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Nanophotonics can guide the design of novel structures for light-trapping in ultra-thin photovoltaic cells. Here, we report on the systematic study of the effect of the angle of incidence of sunlight on the performance of such structures. We also conduct a parametric study of a sinusoidal grating and demonstrate that light intensity in the active region averaged over a range of input angles from 0° to 80° can be enhanced by more than 3 times compared to the bare device. Such a broadband light-trapping nanostructure can increase the total daily energy production of a fixed (non-tracking) device by over 60%, compared to a reference device with an anti-reflection coating.
©2012 Optical Society of America
1. Introduction
Photovoltaic devices with ultra-thin active layers have the advantages of lower manufacturing costs [1], reduced use of expensive material, increased carrier-extraction efficiency [2, 3] and improved open-circuit voltage [4]. Overall, they show significant potential to decrease solar-power costs such that they are on par with power from non-renewable sources. One major challenge in thin photovoltaic cells is their poor light absorption. Several techniques have been proposed to increase the optical length within the active layer to improve light absorption. These techniques include the use of random textures on the top surface [5, 6], dielectric nanospheres embedded within the active layer [7], metallic nanostructures on the top [8, 9] or bottom surface [9, 10], grating structures in a top layer [11–13], and nanophotonic structures [14]. The last of these hold significant promise due to the ability to excite multiple guided resonances that can couple close-to-normally incident sunlight into modes that can travel within the plane of the active layer, thereby increasing the optical path-length by 2 or more orders of magnitude [14, 15].
These previous approaches suffer from myriad limitations. For instance, the addition of metallic nanostructures (for plasmonic trapping) leads to enhanced recombination at the surface of the metal, which can often negate the improvement in light absorption [16]. Dielectric structures avoid the recombination problem. However, the design of dielectric nanostructures for light trapping is computationally expensive and the fabrication of such structures is challenging. Furthermore, the performance of such structures is highly sensitive to the angle of incident light [14, 15]. Previously, we performed a careful numerical analysis of the light-trapping capabilities of several simple one-dimensional (1D) periodic dielectric nanostructures [17]. We showed that with judicious design of the geometrical parameters, light intensity over the entire solar spectrum within an ultra-thin active layer might be enhanced by a factor of up to 6. In this paper, we expand on this previous work to analyze the effect of the angle of incidence on nanophotonic light-trapping. Pursuant to that, we perform a parametric analysis of geometric factors that affects light-trapping for a broad range of input angles. As a result of this analysis, we propose a simple trapping geometry that can enhance short-circuit-current density by a factor of ~3 for angles of incidence averaged from 0° to 80°. We further show that this preliminary light-trapping design increases the daily energy output from a fixed (non-tracking) device by over 60% when compared to an unpatterned device with only an anti-reflection coating and the same active layer thickness.
2. Effect of the angle of incidence
A geometry of interest is depicted as an inset in Fig. 1(A) . The top layer of the device is a scattering layer comprised of a square grating of period Λ, duty cycle d, and thickness ts. The next layer is a cladding layer of thickness tc. Below that is the active layer of thickness ta. The active layer is assumed to be atop a perfect reflector, an approximation of the back-contact. In order to quantify the effect of the angle of incidence, we calculated the average enhancement of light intensity for a fixed incident angle, Fθ within the active layer over the entire solar spectrum compared to the case where the scattering and cladding layers are absent. We also computed the enhancement in the resulting short-circuit current-density, Jθ as a result of adding the scattering and cladding layers. The formal definitions of these enhancement factors are described in section 3. The simulations in Fig. 1(A) assumed ta = 10nm, tc = 30nm, ts = 90nm, Λ = 400nm, and d = 0.6. The active layer was assumed to be monocrystalline silicon, and the scattering and cladding layers were made up of SiO2. Collimated light of AM1.5 spectrum was assumed for the incident illumination. Other details of the simulations were described earlier [17]. Figure 1(A) shows that as the angle of incidence is increased, the enhancement factors drop. However, even at an incident angle of almost 70 degrees, the enhancement is about 1.5, i.e., the nanophotonic structure still improves performance. Figure 1(B) shows the effect of incidence angle on a scattering structure comprised of a sinusoidal grating. The geometric parameters were the same as in Fig. 1(A), except that ts = 120nm. The sinusoidal grating shows higher enhancement at small oblique incidence (<50°) and similar enhancement at large oblique incidence (>50°) compared to the square grating. We can plot the spectrum of the enhancement factor Fθ for each angle as shown in Fig. 1(C) for the square grating and Fig. 1(D) for the sinusoidal grating to gain insight into the nanophotonics. At normal incidence, a strong peak is clearly seen at λ = 500nm depicting a strong guided-mode resonance in the active layer. At small angles of incidence, two peaks symmetric about 500nm are observed. These peaks arise from the symmetric guided modes that are excited for small oblique angles. At angles beyond 20°, the enhancement is about half of that at normal incidence. The sinusoidal grating shows stronger resonances as well as better large-angle enhancement (<50°). Interestingly, wavelengths above 900nm show broadband enhancement for angles of incidence larger than ~80°. This is likely due to the scattering layer acting as an anti-reflection coating (ARC) at long wavelengths (Λ << λ).
