Finite Element Numeric Simulation of Organic Solar Cells with Gold Thin Film

In this paper, we have explored the potential of organic solar cells with gold layers, simulating different geometries and comparing them with the experimental data obtained from the devices produced at the “optoelectronic organic devices laboratory at Ben Gurion University of the Negev, Israel.” Thin-film heterojunction solar devices are analyzed using a basic chemical technology of GLASS/ITO/PEDOT,PSS/P3HT, PCBM, and another type of nanostructure where the gold layer is added. A standard device is realized on top of a transparent substrate such as glass or flexible polymer Polyethylene Terephthalate (PET). he first layer is the anode, which is made of conductive material and is also transparent. In our case, the very common material Indium-Tin-Oxide (ITO) is used. To facilitate the transition between the active layer and the anode, an intermediate layer is introduced. Hole Transport Layer (HTL) 's high hole mobility allows holes to move towards the anode instead of the cathode. On top of these layers the organic active layer is constituted by a blend of two organic materials configuring a multiple junction morphology (Bulk Heterojunction or BHJ). In our case, two commonly organic materials [6,6]-Phenyl C61 Butyric acid Methyl ester and Poly(3-Hexylthiophene-2,5-diyl) (PCBM:P3HT) are used. The cathode on top organic active layer is made of highly conductive opaque metal, mostly Aluminum (Al). The finite-element method has been used to compute the electromagnetic field distributions. The results show that the model with the gold layer increases the electrical performance of organic solar cells. Keywords— power density flow; FEM; organic solar cells.


I. INTRODUCTION
Power generation by solar cells/modules is a promising renewable energy candidate for future cars. Most EFVs are equipped with large-capacity batteries that can be charged with electricity generated by solar cells/modules. It has been reported that installing 800 W rated solar power modules on automobiles can significantly reduce CO 2 emissions from passenger cars. However, the photovoltaic modules need to be installed on the roof and the side doors, engine hood, and the hatch of passenger cars [1]. Green technology includes urban context services for buildings, public infrastructures, and smart community involving sustainable energy generated from solar panels, wind turbines, and biogas. The challenge of providing the world energy demand is aggravating each year, with billions of people still living without proper electricity access.
The conventional energy sources are still costly and highly polluted. In the last decade, large amounts of money in renewable energies have been invested, which are clean, inexpensive, and suited for various applications [2], [3]. Solar energy is the most popular among alternative green energy sources. Recently, organic solar cells (OSCs) have emerged as an efficient and sustainable energy technology. Their prominent attributes of being lightweight, low-cost, mechanically flexible, and enabling ease of largescale fabrication have attracted even more attention from academia and the industry over the decades [4]. These properties can combine to a low-cost large-area device with an undemanding fabrication process [5]- [10].
OSCs may find application in a host of technologies, ranging from smart windows and skins of future buildings to optical displays, glare-control devices, and rearview mirrors in automotive. A photo-electrochromic device with integrated photovoltaic and electrochromic components enables an adjustable transparency glazing where the photovoltaic part supplies the power to drive the coloration. Such stand-alone, self-powered, wireless devices are of commercial interest for integration into glass windows and surfaces of buildings and automotive or aeronautic vehicles.
These devices with smart window applications can be effectively implemented in modern energy-saving buildings [11]. Many resources were invested in pursuing better organic materials, fabrication processes, and device configurations. As evidence, the efficiency of a lab OSC has already reached 11% percent. Yet, there is still a need for extensive investigation to exploit the full extent of this technology. The optical transmittance and conductivity for thin metallic films, such as Au, are critical parameters in organic photovoltaics for obtaining an extra-ordinary improvement in the overall solar cell efficiency (to the order of 49%) when the Au thin film transmittance was increased from 38% to 54% [12].
Gold quantum dots (AuQDs) are employed as photosensitizers in organic thin-film solar cells (OSCs) to improve their photoelectric conversion properties. The enhancement in the polymer solar cells efficiency is related to the increase in their absorptivity due to the far-field and near-field effect of localized surface plasmon resonance. It is induced by the presence of the Gold nanorods and introduced by spin-coating their aqueous solution directly on top of poly(3-hexy lthiophene-2,5-diyl): [6,6]-phenyl-C 61butyric-acid methyl ester layer, in the interface between the photoactive layer and the metallic rear electrode [13]. The periodically arranged colloidal gold nanoparticles integrated at the bottom electrode of organic solar cells (OSCs) and light absorption enhancement in the active organic layer are demonstrated experimentally and numerically investigated in bulk hetero-junction solar cells based on the Finite-Difference Time-Domain (FDTD) and Transfer Matrix Method (TMM) [14]- [17].
In this paper, the optical models relative to two organic samples exhibiting the same structure GLASS/ITO/PEDOT: :PSS/P3HT:PCBM are considered. The only difference between the two consists of an addition of gold layers in one of them. The electromagnetic analysis is aimed at evaluating the electric power obtainable. It was conducted using a Finite Element discretization in which the devices behaviour has been simulated on a large range of frequencies. We have referred to the OSCs fabricated in Optoelectronic Organic Semiconductor Devices Laboratory (OOSDL) (see Fig.1). Fig. 1 The manufactured organic solar cell.
The paper is structured as follows: in section II and III, photoelectric materials and fabrication of OSCs are described in details; in section IV, the FE numerical analysis is illustrated; in section V numerical simulations are compared to experimental data. Conclusions are presented in section VI.

