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We present a novel coupled design method that both optimizes light absorption and predicts electrical performance of fully infiltrated inorganic semiconductor nanowires (NWs) based hybrid solar cells (HSC). This method provides a thorough insight of hybrid photovoltaic process as a function of geometrical parameters of NWs. An active layer consisting of GaAs NWs as acceptor and poly(3-hexylthiophene-2,5-diyl) (P3HT) as donor were used as a design example. Absorption spectra features were studied by the evolution of the leaky modes and Fabry-Perot resonance with wavelength focusing firstly on the GaAs/air layer before extending to GaAs/P3HT hybrid active layer. The highest absorption efficiency reached 39% for the hybrid active layer of 2 μm thickness under AM 1.5G illumination. Combined with the optical absorption analysis, our method further codesigns the energy harvesting to predict electrical performance of HSC considering exciton dissociation efficiencies within both inorganic NWs and a polymeric shell of 20 nm thickness. The validity of the simulation model was also proved by the well agreement of the simulation results with the published experimental work indicating an effective guidance for future high performance HSC design.
© 2016 Optical Society of America
1. Introduction
Hybrid solar cells (HSCs) have attracted great interest due to their potential to substantially reduce material and manufacturing cost for large scale photovoltaic implementation [1,2]. Early work mixed inorganic quantum dots such as CdSe with organic material PCP-DTBT to form bulk heterojunctions [3]. Bilayer structure was also proposed by spin-coating a layer of organics on top of GaAs wafer [4]. However, most of the power conversion efficiencies (PCEs) for the above mentioned structures were below 4% [5]. Since 2009, great leaps have been made by incorporating inorganic nanowires (NWs) with polymer infiltrated around forming ordered heterojunctions as the photoactive layer [1, 5, 6]. On the electrical side, along the NW radial direction, the interdigital ordered heterojunctions reduce the exciton diffusion distance to be dissociated and thus improve exciton diffusion and dissociation efficiencies. Along NW axial direction, the ordered heterojunctions provide direct pathways for the carriers to transport to respective electrodes which increase the carrier transport efficiency by reducing recombination loss [7]. On the optical side, due to sub-wavelength diameter, NWs are able to enhance energy harvesting through localized optical resonant modes that can concentrate and absorb light beyond the geometrical boundaries over micron length [8]. Moreover, the ability to tune the dimensions of NWs, relax of lattice constraint and capability of integration on low cost substrate represent significant potential towards low-cost and high performance HSC [9, 10]. Among a variety of the organic and inorganic material combinations, poly(3-hexylthiophene) (P3HT) and Si or GaAs semiconductor NWs are the most widely reported and the highest PCE reaches 13.2% [11].
Improvement of light absorption of the inorganic NWs is vital to device performance concerning their large absorption coefficients compared with that of the organic material. Therefore, great effort has been devoted to optimize the light harvesting capability of the vertically aligned NWs by adjusting their geometrical parameters such as height, diameter and volume filling ratio (FR) [12, 13]. It was reported that varying the diameter of NWs can tune the radial resonant wavelengths, according to the leaky mode resonant theory [10]. Therefore, through optimization of the diameter of NWs, near-unity broadband absorption was achieved across the incident spectrum [9, 14]. Besides, concerning about periodicity, Martin Foldyna et al. compared squarely and hexagonally periodic NWs and stated that, compared with periodicity, FR mattered greatly to the light confinement [13]. However, when considering adoption of these optimized structures into designs of solar cells, most of the papers end with ultimate efficiency or short circuit current as the assessment standard. This evaluation assumes no recombination other than radiative, so that each exciton contributes to the short-circuit current. Further digging into the electrical performance of the device is neglected.
