1. Introduction

Among crystalline semiconductor materials, indium gallium nitride (InGaN) ternary alloys are of great interest in the field of photovoltaics due to their superior photovoltaic properties, especially the tunable direct band gap covering most of the solar spectrum ranging from ultraviolet to the near-infrared region [1,2], high absorption coefficient (∼10⁵ cm⁻¹) [3], and high carrier mobility [1]. InGaN alloys also exhibit high thermal and chemical stabilities and superior radiation resistance [1,4]. Hence, these alloys have become a potential candidate for photovoltaic device applications in harsh environments. Many previous reports have proposed the fabrication of InGaN-based solar cells with low indium content [5–8]. But, a low indium content in InGaN results in a large band gap of the InGaN alloy. This leads to the absorption of sunlight only for shorter wavelengths, which in turn leads to lower efficiency of the solar cells. Thus, for the realization of a high efficiency InGaN-based solar cell, the indium content in the InGaN active layer must be increased to cover most of the solar spectrum.

Previous studies have reported phase separation in indium-rich InGaN alloy due to solid phase immiscibility between GaN and InN [3,9–12]. Nevertheless, recent reports have shown the growth of high quality, single crystalline InGaN with high indium content can be carried out by controlling the growth temperature and pressure [13–16]. However, with higher indium content, the crystalline quality of the InGaN thin films degrades significantly with increasing layer thickness [17]. Therefore, for high efficiency indium-rich InGaN solar cells, the thickness of the active layer needs to be in the order of a few hundred nanometers. But, decreasing the layer thickness results in poor light absorption in the active region, which then leads to a low-efficiency cell.

To increase the absorption of sunlight in the thin active layer, researchers have proposed several light trapping methods such as surface texturing [8,18], anti-reflection coating [19], and anti-reflection sub-wavelength structures on the top surface of the solar cell [20–23]. Some plasmonic nanostructures have also been demonstrated to confine the sunlight in the thin active layer through surface plasmon resonance (SPR)-based scattering and coupling of incident light into SPR modes or waveguide modes in the active layer [24–27]. Recent studies have shown the use of dual interface nanostructures in silicon and organic solar cells for enhanced performance [28–32]. Although several plasmonic-enhanced silicon and organic solar cells have been proposed in the last few years, there are very few reports of a plasmonic-enhanced InGaN p-n junction solar cell with indium-rich InGaN layers.

In this paper, we present an indium-rich InGaN (with 60% indium content) p-n junction thin-film solar cell with an integrated structure of a 2-dimensional (2D) array of ITO nanodiscs on the top surface and a 2D array of Ag nanodisc in the active layer above the Ag back reflector of the solar cell. A detailed theoretical study of InGaN p-n junction solar cells with varying indium composition from 0 to 100% in the InGaN active region was presented by Feng et al. [33]. They reported that the indium composition of 60% in the InGaN active region leads to maximum power conversion efficiency. Moreover, Pantha et al. [15] have succesfully demonstrated epitaxial growth of InGaN thin films with indium concentrations upto 63% with no phase separation. Hence, an indium composition of 60% in the InGaN active region is chosen for the solar cell structures being proposed here. It is demonstrated that the absorption in the proposed solar cell structure is significantly enhanced across a broad spectral range, thus obtaining significantly larger short circuit current density (J_sc) and power conversion efficiency (PCE) as compared to a solar cell having either no nanostructures or having only the top ITO nanodisc array or only the bottom Ag nanodisc array. The change in J_sc of the solar cell due to the oblique incidence of light was also examined.

However, embedding such metallic or dielectric nanoparticles in the absorbing InGaN epitaxial layers reduces the crystalline quality of these layers because the epitaxial layers have to be grown continuously as high-quality crystalline films. A fabrication process, addressing this, has been proposed to develop the indium-rich InGaN solar cells containing plasmonic nanostructures (Appendix A).

