Particle swarm optimization for performance enhancement of cadmium telluride thin film solar cells by embedded nano-grating structures with a plasmonic metal coating layer

Abstract

As the demand for energy in world is increasing rapidly and there is pursuit for renewable energy sources which is cheap, easy to generate and requires low maintenance, solar energy is a top contender. The world is in dire need of photovoltaic solar cells that can aid in keeping up with the hiking energy demands. However, thin film solar cells (TFSCs) which are developed for cost effectivity, suffer in performance due to reduced thickness. Therefore, this computational study uses Finite-Difference Time-Domain (FDTD) and delves into the scope of using a 1-D nano-grating structure embedded into absorbing layer of cadmium telluride TFSC to enhance the optoelectronic performance. A unique nano-grating structure with SiO₂ at its core and aluminium coating aims to enhance the performance of CdTe TFSC with cost effectivity and ease of fabricability as the main motifs. Additionally, an evolutionary computational technique, Particle Swarm Optimization (PSO), was used to determine the optimal parameters of nano-gratings on CdTe TFSCs, i.e., nano-grating height, angle, duty cycle, aluminium coating thickness and grating substrate thickness. The PSO algorithm resulted in a nano-grating structure that yielded an efficiency increase of 52.86% and increase in short-circuit current density of 25.45% with respect to bare CdTe TFSCs. Subsequently, the performance of the optimal nano-grating structure was also observed to be insensitive to variation of wide range of incidence angle of light, a key feature preferred for versatile application of TFSCs.

1. Introduction

Today's world demands energy from renewable sources at the expense of low cost, easy manufacturing and minimum maintenance. The only source that stands out is solar energy and the field closely related to the exhausting research behind harnessing it is photovoltaics. In that regard, solar cells are still the leading contender for effective conversion of photon energy to electric energy [1]. Although solar cells have been around for a long time with crystalline silicon based solar cells being the market dominant and mass manufactured, it still has not widely replaced fossil fuel-based sources of energy because of its low conversion efficiency and high payback period. Because the traditional crystalline silicon (c-Si) solar cells are quite bulky and expensive, a significant amount of research is taking place towards thin film solar cells (TFSCs) [2]. More so, the cost of purifying these c-Si for fabrication purpose pushes the manufacturing cost higher [3]. As a result, active materials such as poly-crystalline or amorphous silicon (p-Si or a-Si) are currently being used as the active material in such TFSCs. Although these cuts down the cost for manufacturing, they have an added disadvantage of having small diffusion length due to randomness of the crystal structure [4]. Hence, it is important to shift the preferences of substrate material towards a better alternative. Cadmium Telluride (CdTe) with an ideal band gap value of 1.45 eV and absorption co-efficient of 10⁶ cm^-1 at room temperature stands out as the ideal absorbing substrate material [5]. Despite being a direct band gap semiconductor material, CdTe based TFSCs are still lacking behind in terms of performance efficiency [6]. Only effective light trapping mechanisms can push further the performance efficiency of CdTe thin film solar cells and make it more suitable for mass production and wide range of use [7].

Recently, the use of the plasmonic metal nanoparticles/nanostructures has been one of the efficient and effective ways to enhance light absorption in thin film solar cells [8]. Several different techniques have been previously investigated and studied using plasmonic nano-structures such as nanoparticles [9], nano-pillars [10], nano-rods [11], surface texturing [12] and nano-gratings [5]. The plasmonic metal nanostructures mentioned above contribute to the light trapping in one of the following ways, (i) through plasmonic nano-structures placed on top of absorbing substrate which couples incident radiation to wave guide modes and by excitation of surface plasmon polaritons (SPPs) [13]; (ii) introducing plasmonic nano-structures embedded into the light absorbing substrate to enhance electro-magnetic energy through localized surface plasmons (LSPs) [14]; (iii) plasmonic back structures to redirect the unabsorbed or weakly absorbed light back into the substrate via photonic modes or orders [15]. The plasmonic top structures can enhance light trapping by coupling light to longer propagation path but the plasmon resonance occurs only at certain wavelengths blocking considerable amount of incident radiation [16]. Recently, nano-grating structures are being investigated by being placed in different orientations for enhanced light trapping in variety of TFSCs such as silicon, intermediate bandgap solar cell, perovskites, and as well as GaAs photodetectors [17], [18], [19], [20]. Moreover, nano-grating structures are being widely investigated because of its simple geometry and easy fabrication as compared to nanoparticles, optical antennas and split ring resonators [21]. During literature review, it was found that back surface grating structure contribute to excitement of surface plasmon polaritons (SPPs) and thus contribute to absorption especially for wavelength range of 800 nm to 1200 nm of incident radiation [21]. Previously it was investigated that a bulk aluminium nano-grating incorporated within the absorber layer of CdTe TFSC reported performance enhancement [5]. Although it was a good intial study to enhance light trapping mechanism in CdTe TFSCs but it did not address many other parameters and factors that play a vital role in overall efficiency of CdTe TFSCs when grating structures are used at the bottom of the absorbing substrate. Additionally, nanograting structures have been reported to result in absorption enhancement for light having wide angle of incidences. As the light incident on a solar cell varies throughout the day and is seldom perpendicular, hence the aforementioned characteristic of nanograting structures is very crucial [22].