At the same time, carrier transport of the inorganic NWs as the photoactive layer has been explored in axial [15] or radial core-shell p-n junctions structures both theoretically [7, 16, 17] and experimentally [18]. Moreover, the electrical performance of the NWs based HSC is also widely reported. When photon absorption by the inorganic NWs were neglected, Kannan et al. concluded that in order to guarantee high performance, the size and spacing of the NWs should be on the same scale of the carrier diffusion length within the polymer in HSCs [19]. Taken into the absorption of NWs, size and periodicity of NWs within the hybrid active layer were analyzed as well but the diameter of NWs was limited below 50 nm [20]. In most of those electrical performance investigations, light absorption in the nanostructures was estimated in the way similar with that of thin film material. Nevertheless, when the diameters of NWs fall in the range comparable to the solar spectrum wavelengths, their absorption characteristics are influenced both by their geometrical dimensions and material composition [21]. Therefore, optical or electrical optimization [22] alone is not sufficient to guide high performance device design. In this case, an effective coupled opto-electrical design [23] method is greatly desired to fully evaluate device performance accounting both the size effect as well as intrinsic material property [24, 25]. However, there are limited reports that provide a thorough evaluation on device performance. Wang et al. used coupled opto-electrical simulation to describe the conformal coating thickness of the organics on HSC performance [26, 27]. Still, their NWs size and distribution were chosen based on the optimized structures in the air whereas the NWs geometrical parameters effects on absorption in hybrid active layer were neglected. Our work extends the scope of these studies by developing an effective opto-electrical design method to fully investigate HSC performance.
In this paper, a coupled opto-electrical design method is presented to thoroughly explore the performance of a HSC as a function of geometrical parameters of NWs. In particular, the GaAs NWs/P3HT HSCs are simulated in this work. Finite-difference time-domain (FDTD) is employed to compare the light absorption of both the GaAs NWs/air and GaAs NWs/P3HT hybrid active layer. Geometrical parameters of the NWs such as diameter and FR are discussed about their influence on the optical absorption. Upon solar illumination, photogeneration profile of the hybrid active layer is incorporated into our electrical model for simulating the photovoltaic performance. The electrical model is able to calculate the exciton diffusion efficiency, photocurrent density Jph, external quantum efficiency (EQE), current density-voltage (J-V) characteristic, and PCE of the HSCs. The validity of the model is verified by the well agreement between the simulation results and the published experiment work which implies an effective guidance of HSC design.
2. Photovoltaic process
Schematic energy level arrangement and the photovoltaic process of the GaAs NWs/P3HT HSC is shown in Fig. 1. Upon illumination, photons are absorbed by both the inorganic NWs and polymer, and then excitons are generated. Excitons diffuse to the donor-acceptor (DA) interfaces and are dissociated into free carriers. Electrons are held by the inorganic NWs which has higher electron affinity whereas holes are captured by the polymer with low ionization energy. The carriers then transport to the respective electrodes through either inorganic NWs (for electrons) or polymer (for holes) to generate the photocurrent. Photon absorption efficiencies for NWs and polymer are ηA_NW and ηA_Poly. Diffusion efficiencies ηd_NW and ηd_Poly are used respectively to measure the number of excitons that reach the DA interface to the total number of excitons generated in the two materials. Transport efficiencies ηtr_NW and ηtr_Poly are introduced to evaluate the number of excitons that form the photocurrent to the number of excitons that reach the DA interface. EQE is defined to measure the percentage of the number of charge carriers that generate the photocurrent to the number of photons incident on the device [28]. Therefore, EQE equals to the product of the photon absorption efficiency, diffusion efficiency and transport efficiency.
Fig. 1 Schematic of the energy level arrangement and photovoltaic process for inorganic nanowires (NWs) based hybrid solar cell (HSC) (LUMO: lowest unoccupied molecular orbital; HOMO: highest occupied molecular orbital; CB: conduction band; VB: valance band; hυ: incident photon energy).