2. Solar cell structure and numerical calculation method

The device structures of InGaN p-n junction solar cells containing plasmonic or photonic nanostructures are shown in Fig. 1 — a planar solar cell without nanodiscs (Fig. 1(a)), a cell with only Ag nanodiscs on the back electrode (Fig. 1(b)), a cell with only ITO nanodiscs on top (Fig. 1(c)), and finally, a cell with the integrated structure of vertically aligned ITO nanodiscs on top and Ag nanodiscs in the back (Fig. 1(d)). In all these InGaN solar cell configurations, the thicknesses of the Ag, n-InGaN, and p-InGaN layers were taken to be 100 nm, while the thickness of the top ITO electrode was taken to be 20 nm. The Ag bottom layer serves both as a back reflector and the cathode in these solar cells. In the proposed solar cell structures, the radius (R_b) of the bottom Ag nanodiscs, as well as the height (H_t) and radius (R_t) of the top ITO nanodiscs were optimized to maximize the J_sc of the cells. The height (H_b) of the bottom Ag nanodiscs in the back side of the n-InGaN layer was fixed at 50 nm.

 

Fig. 1. Schematic of the InGaN solar cells with and without plasmonic and dielectric nanostructures: (a) a planar solar cell i.e. with no nanostructures, (b) a solar cell with a periodic Ag nanodiscs (ND) array at the bottom, (c) a solar cell with a 2D periodic ITO ND array on the top surface, and (d) a solar cell with an integrated structure of a 2D periodic top ITO ND array and a 2D periodic bottom Ag ND array.

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The finite-difference time-domain (FDTD) method was employed to calculate the absorption in the solar cells using a commercial FDTD simulation software (Lumerical FDTD Solutions). Plane waves with free space wavelengths varying from 300 nm to 900 nm were incident on the top surface of the solar cells. While optimizing the nanodiscs parameters, the incident plane waves were taken to be TM polarized (polarization along x-direction) and were normally incident along the z-direction. After optimizing the nanodiscs parameters, the solar cell performances of the various cells (as shown in Figs. 1(a)–1(d)) were studied under oblique incidence of light for both TM and TE polarizations. As the solar radiation consists of un-polarized light, we obtained an average of the absorptions calculated for the TE and TM polarizations for the calculation of the short circuit current density. Periodic boundary conditions were used in the x- and y-directions, and perfectly matched layer (PML) boundary conditions were used in the z-direction.

In the FDTD simulations, non-uniform grid sizes were taken — 1 nm for the simulation region of the nanostructures (i.e. the region of the Ag and ITO nanodiscs), and 2 nm for the remaining regions of the solar cell. The simulation window had a dimension of 250 nm in both x- and y- directions i.e. the periodicity of the nanodiscs in the x- and y- directions was fixed at 250 nm. The wavelength dependent refractive indices for Ag and ITO were taken from the literature [34] and [35], respectively. Methodology for calculation of the wavelength-dependent refractive indices of the InGaN alloy is described in Appendix B.

FDTD simulations were carried out to obtain the E- and H- fields in the solar cells. Then, the time-averaged power absorbed in the active medium (InGaN) was calculated by the following relation [27]:

3. Results and discussion

The performance enhancement of the solar cells due to the addition of the bottom Ag nanodisc array and the top ITO nanodisc array was demonstrated by a comparative study of the absorption and short circuit current density (J_sc) for the four different device structures shown in Figs. 1(a) − 1(d). The J_sc of the solar cell was maximized by an optimization procedure involving the bottom Ag nanodisc radius (R_b), the top ITO nanodisc height (H_t) and the top ITO nanodisc radius (R_t). The bottom Ag nanodisc height (H_b) was kept constant at 50 nm.

3.1 Bottom Ag nanodisc array

Firstly, the bottom Ag nanodisc parameters were optimized — for normal incidence of solar radiation — to maximize the J_sc of the solar cell. Figure 2(a) shows the absorption in the active medium as a function of wavelength in solar cells containing only 2D bottom Ag nanodisc arrays — for different values of the radii (R_b) of the Ag nanodiscs. For comparison, the absorption spectrum of the planar solar cell is also shown. Figure 2(a) demonstrates that the absorption is higher for wavelengths longer than 450 nm due to the introduction of the bottom Ag nanodisc array. Figure 2(b) shows the enhancement in the J_sc as a function of bottom Ag nanodisc radius (R_b). The J_sc was calculated by integrating the product of the wavelength-dependent absorption and the solar spectrum AM1.5G from wavelength 300 nm to 900 nm as given by Eq. (3). With an increase of the Ag nanodisc radius, the enhancement in J_sc increases to a maximum of ∼19% for R_b = 90 nm and then, decreases. Figure 2(b) also shows that the enhancement in J_sc is more than 14% for the specified range (60 nm-120 nm) of Ag nanodisc radii.

