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The effect of the relative lateral displacement between the front and back sinusoidal textured layers of a conformal grating solar cell on light trapping was investigated. For various amount of relative lateral displacements and thicknesses of the active layer, the external quantum efficiency (EQE) of the misaligned solar cell structures and their EQE enhancement relative to the aligned structure were studied. For both aligned and misaligned solar cell structures, the electric field distribution at the wavelength corresponding to the EQE peaks was analyzed, and the corresponding guided modes were identified. Additional modes were observed in the misaligned grating structures. A 25.1 times enhancement of the EQE at the wavelength of 950 nm and an average of 2.2 times enhancement in the wavelength range from 700 to 900 nm were observed. For the misaligned grating structure with the phase shift β = π/4 and the active layer thickness DSi = 230 nm, a maximum short circuit current density Jsc enhancement of 34% was achieved for normal incidence, and a short circuit current enhancement of more than 15% was obtained for the incident angle between −15° and + 15°.
©2013 Optical Society of America
1. Introduction
The primary objective of research and development on solar cells is to increase their efficiency and to reduce the cost for their manufacturing. Thin film silicon solar cells have a great potential as substantial cost reduction can be realized owning to the significant saving on silicon material in comparison with crystal silicon cells. However, the absorption length of silicon, especially in the infrared region, is much greater than the thickness of thin film silicon solar cells. To maintain the conversion efficiency, light trapping structures have been employed to increase the optical path and/or to enhance the electric field intensity in the active layer. Diffraction gratings [1–9], plasmonics [10–13], and moth eye antireflection coatings [14, 15] are among those structures.
So far, researches on thin film silicon solar cells have been concentrated on the aligned dual grating structures. For thin film silicon solar cells with 1-dimensional (1-D) conformal gratings, Hasse and Stiebig [1] and Dewan and Knipp [2] observed the maximum short circuit current when the solar cell’s grating period and height were in the range of 600 ~700 and 300~350 nm, respectively. Madzharov et al. [3] reported that the phase difference between the front and back grating layer greatly influenced the light trapping ability in microcrystalline thin film silicon solar cells. They observed an increase of the short circuit current from 16.3 mA/cm2 to 19.1 mA/cm2.
Studies on misaligned dual grating structures have been mainly concentrated on optical filters. The phase difference induced by relative lateral displacement of the two gratings can exert strong influence on the resonance modes, resulting in the apperance and disapperance of certain modes or the alteration of the transmission/reflection bandwidth [16, 17]. Such features are applicable to optical switches [18] and tunable spectral filters [19, 20]. Though extensive studies have been carried out on the effect of laterial displacement of the gratings on the spectral characteristics of filters, not much work has been focused on solar cell structures. One of the few research articles on this topic introduced a relative lateral displacement of blazed gratings in a specific configuration and showed improved absorption [6]. However, it did not distinguish the contributions from blazing and shifting. In another one, the efficiency of a 20 μm thick crystalline silicon solar cell with a phase-shifted pyramid structure was calculated [7]. The authors, however, did not provide sufficient discussion on the mechanism for the efficiency enhancement derived from the relative lateral shift of the two pyramid-structured layers. In addition, calculations necessarily assume ideal conditions, which would be a valid assumption only when the silicon layer is thin relative to the lateral dimension of the textured structure. In their calculation, the ratio of the silicon film thickness to the lattice constant is 20/1.2, which likely deviates from the ideal condition. Therefore, the result might not be readily confirmed by experiments.
In this article, we intend to introduce misaligned conformal grating structures into thin film silicon solar cells to improve their efficiency. We anticipate that, by introducing the ralative lateral displacement of the two gratings, symmetry breaking may excite previously inaccessible modes. By carrying out a systematic study of the effect of the displacement scale on the resonance modes, we expect to explore the mechanism of the observed external quantum efficiency (EQE) enhancement caused by the relative displacement of the gratings, and eventualy to design thin film silicon solar cells of higher efficency.
2. Design principle and the proposed structure
For a conformal grating structure, substantial enhancement of the optical path and the electric field intensity in the active layer are observed when the waveguide modes are achieved, resulting in a great increase of the EQE at the resonant wavelengths [21–23]. However, the EQE enhancement derived from waveguide modes only takes place in the narrow region around the wavelengths corresponding to the resonance waveguide modes, which only covers a small portion of the solar spectrum. One way to solve this problem is to introduce more resonance waveguide modes, which can be accomplished by increasing the thickness of the active layer. This, however, in some senses, contradicts to the objective of achieving the maximum efficiency with the minimum thickness of the active layer.