3. Theoretical model
Configuration of the inorganic NW/polymeric HSC is schematically shown in Fig. 2. Inorganic NWs are immersed in polymer forming the active layer which is sandwiched between the anode and cathode. Figures 2(a) and (b) show the side view and top view of the HSC. The simulated region is a unit cell which is the minimum unit of the HSC. Characteristic dimensions of the unit cell are shown in Fig. 2(c). The diameter of the NW is DNW and the period of the unit cell is a which is equal to the center to center distance of the adjacent NWs. FR is defined as πDNW2/4a2 which has a maximum value of π/4 for the case that the cylindrical NW fill in the maximum volume percentage of the unit cell [8]. The length of the NWs is L. Since the thickness of the polymer-only layer LPoly, as shown in Fig. 2(a), is less than 1/100 of the total length of NWs, the thickness of the active layer is approximated as L. In this work, NWs length of 2 μm was chosen for the following simulations. The total photocurrent generated is acquired by summing all the current generated in the unit cells.
Fig. 2 Schematic of the active layer in the HSC including (a) side view, (b) top view and (c) a unit cell with characteristic dimensions for the simulation.
Spectral absorptance of the inorganic NW/polymeric active layer was thoroughly analyzed using the full-field three-dimensional (3D) FDTD electromagnetic simulations (Lumerical FDTD Solutions 8.15). The simulation was carried out in each unit cell in Fig. 2(c) with the periodic Bloch boundary condition applied in x and y directions and infinite boundary condition applied in z direction. The complex refractive indexes of GaAs were obtained from the Palik material data provided by Lumerical whereas the optical constants for P3HT were taken from the reference [27]. The absorbed energy was calculated from total energy illuminated upon the active layer deducting both the reflected and transmitted energy. The electromagnetic field distribution in the inorganic NW/polymer active layer was obtained from the simulation. Accordingly the number of excitons generated per unit volume per unit time, namely, the photogeneration rate in the unit cell was calculated. Through incorporating the photogeneration rate into the electrical model, the photocurrent density and EQE were obtained by accounting the exciton diffusion efficiency under terrestrial AM 1.5G illumination [29]. The J-V curves of the devices were acquired and from which the important electrical parameters such as the open circuit voltage (Voc), short circuit current (Jsc), and PCE were determined. The bandgaps of GaAs and P3HT were taken from the published references [20]. In the simulation, the following assumptions were made: (1) excitons only generated within the diffusion length to the DA interface would contribute to the photocurrent [19]; (2) excitons were dissociated into electron-hole pairs only at the DA interface; (3) carriers dissociated from the excitons would not recombine since the electrons transported through the inorganic semiconductor NWs and the holes transported through the polymer.
3.1 Light absorption of GaAs NWs/P3HT HSC
Light harvesting capability of the GaAs NWs/P3HT hybrid active layer is thoroughly explored as a function of different NW diameters when the FR of the NW array was fixed and compared with that of GaAs NWs/air layer as shown in Fig. 3. For GaAs NWs/air layer, we can clearly find the selectivity of the absorption wavelength from Figs. 3(a) and 3(b). When the FR is 0.05, the leaky mode resonance dominates light absorbing behavior of sparsely distributed NWs [9]. From the simulation result, the resonant wavelengths for HE11 mode are observed to be 491, 561, 645, 720, 809 and 869 nm for diameter of 80, 100, 120, 140, 160 and 180 nm respectively as marked in Fig. 3(b). Redshift of the HE11 mode resonant wavelength as the increase of diameter of NWs can also be observed in Fig. 3(a). When the diameter of NWs is 160 nm, additional resonant peak begins to appear at 458 nm which corresponds to HE12 mode as noticed in Fig. 3(b). At short wavelengths (below 450 nm), the absorption efficiency decreases with the expansion of diameter of NWs. This is because as the increase of NWs’ diameter, for a fixed FR, the periodicity a is no longer comparable to the size of incident wavelengths. When FR is 0.05, the periodicities are 317, 396, 475, 555, 634 and 713 nm for 80, 100, 120, 140, 160, and 180 nm respectively. Consequently, the scattering to the incident wavelengths is significantly reduced, resulting in decrease of light absorption [30].
Fig. 3 Light absorption efficiency changes with diameter of NWs for (a), (b) GaAs NWs/air layer and (c), (d) GaAs NWs/P3HT when filling ratio (FR) is 0.05.