 

Fig. 2. (a) Absorption spectra of InGaN solar cells containing a 2D bottom Ag nanodisc (ND) arrays having different radii (varying from R_b = 60 nm to R_b = 120 nm), and (b) Enhancement in J_sc with respect to a planar solar cell due to the presence of a bottom Ag ND array, plotted as a function of the Ag ND radius (R_b).

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In order to study the enhancement in absorption due to the addition of the bottom Ag nanodisc array, the absorption enhancement in the solar cell containing the optimized bottom Ag nanodiscs was plotted against wavelength, as shown in Fig. 3(a). It can be observed from Fig. 3(a) that the absorption in the active layer is significantly enhanced for longer wavelengths — with ∼ 60% enhancement at a wavelength of 820 nm. Figures 3(b) and 3(c) show the magnetic field distribution in the x-z plane at a wavelength of 820 nm for a solar cell containing the optimized bottom Ag nanodiscs and for a planar solar cell, respectively. Due to the periodic arrangement, the Ag nanodisc array on the Ag back electrode behaves like a 2D plasmonic nano-grating. Figure 3(b) demonstrates significant magnetic field confinement in the active region due to the presence of the bottom Ag nanodisc array. This can be ascribed to two processes. Firstly, the incident light couples into surface plasmon resonance (SPR) modes present at the interface between the Ag nanodiscs (which are present on the Ag back electrode) and the InGaN active layer. This leads to the localization of fields near Ag nanodiscs in the normal direction and scattering of incident light at different angles in the plane of the active medium. Secondly, the scattered light is reflected back from the interface between the InGaN and the ITO layer. Hence, the scattered light couples into waveguide modes for the wavelengths around the band edge of InGaN active material (∼ 835 nm). Thus, the enhancement of absorption in the active region can be attributed to the field confinement in the active region due to the presence of bottom Ag nanodiscs (as shown in Fig. 3(b)). On the other hand, in a planar solar cell, normally incident light is reflected normally from the flat Ag back reflector (Fig. 3(c)), and reflected back into the air, leading to lower absorption in the thin active layer.

 

Fig. 3. (a) Absorption enhancement (left y-axis) as a function of wavelength for a solar cell with an optimized bottom Ag nanodisc array with respect to a planar solar cell. Absorption spectrum (right y-axis) of a planar solar cell and a solar cell with an optimized bottom Ag nanodisc array. (b) and (c) show magnetic field distributions in the x-z plane at a wavelength of 820 nm for a solar cell with a bottom Ag nanodisc array and for a planar solar cell, respectively. The active layer is contained within black dashed lines. In (b), white dashed lines show the periodic array of bottom Ag nanodiscs. Optimized parameters of the bottom Ag NDs, i.e. radius R_b = 90 nm and height H_b = 50 nm have been used for these plots. Same color scale has been taken for (b) and (c).

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An optimization of the parameters of a solar cell containing only the top ITO nanodisc array was also performed, and the results are presented in Appendix C. A maximum J_sc enhancement of 15.71% was obtained by employing only top ITO nanodiscs in the solar cell — for R_t = 110 nm and H_t = 120 nm. However, combining these individually optimized top ITO nanodisc parameters with those of the individually optimized bottom Ag nanodisc parameters leads to a solar cell with a J_sc enhancement of only 16.90%. This is significantly less than the enhancement obtained in the solar cell containing only bottom Ag nanodisc array, which was 19%. Thus, to obtain further enhancement in the J_sc, the top ITO nanodisc parameters were optimized in the solar cell containing the optimized bottom Ag nanodisc array.

3.2 Top ITO nanodisc array integrated with bottom Ag nanodisc array

Figure 4 shows the absorption in the active medium as a function of the wavelength for the solar cell with the integrated structure of a 2D array of ITO nanodiscs on the top surface and a 2D array of Ag nanodiscs at the bottom of the solar cell. For comparison, the absorption spectrum for the planar solar cell and the solar cell with only the bottom Ag nanodisc array are also shown. The optimization of the top ITO nanodisc parameters was carried out by taking the optimized values of the bottom Ag nanodisc parameters i.e. height H_b = 50 nm and radius R_b = 90 nm, and varying only the top ITO nanodisc parameters. The height (H_t) and radius (R_t) of ITO nanodiscs were varied from 60 nm to 140 nm and from 50 nm to 100 nm, respectively — Figs. 4(a), 4(b), 4(c), 4(d), and 4(e) correspond to H_t = 60 nm, 80 nm, 100 nm, 120 nm, and 140 nm, respectively. Figures 4(a) − 4(e) show that the addition of the top ITO nanodisc array to the solar cell containing bottom Ag nanodiscs primarily enhances the absorption for the middle wavelengths from 400 nm to 750 nm. However, as the radius and the height of the ITO nanodiscs increase, the absorption in the active region decreases for wavelengths smaller than 430 nm and for wavelengths greater than 700 nm.

