1. Introduction

Thin-film solar cells based on microcrystalline silicon (μc-Si:H) or amorphous silicon (a-Si:H) have gained considerable attention as promising candidates for future generation of photovoltaics [1,2]. With an absorber layer in the range of 1 μm, complete utilization of light incoupling and light trapping is imperative for realizing efficient thin-film solar cells based on these materials. Efficiencies higher than 10% have been achieved for microcrystalline silicon solar cells by introducing textured interfaces in the solar cell [3–5]. Introducing nano textured interfaces leads to reduced reflection losses and enhanced scattering and diffraction of light in the device. Whilst these optical phenomenons can be measured in the far-field, in order to understand the optical propagation within such thin-film devices, it is imperative to use numerical methods and solve the Maxwell’s equations rigorously. By considering the near field optics, the nano texturing process for efficient solar cells can be understood and optimized. In this work, a Finite Difference Time Domain (FDTD) simulation tool (OptiFDTD®) was used to investigate the wave propagation for nano textured microcrystalline silicon solar cells. So far the optics in such structures has been investigated by solving the Maxwell’s equations using the Finite Integration Technique (FIT) and Finite Element Method (FEM) algorithm [6–9]. FDTD approach has also been used, but to analyze the wave propagation in amorphous silicon solar cells [10]. In this study the nano texturing of the front interface of the microcrystalline solar cell property was investigated by introducing a triangular grating which represents the textured front interface of a real thin-film silicon solar cell. Triangular and pyramidal structures have been extensively investigated for solar cell applications in the past decade [11–13]. But they were mostly addressed for crystalline silicon solar cells, where the period of the structures were larger than the wavelength of the incident light in many folds. Hence, geometric optics was sufficient to understand the behavior of optics for such solar cells. A recent paper has studied pyramidal textures in thin-film silicon solar cells [7]. However, the manuscript does not provide a detailed description of the wave propagation for small surface textures. Such small textures have distinct influence on the incoupling of blue light in the solar cell.

The influence of the period and height of the triangular profile on the short circuit was investigated for a microcrystalline silicon solar cell to determine the optimal geometries. Results on smooth substrates were used as a reference to investigate the influence of the grating parameters on the solar cell parameters. Optimized designs of the triangular structure were derived to maximize the short circuit current and the efficiency of the microcrystalline silicon solar cells. The optical model used to calculate the optical power losses in the individual regions of the solar cell is introduced in Section 2. Simulation results including power loss profiles, quantum efficiencies and short circuits currents are described in Section 3. The manuscript is summarized in Section 4.

2. Optical simulation model

To increase the effective thickness of thin-film silicon solar cells, many different concepts exist. More light can be coupled into or trapped within the solar cell by applying anti-reflection coatings [10,13], optical filters [14], or using highly reflective back contacts [15]. In the case of microcrystalline silicon thin-film solar cells randomly textured contact layers have resulted into the highest efficiencies [4,5]. These textured layers have been realized by direct growth of zinc oxide films by low pressure chemical vapor deposition or etching of sputtered zinc oxide [5,16]. A surface profile of such an etched aluminum doped zinc oxide (ZnO:Al) is shown in Fig. 1 . The sputtered zinc oxide film was etched for 10 seconds in a 0.5% diluted hydrochloric acid (HCl) solution. Figure 1(a) shows a three dimensional surface profile of the substrate. Surface texturing of the film leads to surface morphology that very closely resembles a pyramid-like structure, albeit not perfectly symmetrical ones.

 

Fig. 1 (a) Atomic Force Microscope (AFM) image of a randomly textured aluminum doped zinc oxide (ZnO:Al) film. (b) Surface profile of the same textured substrate, showing the triangular grooves that are formed due to etching by a hydrochloric acid solution.

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A line profile of the nanotextured surface is shown in Fig. 1(b). In this figure, the triangular profiles exhibit an almost periodic arrangement with a period of around 500 nm. Based on these observations, the model investigated in this study consisted of periodic arrangements of triangular gratings. A schematic cross section of the investigated unit cells is shown in Fig. 2 . The microcrystalline silicon solar cell structure consists of a 500 nm thick aluminum doped zinc oxide (ZnO:Al) front contact, followed by a (p-i-n) hydrogenated microcrystalline silicon diode (μc-Si:H) with a total thickness of 1000 nm and a back reflector consisting of an 80 nm thick ZnO:Al layer and a metal reflector. The device structure is consistent with the standard microcrystalline silicon solar cell process used by several research groups like the Research Center Jülich and University of Neuchâtel [17,18].