Compared with GaAs NWs/air layer, the GaAs NWs/P3HT structure displays different light absorbing behavior as shown in Figs. 3(c) and 3(d). When the incident wavelengths are shorter than the P3HT absorption edge (650 nm), the absorption efficiency is high and uniform across the incident spectrum. At this stage, the large amount of P3HT in the unit cell governs the light absorptance when FR is 0.05. The absorption efficiency drops sharply beyond 650 nm since the absorption is mainly contributed by GaAs NWs at this spectral range. Beyond the absorbing edge of P3HT, the resonant HE11 mode takes the lead and the selectivity of wavelength absorption appears. Moreover, the resonant wavelengths are oscillating as the peaks red shifted with the enlarging of NWs diameter. The reason is due to the Fabry–Perot (F-P) effect of the P3HT thin film which tunes the resonant peaks of GaAs NWs as shown in Fig. 3(d). Although the long wavelengths cannot be absorbed to generate excitons by P3HT, they are still effectively trapped inside the active layer due to the high refractive index of P3HT serving as dielectric shell [26]. Therefore, an average absorption enhancement can be observed compared with GaAs NWs/air layer.
A two-dimensional modal analysis of the GaAs NWs/air and GaAs NWs/P3HT layers are carried out to gain an insight of the aforementioned optical properties. The normalized electric field intensity along the vertical cross-section through the middle of the NWs for the 160 nm diameter GaAs NWs both in air or P3HT at 400 nm, 600 nm and resonant wavelengths of HE11 mode are shown in Fig. 4. Compared with GaAs NWs/air, the modes for GaAs NWs/P3HT are more concentrated around NW periphery for 400 and 600 nm incident light. From Figs. 4(d) and 4(e), the existence of P3HT helps absorb light energy effectively below the absorptance bandgap and therefore the electrical field intensity attenuates rapidly along the NWs axis and does not reach the bottom of the NWs. Besides, Fig. 4(c) shows the dipole-like HE11 mode which has two distinct maximum values along the diameter of the NWs. Oscillation of the electrical field intensity becomes obvious in Fig. 4(f), which is mainly because the F-P mode by P3HT layer. Since the FR is fixed at 0.05 for the simulated NWs, the HE11 leaky modes are concentrated in and around the NWs and thus are not affected by the adjacent NWs.
Fig. 4 Electric field intensity distribution of GaAs NWs/air and 160 nm GaAs NWs/P3HT unit cell. Plots at the top (a)-(c) correspond to GaAs NWs/air whereas bottom ones (d)-(f) correspond to GaAs NWs/P3HT layer. Left, middle and right plots correspond to: (a), (d) 400 nm, (b), (e) 600 nm, and (c), (f) resonant wavelengths of 809 and 827 nm for HE11 modes in GaAs NWs/air and GaAs NWs/P3HT layer, respectively. White lines indicate the edges of the NWs.
Figure 5 shows the contour plot of the light absorption efficiency spectra of the GaAs NWs/P3HT active layer as a function of FR with the NW diameter of 80 and 160 nm, respectively. When the incident wavelengths are below the band edge of P3HT, the absorption efficiency of the active layers decreases with the increases of FR for both the 80 and 160 nm diameters. This is mainly due to the modal coupling among adjacent NWs. From the modal analysis shown in Fig. 4, we find that the radial extent of the HE11 resonance mode leaks to the boundary of the unit cell. When the distance between the adjacent NWs narrows down as the FR increases, the competition of the incident photons among the NWs will cause the decrease of the absorption. For 80 nm NWs, when the incident wavelength is longer than 650 nm, the absorption peaks oscillate and the resonant wavelength red shifts as the FR increases as mentioned above. However, this oscillation origins mainly from the F–P modes [31] in the NWs instead of P3HT since the volume ratio of NWs rises. The F-P modes in the NWs are generated as a result of the longitudinal boundary conditions at the two ends of the NW. This generates axial standing wave along the NW length through constructive interference of the guided wave. Besides, as FR increases, the F-P modes mostly pass through GaAs. Since the absorption coefficients of GaAs is much higher than those of P3HT, the absorption builds up with FR. For 160 nm NWs, Fig. 5(b) shows a blue shift at longer incident wavelength which is contrary to the trend displayed in Fig. 5(a). According to a recent publication from Sturmberg et al. [32], the first coefficient of the Rayleigh identity representing the nearest neighbor interactions within the lattice is calculated to be negative for our GaAs NWs/P3HT active layer. This indicates the destructive interference of the HE11 mode. Compared with 80 nm diameter NW, the HE11 mode resonant wavelength for 160 nm extends to 809 nm. Therefore, the blue shift of the resonance peak is observed indicating the destructive interference.
