Light Absorption Enhancement in Organic Solar Cell by Embedding Ag Nanoparticles and Nanochains within the Active Layer

1 School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China 2 Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, Nanjing 210096, China 3 Suzhou Key Laboratory of Metal Nano-Optoelectronic Technology, Suzhou Research Institute of Southeast University, Suzhou 215123, China 4 School of Materials Science and Engineering, Southeast University, Nanjing 211189, China


Introduction
Organic solar cells (OSCs) based on conjugated polymer and fullerene composites, because of the various advantages, such as lightweight, solution processed, mechanical flexibility, and large-area coverage, have been intensively studied as a potential new candidate for solar energy conversion system [1][2][3][4].However, comparing to conventional solar cells, including silicon, GaAs, and CuIn  Ga 1− Se 2 [5][6][7], the OSCs have got relatively lower energy conversion efficiency and can not compete with conventional energy.This demerit is mainly ascribed to the poor light absorption of the active layer in the OSCs.In order to increase the light absorption of the OSCs, the thickness of active layer, usually being a few hundred nanometers (30-150 nm) [8][9][10], should be increased in conventional method.However, the low chargecarrier mobility and small exciton diffusion length of most molecular and polymeric materials limit the increase of the active layer thickness in OSCs [11,12].If the active layer thickness increases, this will in turn result in insufficient carrier generation and low power conversion efficiency.
To overcome the poor light absorption, several light trapping strategies may be explored in the design of OSCs to improve the power conversion efficiency.For instance, Kim et al. utilized solution-based titanium oxide as an optical spacer to harvest more sunlight [13]; Sista et al. employed tandem structure to improve the light absorption [8].Recently, researchers proposed a more novel approach that uses noble metallic nanostructures to obtain effective light trapping for thin-film solar cells [14,15].These nanostructures can excite localized surface plasmon resonances (LSPRs), arising from the collective oscillation of conduction electrons in noble metal nanoparticles when the electrons are disturbed from their equilibrium positions, and usually served as a local field enhancer or a light scattering center depending on the size of metal nanoparticles [16].Up to now, numerous experiment studies on the influence of noble metallic nanostructures in inorganic solar cells have been performed, which involved nanoislands [17,18], spheres, nanorods, nanostars [14], nanogrids [19,20], and so forth.However, comparing to experiment investigation, theoretical study especially of the enhancement mechanism of light absorption has not been well developed.Duche et al. studied the light absorption enhancement induced by silver nanoparticles (SNPs) within the OSCs by finite-difference time-domain (FDTD) method [21]; however, they only modeled a thin film of active layer with nanoparticles in three-dimensional simulations.Shen et al. modeled a multilayer structure with silver nanoparticles imbedded in the middle of the active layer [22], but this structure is difficult to realize in experiment because the preparation process that adds water solvable nanoparticles into photovoltaic material solution (chlorobenzene or chloroform as the solvent) usually is incompatible or complicated.
In this work, we model a more realistic solar cell structure with cathode, active layer, and anode based on the finite element method (FEM).In this model, periodic monodisperse SNPs and silver nanochains (SNCs) composed of adjacent nanoparticles, used as light absorption enhancement structures, are placed in the interface between conductive polymer layer and active layer.Silver is chosen since it allows for low metal absorption loss and it also has a beneficial surface plasmon resonance wavelength suitable for enhancing the P3HT : PCBM OSC.We systematically investigate the effect of numerous factors, such as the size, period of monodisperse SNPs, and the length of SNCs, on the light absorption of the OSCs.Furthermore, the enhancement mechanism of light absorption is analyzed.The result shows that the origin of the light absorption enhancement should be attributed to near electric field enhancement of the nanostructures.

Simulation Models and Methods
We considered the OSCs layout with the schematic cross section shown in Figure 1.Due to the indium scarcity, an indium tin oxide-(ITO-) free structure [23] was used and the ITO was replaced by highly conductive polymer, poly (3, 4-ethylenedioxythiophene) : poly (styrenesulfonate) (PEDOT : PSS) with 30 nm thickness, which is a polymer with good thermal and chemical stability and good flexibility.For the active layer, the typical photovoltaic material, poly (3exylthiophene) : (6,6)-phenyl-C61-butyric-acid-methyl ester (P3HT : PCBM), with 1 : 1 weight ratio was used.Aluminum film with the thickness of 120 nm was used as the cathode.In this work, the light absorption structures include two types: periodic monodisperse SNPs (Figure 1(a)) and periodic SNCs (Figure 1(b)).The refractive index of PEDOT : PSS, silver, aluminum, and P3HT : PCBM are taken from the literature [18,24].Meanwhile, in order to save computation time and memory, we reduce the three-dimensional (3D) simulation to a two-dimensional (2D) one because 2D model can give similar results to a 3D model according to the early literature reported [25].
In this simulation, the calculation of light absorption is carried out by 2D finite element method (FEM).The FEM, which is a popular numerical approach for the solution of many engineering problems, is currently recognized as a powerful tool for the analysis of several optical structures, particularly those with arbitrary shapes, index profiles, nonlinearities, and anisotropies.We assume the light illumination on the device as incident plane waves under TM polarization with wavelengths of 300-800 nm, which is the region of interest for the P3HT : PCBM material.Periodic boundary conditions are set at the left and right boundaries, while perfectly matched layer (PML) absorbing boundary conditions are used at the top and bottom boundaries of the computational domain.In this paper, the absorption () in different parts of OSCs (in active layer, SNPs or SNCs) is calculated by integrating the divergence of the Poynting vector ⃗  (power flow) which is then normalized with input power  inc : in which  refers to the total volume of integration.To quantify the absorption capability of our OSC models in the wavelength region of interest wavelength (300-800 nm), we define a normalized weighted integrated absorption for the AM1.5G spectrum:

Results and Discussion
3.1.Absorption Property of Pristine OSCs.Firstly, we calculate the simulation model for pristine OSCs without any silver nanostructures and investigate the influence of the active layer thickness on the absorption.The absorption spectra of active layer are shown in Figure 2(a).On the whole, these simulation spectra matched the experimental data well [26,27].The three apparent vibronic absorption shoulders near the wavelengths of 500 nm, 550 nm, and 600 nm observed from the absorption spectra can be attributed to the strong interchain-interlayer interactions of P3HT [28].The calculated results proved that the model program is accurate and useful.It also can be obviously seen that the OSCs with thicker active layer harvest more incident sunlight.The values of absorption near 500 nm with 20 nm, 40 nm, 120 nm, and 300 nm active layer thicknesses are 22%, 62%, 87%, and 93%, respectively.However, it is interesting to note that the absorption spectrum with an 80 nm thick active layer is more intense than that with a 120 nm thick active layer in the wavelength range of 370 nm to 800 nm.To explore the reason, we calculated absorption spectra with other thicknesses (20-300 nm) of active layer and integrated the absorption spectra weighted by the AM1.5G solar spectrum (inset in Figure 2(b)).Figure 2(b) shows the integrated absorption  int as a function of the active layer thickness for normal incidence and there are two absorption peaks near 75 nm and 200 nm.These absorption peaks can be ascribed to interference effects of the two interfaces (also called Fabry-Perot effects) of the active layer when sunlight irradiates on the OSCs.This result matched well with previous works and this is why the absorption intensity with 80 nm active layer thickness is stronger than that with 120 nm [22].Obviously, increase of the active layer thickness can promote the incident light absorption.However, as the thickness increases, carrier recombination will become significant, which reduces the external quantum efficiency of the OSCs.To resolve this problem, we embed SNPs into the interface between active layer and buffer layer as absorption enhancement structures to harvest more incident light.This kind of OSCs with SNPs could combine the advantages of thin and thick active layers, in which both high carrier collection efficiency and strong light harvesting can be kept.

OSCs Embedded with Periodic Monodisperse SNPs.
In this section, we systematically investigate the optical property of OSCs embedded with periodic SNPs.In the simulation model, the particles size and the thickness of active layer are set as  (diameter) = 10 nm and  = 60 nm, respectively.The absorption spectra of the active layer which includes P3HT : PCBM and periodic monodisperse SNPs are shown in Figure 3(a), where a broadband absorption enhancement can be observed in the wavelength range of 300-800 nm for all periods.It is also found that the absorption enhancement value is associated with the period.The values of absorption in OCSs near 500 nm with the periods of 30 nm, 60 nm, 90 nm, 150 nm, and 450 nm are 93.4%,91.5%, 90.5%, 89.6%, and 88.3%, respectively.However, these absorption values contain the contribution of the periodic SNPs.In order to calculate the net absorption of P3HT : PCBM, the absorption 300 400 500 600 700 800  spectra of SNPs are calculated and shown in Figure 3(b).The absorption peaks near 380 nm are attributed to dipole resonance, which was caused by the alternating electric field on the SNP surfaces when incident light irradiated on the OSCs [29].Figure 3(c) exhibits the net light absorption of P3HT : PCBM (exclusive of SNPs).The main difference of the spectra from Figure 3(a) is that light absorption enhancement appears only in part of the wavelength range of 403-800 nm and light absorption weakens in 300-402 nm ranges.To achieve the whole absorption enhancement in OSCs embedded with SNPs, the integrated absorption weighted by AM1.5G irradiation was obtained (not exhibited) and relative enhancement (ratio of  int with SNPs to that without SNPs) in the active layer is shown in Figure 3(d).The result shows the light absorption enhancement as a function of the period of SNPs and there exists an optimum period of 30 nm maximizing the absorption enhancement with a factor of around 105.37%.Meanwhile, we also notice that the relative enhancement dropped below 1 when active layer thickness is less than 18 nm.This is because the volume of P3HT : PCBM is reduced and luminous flux decreases when OSCs are embedded with high concentration-density SNPs.
It is well known that the localized plasmon resonance in SNPs can cause near-field enhancement and enhanced scattering cross section, and both of them can be the mechanism to enhance the absorption in a solar cell in previous works.In order to further explore which mechanism of absorption enhancement exists in OCS embedded with SNPs, the active layer was divided into two regions (part I and part II).The region of part I contains the sublayer embedded with SNPs and the region of part II contains the other active layer (see the inset in Figure 4(b)).Figure 4(a) shows the net absorption spectra of P3HT : PCBM in the region of part I.The absorption spectra exhibit a broadband enhancement in the range between around 362 and 650 nm comparing to that in corresponding region of pristine OSC. between SNPs can be sharply enhanced by several orders of magnitude.Therefore, these SNPs are used as nanoantennas to increase the light absorption in this simulation model.
Apart from the case of particle size of 10 nm, we also calculate other OSC models which are embedded with SNPs with the size of 15, 20, 25, and 30 nm to achieve the optimal particle size  and period  of the SNP structures.Figure 5(a) shows relative enhancement in the whole active layer for various particle sizes () and periods ().These enhancement factors exhibit similar tendency as the particle size of 10 nm and highest factors as large as 105.2%, 105.3%, 105.9%, and 107.1% are observed for particle size of 15, 20, 25, and 30 nm, where the corresponding optimal periods are 72 nm, 115 nm, 158 nm, and 200 nm, respectively.From Figure 5(a), it is also found that OSC with big particle size usually needs large period to obtain better light absorption.Figure 5(b) depicts the absorption enhancement for various particle sizes () and periods ().The dash line indicates the position of optimal size and period.It visually demonstrates the relation between enhancement factor and SNP parameters (particle size  and period ) and the relation is summarized as in the following empirical formula: in which  optimum and  optimum refer to the optimal values to obtain highest absorption enhancement.

