Modeling of High-Efficiency Multi-Junction Polymer and Hybrid

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Article Modeling of High-Efﬁciency Multi-Junction Polymer and Hybrid Solar Cells to Absorb Infrared Light

Jobeda J. Khanam and Simon Y. Foo * Department of Electrical and Computer Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-850-410-6474

Received: 7 January 2019; Accepted: 16 February 2019; Published: 22 February 2019

Abstract: In this paper, we present our work on high-efficiency multi-junction polymer and hybrid solar cells. The transfer matrix method is used for optical modeling of an organic solar cell, which was inspired by the McGehee Group in Stanford University. The software simulation calculates the optimal thicknesses of the active layers to provide the best short circuit current (JSC) value. First, we show three designs of multi-junction polymer solar cells, which can absorb sunlight beyond the 1000 nm wavelengths. Then we present a novel high-efficiency hybrid (organic and inorganic) solar cell, which can absorb the sunlight with a wavelength beyond 2500 nm. Approximately 12% efficiency was obtained for the multi-junction polymer solar cell and 20% efficiency was obtained from every two-, three- and four-junction hybrid solar cell under 1 sun AM1.5 illumination.

Keywords: short circuit current density (Jsc); open circuit voltage (Voc); power conversion efﬁciency (PCE); ﬁll factor (FF); organic/polymer solar cell (OSC); hybrid solar cell (HSC)

1. Introduction In the past few years, polymer solar cells (PSCs) have been attracting much attention due to their ease of processing, low cost, flexibility and lightweight nature compared to the traditional inorganic solar cells. The thickness of the materials used in polymer solar cells is limited due to their high absorption coefficient [1–3]. Although the organic solar cell (OSC) has a good future, its efficiency is still very low compared to the silicon solar cell [4]. There have been various methods implemented, such as annealing, device structure tuning and active material modification, to improve the efficiency of the PSC [5]. Among the various methods involving two or more organic junctions, the tandem structure is one of the most effective solutions. Furthermore, the photovoltaic devices using a mixture of inorganic nanoparticles and conjugated polymers, called hybrid solar cells, have gained popularity due to their ability to absorb near-infrared light. To optimize the device performance, it is essential to adjust the thickness of active layers used in tandem photovoltaic cells. The optimization of a tandem structure using trial and error experiments is costly and sometimes ineffective. Simulation is a more effective tool to create the best tandem device structure. The OSC device is mainly made of an organic layer sandwiched between two different metal electrodes. A bulk heterojunction (BHJ) organic solar cell consists of three components: An active layer, band alignment layer and electrodes. The active layer is a homogeneous mixture of donor and acceptor materials. The donor materials are generally conjugated polymers, whereas the acceptor materials are fullerene derivatives. The power conversion efficiency of the most promising structure, which is namely the P3HT:PCBM bulk heterojunction solar cell, has been reported to be 5% [6,7]. Benaissa et al. [8] showed that the hybrid solar cell absorbs light until 800 nm. The study by Islam [9] showed that the one-junction polymer solar cell with a P3HT:PCBM active layer can cover the 800 nm light spectrum with 2.9% efficiency. The study by Swapna et al. [10] showed that the one-junction polymer solar cell with MEHPPV:PCBM active

Polymers 2019, 11, 383; doi:10.3390/polym11020383 www.mdpi.com/journal/polymers Polymers 2019, 11, 383 2 of 16 layer covered the 800 nm light wavelength and only produced a current density of 6.82 mA/cm2. Wei et al. [11] showed the tandem (two-junction) PSC, with the PCPDTBT:PCBM and P3HT:PCBM active layers providing 9% efficiency. In most papers, the simulation and optimization were conducted for the one-junction PSC cells. In our paper, we showed that the multi-junction hybrid solar cell can absorb light beyond 2500 nm and cover the whole solar spectrum with 20% efficiency. We also created a tandem polymer with 12% efficiency. The device structure was arranged in such a way that the high band gap material on the top of the device and lower band gap materials on the bottom of the device were able to absorb the near-infrared spectrum of light. The tandem solar cell voltage was increased due to the multiple junctions and the current also increased as it covered the near-infrared spectrum, hence increasing efficiency.

2. Materials and Methods

2.1. Theoretical Considerations The organic and inorganic materials used in this simulation are shown in Table1. To reduce the charge recombination, two different materials called the electron transport layer (ETL) and hole transport layer (HTL) are used, which collect the electron and hole, respectively, after charge separation in the interface [12].

Table 1. Description of organic and inorganic materials used in the simulation [13].

Symbol Name; Description

SiO2 Silicon dioxide, glass ITO Indium tin oxide; electrode that collects hole/anode PEDOT: PSS Poly polystyrene sulfonate; HTL P3HT Poly(3-hexylthiophene-2,5-diyl), electron donor ICBA Indene-C60 bisadduct, electron acceptor

