The influence of nano textured front contacts on the optical wave propagation within microcrystalline thin-film silicon solar cell was investigated. Periodic triangular gratings were integrated in solar cells and the influence of the profile dimensions on the quantum efficiency and the short circuit current was studied. A Finite Difference Time Domain approach was used to rigorously solve the Maxwell’s equations in two dimensions. By studying the influence of the period and height of the triangular profile, the design of the structures were optimized to achieve higher short circuit currents and quantum efficiencies. Enhancement of the short circuit current in the blue part of the spectrum is achieved for small triangular periods (P<200 nm), whereas the short circuit current in the red and infrared part of the spectrum is increased for triangular periods (P = 900nm) comparable to the optical wavelength. The influence of the surface texture on the solar cell performance will be discussed.
©2009 Optical Society of America
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 . 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 . 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 , or using highly reflective back contacts . 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.
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].
Maximal conversion efficiencies of 10.3% have been achieved for microcrystalline silicon solar cells with an absorber thickness of just 1000 nm . 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 . 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, Ey 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 equationFig. 3 .
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 . 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 equationFig. 4 for a solar cell on a flat substrate, and two solar cells with integrated triangular gratings. The triangular profiles have periods of 100 nm and 900 nm, both with a profile height of 400 nm. For shorter wavelengths (300 – 500 nm), the quantum efficiency for the solar cell with a texture period of 100 nm is higher than that of the flat case. But with increasing wavelength, both devices exhibit the same quantum efficiency. The thickness of the p-layer of the microcrystalline silicon p-i-n solar cell was assumed to be 30 nm for all the cells. For small and very small texture periods (P ≤ 200 nm) the grating acts as effective index matching layer, so that the incoupling of light with short wavelength is improved. Due to the enhanced incoupling, the quantum efficiency for the shorter wavelengths is increased, whereas it remains almost unchanged for longer wavelengths (600 – 1100 nm). For longer wavelengths, the solar cells with grating period of 900 nm exhibits distinctly enhanced quantum efficiency compared to a solar cell on smooth substrates. Compared to that of a solar cell on smooth substrates, the optical path length is increased. For the blue and green part of the optical spectrum the quantum efficiency remains almost constant, since the absorption length for blue and green light is significantly smaller than the thickness of the solar cell. Subsequently the blue and green light will be absorbed within the first few hundred nanometers of the cell.
Based on the quantum efficiency, the short circuit current was calculated for the sun spectra. The short circuit current was determined byFig. 5(a) and 5(b) as a function of the grating period. In Fig. 5(a) the short circuit current was calculated for a spectral range from λmin = 300 nm to λmax = 500 nm. The dashed line represents the short circuit current of a solar cell on a flat substrate. For larger texture periods the short circuit current is comparable to the solar cell on flat substrates. Due to the small penetration depth in this range of the spectrum, light trapping is negligible. For smaller and very small periods an enhancement of the short circuit current is observed. The enhancement of the short circuit current is caused by an improved incoupling of the light. Compared to that of a solar cell on a smooth substrate, enhanced short circuit current in this spectral range is increased from 2.9 mA/cm2 to 3.6 mA/cm2. This increase in the short circuit current is observed for periods smaller than 200 nm. For such small periods the wavelengths of the incident light is much larger than the period of the triangular grating, so that the triangular grating acts as an effective refractive index gradient. The refractive index linearly increases from a refractive index of zinc oxide to the index of microcrystalline silicon. As a consequence the reflection at this particular interface is reduced and more light is coupled in the solar cell. If the grating period is smaller than λ/(2n), where λ is the wavelength of the incident light and n the refractive index of the grating, the behavior of the grating can be described by an effective refractive index gradient. The triangular grating can be approximated by an effective refractive index gradient for periods equal to or less than 100 nm. For texture periods larger than 200 nm the short circuit current starts converging towards the value calculated for the solar cell on a smooth substrate.
The short circuit current under red and infrared illumination (from λmin = 700nm to λmax = 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.
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).
The authors would like to acknowledge the Institute of Energy Research (IEF-5) Photovoltaics, Research Center Jülich. Specifically, the authors thank C. Haase for providing optical data of the thin films. Furthermore, the authors like to acknowledge H. Stiebig from Malibu Solar for helpful discussions. A. S., R. N. and S. P. acknowledge financial support from the Global Climate Energy Project at Stanford and the Department of Energy Solar America Initiative (grant #DE-FG36-08GO18005).
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