 

Fig. 2 Schematic sketch of a thin film microcrystalline silicon solar cell (a) on a smooth substrate and (b) with triangular textured substrate. The different unit cells in Fig. (b) are separated by dashed lines.

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Maximal conversion efficiencies of 10.3% have been achieved for microcrystalline silicon solar cells with an absorber thickness of just 1000 nm [19]. The cross section of a solar cell deposited on a smooth substrate and a triangular texture is shown in Fig. 2(a) and 2(b). In this study the period of the unit cell and height of the triangular profile was varied. The period of the unit cell was varied from 50 nm up to 6000 nm and the height was varied from 0 nm up to 500 nm. Alternatively, the triangular structure can be described by the opening angle of the triangle, which was varied from 6° to 176°. The unit cell was illuminated under normal incidence for the entire spectrum of wavelength 300 – 1100 nm. The complex optical constants used in the model system were determined by optical measurements of the individual layers [20]. Since a two dimensional FDTD algorithm was utilized, it splits the Maxwell’s equations into two independent sets of equations for transverse electric (TE) and transverse magnetic (TM) polarized waves. The polarization of the input wave was assumed to be TE, thus only one component of the electric field, E_y had to be solved.

3. Results and Discussion

In order to compare different textured designs the power loss profiles within the solar cell, the quantum efficiency, the short circuit current were utilized. The power loss was calculated using the equation

 

Fig. 3 Simulated power loss profile for textured unit cell with period 900 nm and profile heights of (a, c) 100 nm and (b, d) 400 nm under monochromatic illumination of (a, b) wavelength 400 nm and (c, d) wavelength 700 nm.

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The period of the triangular profile for all the cases was 900 nm with heights of 100 nm (Fig. 3(a) and 3(c)) and 400 nm (Fig. 3(b) and 3(d)), respectively. The incident light has a wavelength of 400 nm and 700 nm with amplitude of 1 V/m. In the case of short wavelength illumination (λ = 400nm) photons get absorbed within the first 200 nm of the silicon absorber layer. The high absorption coefficient of silicon for wavelength 400 nm inhibits the propagating wave to hit the back reflector. By having a small period height, like in Fig. 3(a), the opening angle is close to 180°. Hence the high power loss pattern concentrated around the front interface almost resembles that of a solar cell on a smooth substrate; it is almost continuous along the boundary. Whereas, by having an opening angle close to 90°, a “flame-like” power loss pattern is seen in Fig. 3(b). The “flame-like” power loss pattern is caused by the formation of evanescent fields at the boundary between the zinc oxide texture and the p-i-n solar cell. Such “flame-like” patterns are observed because the refractive index difference between zinc oxide and silicon is relatively large for short wavelengths. As a consequence a relative large fraction of the incident light is reflected by the interface. Due to the triangular shape of the interface, a standing wave pattern is formed in the region close to the tip of the triangle. Since the electric field at the boundary between zinc oxide and the silicon diode cannot be discontinuous, an evanescent field extends in the silicon diode. The “flame-like” power loss pattern disappears for longer wavelength and smaller periods of the texture.

Due to a low absorption coefficient of silicon for longer wavelengths, the incident light has to be confined in the solar cell. Only if the light completes multiple passes inside the silicon layer the light can be completely absorbed. The power loss profile for a structure under monochromatic illumination of wavelength 700 nm is shown in Fig. 3(c) and 3(d). Diffraction from the front and back grating constructively interfere towards higher absorption. Within the multiple passes, the diffracted light interferes with the backward propagating waves and also with other diffracted waves from neighboring unit cells. By following the path of the different diffracted orders from the front and back grating, the highest intensities are observed where the second diffraction (front grating) orders from the neighboring cells meet at the center of the unit cell. A similar behavior is observed for lamellar gratings integrated in microcrystalline silicon solar cells [21]. The diffraction from the back reflection does not play a significant role in creating high intensities at the center of the unit cell. But the back grating contributes to the formation of high power losses close to the back reflector. The power loss close to the back reflector depends on the confinement angle of the back reflector. If the opening angle is close to 90°, the power loss close to the back reflector, as seen in Fig. 3(d), is maximized.