Fig. 1 Effect of oblique incidence on (A) square-grating and (B) sinusoidal-grating scattering structures atop an ultra-thin active device layer. Fθ and Jθ refer to light-intensity and short-circuit current-density enhancements with respect to a device that does not contain the scattering and cladding layers, respectively. (C) and (D) show the enhancement spectra as a function of incident angle for the square and sinusoidal gratings, respectively. Note the sharp peaks, which indicate specific guided modes that are excited within the active layer.
These results confirm that in order to gain the maximum advantage of nanophotonic light trapping, the photovoltaic device has to track the sun. However, tracking can be expensive. Therefore, it is advantageous to explore nanophotonic designs that can achieve high enhancements over broad angles of incidence. Since the sinusoidal grating shows better performance compared to the square grating, we proceed to use the sinusoidal grating as the default geometry for parametric optimization for broad-angle light trapping.
3. Figures-of-merit for broad-angle light-trapping
We begin by defining the spectrally-cumulative, time-averaged intensity distribution and the total power per unit grating period within the active layer, S.
The intensity is averaged over the two orthogonal polarizations of the incident light field. Note that the coordinate system is illustrated in the inset in Fig. 1(A). The overall light-enhancement factor for all incident angles, F is defined as
where Sref(θ) is the total power per unit grating period within the active layer of the reference device, in which the nanophotonic structure (cladding and scattering layers) is absent. θmax refers to the maximum angle of incidence under consideration. Normalization with respect to the grating period is necessary to evaluate the effect of varying this period with respect to a reference period. In the case of the reference device, where the nanophotonic structures are absent, Λref is the width of the simulation geometry in the x-direction.In addition to light enhancement, we can also evaluate the effect of light trapping on the device performance by directly computing the short-circuit current density, jsc.
where Φ is the local photon flux in the active layer, IQE is the internal quantum efficiency of silicon and c is the speed of light in silicon. The overall enhancement in short-circuit current-density, J is then defined asWith these figures-of-merit in place, we can evaluate the effects of various geometric parameters in the nanophotonic structure. Since the sinusoidal grating shows better broad-angle enhancement compared to the square grating, we utilize this as the default design. The default parameters are Λ = 400nm, ta = 10nm, tc = 30nm, ts = 120nm and θmax = 80°. In the following analysis, each parameter is changed while all others are kept constant to elucidate their individual effects.
4. Parametric analysis
Figure 2 shows the impact of the period of the sinusoidal grating on the enhancement factors. Since the nanophotonic effect is due to the excitation of guided-mode resonances, one would expect a strong dependence on the grating period. On the other hand, the resonance is also expected to be sensitive to the incident angle. When many incident angles are averaged, the impact of the grating period will be less significant. Figure 2(A) seems to confirm this view. As the grating period is increased, the enhancement factors increase slightly reaching a peak at Λ = 400nm. Beyond that, the angle-averaged enhancement seems to be fairly constant. It is illustrative to study the enhancement as a function of incident angle, Fθ as shown in Fig. 2(B). At normal incidence, a strong peak is observed at Λ = 400nm. At larger incident angles, multiple peaks are seen but the strength of each peak is reduced. This is consistent with previous theoretical studies [15]. Note that at large periods (>900nm) the enhancement factor is higher at oblique incidence (θ = 40°). In order to study the individual resonances, it is instructive to plot the spectra of Fθ for a few incident angles. These are shown in Fig. 2(C)-2(F) for θ = 0°, 20°, 40°, and 60°, respectively. At normal incidence (θ = 0°) strong resonance is observed when the incident wavelength in the scattering layer is approximately equal to the grating period. However, for a given grating period, only one strong resonance is observed. As the incidence angle is increased, multiple resonances are seen. For the same grating period, at least two resonances are generated (see θ = 20° in Fig. 2(D), for instance). Generation of multiple resonances at oblique incidence is useful for broadband enhancement of light absorption. However, the strengths of the individual resonances are diminished at oblique incidence. Therefore, one would still expect highest enhancement only for a narrow cone of incidence as indicated by previous studies [15].
Fig. 2 Effect of grating period. (A) Overall enhancement factors as a function of grating period, Λ. (B) Enhancement factor at a given incident angle, Fθ as a function of Λ. (C)-(F) Spectra of enhancement factor, Fθ for θ = 0°, 20°, 40° and 60°, respectively.
The second geometric parameter of interest is the thickness of the cladding layer, tc. As shown in Fig. 3(A) , the overall enhancement factors decrease with increasing tc. This is expected as the closer the scattering layer is to the active layer, the higher the coupling between the incident and the guided modes. Higher coupling will result in larger energy transfer and hence, a stronger resonance. The dependence of Fθ on tc is less strong except at large θ or when tc > ~50nm (Fig. 3(B)). This is borne out in the individual spectra of Fθ, where the location and the strength of the guided-mode resonances are mostly independent of tc (Fig. 3(C)). At oblique angles of incidence, multiple resonances appear as discussed earlier, but their dependence on tc remain weak (Fig. 3(D)). This is also expected since tc << λ and hence, will have little impact on the characteristics of the guided-mode resonance in the active layer. At large θ, the scattering structure mostly serves as an anti-reflection layer and no clear resonances are observed (Fig. 3(E) and 2(F)).
