1. Introduction

Thin-film solar cells have been of great promise for next-generation solar power conversions due to their better flexibility, lighter weights, cheaper processing and ease of integration. Moreover, significantly reduced cell thickness of 1-2 µm for thin-film solar cells makes them more easily meet the requirement that minority carrier diffusion length should be several times the base thickness to have all the photo-carriers collected [1]. As one of the most promising photovoltaic technologies, cadmium telluride (CdTe) solar cells have demonstrated their long-term stability and competitive performance in the thin-film photovoltaics community. CdTe is a direct band gap semiconductor material with the band gap energy of 1.44 eV, similar to GaAs. While the required absorption thickness for direct band gap materials is of the order of 1-10 micrometers, it is still advantageous to reduce the thickness further to minimize cadmium content and tellurium usage per panel and improve carrier extraction. Moreover, absorption can be improved if the Fresnel reflection is reduced. However, standard single layer anti-reflection coatings are ineffective for broadband reflection reduction [2–4]. For this reason, light scattering of nano-patterned plasmonic structures that enhance light trapping and hence absorption has been previously proposed to improve solar cells performance [5–7]. However, most of the reported structures used nano-patterned metal structures or plasmonic nanoparticles as scatterers [8–12] to trap light in the material where electron-hole pairs are generated.

In the past decade, metamaterials have been proposed and experimentally realized in many material systems and frequency regions. Metamaterial is a kind of the engineered artificial material that is composed of sub-wavelength manmade inclusions with rationally designed shapes, sizes, compositions, and mutual orientations [13]. Compared with conventional materials, metamaterials have offered new opportunities of unprecedented control over the electromagnetic properties of matters, such as negative index of refraction and optical magnetic response. Besides the well-known applications such as super resolution [14] and invisibility [15], metamaterials also have also shown intrinsic advantages in light harvesting. Recently, several groups have successfully demonstrated metamaterial absorbers, in which most of the incident electromagnetic waves have been absorbed [16–21]. Such metamaterial perfect absorbers have achieved great successes in microwave and terahertz frequency regions. However, in optical region, the light absorption of metamaterial is strongly limited by the narrow bandwidth and small incident angle induced by the nature of resonance [19]. The narrow bandwidth is usually less than 10% of the bandwidth of solar spectrum and the incident angle is limited for normal incident light. Thus their enhancements of optical absorption are usually strongly limited.

In this work, we theoretically investigate the possibility to further improve the light absorption enhancement and to enlarge the bandwidth of metamaterials. By using an optical magnetic metamaterial as top and bottom conductive electrodes, the absorption of a thin CdTe photovoltaic cell has been significantly increased in a wide wavelength range. The bandwidth of absorption enhancement is more than 400 nm and the maximum enhancement is over 3 times.

2. Design and simulation

2.1 Structure design

In conventional plasmonic and metamaterial structures, the enhancement of optical absorption is mainly generated by the large field enhancement in the vicinity of metallic structures. However, the resonances of plasmonic structures are usually on the order of tens of nanometer, which are too narrow for the solar spectrum. To further improve the light harvesting, it is essential to enlarge the bandwidths of optical resonances. In conventional designs, simply enlarging the bandwidth will also reduce the local field enhancement [22, 23]. Compared with the tradeoff between enhancement factor and bandwidth, we select the magnetic metamaterials that are more promising candidates. In magnetic metamaterials, there are two types of resonances, which are known as electric resonance and magnetic resonance. While their field confinements are different, both of them have strong local field enhancements. Consequently, carefully designing their resonant positions, it is possible to double the bandwidth of absorption enhancement.

In additional to the enlarged bandwidth, it is also important to improve the enhancement factor simultaneously. In metallic structures, two types of absorption can be identified. One is the absorption of metal that is caused by the ohmic loss. The other one is the absorption of the function layer. For CdTe-based solar cells, the enhancement of absorption means the increase of the latter one. Thus more electromagnetic field should be dragged to the region of CdTe layer. Here we use the sandwich structure, whose metal-CdS-CdTe–metal structure can trap more energy inside the CdTe layer with lower dielectric constant.