Fig. 5 Light absorption efficiency changes with incident wavelength and FR when diameter of NW is (a) 80 nm and (b) 160 nm.
Based on the understanding of the absorption characteristics of the active layer, light harvesting of the HSC is evaluated. The exciton diffusion length SD is assumed as 20 nm for P3HT. Therefore, within a unit cell, only the NWs and their peripheral of 20 nm thickness polymeric shells will devote to the device photon harvesting. This organic-inorganic region is thus named as effective region as shown in the dashed red cylindrical area in Figs. 6(a) and 6(b). In Fig. 6(c), light absorption efficiency of the unit cell is summarized under terrestrial AM 1.5G illumination condition with an intensity of (100 mW/cm2) as a function of diameter and FR. The highest light absorption is 0.39. On one hand, a variety of combination of diameters and FR can enter the high absorption region about 0.38. The two high absorption zones are both with large FRs resulting in less redundant polymeric area within unit cell outside the red dashed cylinder as shown in Fig. 6(b). Besides, when FR is fixed, the consumption of GaAs materials remain the same regardless of diameter variation which results in high absorption for large FR. On the other hand, there is a gentle decrease between two high absorption regions. This can be explained as resonant wavelengths variation as diameter change. When the diameter is below 120 nm, the resonant peaks in Figs. 3(b) and (d) are in the blue end away from the P3HT absorptance edge. The corresponding absorptance coefficients are high at those wavelengths leading to high absorption efficiencies. When diameter of the NWs increases to 140 nm, the red shifted of the resonant wavelengths move beyond the P3HT absorption edge (650 nm) which reduce the absorption efficiency. Due to the small amount of the volume ratio of P3HT, the decrease exists but is minor. When the diameter continues to rise, another resonant mode appears in the blue end of the spectral inside the NWs as shown in Fig. 3(b), and thus the absorption grows again.
Fig. 6 Top view (a) and isometric view (b) for effective region and (c) light absorption efficiencies as a function of FR and diameter at AM 1.5G illumination.
According to the photovoltaic process, excitons are generated upon illumination. The photogeneration rates are calculated for the effective region from the divergence of Poynting vector for each configuration. Eqation (1) gives the expression where is the imaginary part of the complex permittivity and is the electric field intensity [33]. The photogeneration rates are then exported to electrical model and important electrical characteristics such as Jph, EQE, J-V, and PCE are all achieved for GaAs NWs/P3HT HSC.
3.2 Electrical characteristics of GaAs NWs/P3HT HSC
According to the photovoltaic process described above, only the excitons generated within the diffusion length to the DA interface will contribute to the photocurrent. The diffusion efficiency ηd_NW represents the ability of an exciton to diffuse through the NWs and arrive at the DA interface without recombination. For inorganic semiconductor like GaAs, the diffusion length is on the order of micrometers which is much larger than the radius of the NWs [34, 35]. Therefore, ηd_NW can be taken as 1. For organic materials, ηd_Poly is closely related to the distance between the locations where the excitons are generated to the DA interface ∆s as shown in Fig. 6(a). Only when ∆s is smaller than SD, the excitons can diffuse to the DA interface to be dissociated. In this case, the diffusion efficiency ηd_Poly can be expressed as ηd_Poly = exp(-∆s/SD) [19]. Besides, after dissociation at organics/inorganics interface, it is assumed that the carriers will not recombine since the electrons transport through the inorganic semiconductor NWs whereas the holes transport through the polymer. Therefore, the carrier transportation efficiency within the NWs and polymer, ηtr_NW and ηtr_Poly, are taken as 1 in the simulation [36]. The total absorbed photons can be obtained by 3D integration of photogeneration rates along the unit cell axes. As a result, the photocurrent density of unit cell Jph_unit of HSC contributed both from P3HT and GaAs NWs can be determined by dividing unit cell illuminating area AreaUnit as shown in Eq. (2). Correspondingly, the photocurrent density Jph and EQEAM1.5G of the device under terrestrial AM 1.5G illumination condition are received by Eqs. (3) and (4) where q is elementary charge, λ is wavelength, I(λ) is light intensity, h is Plank constant and c is speed of light in vacuum. The material parameters of P3HT and GaAs used in the calculation are listed in Table 1.