TiO2 Titanium (IV) oxide, ETL Poly([2,60-4,8-di(5-ethylhexylthienyl) benzo[1,2-b;3,3-b] dithiophene] PTB7-Th {3-ﬂuoro-2[(2-ethylhexyl) carbonyl] thieno[3,4-b] thiophenediyl}), electron donor PCBM [6,6]-phenyl-C71-butyric acid methyl ester, electron acceptor Poly[2,7-(5,5-bis-(3,7-dimethyloctyl)-5H-dithieno[3,2-b:20,30-d] PDTP-DFBT pyran)-alt-4,7-(5,6-diﬂuoro-2,1,3-benzothia diazole); electron donor Al Aluminum; electrode that collects electron/cathode Poly[[2,5-bis(2-hexyldecyl-2,3,5,6-tetrahydro-3,6-dioxopyrrolo[3,4-c] pyrrole-1,4-diyl]-alt- PMDPP3T [30,3”-dimethyl-2,20:50,2”-terthiophene]-5,5”-diyl]; electron donor Poly[2,1,3-benzothiadiazole-4,7-diyl[4,4-bis(2-ethylhexyl)-4H-silolo [3,2-b:4,5-b0] Si-PCPDTBT dithiophene-2,6-diyl]]; electron donor

MaPbI3 Methylammonium lead iodide; semiconducting organic–inorganic material PbS Lead (II) sulphide; semiconducting inorganic material ZnO Zinc oxide; ETL Ag Silver; electrode that collects electron/cathode NiO Nickel (II) oxide; HTL

2.2. Solar Cell Modeling The optical transfer matrix theory describes the optical processes inside a thin ﬁlm layer stack, which is used to evaluate the power conversion efﬁciency of the multi-junction photovoltaic cell [14]. The theory is explained by Roman et al. in detail [15]. When the light that has the energy of a photon Polymers 2019, 11, 383 3 of 16 with angular frequency ω strikes the organic solar cell, local energy dissipation takes place. The local energy dissipated in the organic solar cell at the point z is given by:

1 Q(z) = cε αn|E(z)|2 (1) 2 0

4πk where ε0 is the permittivity of the vacuum; n is the real index of refraction; α (α = λ ) is the absorption coefficient; k is the extinction coefficient; c is the speed of light; λ is the wavelength and E is the optical electric field at the point z. G (z, λ), the exciton generation rate as a function of depth and wavelength, is given by:

Q(z, λ) G(z, λ) = (2) }ω

h where h is the plank constant and } = 2π . Finally, one obtains the exciton generation rate at a depth of z by summing G (z, λ) over the visible spectrum: λ=2500 G(z) = ∑ G(z, λ) (3) λ=300 For active layer thickness = t and assuming 100% internal quantum efﬁciency, the current density 2 (mA/cm )Jsc under AM1.5 illumination is given by:

Z t Jsc = q × G(z)dz (4) 0

We get the J–V characteristics from the following equation: q(V + J·Rs) V + J·Rs J = Jsc − Jo exp − 1 − (5) KT Rsh

q·Voc 2 where Jo = Jsc/(exp ( KT ) − 1).Jo is the saturation current density (mA/cm ) under reverse bias; Voc is the open circuit voltage; Jsc is the short circuit current density; q is the elementary charge; k is the Boltzmann constant; T is the temperature (K;) and V is the output voltage. We consider a serial 2 resistance Rs = 0.1 Ω cm , related to contact and bulk semiconductor resistances and a shunt resistance 2 Rsh = 1000 Ω cm . A very important parameter is the ﬁll factor (FF), which is deﬁned as:

FF = Pmax/(Voc·Jsc) = (Vmax·Jmax)/(Voc·Jsc) (6)

The main parameter related to the cell performances is the power conversion efﬁciency (PCE) η:

V ·J V ·J η = max max = FF oc sc (7) Pin Pin where Jmax and Vmax are the current density and voltage that correspond to the maximum power Pmax −2 delivered by the solar cell. Pin is the incident photon flux (in mWcm ) that corresponds to AM 1.5 −2 (i.e., Pin is 100 mWcm ). The organic absorber materials are composed of a semiconductor-like materials where the band gap corresponds to the difference between the Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO). The Voc can be calculated by the following equation [16,17]: HOMO(D) − LUMO(A) Voc = − 0.3V (8) q Polymers 2019, 11, 383 4 of 16 where HOMO (D) is the highest molecular orbital of donor material and LUMO (A) is the lowest molecular orbital of acceptor materials. The HOMO and LUMO levels of the donor and acceptor used in the paper are shown in Table2. The Voc for the inorganic materials PbS is 0.6V [18]. The MATLAB program has been obtained from the McGehee Group MATLAB software. The transfer matrix method is used to calculate the transmission, reflection and attenuation by using the MATLAB software. The theory for the calculation is described in detail in the literature [19,20]. The input data are the names of materials which build the structure of the cell and their corresponding thickness (nm); as well as the real and imaginary parts of the complex refraction index of each material. From the Index_of_Refraction_library.xls file, the software will use the n and k refraction index for each selected material (See Supplementary Materials Figures S1–S8 for details) [21–23]. Under AM1.5 illumination (assuming 100% internal quantum efficiency) at all wavelengths, the software calculates generation rate (G) and Jsc by using Equation (1) to Equation (4) using these input data. By using the input n and k refraction index data for all the materials used in a cell for a wavelength range, we can determine how much light was absorbed and reflected by the cell. The J–V characteristics are calculated by using Equation (5). The fill factor and power conversion efficiency are calculated by Equation (6) and Equation (7), respectively. We can calculate the Voc from Equation (8) by using the corresponding active layer HOMO and LUMO level. The AM 1.5 illumination used in the simulation [21], where we can see that the globe absorbs the solar irradiance (mW/cm2) up to a wavelength of 2500 nm.

