Light absorption enhancement in ultrathin film solar cell with embedded dielectric nanowires

A novel design of thin-film crystalline silicon solar cell (TF C-Si-SC) is proposed and numerically analyzed. The reported SC has 1.0 µm thickness of C-Si with embedded dielectric silicon dioxide nanowires (NWs). The introduced NWs increase the light scattering in the active layer which improves the optical path length and hence the light absorption. The SC geometry has been optimized using particle swarm optimization (PSO) technique to improve the optical and electrical characteristics. The suggested TF C-Si-SC with two embedded NWs offers photocurrent density (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{ph}$$\end{document}Jph) of 32.8 mA cm−2 which is higher than 18 mA cm−2 of the conventional thin film SC with an enhancement of 82.2%. Further, a power conversion efficiency of 15.9% is achieved using the reported SC.

www.nature.com/scientificreports/ large index contrast with the Si material (n = 3.6). Additionally, the SiO 2 is almost perfectly lossless within the visible spectrum. Under the right circumstances, Si/SiO 2 interfaces may have extremely low interface recombination velocities and dangling bond densities. Further, the growth of SiO 2 NWs can be implemented using oxidation process of Si 10 . The modified TF-SC with two embedded dielectric NWs offers power conversion efficiency (PCE) of 15.9% and an optical absorption enhancement of 82.2% over the conventional planer TF SC. Figure 1 shows the simulation strategy for the SC characterization. First, optical studies are carried out by using 3D finite-difference time-domain (FDTD) via Lumerical software package to calculate the optical absorption ( P abs ) and J ph 11 . To estimate the absorption capability of the TF C-Si-SCs, J ph is calculated under air mass 1.5 (AM 1.5 G) solar spectrum. To further enhance the P abs and J ph of the reported design, the geometrical parameters are optimized using particle swarm optimization (PSO) technique 12 . In this investigation the J ph is used as a fitness function of the PSO algorithm to quantify the broadband absorption capability of the suggested TF C-Si-SC 5 : where e is the electron unit charge, h is the Plank constant, c is the light speed in vacuum, AM1.5 is the solar spectral irradiance AM 1.5 as obtained from the NREL database 2 and P abs is the optical absorption spectrum of the C-Si material.

Simulation strategy
Next, the generation rate of the optimal design is imported into the electrical simulator to quantify the photo-generated electron-hole pairs that can be collected and contributed to the output electrical power. The electrical model is used to calculate both the PCE and J sc using finite element method (FEM) via Lumerical device simulation package 11 .The FEM package solves coupled nonlinear equations of semiconductor (drift-diffusion equations and Poisson continuity) to obtain the power conversion efficiency (PCE) of the reported design [13][14][15] . The PCE can be calculated according to the following equation 7 : where P in is the incident power at AM 1.5, F.F is the fill factor defined as ( F.F = P max /J sc × V oc ), V oc is the open-circuit voltage, and P max is the maximum power.  Fig. 2b,c. Further, the nanowire has a length (L) of 133 nm. The proposed design is optically simulated using computational domain of 750 nm × 750 nm with height of 3 µm with minimum mesh size of 8.0 nm. In addition, periodic boundary conditions are used in the x and y-directions to mimic the effects of an infinitely periodic unit cell. However, the boundary condition along z axis is a perfect matched layer (PML). The suggested design is excited from the top by a plane wave with wavelength range from 300 to 1100 nm. The material refractive indices of silicon and silicon dioxide are predefined in the Lumerical material database based on Palik's model 16 .