In this work, a more efficient 1-D nano-grating structure in terms of both cost and fabrication is being proposed to be embedded at the bottom of the absorbing substrate of CdTe TFSCs. This modified nano-grating structure diffracts incident light towards the absorbing substrate, thus increasing the path length of the trapped light. The proposed study also involved use of the PSO algorithm to optimize five grating parameters and other methods to make the grating structure more efficient and robust for use in all possible conditions without compromising TFSC performance enhancement and at the same time keeping in mind designs that are relatively fabrication friendly. Moreover, this study demonstrates that instead of using a plasmonic metal to fabricate the whole nano-grating structure, it is possible to opt for cost effective SiO₂ grating structure with a thin plasmonic coating layer made of aluminium (Al) for performance enhancement which was not reported before for CdTe TFSCs.

2. Methodology

2.1. Simulation setup

The proposed nano-grating structure has been simulated using the commercially available Ansys-Lumerical software package (in particular FDTD Solutions and CHARGE softwares). The overall simulation can be divided into two parts, optical simulation and electrical simulation. Optical simulations are done in FDTD solver that uses the finite-difference time-domain method to calculate the optical generation rate, optical absorbance A(λ), transmittance T(λ), reflectance R(λ) and electric field intensity data. Later optical generation data was fed into the DEVICE solver to calculate electrical performance parameters such as short -circuit current density (J_sc), open-circuit voltage (V_oc), fill-factor (FF) and efficiency (%η) of the solar cell.

Fig. 1 illustrates the simulation setup of the FDTD solver. Here CdS and CdTe have been stacked together to work as window layer and absorber layer respectively since CdS is the most common window layer for CdTe based TFSCs [23]. A thickness of 100 nm for CdS and 1500 nm for CdTe is taken which allows more than 92% of visible wavelength light to be absorbed [24]. Finally, 100 nm Ag has been added to work as the bottom metal contact. The proposed nano-grating structure has been carefully designed to be embedded at the bottom of the CdTe absorber layer, which consist of SiO₂ triangular nano-grating with metal coating layer. Periodic boundary conditions have been imposed to the x and y direction because of the 1-dimensional periodicity of the nano-grating structure, allowing to simulate a unit cell to represent the whole structure. Alternatively, perfectly matched layer (PML) boundary condition has been taken to both positive and negative z axis which act to absorb the transmitted and reflected light. To illuminate the solar cell structure, a plane wave source of AM1.5G solar irradiance consisting of 400-1100 nm wavelength has been taken. Two 2D power monitors normal to the z axis have been placed to record the amount of reflected and transmitted light, one above the CdS layer and the other below the bottom metal contact as illustrated in Fig. 1. The proposed nano-grating structure has also been studied for the TE mode polarization where the source polarization angle was set to 90°. Electric field data for both the TM and TE mode polarization was recorded by placing another 2D power monitor normal to the y-axis at the center of the nano-grating structure. Lumerical scripting language was used to export generation data for DEVICE solver.

Figure 1.

3D schematic diagram of FDTD simulation setup showing necessary monitors to simulate a unit nano-grating period for optical analysis.