Table 2. The HOMO and LUMO level of donor and acceptor of materials used in the simulation [13].

MATERIAL LUMO (eV) HOMO (eV) PTB7-Th(donor) −3.61 −5.25 PCBM (acceptor) −3.9 −5.9 PMDPP3T(donor) −3.6 −5.2 P3HT (donor) −3.1 −5 PCPDTBT (donor) −3.55 −5.3 MAPbI3 −3.93 −5.46 ICBA (acceptor) −3.74 −5.6 Si-PCPDTBT (donor) −3.55 −5.3 PDTP-DFBT (donor) −3.64 −5.26

3. Results

3.1. Results for Multi-Junction Polymer Solar Cells Three types of multi-junction polymer solar cells were investigated. Based on different active layers, we stacked the cell. The J–V characteristics and variation of light intensity on the cell were analyzed. The power conversion efﬁciency was calculated from the J–V curve. These three types of multi-junction polymer solar cell were simulated.

3.1.1. Type 1: Multi-Junction Polymer Solar Cell By using the high, medium and low bandgap organic materials, we arranged the stack for solar cells. The number of active layers determined the number of junctions. For the ﬁrst multi-junction polymer solar cell, we used three active layers and hence it is called the three-junction polymer solar cell. During the ﬁrst step, we determined the optical properties of a cell whose dimensions are given by: Glass/ITO (110 nm)/PEDOT:PSS (25 nm)/P3HT:ICBA (190 nm)/TiO2 (25 nm)/PEDOT:PSS (25 nm)/PTB7-Th:PCBM 270 nm)/TiO2 (25 nm)/PEDOT:PSS (25 nm)/PDTP-DFBT:PCBM (640 nm)/TiO2 (25 nm)/Al (200 nm). The thickness of the active layer Polymers 2019, 11, 383 5 of 16

affects the open circuit voltage (Voc) as well as the short circuit current (Jsc) and thus the overall power conversion efﬁciency (PCE). To optimize various active layers, we use a general rule of thumb that decreasing the active layer thickness will increase the Voc due to shorter diffusion length, while increasing the thickness will increase the Jsc. Thus, we must optimize the cell to obtain the maximum performance. The active layer thickness was estimated by using the MATLAB code [21]. We can see in Figure1 that the maximum total current that is possible from the type 1 solar cell is 30 mA/cm 2. As the three junctions are connected in series, each junction should provide 10 mA/cm2 to obtain a maximum current of 30 mA/cm2 from the cell. We can see from Figure1 that if we set certain thicknessesPolymers 2019, (19011 FOR nm PEER for REVIEW P3HT:ICBA active layer, 270 nm for PTB7-Th:PCBM active layer and 640 nm5 for PDTP-DFBT:PCBM active layer), we can obtain 10 mA/cm2 for each junction. Using the MATLAB codejunctionPolymers [21 2019], polymer we, 11 similarly FOR andPEER calculatedhybrid REVIEW cells all optimized the multi-junction thickness. polymer The HOMO and hybrid and LUMO cells optimized band diagram thickness. for5 Thethe type HOMO 1 multi-junction and LUMO band PSC diagramis shown for in Figure the type 2. 1We multi-junction can see from PSC Figure is shown 2 that inwith Figure an active2. We layer can junction polymer and hybrid cells optimized thickness. The HOMO and LUMO band diagram for seecontaining from Figure three2 thatdifferent with bandgaps, an active layer we det containingermined that three the different open circuit bandgaps, voltage we V determinedoc is 2.368 V. that the type 1 multi-junction PSC is shown in Figure 2. We can see from Figure 2 that with an active layer the open circuit voltage Voc is 2.368 V. containing three different bandgaps, we determined that the open circuit voltage Voc is 2.368 V.

Figure 1. The thickness of the active layer is varied to obtain the optimal current for type 1 multi- Figurejunction 1. polymerThe thickness solar cells of (PSC). the active layer is varied to obtain the optimal current for type 1 Figure 1. The thickness of the active layer is varied to obtain the optimal current for type 1 multi- multi-junction polymer solar cells (PSC). junction polymer solar cells (PSC).

Figure 2. HOMO and LUMO band diagram for type 1 multi-junction PSC. Figure 2. HOMO and LUMO band diagram for type 1 multi-junction PSC. The stack diagram for the three-junction OSC is shown in Figure3a. From Figure3b, we can see that theThe three stack active diagramFigure layers 2.for HOMO ofthe P3HT:ICBA three-junction and LUMO (high band OSC bandgap),diagram is shown for PTB7-Th:PCBM typein Figure 1 multi-junction 3a. From (medium FigurePSC. bandgap)3b, we can and see PDTP-DFBT:PCBMthat the three active (low layers bandgap) of P3HT:ICBA cover the (high solar spectrumbandgap), with PTB7-Th:PCBM wavelengths (medium of 300–1000 bandgap) nm and and the The stack diagram for the three-junction OSC is shown in Figure 3a. From Figure 3b, we can see PDTP-DFBT:PCBM (low bandgap) cover the solar spectrum with wavelengths of 300–1000 nm and that the three active layers of P3HT:ICBA (high bandgap), PTB7-Th:PCBM (medium bandgap) and the absorbed light intensity is above 70%. From the simulation, we determined that Jsc at each junction PDTP-DFBT:PCBM (low bandgap) cover the solar spectrum with wavelengths of 300–1000 nm and was 10.0194 mA/cm2. The J–V characteristics are shown in Figure 3c. A PCE of 12.73% was achieved the absorbed light intensity is above 70%. From the simulation, we determined that Jsc at each junction with this configuration. was 10.0194 mA/cm2. The J–V characteristics are shown in Figure 3c. A PCE of 12.73% was achieved with this configuration.

