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In this paper, we present the integration of combined front and back 1D and 2D diffraction gratings with different periods, within thin film photovoltaic solar cells based on crystalline silicon layers. The grating structures have been designed considering both the need for incident light absorption enhancement and the technological feasibility. Long wavelength absorption is increased thanks to the long period (750 nm) back grating, while the incident light reflection is reduced by using a short period (250 nm) front grating. The simulated short circuit current in a solar cell combining a front and a back grating structures with a 1.2 µm thick c-Si layer, together with the back electrode and TCO layers, is increased up to 30.3 mA/cm2, compared to 18.4 mA/cm2 for a reference stack, as simulated using the AM1.5G solar spectrum intensity distribution from 300 nm to 1100 nm, and under normal incidence.
©2012 Optical Society of America
1. Introduction
Most of photovoltaic (PV) solar cells are based on crystalline silicon (c-Si), due to its natural abundance, and its nearly ideal energy band gap. However, as the thickness of the c-Si wafer is reduced, the efficiency of solar cells is limited, notably because of the low absorption coefficient of c-Si in the infrared range. This limitation is particularly stringent in the case of thin film solar cells based on c-Si. Indeed, using micrometer-range layers minimizes the cost of a solar cell, due to a reduced amount of active material, but the absorption length should then be higher than the layer thickness. Therefore, light trapping, i.e. the optimization of incident light capture and absorption, has now become one of the major topics in the thin film solar cell research [1,2]. The general objective is to efficiently couple the incident light into optical modes which adjust light-matter interaction, through photon lifetime or, in other words, optical path length in the absorbing medium. Considering the maturity of nanophotonics, various kinds of advanced light trapping techniques may be considered to achieve this goal [3,4]. Absorption enhancement by using diffraction gratings [5–8], surface plasmons [9] or photonic crystals (PCs) [10] were proposed in recent years. In particular, diffraction gratings present a great potential in this field as they can be used either as advanced back reflectors to increase both the path length and the spectral density of optical modes at long wavelengths. Such gratings can be patterned on transparent and conductive oxides (TCO) [11–15] or on metallic layers [3,16,17]. Other groups proposed to use such gratings as front anti-reflection layers [18] to reduce the reflection at the short wavelengths on c-Si [19]. Recently, Mutitu et al. [5], Dewan et al. [6] and K. Wang et al. [20] have developed new designs based on multiple grating structures. This approach is highly promising, but the properties of these simulated structures remain limited by severe design constraints or strong technological challenges.
In this paper, we propose a technologically feasible thin film solar cell based on a c-Si absorber, and including combined front and back gratings together with the necessary set of layers needed to generate a PV solar cell: TCO layers and metallic electrodes. We investigate the respective role of the front and back photonic structures, and evaluate their impact on the collected photocurrent. Each grating is expected to ensure an absorption enhancement in a specific part of the solar spectrum, leading to a broadband enhanced absorption for the whole device. In order to carefully design these photonic structures, the role of key parameters like their period and etching depth should be carefully investigated. We use the finite difference time domain (FDTD) method to optimize the gratings parameters in order to achieve a maximum increase of the absorption in the c-Si layer, with a view to optimize the collected photocurrent. After a presentation of the basic solar cell design and simulation methodology in section 2, the design rules for the front and back gratings are introduced in section 3. Finally the optical behaviour and the performance of PV solar cells based on combined 1D or 2D gratings are discussed in section 4.
2. Simulation methodology and solar cell design
2.1. Simulation methodology
The FDTD method is used to solve Maxwell’s equations in complex geometries [21] and is available into commercial packages [22]. It is suitable to analyze the wave propagation in thin film solar cells including wavelength or sub-wavelength scale patterns [6]. In this work, it has been used to calculate the absorption of incident light in each layer of the patterned solar cells, more precisely the useful and specific absorption in the active c-Si layer and the optical losses by absorption in the other layers. In these simulations, we consider plane waves illuminating the device at normal incidence. Periodic boundaries conditions are used, as well as an inhomogeneous mesh with steps in the 2-5 nm range. Additionally, we take advantage of a method based on nearfield to farfield projection techniques [21] to evaluate the strength of the all the physical orders of the front and back gratings of the device.