Design consideration and numerical results
The TF-SC design with embedded dielectric (SiO 2 ) sphere is previously published in 9 . The power absorption of the planar TF-SC, TF-SC with embedded dielectric sphere 9 and embedded NW is shown in Fig. 2d. It can be seen from this figure that the TF-SC with dielectric scatter has higher absorption than the baseline TF-SC counterpart. Figure 2e illustrates the J ph and the absorption efficiency ( η ) for the three studied designs. It can be seen from this figure that the TF-SC with sphere and NW scatters have J ph and η higher than that of the conventional base line counterpart. The J ph for the planar TF-SC and TF-SC with embedded dielectric sphere and nanowire are equal to 17.73, 21.9, and 24.6 mA cm −2 , respectively. Additionally, η of the planar TF-SC and www.nature.com/scientificreports/ TF-SC with embedded dielectric sphere and nanowire are equal to 20%, 24.65%, and 27.674%, respectively. This enhancement is attributed to the cylindrical geometry of the NW which has a higher scattering efficiency than that of the spherical geometry by 10.9% especially at λ ≥ 500 nm as shown in Fig. 2f. The scattering efficiency ( Q s ) is defined as the ratio between scattering cross-section of a dielectric particle and the physical cross-sectional area 9 . Therefore, higher scattering is achieved for the incident light inside the active layer by the cylindrical NWs. Consequently, the absorption and J ph are enhanced. It is also expected that the two embedded NWs can further improve the light absorption. Next, the coupled optical/electrical modeling techniques are used to explore the cell performance of the proposed SC with three dielectric embedded elements (sphere, single NW, and two NWs) and compered with the conventional baseline SC. These designs are optically simulated using computational domain of 1 µm × 1 µm with height of 3 µm with minimum mesh size of 8.0 nm. Figure 3 shows 3D schematic diagram of the reported 1.0 µm TF C-Si-SC with two embedded nanowires. The suggested design has an antireflection coating of Si 3 N 4 with a thickness of 75 nm 9 . Further, a trapezoidal grating is used as a back reflector with upper and lower bases of L tu and L tb , respectively. The two embedded NWs have an elliptical shape with minor and major diameters of d 1 , d 2 , d 3 , and d 4 , respectively. The NWs are added in the active layer at a depth of Z 1 and Z 2 from the surface of the active layer with rotation angle of Θ rod as shown in Fig. 3. In order to obtain the optimal design dimensions with maximum photocurrent density, the PSO technique is employed for the two embedded elements (single NW and two NWs). Table 1 summarizes the initial and optimized parameters of the reported design with one NW and two NWs cases. There are six optimization parameters which are minor, major diameters, the distance from the surface of the active layer and center of nanowire ( Z NW ), rotation angle of Θ rod and the upper (L tu ) and lower (L tb ) bases of the trapezoid back grating etching. For single NW, Θ rod is the angle between the NW and the x-axis while for the two NWs Θ rod represents the angle between them. The initial and optimized geometrical parameters are listed in Table 1.
Optical characterization. Figure 4a shows the optimization performance for the J ph of SCs with single/ double NWs versus the iterations number. The optimized design offers J ph of 30.2 mA cm −2 and 32.8 mA cm −2 , respectively which exceed the Lambertian limit for 1.0 µm TF C-Si-SC 17 . This enhancement is mainly attributed to the presence of embedded NWs as dielectric scatters. Therefore, an enhancement ratio of 67% and 82.2% respectively are achieved over the conventional planer TF C-Si-SC. It may be also seen from this figure that the optimizer has fast convergence with smaller iteration numbers using two NWs. The improvement in J ph www.nature.com/scientificreports/ is due to cylindrical geometry of the NWs that offers a degree of freedom through NW length (L) variation. Figure 4b shows the scattering efficiencies of the embedded dielectric sphere and NWs with multiple lengths ( L, 2 × L, 3 × L, 4 × L, and 5 × L ). The dielectric elements have a diameter of 200 nm at a depth of 450 nm beneath the C-Si/Si 3 N 4 interface 9 . The scattering efficiency is improved by increasing the length L especially at λ ≥ 500 nm. This enhancement is attributed to the NW length (characteristic length) which increases the scattering