OSCs Embedded with Periodic SNCs.
In previous works, it is found that the localized electric field intensity near metallic nanoparticle surface can be enhanced significantly when nanoparticles get close to neighboring particles [24,30].It is because the overlapped plasmon gap modes distribute mainly at the gap regions or sharp corner area of the adjacent nanoparticles.Therefore, in this section nanochain structures composed of adjacent SNPs are used in OSC to enhance the light absorption.
In the simulation, SNCs including dimmer, trimmer, tetramer, and pentamer, composed of two, three, four, and five SNPs, are used as the light absorption enhancement structures.Thickness of active layer and diameter of SNP (as the unit in SNCs) are 60 nm and 10 nm.The periods for dimmer, trimmer, tetramer and pentamer are 40 nanometers, 60 nanometers, 80 nanometers, and 100 nanometers, respectively.These parameters keep the ratio of period to SNCs length as a constant in every case.For comparison, OSC embedded with periodic monodisperse SNPs was also calculated.The light absorptions with these nanostructures are shown in Figure 6.Comparing to OSC embedded with monodisperse SNPs and the pristine one, we can find that periodic SNCs can significantly boost the light absorption of OSCs when the wavelength is longer than 550 nm, especially in the long wavelength range of 650-800 nm where OSCs with monodisperse SNPs have a weak absorption.This result is contributed to the coupling effect of LSPRs excited on individual SNPs that would cause more powerful electric field around adjacent region in SNCs comparing to monodisperse SNPs.
To quantify the light absorption enhancement of OSCs with SNCs, we also achieved the integrating absorption in the wavelength region of 300-800 nm under AM1.5G irradiation condition.The factors of relative enhancement with the five types of nanostructures (monodisperse SNP, dimmer, trimmer, tetramer, and pentamer) are calculated as 3.13%, 29.1%, 35.5%, 39.4%, and 36.1%,respectively.The behaviors of significant absorption enhancement for SNCs can be ascribed to significant light trapping in the long wavelength range.

Figure 1 :
Figure 1: (Color online) Schemes of the simulation OSCs' models embedded with monodisperse periodic SNPs (a) and SNCs composed of adjacent SNPs (two, three, four, or five; only the case of four was shown).

Figure 2 :
Figure 2: (Color online) Calculations for pristine OSCs without plasmonic structures.(a) Absorption spectra () of active layer with different thicknesses .(b) Integrated absorption  int as a function of film thickness () for normal incidence (inset is AM1.5 solar spectrum).

Figure 3 :
Figure 3: (Color online) Simulation results for OSCs embedded with monodisperse SNPs with different periods.(a) Absorption spectra of active layer (include SNPs); (b) absorption spectra of SNPs; (c) net absorption spectra of active layer (exclusive of SNPs); (d) relative enhancement as a function of particle periods (the red dash line refers to the value of corresponding pristine OSC).

Figure 4 :
Figure 4: (Color online) (a) Absorption spectra of active layer in the region of part I; (b) relative enhancement for the region of part I; the inset shows the OCS model profile; (c) absorption spectra of active layer in the region of part II; (d) relative enhancement for the region of part II.

Figure 4 (Figure 5 :
Figure 4(b)  shows the relative enhancement with different periods and the highest factor can reach to 238.1% in the region of part I.However, for the other region (part II), there is no light absorption enhancement at any wavelength (Figure4(c)) and the enhancement factor drops below 1 (Figure4(d)).Contrasting the optical properties in the two regions, we can conclude that only the region containing SNPs can obtain obvious light absorption enhancement.The phenomenon also implies that the absorption enhancement is mainly attributed to near electric field enhancement and not to enhanced scattering effects; this is because only in the region of part I the electric field in the gap region