 

Fig. 4. Absorption spectra of solar cells containing the integrated structure of a 2D array of ITO nanodiscs (NDs) on the top surface and a 2D array of Ag NDs at the bottom of the solar cell. Plots (a) to (e) show the absorption spectra for different ITO ND heights: H_t = 60 nm, 80 nm, 100 nm, 120 nm, and 140 nm, respectively. The radius of the ITO NDs (R_t) was varied from 50 nm to 100 nm. Optimized parameters of the bottom Ag NDs have been used for these plots, i.e. radius R_b = 90 nm and height H_b = 50 nm.

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Figure 5 shows the enhancement in the J_sc of the solar cell containing the integrated structure of nanodisc arrays (i.e. containing the top ITO nanodisc array and the bottom Ag nanodisc array). The J_sc was calculated by integrating the product of the wavelength-dependent absorption (shown in Fig. 4) and the solar spectrum AM1.5G as given by Eq. (3). Figure 5 shows the enhancement in J_sc with respect to the J_sc of a planar solar cell as a function of ITO nanodisc radius R_t — for varying heights of the ITO nanodiscs. A maximum J_sc enhancement of ∼ 25% was obtained for radius R_t = 75 nm and height H_t = 100 nm. Thus, the optimized integrated structure consists of a bottom Ag nanodisc array having height H_b = 50 nm and radius R_b = 90 nm, with a top ITO nanodisc array having height H_t = 100 nm and radius R_t of 75 nm. Comparing with the planar solar cell, the addition of only bottom Ag nanodisc array enhances the J_sc by 19%, while the addition of the integrated structure of vertically aligned top ITO nanodisc array and bottom Ag nanodisc array enhances the J_sc by 25%.

 

Fig. 5. J_sc enhancement in the solar cell by employing the integrated structure of a 2D array of top ITO nanodiscs (NDs) and a 2D array of bottom Ag NDs. The J_sc enhancement is plotted against the ITO nanodisc radius (R_t) for varying ITO ND heights: H_t= 60 nm, 80 nm, 100 nm, 120 nm, and 140 nm. Optimized parameters of the bottom Ag NDs R_b = 90 nm and H_b = 50 nm were taken for these plots.

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For a comparative study of the various solar cell structures, the absorption and absorption enhancement in the active medium of the solar cells are plotted in Figs. 6(a) and 6(b), respectively. These results demonstrate that a bottom Ag nanodisc array primarily enhances at the longer wavelengths, while the top ITO nanodisc array primarily enhances at the middle wavelengths – from 400 nm to 800 nm. Hence, the integrated structure of the bottom Ag nanodisc array and the top ITO nanodisc array enhances the absorption in a broad spectral range. The solar cell containing the integrated structure has an absorption greater than 0.85 for the wavelength range from 350 nm to 800 nm.

 

Fig. 6. (a) Absorption spectra of the solar cells having – only a bottom Ag ND array (blue), only a top ITO ND array (red), the integrated structure consisting of a top ITO ND array and a bottom Ag ND array (green), and a planar solar cell (black). (b) Absorption enhancement in the solar cells containing the bottom Ag ND array and/or top ITO ND array, with respect to a planar solar cell Optimized parameters for the bottom Ag NDs (radius R_b = 90 nm and height H_b= 50 nm) and for the top ITO NDs (radius R_t = 75 nm and height H_t = 100 nm) were taken for obtaining these plots.