A cross-section and a top view of a fragment in our proposed structure are shown schematically in Fig. 1. It has a basic form of a typical photovoltaic device in a simple planar configuration: an Ag grating substrate (bottom electrode) with thickness t, a CdS window layer with thickness d₁, a CdTe absorber layer with thickness d₂, and the second Ag grating layer (top electrode) with the same geometry as the bottom electrode. The periodicity of Ag grating is p. The silver strips are well aligned and can be connected separately to work as top and bottom electrodes to collect electrons. This kind of structure has been well studied in magnetic metamaterials [24]. Thus it is an excellent candidate to test and prove above analysis. The active layer of such solar cell is CdTe thin film, whose optical and electrical properties have been well studied [25]. In order to match to experimental results, two thin alumina dielectric layers of 10 nm are added on top and the bottom of the whole structure and the top sharp corners are rounded in simulation [26].

 

Fig. 1 Basic structure of a CdTe solar cell with metamaterial electrodes. (a) The cross section of the structure. (b) The three-dimensional sketch of the structure.

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2.2Simulation results and discussions

We use commercial finite element method software (COMSOL Multiphysics) to calculate the optical absorption in the structure of Fig. 1. This method allows us to directly use experimental data for the frequency dependent dielectric constants. The dielectric constant of silver is described as a linear medium with complex, frequency-dependent permittivity obtained from famous experimental data by Johnson and Christy [27]. Similarly, the optical properties of CdS and CdTe are also taken from experimental data [25]. The simulation is processed based on single unit cell. Periodic boundary conditions are used at the left and right boundaries, while perfect matched layer absorbing boundary conditions are applied at the top and bottom boundaries of the simulated domain. A normal incident plane wave is used to excite the device from the air side. The polarization of incident wave is linear polarized along the x-axis as sketched in Fig. 1(b). The reflected and transmitted waves from the structure are collected in the far field. The total absorber’s efficiency of the metamaterial-based CdTe solar cell device is defined as A(λ) = 1− R(λ) −T(λ), where R(λ) and T(λ) are the reflection and transmission, respectively. Simply, the absorption enhancement can be achieved by decreasing the reflection and transmission simultaneously. Because the optical resonance of metamaterials are decided by their geometries, this can achieved by optimizing the impedance, which has been widely explored in literatures [28].

Following the previous reports [29], we first numerically investigate the dependence of absorption spectrum (A(λ)) on the geometric dimensions of nanostructure. By considering the fabrication tolerance, the geometrical parameters are optimized to w = 90 nm, t = 30 nm, d₁ = 50 nm, d₂ = 200 nm, t_Al2O3 = 10 nm and p = 270 nm for the visible optical wavelengths. The corresponding transmission/reflection/absorption spectra are plotted in Fig. 2. Two peaks at 485 nm and 645 nm are observed in the reflection spectrum (black line). Correspondingly, two deeps in transmission spectrum (red dotted line) can also be observed in the same positions. Similar to previous reports, these two peaks are the well-known electric and magnetic resonances of the structure [30]. The blue dashed line in Fig. 2 shows the calculated absorption spectrum of the magnetic metamaterials. In a broad wavelength range from 400 nm to 750 nm, the absorption efficiency is above 38%. This broad absorption bandwidth matches the solar spectrum with most of the solar energy, indicating a nice performance in absorption enhancement in CdTe photovoltaic device. The maximum absorption is even close to 75% and the bandwidth with absorption above 50% is more than 275 nm. Both the maximum value and the bandwidth are much better than previous reports [31, 32].

 

Fig. 2 The transmission/reflection/absorption spectra of the magnetic grating with CdTe layer between silver layers. The parameters are w = 90 nm, t = 30 nm, d₁ = 30 nm, d₂ = 200 nm, t _Al2O3 = 10 nm and p = 270nm.