II. MATERIAL AND METHOD
OSCs are made of sandwiching layers with different functionalities, as shown in Fig. 2. A standard device is realized on top of a transparent substrate such as glass or flexible polymer Polyethylene Terephthalate (PET). The first layer is the anode, which is made of conductive material and is also transparent. In this work, the very com-mon material Indium-Tin-Oxide (ITO) is used. To facilitate the transition between the active layer and the anode, an intermediate layer is introduced. The high hole mobility of the Hole Transport Layer (HTL) allows to holes to move towards the anode instead of the cathode [18]- [20]. These three layers are transparent in order to allow the light to penetrate to the active layer. On top of these layers the organic active layer is constituted by a blend of two organic materials configuring a multiple junction morphology (Bulk Heterojunction or BHJ), in our case two commonly organic materials [6,6]-Phenyl C61 Butyric acid Methyl ester and Poly(3-Hexylthiophene-2,5-diyl) (PCBM:P3HT) are used. The cathode on top organic active layer is made of highly conductive opaque metal, mostly Aluminum (Al). The process of photocurrent generation is shown in Fig. 3. • Photons absorbed in the organic layer (mainly in the P3HT) generates excitons, a quasi-neutral particle composed of an electron and hole bounded together by Coulomb force. The auxiliary energy for dissociation is provided at the interface of the PCBM:P3HT. • The excitons are diffusing toward the organic materials interface. The electron transfers into the adjacent molecule, and a second quasi-neutral particle is generated, a Polaron-Pair (PP). The PP is a state of an electron and hole bounded together by weaker coulomb force and probability dissociating to free charges. Since excitons have a concise diffusion length (few nanometers), efficiently, the carriers dissociate only at the interface of organic materials composed by the active layer. A dense junction layer is required to achieve a BHJ configuration. (3,4) In the next phase, the finite probability for the PP to decay to the ground state or dissociate to free charge carriers depends highly on the internal electric field (Fig. 3). (5) The free charge carriers can then transport via an electric field to electrodes, holes to anode, and electrons to cathode. However, since the device is a BHJ, instead of reaching the electrodes, (6) the free charges can meet with another organic interface to generate again a PP, this process called Back Electron Transport (BET). This is a closed-loop with a finite probability of collecting the charges and produce electricity. Due to fabrication limitations, the transparent anode slightly spreads out from the actual area of the organic layer to make a place connected to the outer circuit. This additional ITO increases power losses. To avoid this, a gold layer was evaporated right next to the location of cells.
This highly conductive later that has a similar work function to the ITO reduces the transition distance of holes inside the transparent ITO. To examine this configuration, a set of OSCs has been produced. A sample of realized device is shown in Fig. 1. The pro-cess steps are as follows: a 12x12 mm glass coated with an ITO with dimensions of 6x12 mm and a thickness of 90 nm and resistivity of 20 Ω/sq is used as a substrate. The substrate is cleaned in an ultrasonic bath with acetone, methanol, and iso-propanol for 15 min each, after which it is placed in a plasma asher for 4 min. The second stage is the thermal evaporation of 30 nm of gold using the shadow mask shown in Fig. 4. The shadow mask was designed in a way that the gold will be well-positioned. The shadow mask consists of 9 modules; each has four strips with a width of 1.5 mm, which defines one solar cell. Thus, on each substrate, four cells are located. Each module consists of different sets of strip lengths providing different cell lengths, from 1 mm to 6 mm. Following the bottom contact formation, a 30 nm of HTL made of the highly conductive, high transparent polymer poly(3,4 ethylene dioxythiophene) polystyrene sulfonate (PEDOT:PSS) is spin-coated, and the device is dried for 1 hour at high temperature to extract the excessive water.