Fig. 2 demonstrates DEVICE simulation setup for electrical simulation where optical generation data was imported extending for multiple nano-grating periods. Similar to bottom metal contact, Ag was used for top metal contact as illustrated in Fig. 2. No charge carrier generation was considered under the area covered by the top metal contact due to its shadowing effect. The nano-grating structure was also discontinued in this region for successful charge carrier collection by the bottom metal contact. CdTe was uniformly doped (p-type) with a concentration of 2×10¹⁴ cm^-3 and CdS (n-type) with a concentration of 1.1×10¹⁸ cm^-3 [25]. A voltage sweep from 0 V to 1.2 V with an interval of 0.05 V was done to obtain the PV and IV characteristics of the solar cell and later FF and efficiency was calculated using Lumerical scripting language. The DEVICE parameters for the electrical simulations are shown in Table 1.

Figure 2.

3D schematic diagram of DEVICE simulation setup for electrical analysis of multiple nano-grating periods.

Table 1.

DEVICE parameters for electrical simulations.

Parameters	Description	Nominal values
μn(CdTe)	CdTe electron mobility	1050 cm2 V-1s-1
μp(CdTe)	CdTe hole mobility	100 cm2 V-1s-1
μn(CdS)	CdS electron mobility	340 cm2 V-1s-1
μp(CdS)	CdS hole mobility	340 cm2 V-1s-1
NA	Uniform acceptor p-doping	2×1014 cm-3
ND	Uniform donor n-doping	1.1×1018 cm-3
Tn(CdTe), Tp(CdTe)	Trap-assisted (Rsrh) carrier recombination lifetime of CdTe	1×10-6 s
Cn(CdTe), Cp(CdTe)	Auger carrier recombination of CdTe	1×10-34 cm6s-1
Cradiative(CdTe)	Radiative recombination of CdTe	1×10-20 cm3s-1
Tn(CdS), Tp(CdS)	Trap-assisted (Rsrh) carrier recombination lifetime of CdS	1×10-6 s
Cn(CdS), Cp(CdS)	Auger carrier recombination of CdS	1×10-34 cm6s-1
Cradiative(CdS)	Radiative recombination of CdS	1×10-20 cm3s-1
T	Simulation Temperature	300 K

2.2. Numerical analysis

The standard solar cell parameters were calculated from the simulations to analyze the performance of the proposed CdTe solar cell structure, using light with the wavelength range of 400 nm to 1100 nm as the source, which is the range of the solar spectrum. Optical analysis was conducted in order to generate the electric field intensity plot and the absorption plot, which help visualize and understand the interaction of light around the nanostructures. The absorbance A(λ) is calculated to determine the amount of light absorbed by the substrate using the formula [26]:

$$A(\lambda )=1-R(\lambda )-T(\lambda )$$ (1)

where R(λ) is the reflectance and T(λ) is the transmittance.

The short-circuit current density (J_sc) indicates the amount of photocurrent generated per unit area when incident light is absorbed by the solar cell substrate. It is the maximum current that can be generated when the solar cell is in short-circuit condition, i.e., voltage across the solar cell is 0. Assuming each photon with sufficient energy striking the solar cell generates one electron ideally, the short-circuit current density is calculated using the following formula [26]:

$$J_{\mathrm{sc}}=e\int \frac{\lambda }{hc}QE(\lambda )I_{\mathrm{AM1.5G}}(\lambda )d(\lambda )$$ (2)

where e is the charge of an electron, λ is the wavelength, h is the plank's constant, c is the speed of light, I_AM1.5G(λ) is the spectral irradiance of incident light.

The open-circuit voltage (V_oc) is the maximum voltage that can be obtained from a solar cell under open-circuit conditions, i.e., the current across the solar cell is 0. It also indicates the voltage at which the dark current and photocurrent generated are equal, hence resulting in no overall current generation. The open-circuit voltage is calculated as follows [27]:

$$V_{\mathrm{oc}}=\frac{nkT}{q}ln(\frac{I_{\mathrm{L}}}{I_{\mathrm{0}}}+1)$$ (3)

where n is the ideality factor, k is the Boltzmann constant, T is the temperature in Kelvin, I_L is the light-generated current, and I₀ is the dark saturation current.