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The enhancement in absorption can be attributed to the high electromagnetic field intensities in the active region due to the coupling of incident light to the plasmonic modes and photonic modes by the bottom Ag nanodisc array and the top ITO nanodisc array, respectively [31]. The absorption enhancement due to the introduction of the bottom Ag nanodisc array has been attributed to the coupling of incident light into plasmonic modes near the Ag nanodiscs and into waveguide modes in the active region. The addition of the ITO nanodisc array on the top surface of the solar cell leads to the coupling of the incident light into photonic Bloch-modes (as shown in Appendix D, Fig. 10) in the active layer [31,37], which results in reduced top-surface reflection from the solar cell. Thus, a greater enhancement in absorption and J_sc is observed due to the addition of the ITO nanodisc array on the top surface of the solar cells containing the bottom Ag nanodisc array.

3.3 Oblique angle incidence on optimized solar cells

We studied the performance of the various solar cell structures under the oblique incidence of light on the top surface. A BFAST source was used as the incident light source for the FDTD simulations with oblique light incidence in the Lumerical software. More than 75% of sunlight incident around midday is at angles smaller than 40° [31]. Therefore, we calculated the absorption of the solar cells for incident angles varying from 0° to 50°. Figure 7(a) shows the short circuit current density (J_sc) as a function of incident angle θ for the solar cells containing optimized plasmonic and dielectric nanostructures – bottom Ag nanodisc array, top ITO nanodisc array, and an integrated structure of these nanodisc arrays, under both TM- and TE-polarized illumination. The results of a planar solar cell are also plotted for comparison. The J_sc of a planar solar cell decreases with an increasing angle of incidence under the TE-polarized light. But for TM-polarized light, the J_sc increases with increasing angle of incidence. This can be explained by the Fresnel’s equations of reflection and transmission at an interface [38]. According to the Fresnel’s equations, transmission through an interface of low refractive index medium to high refractive index medium (examples air/ITO or ITO/In_0.6Ga_0.4N interface) decreases with increasing angle of incidence for TE polarization. On the other hand, under TM polarization, the transmission first increases for increasing angle of incidence up to a certain angle (given by Brewster’s angle) and then decreases beyond that [38]. It is observed from Fig. 7(a) that the J_sc of a solar cell with a bottom Ag nanodisc array and/or a top ITO nanodisc array is greater than the J_sc of a planar solar cell for incident angles 0° to 37° under both TM- and TE-polarized light. Many recent reports have shown the increased solar cell performance due to plasmonic or dielectric gratings as a function of incident light angle [39–43]. When a bottom Ag nanodisc array and/or a top ITO nanodisc array are present in the solar cell, the absorption in the active region is increased due to the excitation of various SPR and photonic modes. This leads to the increment in the J_sc of these solar cells. Figure 7(a) shows that the J_sc of the solar cell containing bottom Ag nanodisc array or top ITO nanodisc array increases with an increasing angle of incidence under the TM-polarized light while decreases with an increasing angle of incidence under the TE-polarized light. This effect of the incident angle on the J_sc is similar to the planar solar cell. But the rate of changing the J_sc with incident angle is different from the rate of changing the J_sc of the planar solar cell (see Fig. 7(a)). This can be attributed to the shifting of the spectral position of SPR and photonic modes with the angle of incidence. The spectral position of these SPR modes and photonic modes depends on the angle of incidence [44,45]. Thus the incident angle of light influences the absorption enhancement in the active layer and hence the J_sc of the solar cells.

 

Fig. 7. J_sc as a function of the incident angle of light for a planar solar cell (black), a bottom Ag nanodisc (ND) solar cell (blue), a top ITO ND solar cell (red), and a solar cell with the integrated structure (green) for: (a) TM (solid lines) and TE (dashed lines) polarized illumination, and (b) Randomly polarized illumination. Optimized parameters for the bottom Ag NDs (radius R_b = 90 nm and height H_b= 50 nm) and for the top ITO NDs (radius R_t = 75 nm and height H_t = 100 nm) were taken for obtaining these plots.

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It is observed from Fig. 7(a) that the J_sc of the solar cell containing integrated structure of top ITO and bottom Ag nanodiscs is larger than that of the other solar cell structures for incident angles from 0° to 43° under both TM and TE polarized incident light. The J_sc of the solar cell containing integrated structure slightly decreases with an increasing angle of incidence under the TM-polarized light while under TE polarization the J_sc increases initially with the angle of incidence up to ∼ 30° and then starts decreasing. When both the layers of nanostructures — the bottom Ag nanodisc array and the top ITO nanodisc array are present in the solar cell, then the plasmonic and photonic modes (excited in the active region of the solar cell) interact with each other [45]. This mode-interaction is affected by the angle of incidence of light [45]. Therefore the overall effect of the angle of incidence on the absorption as well as on the J_sc depends on the modes excited in the active layer and on the interaction between these modes.