Polymers 2019, 11, 383 6 of 16

absorbed light intensity is above 70%. From the simulation, we determined that Jsc at each junction was 10.0194 mA/cm2. The J–V characteristics are shown in Figure3c. A PCE of 12.73% was achieved withPolymers this 2019 conﬁguration., 11 FOR PEER REVIEW 6

(a) (b)

(c)

Figure 3.3.( a()a Stack) Stack diagram; diagram; (b) variation(b) variation of light of intensity light intensity versus wavelength; versus wavelength; and (c) J–V characteristicsand (c) J–V ofcharacteristics three-junction of organicthree-junction solar cell organic (OSC) solar with frontcell (OSC) P3HT:ICBA, with front middle P3HT:ICBA, PTB7-Th:PCBM middle and PTB7- rear PDTP-DFBT:PCBMTh:PCBM and rear PDTP-DFBT:PCBM active layers. active layers.

3.1.2. Type 2: Multi-Junction Polymer Solar Cell The optical properties properties of of the the second second three-junc three-junctiontion OSC OSC were were investigated. investigated. The The dimensions dimensions of of the cell are described as follows: Glass/ITO (110 nm)/PEDOT:PSS (25 nm)/P3HT:ICBA the cell are described as follows: Glass/ITO (110 nm)/PEDOT:PSS (25 nm)/P3HT:ICBA (235 nm)/TiO2 (235 nm)/TiO (25 nm)/PEDOT:PSS (25 nm)/Si-PCPDTBT:PCBM (290 nm)/TiO (25 nm)/PEDOT:PSS (25 nm)/PEDOT:PSS2 (25 nm)/Si-PCPDTBT:PCBM (290 nm)/TiO2 (25 2nm)/PEDOT:PSS (25 (25 nm)/PMDPP3T:PCBM (1000 nm)/TiO (25 nm)/Al (200 nm). The HOMO and LUMO band nm)/PMDPP3T:PCBM (1000 nm)/TiO2 (25 nm)/Al2 (200 nm). The HOMO and LUMO band diagram diagramfor the type for the2 multi-junction type 2 multi-junction PSC is shown PSC is in shown Figure in 4. Figure We can4. We see can from see Figure from Figure4 that4 with that an with active an active layer of three different bandgaps, we determined that the open circuit voltage V is 2.07 V. layer of three different bandgaps, we determined that the open circuit voltage Voc is 2.07oc V.

Polymers 2019, 11, 383 7 of 16 Polymers 2019, 11 FOR PEER REVIEW 7

Polymers 2019, 11 FOR PEER REVIEW 7

Figure 4. HOMO and LUMO band diagram for type 2 multi-junction PSC.PSC . Figure 4. HOMO and LUMO band diagram for type 2 multi-junction PSC . The stack diagram for the three-junction OSC is shownshown in Figure5 5a.a. FromFrom FigureFigure5 b,5b, we we can can see see that the threeThe stack active diagram layers for of theP3HT:ICBA, three-junction Si-PCPDTBT:PCBM OSC is shown in Figure and 5a.PMDPP3T:PCBM From Figure 5b, we (low can bandgap) see that the three active layers of P3HT:ICBA, Si-PCPDTBT:PCBM and PMDPP3T:PCBM (low bandgap) cover the solar spectrum with wavelengths of 300–1000300–1000 nm and the light intensity is above 70%. J–V characteristicscover the solar are spectrum shown in with Figure wavelengths5c. From of the 300–1 simulation,000 nm and we the determined light intensity that is Jaboveat each70%. J–V junction characteristics are shown in Figure 5c. From the simulation, we determined that Jscsc at each junction characteristics are2 shown in Figure 5c. From the simulation, we determined that Jsc at each junction was 10.1962 mA/cm2 . A PCE of 10.03% was achieved with this conﬁguration with FF of 47.52%. was 10.1962was 10.1962 mA/cm mA/cm. A2. PCEA PCE of of 10.03% 10.03% was was achievedachieved with with this this configuration configuration with with FF of FF 47.52%. of 47.52%.

(a) (b)

(c)

FigureFigure 5. (a )5. Stack (a) diagram;Stack diagram; (b) variation (b) variation of light of intensity light intensity versus wavelength;versus wavelength; and (c) J–Vand characteristics (c) J–V for OSCcharacteristics with P3HT:ICBA, for OSC with Si-PCPDTBT:PCBM P3HT:ICBA, Si-PCPDTBT:PCBM and PMDPP3T:PCBM and PMDPP3T:PCBM active layers. active layers. (c) Figure 5. (a) Stack diagram; (b) variation of light intensity versus wavelength; and (c) J–V characteristics for OSC with P3HT:ICBA, Si-PCPDTBT:PCBM and PMDPP3T:PCBM active layers.