The fill factor (FF) is an indication of the quality of the solar cell. It is the ratio of the maximum possible power that can be obtained from the solar cell to the product of the short-circuit current density and the open-circuit voltage. It can be calculated using the formula as given below [28]:

$$FF=\frac{P_{\max }}{J_{\mathrm{sc}}\text{*}{V}_{\mathrm{oc}}}$$ (4)

The efficiency (η) is a measurement of how much of the input energy from the incident light can be converted to useful energy for current generation by the solar cell. It is calculated by determining the ratio of the maximum possible power generated from the solar cell to the incident energy from the source, as shown in the formula below [29]:

$$\eta =\frac{FF\text{*}{J}_{\mathrm{sc}}\text{*}{V}_{\mathrm{oc}}}{P_{\mathrm{in}}}$$ (5)

where P_in = 1000 Wm^-2 for AM 1.5 solar irradiance.

3. Result analysis

3.1. Coating material study

The nano-grating structure placed at the bottom of the absorbing substrate usually diffracts lights of longer wavelength at specific angles creating a spectrum of diffracted lights in both sides of the incident radiation. The extent of diffraction depends on the interface between the semiconductor material and the nano-grating material. Previous works used plasmonic materials like aluminium and silver to construct the entire nano-grating used in their design [5], [21]. This makes the fabrication of TFSCs expensive. This study proposes use of a plasmonic coating layer over SiO₂ grating structure which is quite inexpensive and has industry efficient fabrication advantages as well [30]. To investigate which plasmonic metal can be used as a coating layer for CdTe TFSCs, we conducted a study on a recently proposed structure of CdTe TFSC where the nano-grating material was aluminium [5]. In this study, SiO₂ nano-gratings with similar parameters to those studied previously were used [5], but with an additional modification that the SiO₂ gratings were coated with a 10 nm thin layer of different kinds of plasmonic metals, respectively. The materials chosen for this study were aluminium (Al), silver (Ag), gold (Au) and titanium (Ti). From the results shown in Fig. 3, it can be stated that aluminium (Al) stands out as the leading material of choice in terms of important TFSC performance parameters such as short-circuit current density (J_sc) and efficiency. The short-circuit current density (J_sc) and efficiency were 29.24 mA/cm² and 22.29% respectively for Al while titanium (Ti) was the second best performing coating material. From Fig. 4, it can also be observed that of all the materials studied for suitable coating layer material, aluminium (Al) has the largest absorption peaks beyond the edge of visible spectrum. These peaks contribute to efficient light matter interaction at the interface of absorbing substrate and embedded nano-grating structure which ultimately leads to enhanced absorption and overall efficiency. For further investigations of this study, we used Al as the plasmonic coating layer metal for the finally proposed design of highly efficient CdTe TFSC.

Figure 3.

Short-circuit current density (J_sc) and efficiency for bare CdTe TFSC, CdTe TFSC with only SiO₂ nano-grating and CdTe TFSC with coated (Ag, Al, Au and Ti) SiO₂ nano-grating structure.

Figure 4.

Optical absorption spectra for bare CdTe TFSC and CdTe TFSC with SiO₂ nano-grating structure coated with plasmonic metals for λ between 400-1100 nm.

3.2. Period study

A nano-grating redirects incident radiation into multiple directions depending on the angle of incidence on the grating itself and the periodicity of the grating structure. Effective light trapping by the nano-grating structure depends on the number of diffracted modes and the angle at which they are being diffracted to. Depending on the angle of diffraction, the enhanced path length is determined which is traveled by the redirected light causing higher optical absorption. Depending on the periodicity, this phenomenon happens where surface plasmon polaritons (SPPs) are effectively coupled into guided resonance modes traveling back towards the substrate after diffraction. The following equation can be stated to explain this relationship:

$$p\text{*}n\text{*}sin({\theta }_{\mathrm{m}})=m\text{*}\lambda$$ (6)