Fig. 3 Effect of cladding-layer thickness, tc. (A) Overall enhancement factors as a function of tc. (B) Enhancement factor, Fθ as a function of tc. (C)-(F) Spectra of enhancement factor, Fθ for θ = 0°, 20°, 40° and 60°, respectively.
As described earlier [18], the scattering-layer thickness, ts has an important impact on the enhancement factors. Figure 4(A) shows that the overall enhancement factors reach a maximum when ts = 120nm. Most of this peak enhancement is achieved due to the sharp increase in the light intensity under normal incidence as illustrated in Fig. 4(B). Significant decrease in Fθ is observed at larger angles, irrespective of ts. The spectra of Fθ clearly illustrate the presence of strong guided-mode resonances (one at normal incidence, two at θ = 20°, and so on). At θ greater than about 40°, the anti-reflection properties seem to dominate and broadband enhancement is achieved, albeit at lower absolute values (Fig. 4(E) and 4(F)).
Fig. 4 Effect of scattering-layer thickness, ts. (A) Overall enhancement factors as a function of ts. (B) Enhancement factor, Fθ as a function of ts. (C)-(F) Spectra of enhancement factor, Fθ for θ = 0°, 20°, 40° and 60°, respectively.
5. Enhancement of daily energy output
It is well known that the daily energy output from a flat non-tracking photovoltaics panel is determined by the angle that the sun makes with the normal to the panel [19]. Therefore, the panel produces significantly lower power during the early morning and the late afternoon hours. It is illustrative to compare the effect of the subject nanophotonic structure on the total daily energy output of a flat non-tracking thin photovoltaic device. In order to simplify our calculations, we assumed that the device is placed horizontally at the equator. We also assumed that the incident solar spectrum, AM1.5 does not change over the course of the day. Furthermore, we assumed that the azimuthal angle of the sun is 0°. Finally, any effects of the atmosphere including shading due to clouds is ignored. The short-circuit current-density can be calculated by Eq. (4). The incident angle is assumed to vary from −90° to 90°.
Next, we compute the open circuit voltage via a semiconductor-device model [20, 21].
where Eg is the bandgap, k is Boltzmann’s constant, T is the absolute temperature, n is the refractive index of the active material and q is the electronic charge. The output power-density for a fixed incident angle θ is then,where FF is the fill factor. In this paper, we assumed Eg = 1.12eV (c-Si) and FF = 0.6. And θ is a function of time within a day. Finally, the daily output energy-density is given byFor comparison, we computed E for a bare reference device with 10nm-thick active layer, a device with an anti-reflection coating (a uniform 85nm-thick fused silica layer on top of the 10nm-thick active layer) and the designed device with the optimized nanophotonic structure on top of the active layer. The results are summarized in Fig. 5 . The parametric values were ta = 10nm, tc = 10nm, ts = 120nm and Λ = 400nm. The nanophotonic structure increases daily energy output in the non-tracking system by a factor of 2.58X compared to the bare reference device. Even when compared to the standard device with an anti-reflection coating (ARC), the daily energy output is increased by about 1.62X.
Fig. 5 Daily energy output per unit area in the non-tracking configuration for a bare device (left), a device with an anti-reflection coating (ARC) (center), and a device with the nanophotonic structure (right).
6. Conclusions
In this paper, we demonstrated that simple periodic nanostructures could be used to scatter sunlight from a broad range of angles into resonant-guided modes within an underlying active layer resulting in significant increase in broadband light trapping. We performed a preliminary optimization of the geometric factors in a sinusoidal grating and demonstrated that the short-circuit current-density could be increased by a factor of over 3 compared to a bare reference device averaged over incident angles from 0° to 80°. This approach can, therefore increase the daily energy output of a non-tracking PV device by over 60%, compared to the device with the same active layer thickness and an optimal ARC layer. Significant improvements in light-trapping can be expected by considering more complex geometries as well as two-dimensional geometries [13, 15, 16]. It has been proposed that optimized 2-D nanostructures could overcome the classical Yablonovitch limit for light-trapping [14–16]. It must be noted that all such nanostructures present significant challenges in fabrication, primarily due to the requirement of large-area coverage. Advances in scalable nanofabrication such as roll-to-roll nanoimprint lithography will be critical for practical implementation of such schemes [22]. Although, we assumed ultra-thin layers of c-Si for our active layer, it is obvious that the principles apply equally to organic photovoltaic devices as well [23, 24]. The improvement in electrical performance for such devices is expected to significant at the very small thicknesses as considered here [9]. The approach presented here can provide guidance when designing light-trapping nanostructures for ultra-thin devices that need to operate under normal and oblique illumination conditions.
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