Afterward, 100 nm of the organic layer (PCBM:P3HT) is spin-coated inside a nitrogen environment to avoid moisture and oxygen exposition. Then, 80 nm of Aluminum is evaporated through the same shadow mask shown in Fig. 4. In this step, the substrate is rotated 180° and placed in the corresponding module to create a continuous strip con-sisted of gold on one side and Al on the other side. To further increase performance, the device is annealed at 140 ° for 20 minutes. To complete the device, eight electric wires are then glued using conductive silver epoxy to the device, one for each electrode. Then, a small piece of glass is glued on top of the device for encapsulation. The following equations govern the electromagnetic field distribution for OSCs: Where ω is the angular frequency, µ 0 and ε 0 are the permeability and permittivity of free space, respectively µ r is the relative permeability and ε r is the relative permittivity which is assumed to be constant in each material. By combining (1) and (2) the following equation is obtained: Where k 2 0 = ω 2 ε 0 µ 0 . The physical organic devices derive the three-dimensional models with pe-culiar geometries, and materials are shown in Fig. 5 and Fig. 6. The first model consists of the following layers from the bottom: glass, ITO, PEDOT: PSS layer, PCBM: P3HT, and Aluminum representing the basic components of the solar cell without the encapsulation and protective cover. The component and its arrangement are shown in Fig. 5. The glass substrate is 0.7 mm thick, ITO layer and Aluminum are respectively 90 nm and 80 nm thicks, PCBM: P3HT is 200 nm thick, and PEDOT:PSS is 30nm thick. The aluminum layers are the smallest in size and thus determine the mesh size's slightest extent. In the second model, the layers are arranged as shown in Fig. 6 with the same basic model configuration, but a 30 nm thick gold layer is added between ITO and PEDOT: PSS. The FE solutions of equation (3) for the two 3D models are carried out using the RF Module of commercial product COMSOL Multiphysics. In the discretization, meshes are used at 2.5 nm length. The model meshes with coarse size mesh on the broader region, and the mesh is finer at the narrow regions such as the interface aluminum and active layers. Absorbing boundary conditions, perfectly matched layer (PML), are used in the simulations. Thin multi-layered structure procures the optical interference effect in each layer having distinct electrical conductivity. For this purpose, the optical and physical properties of organic materials are described by complex wavelength-dependent refraction index (n) and extinction coefficient (k) taken from the literature. For the gold the refractive index and extinction coefficient used in these simulations are: k = 3.5427, n = 0.16541 related to a wavelength of 6.644 µm. To represent the light in the simulations was used as an electric field incident in the device with wavelength ranging from 400 nm to 800 nm ( Fig.  7 and Fig. 8). We have compared the power spectral density for values obtained by simulation model with and without a layer of gold referred to the wavelength range between 400 nm and 800 nm and the electric power values obtained by experimental data for each organic solar cell.

III. RESULTS AND DISCUSSION
The device was characterized by measuring of currents and voltages. The measurements were performed under illumination using a solar simulator that produces light with 100 mW/cm 2 to reproduce the sun spectrum (AM 1.5). The IV traces were obtained using the source-measure unit Keithley 2420. The current-voltage characteristics of OSCs with and without a thin film of gold ranging from 0 to 0.7 Volts as shown in Fig. 9. It is worth noticing that the OSC containing a gold layer exhibited better performances. Fig. 10 shows the electric power extracted by the I-V characteristic of an organic solar cell with length of 5.50 mm in the organic sample (12 mm x 12 mm). The configuration model with layer of gold reaches a maximum electric power peak of 0.0239 mW while the maximum value for Osc without layer of gold is 0.01mW. This latter value is considerably lower, so proving that gold layer increases the efficiency and performance of organic devices.

IV. CONCLUSIONS
In this paper, two organic cell models are analyzed: the first exhibiting a gold layer for multilayer structure GLASS/ITO/PEDOT:PSS/P3HT: PCBM and the other organic sample without it. These structures have been implemented and compared with simulated models derived from physical devices. The results and comparison show that the gold layer model has increased the electrical performances with respect of others.