in the horizontal direction compared to spherical counterpart. Figure 4c shows the P abs of the conventional planer TF C-Si-SC (baseline), TF C-Si-SC with embedded SiO 2 nano-spheres 9 , single SiO 2 NWs, and two SiO 2 NWs. It may be seen from this figure that the SiO 2 scatter will enhance the optical absorption compared to the planar reference SC device. As λ increases further than 450 nm, P abs of the planar device is decreased due to the low absorption coefficient of C-Si material at mid and high wavelength band 8,9 . However, by introducing the embedded NWs, the absorption enhancement is increased rapidly in the mid and high wavelength band owing to the geometry and configuration of the nanowires. Additionally, due to the improved impedance mismatch between the air and C-Si layer, more scattering occurs through the active layer with more light absorption. The J ph of the planer conventional TF-SC, TF-SC with embedded nanospheres, one and two NWs are 18.3, 25.9, 30.2 and 32.8 mA cm −2 , respectively. Figure 5b illustrates the normalized absorption distribution at cross sectional plane ZU shown in Fig. 5a. It may be seen that the light is highly trapped and absorbed below the NWs. For further investigation, another monitor is placed along the side plane (ZX) for the NWs as shown in Fig. 5c. The normalized absorption distributions at the edges of the TF C-Si-SCs is described in Fig. 5d where the light path is plotted red dotted line. Such figures confirm that the presence of NWs produces volume light scattering in the active layer which improves the optical absorption by tuning the scattering mean free path to the material absorption length.  www.nature.com/scientificreports/ Figure 6a shows a schematic diagram of the reported SC with embedded two NWs under the excitation of transverse electric (TE) and transverse magnetic (TM) modes. In this study, the incident angle (β) for both excitation modes is swept from − 50° to 50°. Figure 6b shows the photon current density J ph versus the incidence angle for TE and TM polarizations. It may be seen from Fig. 6b that the J ph for TE and TM modes are nearly the same at normal incidence (β = 0°) and is equal to 32.9 mA cm −2 . Additionally, a second maximum of J ph is achieved at β = 30° which is equal to 29.5 and 25.4 mA cm −2 for TE and TM excitations, respectively. The angular photocurrent response can be explained by the polarization angle effect. At the incident angle (β) = 0°, the light is nearly fully transmitted into the absorber without any reflection 18 . At β = 30°, the absorption enhancement is due to the increment of the optical path length in addition to the angular scattering from the two NWs. The difference between the J ph according to the TE and TM modes is due to the asymmetry of the two NWs in y-axis and x-axis. In this context, the tilted incident angle will increases the influence of the asymmetry of the NWs 18 .
Electrical characterization. Figure 7a shows the schematic diagrams of the reported TF-SC with p-i-n doping (p-type/intrinsic/n-type) mounted on Si substrate. The proposed design utilizes the silicon nitrate and aluminum as the emitter and base electrodes, respectively as shown in Fig. 7a. In this study, the doping concentrations of P + and N + regions are equal to 5 × 10 17 and 1 × 10 19 cm −3 , respectively 8,19 . However, the doping P + and  www.nature.com/scientificreports/ N + regions are on the front and rear part of the SCs with thicknesses of L p and L n , respectively. Also, the carrier lifetimes of P + , N, and N + region are 10, 1000, and 5 μs, respectively. The surface recombination velocity is 2 × 10 5 cm s −18 . Additionally, the Auger coefficients for electrons and holes are 9.9 × 10 -32 and 2.2 × 10 -31 cm 6 s −1 , respectively 19 . The bimolecular radiative coefficient is also taken as 9.5 × 10 -15 cm 3 s −119 . The thickness of the doping regions L i can be selected from Fig. 7b in order to increase the conversion efficiency with a saturated J sc of 30.91 mA cm −2 at L i equals to 800 nm. In this investigation, the thickness of L p and L n is equal to 100 nm. Figure 7c,d present an electrical comparison between three different embedded dielectric elements with the planer solar TF C-Si-SC. The dimensions of embedded single NW and two nanowires are mentioned in Table 1. The calculated J sc , the open-circuit voltage ( V oc ), PCE, and the fill factor (F.F) for the three embedded elements are listed in details in Table 2.