Figure 7(b) shows the J_sc as a function of incident angle θ of these solar cells, under un-polarized illumination — evaluated as the average of J_sc under TM- and TE-polarization. It is observed that the addition of the integrated structure of top ITO and bottom Ag nanodiscs into the solar cell leads to significant enhancement in the J_sc for incident angles of 0° to 50°, as compared to cells having either no nanostructures or having only the top ITO nanodisc array or only the bottom Ag nanodisc array. More importantly, the solar cell containing the integrated structure exhibits a substantially large J_sc for a range of incident angles from 0° to 40°, as shown in Fig. 7(b). This result reveals a significant advantage of the integrated structure of top ITO and bottom Ag nanodiscs in these solar cells.

3.4 Efficiency characteristics

The J-V characteristics of the various solar cell structures shown in Fig. 1 were evaluated by employing the procedure described in Appendix E and plotted in Fig. 8. A summary of the photovoltaic characteristics of these solar cells is presented in Table 1. It was observed that the optimized integrated structure can enhance the J_sc and the power conversion efficiency (PCE) of the solar cell by ∼25% and ∼26%, respectively, which are significantly large as compared to cells having either only the top ITO nanodisc array or only the bottom Ag nanodisc array. Since it was assumed that the presence of the Ag nanostructures and the ITO nanostructures do not make a difference in the InGaN semiconductor properties or in the contact quality, the open circuit voltage and the fill factor do not change significantly.

 

Fig. 8. J-V characteristics of the planar solar cell (black), and the solar cells containing – only bottom Ag nanodiscs (NDs) (blue), only top ITO NDs (red), and the integrated structure of top ITO NDs and bottom Ag NDs (green). Optimized parameters for the bottom Ag NDs (radius R_b = 90 nm and height H_b= 50 nm) and for the top ITO NDs (radius R_t = 75 nm and height H_t = 100 nm) were taken for obtaining these plots.

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Table 1. Photovoltaic characteristics of the planar solar cells, solar cells with only bottom Ag nanodisc array, only top ITO nanodisc array, and bottom Ag nanodisc array along with top ITO nanodisc array.

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4. Conclusions

In this paper, the improved photovoltaic characteristics of various configurations of In_0.6Ga_0.4N thin-film solar cells — containing either only top ITO nanodisc arrays or only bottom Ag nanodisc arrays or both top ITO and bottom Ag nanodisc arrays — were discussed. It was determined that the introduction of an integrated structure consisting of both the top ITO nanodisc array and the bottom Ag nanodisc array leads to a greater enhancement in the solar cell performance as compared to either of the individual nanodisc arrays. The Ag nanodisc array at the bottom of the solar cell enhances absorption primarily for longer wavelengths of light (with ∼ 60% absorption enhancement at a wavelength of 820 nm). This was attributed to the excitation of surface plasmon-based scattering and coupling of incident light into waveguide modes. The ITO nanodisc array on the top surface leads to an enhanced absorption primarily for the middle wavelengths from 400 nm to 800 nm. This was associated with the coupling of incident light to photonic modes. Hence, a broadband absorption enhancement was obtained by employing the integrated structure of the nanodisc arrays. The optimized integrated structure of the nanodisc arrays enhances the J_sc and PCE of the InGaN solar cell by 25% and 26%, respectively. Moreover, the study of oblique light incidence demonstrates significantly larger J_sc of the solar cell containing the integrated structure of nanodisc arrays as compared to the cells having no nanostructures or having only the top ITO nanodisc array or only the bottom Ag nanodisc array.