Polymers 2019, 11, 383 8 of 16

Polymers 2019, 11 FOR PEER REVIEW 8 3.1.3. Type 3: Multi-Junction Polymer Solar Cell 3.1.3. Type 3: Multi-Junction Polymer Solar Cell The third three-junction OSC was investigated. The dimensions of the cell were Glass/ITOThe third (110 three-junction nm)/PEDOT:PSS OSC was (25 investigated. nm)/P3HT: The ICBA dimensions (200 nm)/TiO of the cell2 (25 were nm)/PEDOT:PSS Glass/ITO (110 nm)/PEDOT:PSS(25 nm)/Si-PCPDTBT:PCBM (25 nm)/P3HT: (290 nm)/TiOICBA (2002 (25 nm)/TiO nm)/PEDOT:PSS2 (25 nm)/PEDOT:PSS (25 nm)/PDTP-DFBT:PCBM (25 nm)/Si- PCPDTBT:PCBM(1000 nm)/TiO2 (25(290 nm)/Alnm)/TiO (2002 (25 nm)/PEDOT:PSS nm). The HOMO (25 andnm)/PDTP-DFBT:PCBM LUMO band diagram (1000 for nm)/TiO the type2 (25 1 nm)/Almulti-junction (200 nm). PSC The is HOMO shown and in Figure LUMO6. band We can diagram see from for the Figure type6 1that multi-junction with an active PSC layeris shown of inthree Figure different 6. We bandgaps, can see from we determined Figure 6 that that with the open an active circuit layer voltage of Vthreeoc is 2.17different V. bandgaps, we determined that the open circuit voltage Voc is 2.17 V.

Figure 6. HOMO and LUMO band diagram for type 3 multi-junction PSC.

The stack diagram for the three-junction OS OSCC is shown in Figure 7 7a.a. FromFrom FigureFigure7 7bb,, we we can can see see that thethe threethree active active layers layers of of P3HT:ICBA, P3HT:ICBA, Si-PCPDTBT:PCBM Si-PCPDTBT:PCBM and and PDTP-DFBT:PCBM PDTP-DFBT:PCBM cover cover the solar the solarspectrum spectrum with with a wavelength a wavelength in the in range the range of 300–1000 of 300–1000 nm andnm theand light the light intensity intensity is above is above 80%. 80%. J–V J–Vcharacteristics characteristics are shown are shown in Figure in Figure7c. From 7c. theFrom simulation, the simulation, we determined we determined that the Jthatsc at the each Jsc junctionat each 2 wasjunction 10.0130 was mA/cm 10.0130 .mA/cm A PCE2 of. A 10.90% PCE of was 10.90% achieved was usingachieved this using conﬁguration this configuration with FF of 50.17%.with FF of 50.17%.

Polymers 2019, 11 FOR PEER REVIEW 9 Polymers 2019, 11, 383 9 of 16

(a) (b)

(c)

Figure 7.7.( a)(a Stack) Stack diagram; diagram; (b) variation (b) variation of light of intensity light versusintensity wavelength; versus wavelength; and (c) J–V characteristicsand (c) J–V ofcharacteristics OSC with P3HT:ICBA, of OSC with Si-PCPDTBT:PCBM P3HT:ICBA, Si-PCPDTBT:PCBM and PDTP-DFBT:PCBM and PDTP-DFBT:PCBM active layers. active layers.

3.2. Results for Two-, Three-Three- andand Four-JunctionFour-Junction HybridHybrid SolarSolar CellCell Here, two-,two-, three- three- and and four-junction four-junction hybrid hybrid solar sola cellsr cells were were investigated. investigated. Based Based on different on different active layers,active layers, we stacked we stacked the cell. the The cell. J–V The characteristics J–V characteristics and variation and variation of light of intensitylight intensity on the on cell the were cell analyzed.were analyzed. The power The power conversion conversion efficiency efficiency was calculated was calculated from thefrom J–V the curve. J–V curve. 3.2.1. Two-Junction Hybrid Solar Cell 3.2.1. Two-Junction Hybrid Solar Cell First, the two-junction hybrid solar cell (HSC) was simulated. The lead sulfide (PbS) was First, the two-junction hybrid solar cell (HSC) was simulated. The lead sulfide (PbS) was used used as a low bandgap material to absorb light beyond the infrared spectrum. The active layer as a low bandgap material to absorb light beyond the infrared spectrum. The active layer MaPbI3 is MaPbI is organic and inorganic while PbS in HSC is inorganic in nature. During the first organic3 and inorganic while PbS in HSC is inorganic in nature. During the first step, we determined step, we determined the optical properties of a cell whose dimensions are given by: Glass/ITO the optical properties of a cell whose dimensions are given by: Glass/ITO (100 nm)/PEDOT:PSS (20 (100 nm)/PEDOT:PSS (20 nm)/P3HT:ICBA (300 nm)/TiO2 (25 nm)/PEDOT:PSS (20 nm)/MaPbI3 nm)/P3HT:ICBA (300 nm)/TiO2 (25 nm)/PEDOT:PSS (20 nm)/MaPbI3 (1110 nm)/TiO2 (25 (1110 nm)/TiO (25 nm)/PEDOT:PSS (20 nm)/PbS (3000 nm)/ZnO (25 nm)/Ag (200 nm). The stack nm)/PEDOT:PSS2 (20 nm)/PbS (3000 nm)/ZnO (25 nm)/Ag (200 nm). The stack diagram for the three- diagram for the three-junction OSC is shown in Figure8a. From Figure8b, we can see that the two junction OSC is shown in Figure 8a. From Figure 8b, we can see that the two active layers of MaPbI3

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Polymers 2019, 11 FOR PEER REVIEW 10 active layers of MaPbI3 and rear PbS active layers cover the solar spectrum with wavelengths of 300–2500 nm and the light intensity is above 80%. From Figure8c, we can see that only the active and rear PbS active layers cover the solar spectrum with wavelengths of 300–2500 nm and the light layers are creating excitons. intensity is above 80%. From Figure 8c, we can see that only the active layers are creating excitons.