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Based on the large absorption of the magnetic metamaterials based CdTe solar cell device, it is important to calculate the exact absorption enhancement factor. As we mentioned above, the magnetic metamaterials have both the ohmic loss and absorption inside the active layer. Consequently, we have to calculate the absorption of only CdTe layer inside metamaterials to determine the enhancement factor. The exact absorption spectrum of the 200 nm CdTe layer without metamaterials electrodes is plotted as black line in Fig. 3. We can see that the CdTe absorber layer without metamaterials exhibits a low absorption with wavelength around 500 nm. This absorption spectrum is attributed to the absorption of CdS window layer and is consistent with previous reported [27]. When the CdTe absorber layer is embedded into magnetic metamaterial, the absorption becomes complicated. To calculate the absorption only within the CdTe absorber layer, we have calculated the total electromagnetic power loss in CdTe absorber layer, modeled as G_org = ${\displaystyle {\int }_s{Q}_e}ds$, across the 400-800 nm. Here, Q_e is the electromagnetic power loss density and the integral area is through the CdTe absorber layer region. As shown in Fig. 3, the CdTe layer absorption is significantly enhanced and broadened in the visible light range. Similar to the absorption spectrum in Fig. 2, here the absorption consists of two peaks and covers most of the strongest emission region of solar spectrum. The blue dotted line in Fig. 3 shows the corresponding absorption enhancement factor, defined as the ratio of the energy absorbed by CdTe layer with metamaterial G_{org_w} to without metamaterial G_{org_w/o}, as a function of wavelength. We can see that the enhancement factor is above 1.5 times among the wavelength from 400 nm to 800 nm, which matches to the solar spectra well. The maximum enhancement factor reaches 3.2 times at 645 nm. The second highest enhancement factor occurs at 485 nm. Both peaks are consistent with the positions of electric and magnetic resonances in Fig. 2. It is interesting to note that the enhancement factor at 645 nm is around 22% higher than the one around 485nm. This indicates that the magnetic resonance can improve the optical absorption more dramatically than the electric resonance even though both of them can increase the light absorption in CdTe absorber layer.

 

Fig. 3 The electromagnetic power loss for CdTe layer with and without grating and the wavelength dependent absorption enhancement factor.

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Figures 4(a) and 4(b) show the electromagnetic energy loss density distribution at different incident wavelengths of 485 nm and 645 nm. In both cases, most of energies are localized around the interface between top metal and CdS window layer and between CdTe absorber layer and bottom metal. This clearly demonstrates the effects of localized surface plasmon in metamaterials. Interestingly, most of energy dissipations happen within the CdTe absorber layer, indicating that the contributions of resistive heating of metal are very little in this design. Thus the proposed metamaterials based CdTe solar cell device cannot only increase the solar energy absorption, but also effectively confines the absorbed energy inside the CdTe absorber layer. As a result, high efficiency CdTe thin film solar cell can be achieved. The different enhancement effects of magnetic resonance and electric resonance can also be observed here. The field dissipation of magnetic resonance at the interface between bottom metal and CdTe absorber layer is much higher than that of electric resonance. Meanwhile, the field dissipation inside the metal of magnetic resonance is much weaker. Therefore, the magnetic resonance can confine more energy within the CdTe absorber layer and thus have better effect in absorption enhancement.

 

Fig. 4 The electromagnetic energy loss density distribution. (a) at 485 nm. (b) at 645 nm.

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3. Discussion

The physical origin of the absorption enhanced effect relies on the excitation of localized magnetic and electric resonances. To well understand the enhancement in optical absorption and the difference between magnetic resonance and electric resonance, it is thus necessary to study the corresponding magnetic field distributions and the electric displacement at the resonant wavelengths of 485 nm and 645 nm. All the results are shown in Fig. 5. The arrows represent the electric displacement whereas the color map represents the magnetic field. At the magnetic resonance shown in Fig. 5(b), the electric displacement forms a loop resulting in an artificial magnetic moment. We also note a strong magnetic field inside the loop. At the electric resonance shown in Fig. 5(a) the electric displacement is predominantly aligned along one direction with two small circulating component. The magnetic field is also lower when compared to the magnetic resonance. The small circulating component of the electric displacement results in a small magnetic moment which manifests itself as the magnetic anti-resonance. These kinds of field confinements show that both electric and magnetic resonances can improve the light distributions within the CdTe absorber layer well. This is consistent with above results and confirms that the magnetic metamaterials can significantly extend the bandwidth of absorption enhancements, through combing electric and magnetic resonances.