In the next step the quantum efficiency was determined The quantum efficiency is defined as the ratio of the power absorbed in the silicon layer with respect to the total power incident on the unit cell. The quantum efficiency was calculated using the equation

 

Fig. 4 Comparison of quantum efficiency for solar cell on smooth substrate with triangular structures of height 400 nm and periods of 100 nm and 900 nm.

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Based on the quantum efficiency, the short circuit current was calculated for the sun spectra. The short circuit current was determined by

 

Fig. 5 Short circuit current for different triangular profile heights as a function of the period of the unit cell under (a) blue illumination (wavelength 300 – 500 nm) and (b) red and infrared illumination (wavelength 700 – 1100 nm).

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The short circuit current under red and infrared illumination (from λ_min = 700nm to λ_max = 1100 nm) as a function of the period is shown in Fig. 5(b). The highest short circuit current is achieved for periods of 700 nm and 900 nm and a triangular profile height of 400 nm to 500 nm. Compared to the short circuit current of a solar cell on a smooth substrate, the short circuit current is increased by almost 200% from 2.5 mA/cm² to 7 mA/cm². The gain in the short circuit current for this part of the optical spectrum is due to light trapping of the incident light inside the silicon absorber layer. Figure 5(b) can be divided into three regions. For texture periods much smaller than the incident wavelength, the triangular grating can be described by an effective refractive index gradient. One might expect an effect similar to the previously described situation under blue illumination. However, the refractive index difference between zinc oxide and microcrystalline silicon is small for longer wavelengths, whereas the refractive index difference for short wavelength is relatively large. For a wavelength of 400nm 21% of the incoming light is reflected by the interface between zinc oxide and microcrystalline silicon, whereas the reflection is reduced to 12% for a wavelength of 800 nm. Therefore, the effective refractive index gradient has a distinct influence under blue illumination, whereas the influence is significantly reduced for red and infrared illumination.

For texture periods which are much larger than the incident wavelengths (Period > 3 µm); the short circuit current drops as well. Light is only diffracted at small diffraction angles, which can be seen by the grating equation

If the period of the triangular grating is comparable to the incident wavelengths the diffraction angles are large enough to propagate into their neighboring unit cell. Diffracted waves can thus interfere constructively within the thin absorber layer contributing to the higher short circuit current that is observed for periods of 700 nm and 900 nm. The higher current values are obtained for structures with triangular profile heights of 300 nm and above.

For the entire spectrum (300 nm – 1100 nm) the short circuit current was calculated to be 12.3 mA/cm², 15.33 mA/cm² and 18.9 mA/cm² for the solar cell on smooth substrate, with triangular structures of period 100 nm and 900 nm, respectively. The latter, where the period is in the range of the incoming wavelengths, has the highest short circuit current because it best utilizes the diffraction and scattering of light. The enhancement comes from light trapping of the longer wavelengths. On the other hand, with a texture period of 100 nm, the small gain in short circuit current is due to its better incoupling of the shorter wavelengths into the cell.

4. Summary

Light trapping and incoupling of light in thin-film microcrystalline silicon solar cells with periodic triangular profiles was investigated. Compared to that of a solar cell on a smooth substrate with 1 µm thick absorber layer, the short circuit current and quantum efficiency are enhanced with the introduction of triangular texturing. The degree of enhancement highly depends on the period of the triangular profile unit cell. When periods of the texture are smaller than the incident wavelength, enhancement in the shorter wavelengths (300 – 500 nm) of the spectrum comes as a result of better incoupling of the light into the absorber layer. For longer wavelengths (700 – 1100 nm) the short circuit current is distinctly enhanced if the period of the triangular profile unit cell is in the range of the incident wavelength. Along with the period, combination of the period and height of the triangular unit cell is also important. Optimal dimensions were found to be for combinations of the triangular profile where the opening angle of the triangle is equal or close to 90°. The total short circuit current for the entire spectrum is increased from 12.3 mA/cm² by 60% up to 20 mA/cm² for the best case triangular profile (period of 700 nm and height of 500 nm).