In this framework, it is noticeable that a single FDTD calculation (using a polychromatic pulse as a source) provides the same results for the gratings as using Rigorous Coupled Wave Analysis (RCWA) method, but within a shorter time (few minutes for 1D gratings and about 4 hours for 2D gratings on normal PC). Indeed, RCWA would require as many calculations as wavelengths in the spectra.
The global performance of the device will simply be assessed by the short circuit photocurrent density Jsc, defined as [8,23]:
in which e is the elementary charge, h the Planck constant, c the speed of light in vacuum, λ the wavelength, considering the 300-1100 nm range, A(λ) the absorption in c-Si, and dI/dλ the incident solar radiation intensity per unit wavelength, considering the AM1.5G distribution, and assuming a carrier collection efficiency of 1.2.2. Solar cell design and main parameters
The whole solar cell structure investigated in this work is a stack composed, from the back to the front, of a 100 nm thick silver (Ag) layer, a 120 nm thick zinc oxide (ZnO) layer, a c-Si layer with a thickness in the 1-2 µm range, used as the active material (p+-i-n+ junction), overlaid by an 80 nm thick indium tin oxide (ITO) layer (see Fig. 1(a) ). On the back side, the c-Si/ZnO interface is patterned as a 1D / 2D grating, whereas on the top, the c-Si and ITO layers are patterned as a 1D / 2D grating with a different period (Fig. 1(b)) The optical indices of the materials (ITO, c-Si, ZnO [24] and Ag [24]) are included in the Appendix.
Fig. 1 Schematic views of the investigated complete (a) unpatterned stack (reference) and (b) patterned stack with the front and back 1D diffraction grating with different periods.
The thickness of 80 nm for the ITO layer is high enough to enable a low sheet resistance, so low lateral transport losses of the carriers over hundreds of microns to lateral metallic contacts. In the same time, this value yields a low optical absorption. In an unpatterned solar cell, this ITO layer, with its refractive index around 2, also plays the role of an anti-reflection coating for red light. In the case of patterned solar cells, this material will further contribute to the anti-reflective effect of the front grating. On the back side of the cell, the silver electrode also acts as an almost perfect reflector. It is assisted by the ZnO TCO layer which prevents from the diffusion of Ag to c-Si [10], and which exhibits a particularly low optical absorption (see appendix). Incident light is then expected to be preferentially absorbed in the c-Si layer, while the photogenerated carriers are collected by the ITO and ZnO/Ag layers. A grating filling fraction (ff) of 50% will be considered, a value easily achievable by most of the nanopatterning technologies [8, 25].
3. Design rules, 1D front and back gratings
In this section, we discuss on the respective roles of the front and back gratings. For the sake of simplicity, and to provide simple guidelines for the design of these structures, non dispersive materials will be considered, with n = 4 and k = 0 for c-Si; n = 2 and k = 0 for ZnO and ITO. We consider 1D gratings and an incident plane wave with a TM polarization (along the y axis, i.e. electric field orthogonal to the slits).
3.1 Design of the back grating
The expected role of the back diffraction grating is to trap the incident light at long wavelengths into guided modes, in such a way to increase photon lifetime in the active medium. To reach this goal, a periodic grating is implemented on the ZnO layer, on top of the Ag electrode (see Fig. 2 ), in order to diffract back the incident light into c-Si.
Fig. 2 Schematic view of the back grating structure (a); influence of the grating depth (b) and period (c) on the light intensity distribution on the diffracted orders, for a TM polarization.
In the case of a simple 1D diffraction grating, the angles of the diffracted orders are calculated using the grating equation:
where nd is the refractive index, λ is the wavelength in vacuum, Λb is the grating period, m is the diffraction order (0, ± 1, ± 2…), θi is the incident angle, θm is the diffraction angle for the mth order. As the main purpose of the back grating is to increase the absorption at longer wavelengths (from 700 to 1100 nm for c-Si), the specular reflection in the order 0 should be attenuated for the profit of diffracted orders with . Incident light will then be reflected with a larger propagating angle θm, thereby increasing the optical path length, and potentially trapping photons into guided modes in the c-Si layer. Following these considerations, a relatively large lattice parameter should be selected in order to generate non zero diffraction orders [26].In order to determine in a more quantitative way the opto-geometrical parameters of the back grating, we now consider the structure displayed Fig. 2(a), and combining the patterned 120 nm ZnO layer, the 100 nm thick Ag reflector and the c-Si medium, here considered as semi-infinite. This structure is simulated by FDTD, with a view to investigate the impact of the corrugation depth (hb) and of the lattice parameter of the grating.