Table 1. Summarized parameters used in the simulation
Figure 7 shows the photocurrent density and EQEAM1.5G changing with diameter of GaAs NWs and FR. In general, dependence of Jph on the diameter of NWs and the FR shows very similar values for large range of parameters. This indicates that GaAs NWs/P3HT active layer have high tolerance to manufacturing process. It is important to notice the best potential values of Jph is 22.55 mA/cm2. For the low FR value of 0.4, a general increase of the Jph can be observed when increasing diameter of NWs from 80 to 190 nm. This trend arises from the excitation of multiple resonance modes for a fixed FR, as discussed above. When FR is larger than 0.4, the NWs are so closely packed that the competition of incident photons among adjacent NWs reduce the Jph. On the other hand, for a fixed diameter of NWs, the increase of FR will generally lead to the rise of Jph and EQEAM1.5G. This is because when FR is small, there is large portion of P3HT in the unit cell. Due to the short diffusion length, the excitons outside the effective region will recombine and lost before they transport to the DA interface to be dissociated. When FR increases, NWs account for more volume ratio within the unit cell, and at the same time, larger percentage of photons generated from P3HT will contribute to the photocurrent. However, further increase of FR will result in a decrease of Jph. The reasons mainly lie in the destructive interference among adjacent NWs which can also be confirmed by Fig. 6(c). EQEAM1.5G has a resembling trend as Jph and the highest value is 36.76% at diameter of 161.5 nm.
Fig. 7 Photocurrent density (a) and external quantum efficiency (EQEAM1.5G) (b) change with diameter of NWs and FR.
From the device fabrication point of view, the P3HT has long and entangled molecular chains. Too large value of FR will make P3HT difficult to penetrate into the gaps between the NWs. The narrowest spacing for P3HT to infiltrate in will vary due to the polymeric concentration and process. From the published experimental results, we set 20 nm as the minimum spacing Smin among adjacent NWs to ensure the full penetration of P3HT. This requirement is marked as the dash-dot line in the Fig. 7. Along the Smin, the Jph is about 20 mA/cm2 and EQEAM1.5G is 32%.
Figure 8 shows the simulated J-V curves of the GaAs NWs/P3HT HSCs with different NW diameters and the FRs. The equivalent circuit of the HSC adopted in this simulation is included in the inset of Fig. 8(b). The photocurrent source Jph describes the ability of converting photons into free carriers under illumination. A diode parallel to the photocurrent source generates the dark current, which represent how device behaves like a diode without illumination. The series resistance Rs origins from the resistance of active layer and contact resistance with electrodes whereas the shunt resistance Rsh accounts for the leakage current in the device. Since the Rsh is usually an order of magnitude greater than the series resistance, it is neglected in the analysis [37]. The final form of the J-V relation of the HSC is displayed in Eq. (4). Reverse saturation current density Jsat is less affected by the FR of NWs according to the Richardson’s thermionic emission equation and is set as 10−10 A/cm2 [38]. kB is Boltzmann constant and T is absolute temperature. Since the carrier mobility within the inorganic NWs is a few orders of magnitude higher than those in polymers, therefore the Rs is chosen as a fixed value which is on the order of 10−3 Ωm2 [5].