 

Fig. 5 The magnetic field distribution and the electric displacement inside the metamaterials based CdTe solar cell structure at (a) 485 nm. (b)645 nm.

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There are also some differences between Fig. 5(a) and Fig. 5(b). In the case of electric resonance, most of energy is confined within the whole CdTe absorber layer even though it is also stronger at two metal-dielectric interfaces as surface plasmon. In contrast, the field confinement is more uniform within the CdS and CdTe layer even though it is also stronger at two metal-dielectric interfaces at magnetic resonance. This is mainly caused by the capacity effect between two metallic layers with opposite current direction. Moreover, the closed loop of electric displacement at magnetic resonance can form quite strong artificial magnetism inside it. Besides better absorption enhancement in Fig. 3, the electric resonance and magnetic resonance shall have more advantages. When the devices are illuminated by stronger incident light, the plasmonic devices usually reach the absorption threshold easily due to the presences of hot spots in light dissipations and the limited number of exciton [33]. Instead, the magnetic field confinement spreads well within the CdS and CdTe layer in Fig. 5(a) and Fig. 5(b). Thus, the enhancement of electric resonance and magnetic resonance have larger tolerance on high power of incident light.

The aim of this study is to improve the performance of CdTe solar cells using plasmonic nanostructures. By utilizing the magnetic and electric resonances in metamaterials, the bandwidth of absorption enhancement has been significantly extended and the maximum enhancement has been improved at the electric resonance and magnetic resonance. In addition, here we would like to further show that our designed metamaterial structure can also work well over a wide range of angles of incidence, which is also very important in real solar cell devices [34]. Figure 6 demonstrates the effect of incident angle on the absorption enhancement factor, including the CdTe layer absorption r for TM configuration. A peak absorptions enhancement above 3 times is obtained at incidence of 10° for the resonances at 645 nm. The absorption will decrease with further increasing of incident angle. However, the absorption enhancement is weakly dependent on the angle of incidence, with the enhancement factors among the wavelength range from 465 nm to 795 nm still remain as high as 1.2 times at the angle of incidence of 50°. This is due to the fact that the electric and magnetic modes are broadband and excited for a wide range of angles of incidence. When the incident angle is below 10°, the increase of the CdTe layer thicknesses induces the slightly absorption enhancement compared to normal incident light. However, further increasing the incident angle, the incident wave can no longer efficiently drive circulating currents between the two metallic layers at magnetic wavelength. As a result, the total absorption enhancement factor shows a decreasing trend. Moreover, These peaks can be tuned through the visible light and near-infrared regime and further increased by scaling the dimensions of the metamaterials structure.

 

Fig. 6 Wavelength dependent absorption enhancement factor of the metamaterial based CdTe solar cell structure under different incident angles.

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4. Conclusion

Overall, we have studied the influence of magnetic metamaterials on absorption enhancement of CdTe solar cells. Compared with conventional CdTe-based photovoltaic device, we show that the bandwidth of absorption enhancement can be more than 1.5 times larger and thus covers the strongest regions of solar spectrum well. This is mainly caused by the coexistence of electric and magnetic resonances in magnetic metamaterials. Due to the capacity effect of the magnetic resonance, the field absorption within the CdTe layer, the maximum enhancement factor in light absorption has also been increased. The largest value is more than 3.2, which is also much better than previous reports. In additional to the extended bandwidth and improved enhancement factor, the magnetic metamaterials are also found to be robust to the angles of incidence. The absorption enhancement has been observed from normal incident to more than 50 degree. All these results reveal that the magnetic metamaterials can be nice candidates for further improving the performances of ultrathin CdTe solar cells.