(a) (b) ) 3 Generation rate /(sec-cm rate Generation

(c)

FigureFigure 8. 8.( a(a)) Stack Stack diagram; diagram; ( b(b)) variation variation of of light light intensity intensity versus versus wavelength wavelength for for HSC HSC MaPbI MaPbI3 3and and rearrear PbS PbS active active layers; layers; and and ( c()c) exciton exciton generation generation rate rate vs. vs. position position of of device device for for two-junction two-junction hybrid hybrid solarsolar cell. cell.

3.2.2.3.2.2. Three-JunctionThree-Junction HybridHybrid SolarSolar Cell Cell TheThe secondsecond solar solar cell cell investigated investigated was was the the three-junction three-junction HSC. HSC. The Theactive active layer layer of P3HT: of P3HT: ICBA ICBA is organic but MaPbI is both inorganic and organic and PbS is inorganic in nature. is organic but MaPbI3 is both 3inorganic and organic and PbS is inorganic in nature. During the first Duringstep, we the determined ﬁrst step, wethe determinedoptical properties the optical of a propertiescell whose ofdimensions a cell whose are dimensions given by: Glass/ITO are given (100 by: Glass/ITO (100 nm)/PEDOT:PSS (30 nm)/P3HT:ICBA (2000 nm)/TiO (15 nm)/NiO (20 nm)/MAPbI nm)/PEDOT:PSS (30 nm)/P3HT:ICBA (2000 nm)/TiO2(15 nm)/NiO2 (20 nm)/MAPbI3 (17003 (1700 nm)/TiO (15 nm)/NiO (20 nm)/PbS (1000 nm)/ZnO (15 nm)/Ag (200 nm). The stack diagram nm)/TiO2(15 nm)/NiO2 (20 nm)/PbS (1000 nm)/ZnO (15 nm)/Ag (200 nm). The stack diagram for the forthree-junction the three-junction OSC is OSCshown is shownin Figure in 9a. Figure From9a. Figu Fromre Figure9b, we9 canb, we see can that see the that three the active three layers active of layers of P3HT: ICBA, MaPbI and rear PbS active layers cover the solar spectrum with wavelengths of P3HT: ICBA, MaPbI3 and rear3 PbS active layers cover the solar spectrum with wavelengths of 300– 300–2500 2500nm and nm the and light the lightintensity intensity is above is above 80%. 80%.From FromFigure Figure 9c, we9c, can we see can that see the that three the threeactive active layers layersare producing are producing excitons. excitons.

Polymers 2019, 11, 383 11 of 16 Polymers 2019, 11 FOR PEER REVIEW 11

(a) (b)

(c)

FigureFigure 9.9.( a()a Stack) Stack diagram; diagram; (b) variation(b) variation of light of intensitylight intensity versus wavelength;versus wavelength; and (c) exciton and ( generationc) exciton rategeneration vs. position rate vs. of deviceposition for of three-junction device for three-junction hybrid solar hybrid cell. solar cell.

3.2.3.3.2.3. Four-Junction HybridHybrid SolarSolar CellCell TheThe third solar cell cell that that was was investigated investigated was was the the four-junction four-junction HSC. HSC. During During the thefirst ﬁrst step, step, we wedetermined determined the theoptical optical properties properties of a of cell a cellwhose whose dimensions dimensions are aregiven given by: by:Glass/ITO Glass/ITO (100 (100nm)/PEDOT:PSS nm)/PEDOT:PSS (20 nm)/P3HT:ICBA (20 nm)/P3HT:ICBA (500 (500nm)/TiO nm)/TiO2 (15 2nm)/NiO(15 nm)/NiO (20 nm)/PTB7-Th:PCBM (20 nm)/PTB7-Th:PCBM (2000 (2000nm)/TiO nm)/TiO2 (20 nm)/NiO2 (20 nm)/NiO (15 nm)/PMDPP3T:PCBM (15 nm)/PMDPP3T:PCBM (1100 (1100nm)/TiO nm)/TiO2 (20 nm)/NiO2 (20 nm)/NiO (15 nm)/PbS (15 nm)/PbS (1000 (1000nm)/ZnO nm)/ZnO (20 nm)/Ag (20 nm)/Ag (200 nm). (200 The nm). stack The diagram stack for diagram the three-junction for the three-junction OSC is shown OSC in is Figure shown 10a. in FigureFrom Figure 10a. From 10b, Figurewe can 10 seeb, that we canthe seethree that active the threelayers active of P3HT: layers ICBA, of P3HT: PTB7-Th: ICBA, PCBM, PTB7-Th: PMDPP3T: PCBM, PMDPP3T:PCBM and PCBMPbS cover and the PbS solar cover spectrum the solar with spectrum wavele withngths wavelengths of 300–2500 of nm 300–2500 and the nmlight and intensity the light is intensityabove 80%. is aboveFrom 80%.Figure From 10c, Figurewe can 10 seec, wethat can the see four that active the fourlayers active are producing layers are producingexcitons. excitons.