Fig. 8 Current density-voltage (J-V) curves (a) and power conversion efficiency (PCE) (b) of the GaAs NWs/P3HT HSC change with diameter and FR.
As shown in Fig. 8(a), the open circuit voltage is almost the same for all the devices with different NW diameters and FRs. This is because Voc of a HSC is mainly affected by the electron affinity of the acceptor and the highest occupied molecular orbital (HOMO) of the donor [36]. Since only the diameter and spacing of the acceptor NWs have changed, Voc of the cell will remain unaffected. The short circuit current Jsc of the device is primarily determined by the photocurrent density. In the ideal case, the upper limits of Jsc can be taken as the Jph when Rs is very small and Rsh is sufficiently large [5]. Therefore, Jsc has similar trend as the Jph. Two specific FRs are chosen for analysis. For a given FR, despite the diameters of the NWs, the amount of NWs’ material consumption is the same. The larger FR is, the higher the amount of GaAs material consumes and thus the higher the cost of the device. Besides, the FR should not be too large, so that there is sufficient spacing among the NWs. For FR is 0.6, the rise of diameter of NWs will decrease the Jph and PCE. This is because of the destructive interference among NWs as shown in Fig. 3. At the same time, the FR should also be larger than 0.3 since too low FR will lead to PCE to below 9% as shown in Fig. 8(b). When FR has a small value of 0.3, the coupling among NWs is reduced and with the increase of diameter, the light harvesting efficiency increase which results in high Jph and PCE.
From the calculated J-V curves of the GaAs NWs/P3HT HSCs, their PCEs are calculated by the ratio of the maximum power over the incident light energy as shown in Fig. 8(b) and Eq. (5). Since Pin is a constant for a given illumination and voltage for maximum power generated for the HSC Vm varies within a small range in the J-V curve for different diameters of NWs and FRs. The current density for maximum power Jm determines the maximum output power, Pm. Since Jm can be approximated as Jsc which is proportional to EQEAM1.5G by a factor of constant incident illumination density, therefore the trend of PCE is also similar with that of EQEAM1.5G.
Using this model, the PCE of the GaAs NWs and P3HT HSC published by Jiun-Jie Chao et al. was calculated [39]. The PCE of the solar cell is 10.1% with the cell’s structure parameters given, which is very close to the experimental results of 9.28%. Considering the exciton recombination during transportation and carrier collection loss in actual device, the predicted value demonstrates the effectiveness of our opto-electrical model.
4. Conclusion
In this paper, coupled opto-electrical design method for GaAs NWs/P3HT HSCs is presented. Light absorption of the GaAs NWs/P3HT active layer is studied using the 3D FDTD simulation and compared with that of a GaAs NWs/air layer an increased light harvesting is received. Along with the leaky resonant modes of the GaAs NWs for light trapping, addition of the polymeric layer serves as dielectric shell which confines light both below and beyond the absorptance band edge. Geometrical parameters including diameter of NWs and FR are assessed on their influence of the light absorption efficiency. The light absorption efficiency of 2 μm thickness hybrid active layer is also evaluated at solar illumination achieving the highest value of 0.39. Moreover, photogeneration rates are calculated and incorporated to an electrical model which is built relating to the diffusion efficiency of the excitons both in organic and inorganic materials. Current density-voltage characteristics illustrate that the Voc remains unchanged for various unit cell dimensions whereas the device’s Jsc changes following the trend of Jph. In general, device’s PCE rise with FR but it is also limited by both P3HT infiltration spacing and high cost. For a high FR, the device’s PCE decrease with the rise of diameter of NWs, whereas opposite trend is observed when the FR is small. This corresponds to the light absorption efficiency variation trend in the optical simulation. The proposed opto-electrical model is used to reconstruct published work and the well match of the device performance indicating the effectiveness of the model.
Funding
Academic Research Fund (RG97/14) of the Ministry of Education of Singapore; National Natural Science Foundation of China (Grant No. 51402148); Guangdong High Tech Project (Grant No. 2014A010105005, No. 2014TQ01C494); Shenzhen Innovation Project (Grant No. KC2014JSQN0011A).
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