where ‘p’ denotes periodicity, ‘n’ denotes refractive index of the medium after diffraction, θ_m represents angle of diffraction and ‘m’ denotes order of diffraction. Since the nano-grating structure under this study is one dimensional, i.e., it is uniform in y-direction and periodic in x-direction, hence, the diffracted beam always lies in x-z direction. This study is important because if the period of the nano-grating structure is too large, the diffraction angle reduces which reduces the enhanced path length of the diffracted light beams. On the other hand if the period is too small, the number of guided resonance modes decreases [31]. It is important to find the trade off between these extremely large and short periods and hence this period study is conducted within a range of 450 nm to 1000 nm. Since the aim is to decide upon a period for the nano-grating structure which helps in absorption of large wavelengths or broadband absorption, from Fig. 5, it can be noticed that 600 nm period has the highest number of resonance peaks. These peaks when aggregated together contribute to enhanced absorption especially beyond the band edge of visible spectrum and in the near-IR region. To further justify the choice of this period, performance of the structure proposed in previous studies was also investigated in terms of TFSC performance parameters such as short-circuit current density (J_sc), open-circuit voltage (V_oc) and efficiency. From Fig. 6, it can be seen that for 600 nm period, the J_sc and V_oc are 29.24 mA/cm² and 1.0168 Volt respectively. The performance values for other periods studied kept decreasing as the value of the periodicity kept increasing. This trend can also be seen from previously conducted study where with increasing period, the enhancement is reduced [15]. From Fig. 7, it can be also been seen that in terms efficiency, 600 nm period is an ideal choice for the nano-grating structure as it recorded an efficiency value of 22.29%.

Figure 5.

Absorption curve for bare and CdTe TFSC with nano-grating structure having periodicity (450 nm, 500 nm, 600 nm, 750 nm, 900 nm, 1000 nm) for wavelength between 400 nm to 1100 nm.

Figure 6.

Short-circuit current density (J_sc) and open-circuit voltage (V_oc) for bare CdTe TFSC, CdTe TFSC with only SiO₂ nano-grating and CdTe TFSC with Al coated SiO₂ nano-grating having varied periods (450 nm, 500 nm, 600 nm, 750 nm, 900 nm and 1000 nm).

Figure 7.

Efficiency of bare CdTe TFSC, CdTe TFSC with only SiO₂ nano-grating and CdTe TFSC with Al coated SiO₂ nano-grating having varied periods (450 nm, 500 nm, 600 nm, 750 nm, 900 nm and 1000 nm).

3.3. PSO optimization

The nano-grating structure used so far under this investigation was the proposed design in previously-conducted study [5] upon which further optimal period finding was conducted by replacing the aluminium-based bulk nano-grating structure with SiO₂ nano-grating, and concluded that aluminium coating of 10 nm thickness to be a desirable material for coating. The structural parameters associated with the nano-grating are namely nano-grating height, nano-grating angle, nano-grating duty-cycle, nano-grating substrate thickness and nano-grating coating layer thickness which are described in Fig. 8. It is vital that the geometry associated with the nano-grating structure under this study is optimized so that performance enhancement can be ensured to its highest limit. Fabrication of such structures and physical verification of performance enhancement is quite expensive and complex. Hence it is important that the structural parameters of this nano-grating are optimized using simulations. But optimization of so many structural parameters using only FDTD simulations is a long and tedious process which will require hundreds or thousands of iterations for optimization of single parameter and very high computational power and time. As a result, it is important that an algorithm is used that can factor in multiple structural parameters and return their optimized value where the combination of all the optimized parameters returns the highest performance efficiency of CdTe TFSC.

Figure 8.

Structural parameters of nano-grating structure considered for Particle Swarm Optimization.

The Particle Swarm Optimization (PSO) algorithm is an evolutionary algorithm based on the social behavior of animals flocking or moving together [32]. This algorithm has been used in this study with a goal of optimizing the above mentioned nano-grating parameters with a single objective of maximizing the short-circuit current density (J_sc) of the finally proposed CdTe TFSC with optimized nano-grating parameters, also called fitness function within the algorithm. In this algorithm, a random particle population is generated and distributed where each particle represents a multi-dimensional vector. Each particle's position and movement is influenced by its neighboring particles towards a global maxima while improving their local maxima with consecutive iterations. The work flow followed by this algorithm is shown using the flowchart mentioned in Fig. 9.

Figure 9.

Flowchart for Particle Swarm Optimization.

Here, in this flow chart, r₁, r₂ represents random value between 0 to 1 and C₁, C₂ represent cognitive and social attributes respectively for each particle. For this study, number of generations was set to be 20 and within each generation 10 simulations were run for maximizing the fitness function as stated above. Table 2 shows the structural parameters set for PSO with their range and the returned value after optimization.

Table 2.

Parameter range and their optimized values after Particle Swarm Optimization.