PolymersPolymers2019 2019,,11 11, 383FOR PEER REVIEW 12 of 1612

(a) (b)

(c)

FigureFigure 10.10. (a) Stack diagram;diagram; (b) variationvariation ofof lightlight intensityintensity versusversus wavelength;wavelength; andand ((cc)) excitonexciton generationgeneration raterate vs.vs. positionposition inin devicedevice forfor two-junctiontwo-junction hybridhybrid solarsolar cell.cell. 4. Discussions 4. Discussions 4.1. Result Analysis for Three Types of Multi-Junction PSC and HSC 4.1. Result Analysis for Three Types of Multi-Junction PSC and HSC For the three types of multi-junction polymer solar cells, the efficiency compared to fill factor graphsFor are the shown three in types Figure of 11multi-junction. In Figure 11 ,polymer we observed solar that cells, the the efficiency efficiency for compared all three types to fill of factor PSCs aregraphs above are 10%. shown However, in Figure the 11. P3HT:ICBA, In Figure 11, PTB7-Th:PCBM we observed that and the PDTP-DFBT:PCBM efficiency for all three three-junction types of PSCs PSC hasare 12%above efficiency. 10%. However, The J–V the characteristics P3HT:ICBA, forPTB7 two-,-Th:PCBM three- and and four-junction PDTP-DFBT:PCBM hybrid solarthree-junction cells are PSC has 12% efficiency. The J–V characteristics for two-, three- and four-junction hybrid solar2 cells shown in Figure 12a, where we observed that two junctions produce a high Jsc of 30 mA/cm and are shown in Figure 12a, where we observed that two junctions produce a high Jsc of 30 mA/cm2 and four junctions produce a high Voc of 2.8 V. In Figure 12b, we also observed that the power conversion efficiencyfour junctions is above produce 20% fora high the V two-,oc of three-2.8 V. In and Figure four-junction 12b, we also hybrid observed solar cells. that Inthe Figure power 12 conversionb, we can efficiency is above 20% for the two-, three- and four-junction hybrid solar cells. In Figure 12b, we can see that MAPbI3 and PbS two-junction hybrid solar cell provides 22% efficiency with a 55% fill factor. see that MAPbI3 and PbS two-junction hybrid solar cell provides 22% efficiency with a 55% fill factor. As the fill factor was close to 50% for all cells, this proves that there was reasonable series resistance (Rs) and parallel resistance (Rsh) during the calculation of current density.

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As the ﬁll factor was close to 50% for all cells, this proves that there was reasonable series resistance Polymers(Rs)Polymers and 20192019 parallel,, 1111 FORFOR resistance PEERPEER REVIEWREVIEW (Rsh ) during the calculation of current density. 1313

FigureFigure 11. 11. EfficiencyEfﬁciencyEfficiency vs. vs. fill ﬁllfill factor factor for for multi-junction multi-junction PSC. PSC.

((aa)) ((bb))

FigureFigure 12. 12. ((aa)) J–V J–V characteristics characteristics for for two-,two-, three-three- and and four-junctionfour-junction hybrid hybrid solar solar cells. cells. (( bb)) FillFill factorfactor factor vs.vs. vs. efficiencyefﬁciencyefficiency for for two-,two-, three-three- andand four-junctionfour-junction hybridhybrid solarsolar cells.cells. 4.2. Brief Fabrication Methodology for Multi-Junction Solar Cell 4.2.4.2. BriefBrief FabricationFabrication MethodologyMethodology forfor Multi-JunctionMulti-Junction SolarSolar CellCell Future works should focus on the fabrication of the multi-junction PSC and HSC. FutureFuture worksworks shouldshould focusfocus onon thethe fabricationfabrication ofof thethe multi-junctionmulti-junction PSCPSC andand HSC.HSC. TheThe solution-solution- The solution-processed multi-junction solar cells can be fabricated as shown in Figure 13. First, the processedprocessed multi-junctionmulti-junction solarsolar cellscells cancan bebe fabricatfabricateded asas shownshown inin FigureFigure 13.13. First,First, thethe ITO-coatedITO-coated ITO-coated glass electrode needs to be cleaned and prepared. After that, the spin coating is performed glassglass electrodeelectrode needsneeds toto bebe cleanedcleaned andand prepared.prepared. AfAfterter that,that, thethe spinspin coatingcoating isis performedperformed forfor eacheach for each layer of multi-junction PSC and HSC. After each spin coating, annealing is performed. Finally, layerlayer ofof multi-junctionmulti-junction PSCPSC andand HSC.HSC. AfterAfter eacheach spinspin coating,coating, annealingannealing isis performed.performed. Finally,Finally, thethe the cathode electrode is deposited using thermal evaporation. cathodecathode electrodeelectrode isis depositeddeposited usingusing thermalthermal evaporation.evaporation.

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Glass Substrate preparation and cleaning

Spin coating the solution material on Substrate

Annealing

Deposition of Contacts using thermal evaporation

Figure 13. Fabrication methodology for multi-junction polymer and hybrid solarsolar cell.cell.