Appendix A. Fabrication processes for indium-rich InGaN solar cells

In order to develop the proposed InGaN solar cell containing bottom Ag nanodisc array and top ITO nanodisc array, a multi-step fabrication process can be followed. In this process, the indium-rich In_xGa_1-xN (x = 0.6) layer can be grown on GaN/Al₂O₃ epitemplates by metal organic chemical vapor deposition (MOCVD) or by molecular beam epitaxy (MBE) with the required doping levels for the n-InGaN and p-InGaN regions [14,15]. The indium content can be controlled by the growth temperature and pressure. To develop the Ag- and ITO- nanodisc arrays into the solar cell, first, a 2-dimensional array of nano-circles (radius R_b and period P) can be etched in n-InGaN up to height H_b using deep UV lithography or electron beam lithography and inductively coupled plasma reactive-ion etching. This can be followed by Ag deposition, mechanical polishing, and planarization, such that the required Ag layer thickness is obtained. Subsequently, this structure can be transferred onto a suitable substrate. The Al₂O₃ layer, now on top, can be removed using laser lift-off. A uniform ITO layer of the required thickness can be deposited on top. Finally, the 2D array of ITO nanodiscs can be developed on the ITO layer by using deep UV lithography or electron beam lithography and inductively coupled plasma reactive-ion etching.

Appendix B. Calculation of real and imaginary parts of the refractive indices for InGaN alloy

The refractive indices of InGaN alloy depend on its band gap (E_g), which is a function of indium composition (x) of In_xGa_1-xN and given by [2]:

(4)$${E_g} = 3.42({1 - x} )+ 0.77x - 1.43x({1 - x} )\;eV$$

The real part of the refractive index of In_xGa_1-xN is given by the following relation [46]:

(5)$$n({h\upsilon } )= {\left\{ {a(x ){{\left( {\frac{{h\upsilon }}{{{E_g}}}} \right)}^{ - 2}}\left[ {2 - {{\left( {1 + \left( {\frac{{h\upsilon }}{{{E_g}}}} \right)} \right)}^{0.5}} - {{\left( {1 - \left( {\frac{{h\upsilon }}{{{E_g}}}} \right)} \right)}^{0.5}}} \right] + b(x )} \right\}^{0.5}}$$

where h is the Planck’s constant, $\upsilon $ is the incident light frequency; and $a(x )$ and $b(x )$ are fitting parameters given by

(6)$$a(x )= 13.55x + 9.31({1 - x} )$$

(7)$${\textrm{and}}\;b(x )= 2.05x + 3.03({1 - x} )$$

The absorption coefficient of In_xGa_1-xN was taken from the literature [47]:

(8)$$\alpha = {10^5}\sqrt {A({h\upsilon - {E_g}} )+ B{{({h\upsilon - {E_g}} )}^2}} {\textrm{c}}{{\textrm{m}}^{ - 1}}$$

where A and B are dimensionless fitting parameters found by linear interpolation of any indium composition in InGaN compound from Table 2.

Table 2. Fitting parameters used to calculate the absorption coefficient of In_xGa_{1_x}N alloys.

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The imaginary part of the refractive index of In_xGa_1-xN is evaluated as:

(9)$$k = \frac{{\alpha{\lambda _0}}}{4 \pi},$$

where λ₀ is the free space wavelength of incident light.

Appendix C. Optimization of height and radius of ITO nanodiscs present on top of the solar cells

To obtain the maximum enhancement in J_sc due to the presence of a top ITO nanodisc array, the height and radius of the ITO nanodiscs were varied from 60 nm to 160 nm and from 70 nm to 120 nm, respectively. Figure 9(a) shows the J_sc enhancement as a function of ITO nanodisc radius R_t, when the ITO nanodisc height (H_t) was varied from 60 nm to 160 nm. A maximum J_sc enhancement of 15.71% was obtained for H_t = 120 nm and R_t = 110 nm. Figure 9(b) shows the absorption in the active region of the solar cell containing top ITO nanodiscs of height 120 nm, with the nanodisc radius varying from 80 nm to 120 nm.

 

Fig. 9. (a) J_sc enhancement in the solar cell by employing the 2D array of top ITO nanodiscs (NDs) as a function of ITO nanodisc radius (R_t) for varying height – H_t= 60 nm, 80 nm, 100 nm, 120 nm, 140 nm, and 160 nm. (b) Absorption spectrum for solar cells containing a 2D top ITO ND array with height H_t = 120 nm and radius varying from R_t = 80 nm to 120 nm.