Parameters	Range	Optimized value
NG substrate thickness (nm)	50 - 300	300 nm
NG coating thickness (nm)	2 - 20	14.09 nm
NG height (nm)	80 - 150	141.18 nm
NG duty cycle	0.3 - 0.9	0.54
NG angle (degree)	10 - 85	47.24

The PSO algorithm returns an optimized nano-grating structure with enhanced performance which is capable of performing better than bare CdTe TFSCs in both TM and TE polarization mode as shown in Fig. 10. From Fig. 10, it can be seen that absorption peaks are visible for both TM and TE polarization modes beyond the band edge of visible spectrum for longer wavelengths which are usually not absorbed in single transmission for TFSCs. The proposed design is more responsive towards TM polarization as enhanced absorption peaks are more observed for TM polarization. These absorption peaks together contribute to the overall performance enhancement of CdTe TFSC using PSO optimized nano-grating structure where 5 structural parameters were optimized. Due to well defined absorption peaks beyond the band edge of visible spectrum, average absorption of 83% and 74% were achieved for TM and TE polarization, respectively.

Figure 10.

Absorption spectra for bare CdTe TFSC and CdTe TFSC with proposed nano-grating structure under TE and TM polarization mode for wavelength between 400 nm to 1100 nm.

Fig. 11 gives a visual representation about how much solar spectrum is being incident on CdTe TFSC under AM 1.5 radiation and how much solar spectrum is being successfully absorbed by the bare CdTe TFSC and CdTe TFSC with optimized nano-grating structure proposed above. It is evident that the proposed design of CdTe TFSC is allowing broadband absorption and this broad band absorption can be attributed to the resonance peaks found in the region of longer wavelengths. I-V and P-V curves are crucial to determine and realize overall performance efficiency of the proposed study. So from Figure 12, Figure 13, it can be clearly observed that the proposed design with optimized nano-grating structure covers a larger area under the I-V and P-V curve compared to bare CdTe TFSC. This is an indication of enhanced performance efficiency. Performance of the proposed CdTe TFSC is compared with recently investigated CdTe TFSCs in terms of significant solar cell performance parameters such as short-circuit current density (J_sc), open-circuit voltage (V_oc), fill factor, and efficiency in Table 3. Integrating the proposed nano-grating structure pushes the solar cell efficiency to the highest value as compared to other light trapping techniques. Although the CdTe TFSC investigated in [33] has a higher value of open-circuit voltage and fill factor; short-circuit density and efficiency are the most crucial parameter for evaluating TFSC performance [29].

Figure 11.

Spectral intensity received and absorbed for bare and proposed CdTe TFSC with optimized nano-grating structure with respect to AM 1.5G.

Figure 12.

I-V curve for bare CdTe TFSC and CdTe TFSC with proposed nano-grating structure.

Figure 13.

P-V curve for bare CdTe TFSC and CdTe TFSC with proposed nano-grating structure.

Table 3.

Performance comparison of recently investigated and proposed CdTe thin film solar cells.

Solar cell structure	Light trapping technique	Jsc (mA/cm2)	Voc (V)	FF	Efficiency (%)	Reference
SiO2/Si(DBR)/ ZnTe/CdTe/CdS/ ZnO/FTO/glass	SiO2/Si DBR	10.98	1.200	0.82	10.39	[33]
Au/ITO/CdTe/ CdS/ITO/glass	Au NPs	24.80	0.790	0.46	9.00	[34]
Au/ZnO/CdS/ CdTe/Au	ZnO Nanopillar	16.90	1.008	0.75	12.60	[35]
ITO/CdS/ CdTe/Ag	Micro-texturing	24.29	0.798	0.57	10.98	[36]
Ag/CdS/ CdTe/Al(coating)/ glass(grating)/Ag	Nano-grating	30.52	1.020	0.75	23.48	This work

3.4. Electric field intensity plot analysis

To further understand the underlying physics behind the enhanced absorption of the proposed nano-grating structure, the electric field distribution profile has been plotted in Fig. 14(a-l). For a wavelength of 600 nm, 870 nm, 952 nm and 1070 nm, electric field intensity has been plotted for both TE and TM mode polarization and compared with bare CdTe TFSCs (without any nano-grating structure embedded). These wavelengths are particularly chosen compared to the other wavelengths because of strong light matter interaction in the close vicinity of the grating structure. As bare CdTe TFSCs structure is symmetrical from a polarization perspective, the electric field intensity plot for TE and TM mode polarization are the same. Shorter wavelength (<800 nm) light is found to be hardly penetrating through the CdTe substrate which has a bandgap of roughly 1.44 eV as seen in Fig. 14(a-c). Thus, the nano-grating structure plays very little role in enhancing the absorption in the shorter wavelength range. However, at the longer wavelength (>800 nm) range, light passes through the bare CdTe substrate without being absorbed, thus resulting in poor absorption as seen in Fig. 14. This is due to the quick drop in absorption coefficient value after this wavelength (800 nm) [37].