4.3. Stability Analysis of PSC and HSC Organic solarsolar cells degrade extremely fast.fast. The efficiencyefficiency of organic solar cell changes according toto moisturemoisture levels.levels. MaximMaxim etet al.al. reportedreported thatthat water water is is the the key key factor factor determining determining the the degradation degradation in in a solara solar cell. cell. Thus, Thus, there there should should be encapsulationbe encapsulation of the of cellthe socell that so thethat oxygen the oxygen and moistureand moisture cannot cannot come income contact in contact directly directly with the with materials the materials of the solar of cell.the solar Future cell. studies Future should studies determine should thedetermine variation the in thevariation efficiency in the of efficiency the fabricated of the PSC fabr andicated HSC PSC with and humidity HSC with [24 humidity]. [24]. 5. Conclusions 5. Conclusions Theoretical settings have been shown to improve the efficiency of the organic solar cells, which Theoretical settings have been shown to improve the efficiency of the organic solar cells, which were determined by optical modeling using the transfer matrix. We showed how we optimized were determined by optical modeling using the transfer matrix. We showed how we optimized the the various active layers for a type 1 multi-junction PSC. In multi-junction cells, the junctions are various active layers for a type 1 multi-junction PSC. In multi-junction cells, the junctions are connected in series, hence each junction current should be equal. By varying the active layer, we found connected in series, hence each junction current should be equal. By varying the active layer, we the optimum current for each junction. The open circuit voltage was calculated by the HOMO and found the optimum current for each junction. The open circuit voltage was calculated by the HOMO LUMO levels of the materials, which were used as active layers in OSCs and HSCs. The simulations and LUMO levels of the materials, which were used as active layers in OSCs and HSCs. The were performed using the Stanford model. The performance of the device varied with the active simulations were performed using the Stanford model. The performance of the device varied with layer thickness. From the results of our simulations, we showed that our multi-junction polymer the active layer thickness. From the results of our simulations, we showed that our multi-junction solar cell and hybrid polymer solar cell can provide high efficiencies. The maximum PCE of 12.73% polymer solar cell and hybrid polymer solar cell can provide high efficiencies. The maximum PCE of was achieved from the multi-junction polymer solar cell with the three active layers of P3HT: ICBA, 12.73% was achieved from the multi-junction polymer solar cell with the three active layers of P3HT: Si-PCPDTBT:PCBM and PMDPP3T:PCBM. Lead sulfide (PbS) was shown to be the most promising ICBA, Si-PCPDTBT:PCBM and PMDPP3T:PCBM. Lead sulfide (PbS) was shown to be the most low bandgap inorganic material, as it can absorb sunlight beyond the infrared spectrum. By using promising low bandgap inorganic material, as it can absorb sunlight beyond the infrared spectrum. inorganic PbS and high band organic materials, we created a solar cell that absorbs sunlight beyond By using inorganic PbS and high band organic materials, we created a solar cell that absorbs sunlight wavelengths of 2500 nm. The two-, three- and four-junction hybrid solar cells provided a PCE above beyond wavelengths of 2500 nm. The two-, three- and four-junction hybrid solar cells provided a PCE 20%. The two-junction hybrid solar cell provided a high current of 30 mA/cm2 and the four-junction above 20%. The two-junction hybrid solar cell provided a high current of 30 mA/cm2 and the four- hybrid solar cell provided a high voltage of 2.8 V. junction hybrid solar cell provided a high voltage of 2.8 V. 6. Patents 6. Patents A patent has been filed with Florida State University and it is pending. A patent has been filed with Florida State University and it is pending. Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4360/11/2/383/s1, FigureSupplementary S1: Refrative Materials: index (n,k) The vs following wavelngth are for available PbS, Figure online S2: at Refrative www.mdpi.com/xxx/s1, index (n,k) vs wavelngth Figure S1: for Refrative MAPbI3, Figureindex (n,k) S3: Refrative vs wavelngth index for (n,k) PbS, vs wavelngthFigure S2: Refrative for P3HT:ICBA index blend,(n,k) vs Figure wavelngth S4: Refractive for MAPbI index3, Figure (n,k)vs S3: wavelngth Refrative for PMDPP3T:PCBM blend, Figure S5: Refractive index (n,k) vs wavelength for PTB : PCBM blend, Figure S6: index (n,k) vs wavelngth for P3HT:ICBA blend, Figure S4: Refractive index 7 (n,k) vs wavelngth for Refrative index (n,k) vs wavelngth for PDTPDFBT: PCBM blend, Figure S7: Refractive index (n,k) vs wavelength forPMDPP3T:PCBM Si-PCPDTBT: PCBM blend, blend, Figure Figure S5: Refractive S8: Refractive index index (n,k) (n,k) vs wavelength vs wavelength for for PTB PCDTBT:7: PCBM PCBM blend, blend. Figure S6: Refrative index (n,k) vs wavelngth for PDTPDFBT: PCBM blend, Figure S7: Refractive index (n,k) vs wavelength for Si-PCPDTBT: PCBM blend, Figure S8: Refractive index (n,k) vs wavelength for PCDTBT: PCBM blend.

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Author Contributions: For research Methodology, J.J.K.; Resources, S.Y.F.; Software, J.J.K.; Supervision, S.Y.F.; Validation, J.J.K. and S.Y.F.; Writing—original draft, J.J.K.; Writing—review & editing, S.Y.F. Funding: This work is funded in part by Florida A&M University and Florida State University. Conﬂicts of Interest: The authors declare that there is no conﬂict of interest.

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