The enhancement in J-V characteristics for the proposed design with single NW and two NWs can be attributed to the absorption enhancement shown in Fig. 4c. Accordingly, it is expected that the (J-V) results of the proposed design show better electrical performance than that of others. It may be seen from J values presented in Figure 7. (a) The p-i-n axial doping, (b) the J sc and V oc dependence on the L i , (c) J-V characteristics of the C-Si TF planer and with different embedded dielectric elements: sphere, single NW, and two NWs, and (d) power density curves for C-Si TF planer and with different embedded dielectric elements: sphere 9 , single NW, and two NWs.  12 . It is also evident from Fig. 7c that there is a slight improvement in V oc , which is mainly determined by the internal dark-current response owing to the increase of J sc . As for power conversion efficiency (PCE), it can be shown from Table 2 and power density curves in Fig. 7d that the proposed designs with dielectric two embedded NWs and single NW have better power conversion efficiencies than that of the SiO 2 nano-sphere and planer based C-Si TFSC with 15.91%, 14.48%, 10.1%, and 8.58%, respectively. The fabrication of the suggested design can be achieved by using physical vapor deposition, atomic chemical vapor deposition, and wet etching process according to the following steps shown in Fig. 8. First, a Si 3 N 4 layer is deposited with a thickness of 75 nm using atomic chemical vapor deposition. A P-type silicon substrate is exposed to ammonia and hexamethyldisiloxane (HMDSO) gases with flow rates of 80 and 40 SSCM, respectively 20 . A deposition time of 15 min and temperature of 825 °C are needed to obtain a silicon nitride film of 75 nm thickness 20 . Then, a thin layer of silicon is deposited with a thickness of 100 nm at 1000 °C using dichlorosilane (DCS) or Silane (SiH 4 ) and diborane (B 2 H 6 ) to obtain a heavily doped p-type silicon layer with doping concentration 5 × 10 17 cm −321, 22 . Such a layer is then annealed in vacuum at a temperature of 1000 °C for crystallization as shown in Fig. 8b [21][22][23][24][25][26] . Figure 8c shows the deposition of the second silicon layer with a thickness of 236 nm on p-type silicon and Si 3 N 4 layer at a temperature of 690 °C. The substrate is annealed in vacuum at 1000 °C for 30 min to achieve fully crystalline silicon film 23 . Next, photolithography process is used to make an isotropic etching of the required cleavages to anchor the first layer of NWs 27 . The NWs can be fabricated by using metalassisted chemical etching (MACE) method 27,28 . The Si NWs are subjected to thermally oxidizing flow to form the SiO 2 NWs. After that, the SiO 2 NWs are horizontally transferred by pressing NWs substrate vertically onto the <110> crystalline silicon substrate as shown in Fig. 8d 27 . The SiO 2 NWs can be aligned to silicon cleavage through spinning process along the surface of the C-Si layer as revealed from Fig. 8e 27,29 . An additional silicon layer of 100 nm thickness is deposited and annealed to obtain the C-Si layer. Then, the isotropic etching and spinning process are repeated for positioning the second batch of the SiO 2 NWs.
A layer of Si with thickness of 464 nm is next deposited using argon gas and is annealed in vacuum at 1000 °C for 30 min 23 . Additionally, n-thin layer of silicon is deposited with a thickness of 100 nm at 1000 °C using dichlorosilane (DCS), and phosphine (PH 3 ) as N-dopants with doping concentration of 1 × 10 19 cm −322 .
Finally, an aluminum layer is deposited on sacrificial silicon substrate 30 or on polyethylene terephthalate (PET) layer 31 . The grating can be etched using mold-assisted chemical etching to achieve the optimized dimension mentioned in Table 1 32,33 . After that, the aluminum grating layer is transferred to the proposed solar cell using flip transfer method 34 . Such sacrificial layer is later exposed to KOH for removal. www.nature.com/scientificreports/

Conclusion
A novel design of TFC-Si-SC with embedded dielectric NWs is presented in order to improve the light-harvesting efficiency. The performance of the suggested design is optimized using PSO technique to maximize the light absorption through the active layer. The optimized SC offers photocurrent density of 32.9 mA cm −2 and 30.2 mA cm −2 using single/double NWs, respectively. In addition, corresponding power conversion efficiencies of 14.48% and 15.91%, are achieved. Therefore, this work shows the ability of using volume scattering of embedded dielectric NWs for increasing the light trapping and power conversion efficiencies in TFSC. www.nature.com/scientificreports/