Introducing symmetry breaking into a symmetrical system is an effective technique to excite modes that are previously inaccessible without increasing the thickness of the active layer [6, 24]. The modes can be derived by employing blazed gratings [25], supercell grating structures [26], off-normal incidence of light [27], and misaligned dual grating structures. By misaligning the gratings, the system becomes asymmetric providing the possibility for the coupling of the incident light to asymmetric modes in the system. In misaligned structures, the new modes can therefore be derived from guided modes with antisymmetric field profiles in the aligned structure.
In this article, we propose to introduce a lateral displacement of one of the gratings in the conformal grating structure. The displacement would cause symmetry breaking in a multilayer waveguide and the split of the degenerate waveguide modes of the aligned grating structure. This approach, which is similar to the oblique incidence of lights onto the conformal solar cells, increases the number of the waveguide modes without increasing the thickness of the active layer.
The structure of the solar cell proposed is illustrated in Fig. 1. Silicon used in this study is assumed to be 90% polycrystalline and 10% amorphous. The thickness of the uniform silicon layer is denoted as dsi. The gratings consisting of silicon and ZnO adopt a conformal sinusoidal profile. For misaligned conformal gratings, the profile of the front grating is described as dsin(2πx/p)/2 and that of the back grating as dsin(2πx/p + β)/2, where d is the height of the grating layer, p the period, and β the phase shift satisfying 0 < β ≤ π. Aligned conformal grating corresponds to the special case where β = 0. It ought be noted that, the conformal grating with β = 0 is not the one with β = π which is called “in phase” in [6].
Fig. 1 Schematic of the thin film silicon solar cell with misaligned conformal grating structure, where A-B, B- C, C- D, D –E, E- F, and F- G denote the region of the transparent conducting ZnO layer, the sinusoidal front grating layer, the silicon absorption layer, the back grating layer, the ZnO layer, and the Ag layer, respectively.
The relative lateral displacement of the two grating layers is characterized by β. The thickness of the active layer is denoted as DSi, which equals to dsi + d. The thickness of the uniform front and back ZnO layer is 50 and 80 nm, respectively. The thickness of the Ag back electrode is 500 nm. For the following discussions, d and p are assumed to be 300 and 600 nm, respectively, as researches have shown that the maximum short circuit current can be achieved for these parameters [1–3].
The refractive index of Ag was taken from [28], while those of the silicon and ZnO were acquired from the index website [29]. The electromagnetic wave propagation was investigated using the Rigorous Coupled Wave Analysis (RCWA) of Rsoft DiffractMod [30]. Assuming all electron-hole pairs contribute to photocurrent, the short circuit current density Jsc, that characterizes the overall efficiency of a solar cell, is given by
where e is the charge of an electron, λ the wavelength, h the Plank’s constant, c the speed of light in the free space, EQE the external quantum efficiency defined as the ratio of the light energy retained by the active layer to that of the incident light, and IAM1.5 the AM 1.5 solar spectrum [31].3. Results and discussions
In order to investigate the influence of the relative displacement of the two gratings on the resonance modes, the EQE of the solar cell illustrated in Fig. 1 was calculated for the TE incidence, under which polarization is parallel to the grating grooves, and β in the range from 0 to π/4. The result was shown in Fig. 2. For the intermediate wavelengths ranging from 700 to 900 nm, it is obvious that there is an enhancement in the EQE in the wavelength ranges 700 – 750 and 800 – 900 nm with the increase of β, which might be attributed to the phase difference of the front and back gratings. Madzharov et al., who studied solar cells with a similar period but aligned grating structures, observed that the absorption in the intermediate wavelength range was affected by the height of the gratings, which controlled the phase difference [3]. The destructive interference condition might no longer be satisfied when the phase difference deviated from its initial value corresponding to β = 0.
Fig. 2 External quantum efficiency as a function of wavelengths for different lateral displacement when DSi = 300 nm.
For the long wavelengths ranging from 900 – 1100 nm, sharp absorption peaks are observed. In comparison with the aligned grating structure (β = 0), additional absorption peaks are observed at wavelength positions of a, c, and e for the misaligned grating structure. With the increase of β from π/16 to π/4, the height of the resonance peak at a reduces while that at c increases, which is likely due to the deviation from the resonance condition for the former and the approach to that for the latter.
Figure 3 displays the light external quantum efficiency as a function of the wavelength and the thickness of the active layer DSi for the aligned grating structure (β = 0) and the misaligned grating structure (β = π/4) under TE incidence. The five dots marked as a, b, c, d, and e in Fig. 3(b) correspond to the five peaks in Fig. 2, respectively.
Fig. 3 External quantum efficiency as a function of wavelengths and silicon active layer thickness for (a) β = 0 and (b) β = π/4
It is obvious that the resonance modes in the aligned grating structure remain and additional resonance modes in the misaligned grating structure appear. These additional modes are derived from the split of the degenerate modes of the aligned grating structures, which can be attributed to the symmetry breaking taking place in the misaligned grating structures.
