and acts as a hole transfer layer (HTL) and have been fitted from [25].
Metallic nanoparticles can enhance the absorption of light due to two mechanisms. One of them is the increasing of forwarding scattering cross-section and the second is a near-field enhancement [34]. Previous experimental literature has shown that metal NPs position is one of the most important factors for the efficiency enhancement of OSCs [10,14,35]. There are different fabrication methods such as electrodeposition [36], thinfilm evaporation [37], and chemical synthesis [38] which are used to combine metal NPs into OSCs.
The size, shape, and position of nanoparticles affect drastically improve the efficiency and performance of different geometries of OSCs. Typically, the nanoparticles are embedded in the active and buffer layer [39,40]. In this work, the position of nanoparticles has been optimized for the first time for this structure of OSC. Table 1 shows short circuit current density (Jsc), current, and generation rate for different positions of Au NPs with a diameter of 30 nm. It is clear that when NPs are located at the lowest part of AIL (the interface of AIL and active layer) Jsc is maximum. According to equation (1), PCE depends on Jsc thus, in this position we can have an increase in PCE.
where FF is the Fill factor, Voc is open-circuit voltage and Pin is the power density of incident light [41]. This device structure has optical parameters enhancement in comparison with previous works [42]. Figure 1 shows the schematic drawing of a standard polymer heterojunction solar cell. We have used Au nanospheres inside the active layer and AIL and have investigated the effect of the position of nanoparticles on the efficiency enhancement of OSC with 3D FDTD simulation. The generation rate is according to the following equation, where G is the exciton generation rate, P is the electromagnetic energy dissipation rate, ε″ is the imaginary part of complex permittivity, ω is the angular frequency of the electromagnetic wave and E is the local electric field [43].
In figure 2 we can see the transmission spectrum of a standard OSC and embedded OSCs with nanoparticles in different positions. We use Au NPs with a diameter of 30 nm inside the AIL with a thickness of 140 nm. It seems that the position of nanoparticles can affect the transmission spectrum. In this case, standard OSC has a maximum transmission, especially in the visible spectrum. Figure 3 compares the power absorption of OSC in different modes. As can be seen, the difference of power absorption spectra in the near-infrared region (NIR); 635-750 nm, is more than the visible wavelength. Moreover, the power absorption of OSC when the NPs are located in the lowest part of AIL for the NIR region is greater than others.

Silver (Ag) NPs located inside anode interface layer
Gold, silver, copper, and aluminum are used in photovoltaic devices as metallic nanoparticles because these metals can strongly interact with sunlight [44]. Here we use Ag NPs with a radius of 30nm inside the middle of AIL and compare the transmission and power absorption spectrum with Au NPs with a 30 nm radius. Figure 4(a) illustrates the transmission spectrum of OSC with Au and Ag NPs. As we can see, approximately there is no difference between the transmission spectrum of OSC when Ag and Au NPs are located at AIL. In fig 4  (b) it is clear that the power absorption spectrum of OSC for Au NPs is more than Ag for the middle range of wavelength spectrum and these results agree with previous works [44].

Variation of AIL thickness
Thickness-insensitive is an advantage for materials which use as an anode interface layer. There are many studies on the different materials to find thickness-insensitive materials [45].  In this section, the AIL thickness of standard OSC from 140 nm to 50 nm has been changed and the effect of thickness on light transmission, power absorption, and other device parameters has been investigated. As shown in figure 5(a) light transmission especially in visible range decreases with reducing the thickness of AIL. Figure 5(b) illustrates the absorption spectrum for different thicknesses. For the wavelength between 424-522 nm, the absorption increases with the growth of thickness of AIL. Moreover, for long-wavelengths, the absorption drastically depends on increase the thickness of AIL. In table 2 we can see the optical device parameters. Our results show that PEDOT: PSS is approximately a thickness-insensitive material because there aren't significant differences in the optical parameters in the table ((2). However, according to equation (1) device with AIL thickness 140 nm can have maximum PCE because of maximum Jsc.

Conclusions
In this work, the role of NPs position in the optical parameters of OSC has been investigated, and has been found that the position of NPs in the AIL and active layer is an important factor that modifies the optical parameters of OSC. I also compared the light transmission and power absorption spectrum for Au and Ag nanoparticles when they are located in the middle part of AIL and found that the absorption spectrum of Au NPs is greater than Ag for the visible wavelength thus they are more appropriate for the visible spectrum. I also optimized the thickness of AIL in this device structure and found that PEDOT: PSS is a thickness-insensitive material for visible wavelength and a good choice for AIL. This study opens new aspects in OSCs for light management.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).