Figure 2(b) illustrates the influence of hb, considering a 500 nm period. Since this depth should be limited considering the processing time and feasibility, a value of 100 nm appears as an optimum since the 0th order is then minimized, while all the light is almost fully diffracted on the +/−1 orders.
The impact of the grating period is then evaluated (see Fig. 2(c)), for a 100 nm corrugation depth. As expected, additional orders appear for increased periods, but the intensities corresponding to orders larger than 1 remains very limited, even for a 1µm period. Considering these results, together with the tendencies expected from the grating Eq. (2), the choice of the period is thus a compromise between a large period to increase the number of diffraction orders, and to reduce the intensity on the order 0, and a small period, to keep a large enough diffracted angle for the first order mode. The grating period will therefore be set to 750 nm.
3.2. Design of the front grating
As for the case for the back grating, the period (Λf) is also a key parameter for the design of the front grating. In this section, we will consider a periodic structure composed of ITO/c-Si patterns, as depicted in Fig. 3(a) . Its behavior will be explored in the 300-1100 nm wavelength range, considering a semi-infinite c-Si medium. The main objective is to reduce the reflection at the front surface, while considering technologically feasible geometrical parameters. For these reasons, we will consider patterns with an ITO section of 80 nm thick and a c-Si section of 100 nm deep. Figure 3(b) shows the influence of the front grating period, tuned from 100 nm to 750 nm, on the amount of light reflected at the front surface.
Fig. 3 Schematic view of the front grating (a), and reflected intensity versus the wavelength, for various grating periods and considering a TM polarization, and a 50% ff; the reference corresponds to a planar Si surface covered by a 80nm thick ITO layer (b).
While the ITO layer of the planar ITO/c-Si reference acts as an efficient anti-reflector around 600 nm, it is much less the case for the lower wavelength range, i.e. below 500 nm. On the contrary, the simulated spectra show that the patterned structures exhibit a lower global reflection compared to the reference for all the considered periods, in the whole 300-450 nm wavelength range. It means that the patterned ITO/c-Si acts as an efficient anti-reflector to decrease the global reflection in this short wavelength range. This can be attributed to a better impedance matching between air and silicon, but also to diffraction processes. In particular, for periods smaller than the wavelength, light is not reflected in diffraction orders than 0 in air, whereas transmission into c-Si is made possible through more diffraction orders (0 and +/− 1). In the specific case of the patterned interface with a 250 nm period, the simulated spectrum demonstrates a low global reflection in the short (300-450 nm), mid (450-700nm) and long-wavelength (700-1100 nm) ranges. This period will therefore be selected for the front grating, in order to trap most of the incident light into the c-Si active layer.
4. Combined front and back grating solar cell: global design and analysis
So far, the front and the back gratings have been introduced and optimized separately, with a view to select their geometrical parameters. In this section, we propose to implement a double grating structure from the design rules previously derived. The role of each grating can be understood from the previous studies. On the one hand, the short period front grating is intended to reduce the reflection and thus to diffract the incident light in the shorter wavelength range into the active c-Si layer. On the other hand, the large period back grating is intended to diffract back the incident light into the active layer, mainly in the red to near infrared ranges of the spectrum (700-1100 nm). In this section, we consider the complex indices and dispersion characteristics of all the real materials used. The optical indices of ITO [from ellipsometric measurement] and c-Si [from ellipsometric measurement], ZnO [24] and Ag [24] are included in Appendix. We derive the photocurrent along with the methodology introduced in section 2.1.