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Appendix D. Cross-sectional view of magnetic field distributions in the solar cells containing top ITO nanodisc arrays and/or bottom Ag nanodisc arrays

Figure 10 shows the distributions of the magnetic field enhancement in the different configurations of the In_0.6Ga_0.4N thin-film solar cells, when the wavelength of the incident optical radiation was taken to be 600 nm. The addition of the ITO nanodisc array on the top surface of the In_0.6Ga_0.4N solar cells leads to the coupling of the incident light into photonic Bloch-modes in the active layer (as shown in Figs. 10(c) and 10(d)), which results in reduced top-surface reflection from the solar cells as compared to solar cells without any nanostructures (as shown in Fig. 10(a)). Figure 10(d) shows that there is a greater magnetic field enhancement in presence of the integrated structure consisting of a top ITO ND array and a bottom Ag ND array, thereby leading to greater absorption in the active layer.

 

Fig. 10. Distributions of the magnetic field enhancement (in the x-z plane for the solar cells) in the different configurations of the In_0.6Ga_0.4N thin-film solar cells having: (a) no nanostructures, (b) only a bottom Ag ND array, (c) only a top ITO ND array, and (d) the integrated structure consisting of a top ITO ND array and a bottom Ag ND array. The wavelength of the incident optical radiation was taken to be 600 nm. Optimized parameters for the bottom Ag NDs (radius R_b = 90 nm and height H_b= 50 nm) and for the top ITO NDs (radius R_t = 75 nm and height H_t = 100 nm) were taken for obtaining these plots.

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Appendix E. Calculation of J-V characteristics of the solar cells

The open circuit voltage (${V_{oc}}$) was calculated using the J_sc of the solar cells obtained from Eq. (3) in the following relationship [36]:

(10)$${V_{oc}} = \frac{{kT}}{e}\ln \left( {\frac{{{J_{sc}}}}{{{J_0}}} + 1} \right)$$

where k is the Boltzmann constant, T is the absolute temperature, and $\;{J_0}$ is the reverse saturation current for the p-n diode given by [36]:

(11)$${J_0} = en_i^2\left( {\sqrt {\frac{{{D_n}}}{{{\tau_n}}}} \frac{1}{{{N_A}}} + \sqrt {\frac{{{D_p}}}{{{\tau_p}}}} \frac{1}{{{N_D}}}} \right).$$

Here, ${D_n}$ and ${D_p}$ are diffusion constants of electrons and holes, ${\tau _n}$ and ${\tau _p}$ are life-times of electrons and holes, ${N_A}$ and ${N_D}$ are donor and acceptor concentrations (both assumed to be 5 × 10¹⁷ cm⁻³), and ${n_i}$ is the intrinsic carrier concentration in a semiconductor under thermodynamic equilibrium conditions. ${n_i}\;$is evaluated as [36]:

(12)$$n_i^2 = {N_c}{N_v}exp\left( { - \frac{{{E_g}}}{{kT}}} \right)$$

where ${N_c}$ and ${N_v}$ are given by $2{({2\pi kTm_e^\ast{/}{h^2}} )^{3/2}}$ and $2{({2\pi kTm_p^\ast{/}{h^2}} )^{3/2}}$, respectively. The J-V curve was plotted using the equation:

(13)$$J = {J_0}\left( {{e^{\frac{{eV}}{{kT}}}} - 1} \right) - {J_{sc}}$$

The power conversion efficiency (PCE) of the solar cells is defined as:

(14)$$\eta = \frac{{{V_{oc}}\;{J_{sc}}\;FF}}{{{P_{in}}}}$$

where FF is the fill factor of the solar cell, calculated from the J-V curve (ratio of maximum power from the solar cell to the product of ${J_{sc}}$ and ${V_{oc}}$) and ${P_{in}}$ is the incident source power (1000 W/m²). The semiconductor parameters for InN and GaN are listed in Table 3 and can be calculated for In_xGa_1-xN material for given indium composition (x) by linear interpolation.

Table 3. The parameters of wurtzite InN and GaN used for calculation of J-V characteristics [33].

View Table | View all tables in this article

Here, m_e is the electronic rest mass i.e. m_e = 9.109 × 10⁻³¹ Kg.

Funding

Ministry of Human Resource Development (RP03246G: UAY program, RP03417G: IMPRINT program); Science and Engineering Research Board (RP03055G); Department of Biotechnology , Ministry of Science and Technology (RP02829G, RP03150G); Defence Research and Development Organisation (RP03356G, RP03436G).

Acknowledgments

We would also like to thank the Digital India Corporation. This publication is an outcome of the R&D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (formerly Media Lab Asia).

Disclosures

The authors declare no conflicts of interest.

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