Figure 14.

The normalized electric-field intensity, |E|² profile of bare CdTe (same for TM, TE mode), optimized nano-grating structure for TM and TE mode polarization of light at a wavelength of 600 nm, 870 nm, 952 nm, and 1070 nm.

To harness the light of near IR region, the substrate thickness has to be increased. However, the proposed nano-grating structure can harness energy at a longer wavelength without compromising the substrate thickness (i.e., with a thin absorber substrate). The enhanced absorption at the longer wavelengths by the optimized nano-grating structure can be attributed to two mechanisms, cavity resonance and surface plasmon polariton (SPP) excitation [16], [38]. Conventionally bare CdTe TFSCs support Fabry-Perot resonances and the mode intensity increases with the increase in wavelength as seen in Fig. 14(a,d,g,j) [39]. For TM mode polarization, cavity resonance modes can be seen in the region between the two nano-grating periods at 870 nm wavelength of light for the optimized nano-grating structure (Fig. 14(f)) [16], [40]. Nonetheless, it is visible from Fig. 14(i) that SPP dominates at the bottom of the CdTe absorber layer to enable charge carrier generation at a wavelength of 952 nm. At 1070 nm wavelength of light, strongly enhanced electric field around the nano-grating can be attributed to a hybrid mode, created by both cavity resonance and SPP (Fig. 14(l)) [40], [41]. On the other hand, for TE mode polarization, a continuous pattern of constructive and destructive interference throughout the substrate is visible in Fig. 14(e,h,k). However, SPP excitation by the nano-grating metal coating is not significant for TE mode. This may be due to the fact that SPP excitation requires electric fields normal to the metal-semiconductor interface to create surface charges at the metal layer, which is in this case due to the TM mode light [42].

3.5. Angle response by the optimal structure

Due to the apparent solar path taken by the sun, the light that is incident on a horizontal flat solar cell is not always normal to the surface, i.e., the rays of the sun fall on the surface of a solar cell at angles greater than or less than 90 degrees (i.e., normal incidence). Angle of incidence is defined as the angle that a light ray makes with the zenith. Therefore, the effect of angle of incidence of light is an important factor to be considered for the robustness of a solar cell's use in wide range of applications. Hence, after the PSO method was applied, the performance of the CdTe TFSC with optimal nano-grating parameters was studied at oblique angles. It was observed from Figure 15, Figure 16 that there was an enhancement in short-circuit current density and efficiency in the optimal CdTe TFSC compared to bare CdTe TFSC for angles ranging from 10° to 40°. There is a slight decrease in performance for incident angles larger than 40°. It can be said that the optimal structure is adaptive to angle deviations in the range 10° to 40°. Aspect ratio can be one factor associated to the incident angle insensitivity. The aspect ratio, defined as the ratio of nano-grating height to the nano-grating base length, for the optimal structure was found to be 0.44. Previously, experimental studies for a-Si TFSC showed that similar nano-grating structures with aspect ratio ranging from 0.1-0.4 tend to be responsive to wide range of angles as these structures scatter light efficiently inside the absorbing substrate, and there is improved coupling to guided mode resonance [43]. Subsequently, numerical studies for Gallium Arsenide (GaAs) TFSCs have also shown that reflective losses of light vary with incident angle, and it is minimal for grating structures with aspect ratios ranging from 0.1-0.5 [44]. Hence the angle insensitivity of the optimal structure can be attributed to the potential aspect ratio factor.

Figure 15.

Short-circuit current density (J_sc) as a function of solar incidence angle for bare CdTe TFSC and CdTe TFSC with Al-coated nano-grating structure.

Figure 16.

Efficiency (%η) as a function of solar incidence angle for bare CdTe TFSC and CdTe TFSC with Al-coated nano-grating structure.