4.1 Analysis of the double 1D grating solar cell
We first analyze the spectral behavior of the double grating solar cell structures, considering the design parameters derived from section 2, including a 250 nm period front grating, a 750 nm period back grating, and 50% filling fraction for both gratings. This set of parameters also enables the use of a simple unit cell for the FDTD simulation. A 1.2 µm thick c-Si layer is considered, including the 100 nm thick corrugated sections on the top and on the bottom parts of the layer. Figure 4 shows the absorption spectra for such a device, considering only the useful part of the absorption, i.e. in the c-Si layer. The double grating structure is compared to structures including only the front or the back grating. Figure 4(a) exhibits the spectra corresponding to a TM polarized incident light, as in the case of section 2, while Fig. 4(b) correspond to a TE polarized light. Below 500 nm, the absorption is always higher when a front grating is integrated, as compared to the device including only the back grating. This confirms that the front grating acts as an efficient anti-reflecting structure, for both polarizations. One should note that in this short wavelength range, no absorption peaks appear, since the absorption length of c-Si is lower than the layer thickness. In the intermediate wavelength range, i.e. between 500 and 700 nm, most of the absorption peaks are regularly spaced, and attributed to Fabry-Perot-like resonances. Apart from a slightly higher mean absorption in the case of the double grating structures, all the devices exhibit a qualitatively similar behavior. Above 700 nm, the spectra exhibit a very dense and irregular series of intense absorption peaks. Figure 4(c) is a close-up of the spectrum corresponding to the TE polarization, also including the reference spectrum corresponding to the flat device, without any grating. A first observation is that the highest absorption is achieved for the devices including a back grating, which spectrum also exhibits a higher spectral density of resonant modes. This is particularly illustrated above 900 nm, where only one broad peak appears in the case of the reference and front grating devices, whereas the structures including a back grating exhibit 4 resonances, with a reduced linewidth and a higher absorption maximum. Indeed, in this long wavelength range, and considering the low absorption coefficient of c-Si, a longer photon lifetime is necessary to take full profit of the optical resonances of the structure, and to get closer to the critical coupling conditions [25]. Such properties are only offered provided an efficient light trapping scheme, which is achieved here thanks to the back grating diffraction process.
Fig. 4 Absorption spectra of the c-Si layer for the front grating, the back grating and the double grating optimized structures, for (a) TM and (b) TE polarized incident light, (c) with a close-up of the spectra for TE polarized light between 800 and 1000 nm.
In order to further analyze the origin of the absorption peaks which appear in the long wavelength range, the electromagnetic field maps of the corresponding modes have been simulated by FDTD for TE polarized light, and for all the four investigated structure configurations, see Fig. 5 .
Fig. 5 |E|2 field maps, for TE polarized incident light in the double grating structures (peaks 1-2), in the front grating structures (peaks 3-4), in the back grating structures (peaks 5-6), and in the planar device (peaks 7-8) of Fig. 4(c).
For the planar structure, the mode profiles are typical of vertical Fabry-Perot resonances. On the contrary, most of the modes corresponding to absorption peaks observed in simple and double grating structure exhibit a Bloch mode-like diffraction pattern, with a periodicity in the horizontal x-direction. The higher value of the maximum of |E|2, together with the reduced linewidth of the corresponding absorption peaks, illustrate the longer lifetime of the photons trapped in the c-Si layer. Only the mode corresponding to peak 4, for the front grating device, exhibits a field pattern which is characteristic of a vertical Fabry-Perot-like resonance, together with a larger and less intense absorption peak. Finally, the higher absorption efficiencies of the grating structures are attributed to the large number of in-plane Bloch mode-like resonances, which quality factor is significantly higher than that of vertical Fabry-Perot modes.
4.2. Performance of 1D and 2D double grating solar cells
Considering the design parameters introduced above, and given the properties of the photonic gratings for light trapping and absorption control, we now discuss on the performance of such solar cells. In this section, we will first compare the four configurations introduced above, with an additional device including 2D planar gratings. Indeed, it has been shown that the expected efficiency of solar cells including 2D patterns significantly exceeds that of a 1D patterned device [25, 27,28]. We consider the same lattice parameters, layer thicknesses and corrugation depths as in the case of 1D grating structures. Different configurations have been considered in terms of air-surface filling faction (sff) for the front and back gratings, in the 32-75% range, which remains accessible with available lithography and etching processes. The schematic cross section and top views of the 1D and 2D patterned devices are shown in Fig. 6(a-c) .
Fig. 6 Schematic view of the double side structure (a), the top view of the patterned structure with 1D (b) and 2D (c) diffraction gratings.