The guided modes for the aligned grating structure and those additional ones for the misaligned grating structure are denoted by TEi,m, where the subscript i represents the diffraction order and m the mode order [32]. The value of j = 2i and m represents the electric field node number along x and z axis, respectively. These orders can be identified from their electric field distributions such as those shown in Fig. 4. For the misaligned grating structures, the ith diffraction mode splits into two modes ± ith, which are degenerated in the aligned grating structures. According to the effective waveguide refractive index N = nsinθ - iλ/p [33], the wavelength for the diffraction mode + i is greater than that for -i for the same Dsi. For TE incidence, the wavelength for a resonance mode, which happens to be the wavelength at which EQE enhancement takes place, can be tuned by altering the thickness of the active layer, as demonstrated in Fig. 3. Identical conclusion can be derived for TM incidence.
Fig. 4 The electric field distribution for different modes of the misaligned grating structure (β = π/4); (a) λ = 1085 nm, (b) λ = 990 nm, (c) λ = 950 nm, and (d) λ = 930 nm.
In Fig. 3(b), it is apparent that there is a sudden change around 910 nm wavelength throughout the whole thickness range we considered. It is due to the waveguide characteristic of the grating structure. According to the theory of multilayer waveguide, the condition for allowed first order diffraction mode is [34]
where ns is the refractive index of the substrate. By inserting the values of the period and refractive index of the substrate into Eq. (2), the wavelength λ will be 912 nm. Consequently, the light with wavelength less than 912 nm will not propagate as a resonance mode since it will leak out into the surrounding medium. Also there is a feature that the mode TE-1,3 seems disappeared at around Dsi = 270 nm. We calculated the EQE as a function of wavelengths and silicon active layer thickness for the misaligned structure as shown in Fig. 3(b) at a 2° off-normal light incidence. Results show that the absorption peak corresponding to the TE-1,3 mode at around Dsi = 270 nm appear. The electric field distribution calculation shows that the field profile remains unchanged. Therefore, we attribute the disappearance of the TE-1,3 to the low efficiency of the structure in scattering the incident plane wave into the TE-1,3 mode under this structure configuration [35].The EQE of solar cells is primarily governed by the product of the electric field intensity and the imaginary part of the permittivity of the active material. We adopt electric field distribution to characterize the resonance modes in the entire solar cell structure, since it does not depend on the absorption coefficient of the material in the structure. The electric field distribution of the resonance modes of the misaligned grating structure (β = π/4) is shown in Fig. 4, where patterns (a) to (d) correspond to the wavelengths marked by the dots in Fig. 3(b). Note that the scale bars are different for the four patterns. The field intensity is normalized to that of the incident light. The maximum field intensity for the resonance mode at 950 nm is ca.11.41 as shown in Fig. 4(c), while that for the resonance mode at 1085 nm is ca. 5.31 as shown in Fig. 4(a), which is 2.15 times lower than that for the former. In addition, the maximum field for the former is located in the active layer while that for the latter is in the ZnO layer. The combined effect of these two features is manifested by the significantly stronger absorption around 950 nm than that around 1085 nm. The antisymmetric electric field distributions shown in Fig. 4(a), (c) indicate that their corresponding modes are “dark”, while the symmetric ones shown in Fig. 4(b), 4(d) are “bright” [6].
The contribution from each mode to the EQE enhancement, defined as the ratio of the EQE of the misaligned grating structure to that of the aligned one, can be readily identified from Fig. 5. The enhancement originated from the excited TE-1, 2 mode at 1085 nm is ca. 4.5, while that originated from the TE-2, 2 mode at 880 nm is ca. 3.75. Both modes exist only in the misaligned grating structures. The peak at 950 nm is ca. 25.1, which can be attributed to the superposition of the contribution from the first and the second diffraction order waveguide mode. In addition to the guided modes, the diminishing of the destructive interference due to the improvement in phase matching between the front and back gratings caused by the relative lateral displacement may contribute to the EQE enhancement in the intermediate region. The effect of the relative lateral displacement on the phase matching has been reported [18–20]. In this region, an average enhancement of ca. 2.2 is observed.
Fig. 5 External quantum efficiency enhancement for the misaligned grating structure (β = π/4) when DSi = 300 nm.
To assess the performance of a solar cell, EQE enhancement over the entire solar spectrum should be taken into consideration. Here, we adopt the average value of the short circuit current density Jsc over the wavelength range 400 – 1100 nm under both TE and TM incidence, as the evaluation function. The result shows that Jsc is approximately a linear function of the thickness of the active layer. The Jsc of the aligned grating structure increases from 7.76 to 20.87 mA/cm2 when the silicon thickness increases from 100 to 700 nm. The enhancement of Jsc, defined as the ratio of Jsc of the misaligned grating structure to that of the aligned one, as a function of both β and DSi is shown in Fig. 6.