4. Potential fabrication techniques

Although a large number of growth techniques have been used to grow CdTe, only two methods, electrodeposition and CSS, have successfully passed through the scaling up and commercialization program [45]. For device fabrication, it is essential to grow CdTe on glass/FTO/CdS substrates [46]. In addition to enhancing electrodeposited layers through heat treatments and processes like CdCl₂ treatment, the fabrication of CdS/CdTe solar cells involves successive deposition of CdS and CdTe layers. After processing these structures, the final step is the deposition of the back metal contact. The grating structure proposed in this investigation is a 1-D glass grating which has been used for enhanced light trapping and also has been successfully fabricated previously depending on numerous properties such as cost effectiveness, heat resistance and corrosion resistance [47]. To further increase the light trapping in this investigation, an aluminium coating layer has also been used. There are different manufacturing processes for these nano-structures having their own advantages and disadvantages in terms of grating period, grating groove shape, diffraction efficiency, wavefront quality, manufacturing cost, stray light, roughness [48]. Fabrication of such surfaces like nano-grating structure with plasmonic coating requires high end lithography technique, high energy density beam processing, ultra-precision processing technology [48], [49]. To achieve the spectral range demonstrated by simulation results in this study, it is suggested to opt for high energy density beam processing where one of the significant general materials is glass and reported diffraction efficiency is also higher [48].

Integrating a nano-grating structure within a CdTe thin-film solar cell has its own opportunities and challenges. While this light trapping structure can result in enhanced absorption of solar energy within the absorber layer of CdTe thin-film solar cell, it eventually boosts the overall efficiency of the thin-film solar cell. Moreover, fine tuning the grating parameters can help in better spectral matching with the solar spectrum. The advantages of incorporating such light trapping structures come along with their own challenges as well. Fabrication of such nano-grating structures with high precision can be complex and costly [48]; extremely delicate gratings may reduce the robustness of structure [45]; such nano-structures can also lead to increased recombination losses at the interface [50]. Previously conducted studies show that even if the fabrication technique is not the most ideal one or high tech/precision one, the manufacturers can always opt for cost effective techniques for fabricating the nano-structures and can still get better performance as compared to bare CdTe TFSC [51].

5. Conclusion

This computational study investigates the potential performance enhancement of CdTe TFSCs consisting of an embedded SiO₂ nano-grating structure with a thin aluminium coating layer. The purpose of this investigation was to use cost-effective grating materials that are easy to fabricate, without compromising on performance enhancement. Therefore, a thin plasmonic coating layer of aluminium was used on top of SiO₂ nano-grating structure which stood out among other coating materials studied. Upon selecting the proper grating substrate and coating materials, initial simulations were done to find an optimal nano-grating period that provides necessary guided resonance for broadband absorption. The results reveal that the nano-grating period of 600 nm has the highest short-circuit current density of 29.24 mA/cm² and efficiency of 22.29%, significantly higher than that of bare CdTe TFSCs. Subsequently based on these findings, Particle Swarm Optimization algorithm was used to optimize the height, angle, duty cycle, substrate thickness, and coating layer thickness of the nano-grating structures to push further the performance of CdTe TFSCs. The optimized nano-grating structure obtained resulted in a short-circuit current density and efficiency of 30.52 mA/cm² and 23.48% respectively. Compared to bare CdTe TFSCs, short-circuit current density shows a 25.45% increase while efficiency shows a 52.86% increase, respectively. It is noteworthy that the optimal nano-grating structure shows insensitivity to the incident angle as elaborated in the later section, owing to its optimal period and aspect ratio. The viability of the proposed structure in terms of fabrication was also discussed. However, maintaining high precision in fabrication might add additional cost and reduce robustness. Recombination at the interface might also degrade the performance. Therefore, such limitations require extensive studies in the future to overcome. This work can also be extended by incorporating a 2D nano-grating structure and investigating other artificial intelligence or optimization algorithms to further improve the grating structure.

CRediT authorship contribution statement

Rifat Bin Sultan: Writing – review & editing, Writing – original draft, Validation, Software, Project administration, Investigation, Formal analysis, Data curation, Conceptualization. Asif Al Suny: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Data curation. Md. Hasibul Hossain: Writing – review & editing, Writing – original draft, Visualization, Software, Resources, Methodology, Data curation. Tazrian Noor: Writing – review & editing, Writing – original draft, Software, Resources, Formal analysis. Mustafa Habib Chowdhury: Writing – review & editing, Supervision, Software, Project administration, Formal analysis.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.