Figure 7(a) displays the spectra calculated for the flat unpatterned reference, together with patterned structures including 1D and 2D front and back gratings. A first conclusion is that the devices which integrate 1D and 2D gratings exhibit a higher absorption over the whole wavelength range, from 300 to 1100 nm. In the case of the 2D structure, the increase is particularly high in the short and longer wavelength ranges with, respectively, a broad absorption plateau around 450 nm, and many sharp and intense absorption peaks in the near-infrared. Moreover, considering the shape of the absorption spectra, one can conclude that the nature of the resonant modes is similar for the devices including 1D or 2D patterns. Figure 7(b) shows the short circuit photocurrent density for all the investigated structures. While a single 1D diffraction grating enables a 25% relative increase of the photocurrent density with regards to the flat unpatterned reference, the integration of both a front and a back grating yields a 43% increase. Now considering such a double side grating devices, but with 2D patterns, the increase is up to 65%, with a current density of 30.3 mA/cm2. Therefore, compared to the case of optimized devices including 1D gratings, the results obtained with a few configurations including 2D gratings clearly illustrate their higher potential for photocurrent enhancement. Compared to results obtained by other groups a few years ago [5,6] or very recently [20], we achieve higher current density for a similar c-Si thickness [6], or a similar value but for a thinner active layer, or more simple and technologically feasible patterns [5, 20].
Fig. 7 Absorption spectra for the flat unpatterned reference, compared to the 1D double grating structure, considering the average of spectra corresponding to TE and TM polarized incident light, and the 2D double grating structure (a), and short circuit current density for all the structures investigated, with a total c-Si layer thickness of 1.2 µm (b). As a comparison, a full absorption of the incident light would lead to a 43.5 mA/cm2 current density (dotted line).
Lastly, the effect of the thickness of the c-Si layer is investigated in the case of the double grating structure based on 1D gratings, with the geometrical parameters mentioned in Fig. 8 (a) . While the Ag, ZnO and ITO layer thicknesses and grating depths are kept constant, the total c-Si thickness (h) is tuned from 600 nm to 2000 nm with steps of 200 nm, and the collected photocurrent is then derived, see Fig. 8 (b).
Fig. 8 Schematic cross section view of the optimized front and back gratings solar cell stack (a), and photocurrent versus the c-Si layer thickness, for a TM polarized incident light (b).
As one could expect, the short circuit current is increased with the c-Si layer thickness. This increase is not perfectly regular since it depends on the number of resonant modes which are generated in the 300-1100nm wavelength range. Still, the photocurrent variation is monotone; this tends to prove that the front and back 1D gratings are not fully coupled. Indeed, a strong coupling between the gratings should lead to a more complex variation of the short circuit current versus the thickness. This trend was also observed by Bozzola et al, for 1D and 2D patterned c-Si cell and a-Si, with a single side grating, and therefore a lower short circuit current [28]. In the case of our double side 1D patterned device, a 30.42 mA/cm2 photocurrent could be achieved with 2 µm thick c-Si layer.
5. Conclusion
Thin-film photovoltaic solar cells structures based on c-Si, and integrating simultaneously a front and a back 1D and 2D diffraction grating with different periods have been designed and analyzed. The geometrical parameters of both gratings have been designed separately, considering the need to increase photon lifetime in c-Si, efficient anti-reflection at the front surface, and the compatibility with standard processing techniques. These considerations led to a back grating located at the c-Si/ZnO interface, with a period of 750 nm, and a front grating made of ITO and c-Si, with a period of 250 nm. In both cases, rectangular pattern shapes and 50% surface filling fraction were selected to ensure the technological feasibility of the photonic structures with already established technological processes. The spectral properties and resonant mode nature were then analyzed, and the performance of the double grating solar cell device were simulated and compared to flat or single grating references. As a result, for a 1.2 µm thick c-Si layer, a photocurrent density of 26.5 mA/cm2 is achieved for a 1D patterned double grating structure, i.e. a 43% increase with regards to the flat reference. The photocurrent density can be further increased considering the degrees of freedom corresponding to the photonic pattern dimensionality and the active layer thickness, and without affecting the technological feasibility of the device. In particular, a value of 30.3 mA/cm2 is expected in the case of similar structures with 2D patterns.
Appendix
The refractive indices and extinction coefficients considered in the optical simulations and corresponding to c-Si, ZnO, Ag and ITO, are displayed in Fig. 9 (a-d) .
Acknowledgments
X. Meng acknowledges the China Scholarship Council (CSC). This work was partly funded by the region Rhône-Alpes, France. The ellipsometric measurements were provided by LPICM, Palaiseau, France.
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