Fig. 6 Jsc enhancement as a function of DSi and β when the height of the grating d = 300 nm and the period p = 600 nm.
A positive Jsc enhancement is observed for the thickness of the active layer ranging from ~100 to ~700 nm. For both relative thin (e.g. 200 nm) and thick (e.g. 700 nm) active layers, great efficiency enhancement can be achieved by adjusting the relative displacement of the front and back gratings.
The area marked by tilted lines in Fig. 6 corresponds to the structures where the top and bottom layers overlap to each other, which is practically useless for solar cell application due to short-circuiting. Though Jsc enhancement reaches its maximum near the overlapping region, the two gratings, which serve as the electrodes of a solar cell, are so close to each other that they could possibly cause quantum tunneling effect. We, therefore, chose the local maximum at position A for detailed discussions. Jsc enhancement reaches its maximum value of 1.34 when β = π/4 and DSi = 230 nm, corresponding to the increase of the Jsc from 13.44 for the aligned grating structure to 17.98 mA/cm2 for the misaligned one. It is worth emphasizing that, to achieve the same Jsc the misaligned structure only requires 60.5% of the active layer thickness comparing to what the aligned structure requires.
Furthermore, it is evident from Fig. 6 that more than 10% enhancement can be realized when β and Dsi are in the range from π/8 to 3π/8 (equivalent to a relative displacement range of 37.5 – 112.5 nm) and from 200 to 400 nm, respectively. This is an attractive feature for practical applications as the high degree of tolerance makes their fabrication relatively easy. Sinusoidal gratings can be readily achieved by conventional photolithography [36]. Misaligned thin film silicon solar cells can be fabricated by conformal growth [22] using glancing angle deposition method [37].
For practical applications of solar cells, not only direct sunlight, but also diffused light contributes to their efficiency. Moreover, for widely used low-cost non-tracking solar cells, sunlight is mostly oblique incident. The incident angle response of a solar cell, therefore, is another crucial aspect. To evaluate this property, the dependence of Jsc of the aligned (β = 0) and misaligned (β = π/4) grating structure on the incident angle was investigated, and the results as well as the enhancement were shown in Fig. 7.
In the angular range of ± 20°, the Jsc for the misaligned grating structure is in the range of 15.6 – 18.2 mA/cm2 while that for the aligned one is in the range of 13.5 – 15.2 mA/cm2. Moreover, in the range of ± 15°, more than 15% enhancement is achieved. The Jsc of the misaligned grating structure, therefore, not only is greater but also depends less on the incident angle in comparison to that of the aligned one.
The calculation of the EQE and the electric field distribution for the aligned grating structure under oblique incidence shows that the previously degenerate modes split and additional waveguide modes appear. This causes great enhancement in Jsc as can be seen from the curve for β = 0 shown in Fig. 7. However, the aligned grating structure yields a smaller Jsc for the incident angles between −20° and + 20° in comparison with the misaligned grating structure. It indicates that, in this angular range, the misaligned grating structure proposed in this article possesses much better characteristics. Therefore, thin film silicon solar cells with better light trapping properties under both normal and inclined incidence can be prepared by intentionally introducing displacement in the conformal grating structure, which is equivalent to the introduction of additional guided modes in the structure.
Based on the schematic shown in Fig. 1, a realistic solar cell would have conformal coating of at least one of the electrodes. We investigated the case when the front 50nm ZnO layer has the same profile as the Si layer. Results show that the β and DSi for the maximum Jsc enhancement shift to π/4 and 200 nm, respectively and the Jsc is 15.53 mA/cm2 at this position. The additional modes also appear and make great contribution to the light trapping enhancement in the solar cells when the two grating have a relative lateral displacement.
4. Conclusions
In conclusion, to increase solar cell efficiency, a relative lateral displacement between the front and back gratings was introduced into thin film silicon solar cells with conformal gratings. In addition to the resonance modes observed in the aligned grating structure, new ones were observed in the misaligned grating structure. The increase in the amount of the resonance modes enabled the misaligned grating structure to make use of a wider solar spectrum than the aligned one. The phase matching between the front and back gratings was improved by the introduction of the misalignment in the gratings, resulting in a 25.1 times enhancement at the wavelength of 950 nm which is the superposition of the contribution from both the first and the second diffraction order waveguide mode and an average of 2.2 times enhancement of the EQE in the wavelength range from 700 to 900 nm. For the misaligned grating structure with β = π/4 and DSi = 230 nm, a maximum Jsc enhancement of 34% is achieved for the normal incidence and a short circuit current enhancement of more than 15% is obtained for the incident angle between −15° and + 15°. This approach can be likely applicable to 2-D conformal gratings for enhancing light trapping in thin film solar cells.
Acknowledgments
This research was sponsored by the National Natural Science Foundation of China (No.60977028) and Key Project Foundation of Shanghai (No. 09JC1413800).
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