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We study the optical properties of a 2D Photonic Crystal (PC) inserted in the upper ITO electrode of a classical P3HT:PCBM solar architecture with an ultra-thin active layer. First, we analyze the optical response of the system when only the active layer is supposed to absorb light. This allows us to observe clear photonic crystal resonances in the absorption spectrum, which increase the cell efficiency even if the period of the PC is higher than the wavelength. This is in apparent contradiction with the common belief that PC should work in subwavelength regime. Then, by turning to a real system (with optical losses in all the layers), an optimized PC design is proposed, where the maximum of efficiency is obtained for a PC period of 1200 nm, much larger than visible wavelength.
© 2014 Optical Society of America
1. Introduction
Today’s photovoltaic devices have an active material thickness which is smaller than the wavelength of visible light. Despite a high absorption coefficient, classical organic blends such as P3HT: PCBM with a thickness of a few dozens of nanometer may not achieve complete broadband absorption. In this context, recent theoretical and experimental studies [1–6] have been made on finding nanostructures that can enhance the absorption efficiency into (in)-organic solar cells. 2D photonic crystals take advantage of specific resonances, increasing optical thickness of the absorbing layer. The nature of the excited modes in the periodic plane depends on the photonic crystal structures, which can be perfectly ordered [7–10], disordered [11,12] or with periodic defects [13,14].
In this work, a 2D perfectly ordered Photonic Crystal (PC) is used to enhance the efficiency of a solar cell. In particular in our typical organic bulk heterojunction solar cells, there is a well known trade-off between light absorption and charge transport: the higher the thickness the higher the recombination in the active layer. Therefore, a specific challenge of our works is to use a PC light trapping effect in order to have simultaneously an ultra thin active layer and a good absorption rate. To achieve it, we study the optical behavior of a patterned ITO electrode (upper electrode of the solar cell) that contains a 2D cubic air holes array. Note that ITO/Polymers 2D PC have already been studied for both solar cells [15] and LEDs [16] applications.
In section 2, we present the organic solar cell architecture and the numerical methods we have used. Before studying the absorption enhancement of the real structure, in Section 3, we consider an ideal cell where all the layers but the active one are transparent. As the losses in passive layers smooth out the PC resonances, considering directly a realistic structure would indeed entail some important physics and lead us to think that patterned multilayer behaves as a planar structure without PC.
In section 3, absorption is calculated in each layer. We show that the ineffective absorption (absorption in all the layers but the active one) reduces the light trapping efficiency and the associated PC resonances. Finally an optimized design, with a period larger than the wavelength, is proposed.
2. P3HT:PCBM as the only absorbing layer
Organic solar cells typically make use of ITO (indium tin oxide) as a “transparent” holes collecting electrode (180 nm-thick), see Fig. 1. Below it, a thin layer of PEDOT: PSS (35 nm) is used as a hole transporting material. Close to the semiconducting blend of P3HT: PCBM (50 nm), the active material, an aluminum layer (200 nm) acts as a mirror and an electrode that collects electrons.
Fig. 1 Schematic view of global nanopatterned solar cell. The ITO electrode contains a 2D cubic air holes photonic crystal of period a and diameter d.
As shown by previous studies, patterning some of these layers may enhance the absorption efficiency. Various schemes involving a patterning of the metallic electrode [17], active layer [18], and hole transporting layer [15] have already been designed and tested theoretically and experimentally. We have chosen to pattern the ITO electrode [15], as this is easier to fabricate than a patterned active layer. In such device, due to the weak index [19,20] gradient in the multilayer, the spatial modulation of field intensity in the PC layer spreads in the absorbing layer. In such situation, absorption is proportional to the overlap integral between the (resonant) slab mode and the absorbing material - see Eq. (12) in [21].
Using a FEM method, structures are excited by a Transverse Electro-Magnetic (TEM) plane wave at normal incidence and we can rotate the polarization axis so as to make average on the (random) polarization of the incident light. Real and imaginary part of the refractive indexes of polymer materials were measured by spectroscopic ellipsometry and metal indexes were taken from literature [22]. Finally the light absorption spectra A(ω) are obtained by spatial integration of the electric field intensity according:
Here, ω is the pulsation of the incoming wave. ε0 and εr and are respectively the vacuum permittivity and the relative permittivity of the material.To model the 3D system, we have used a 2.5D method [23] by calculating 2D band diagram (with Plane Wave Method) combined to an effective index approximation that allows taking into account the finite height of the structure. As refractive indexes of ITO and P3HT: PCBM are comparable, it is a reasonable approximation.
In this section, we consider that only the active layer absorbs, whereas Im(n) is set to zero for all the other layers. Even though this is a strong approximation, it permits to show clearly that a photonic crystal effect is present for periods larger than the wavelength.
First we calculate the absorption spectrum of the active layer for several values of PC period a varying from 200 to 1000 nm and for a reference structure without PC, while keeping fixed the air filling factor of 0.44 (see Fig. 2(a)). The value of the integrated absorption enhancement G (normalized by the absorption of the reference structure) is given for each period.
Fig. 2 (a) Absorption spectrum in the active layer for several values of PC period a. The air filling factor is fixed at 0.44. The integrated absorption enhancement G, normalized by the reference, is given for each value of period. (b) Spectral density of absorbed photons per unit of area and time, and integrated absorption enhancement G, weighted by the AM1.5 solar spectrum.
One observes two regimes in Fig. 2(a), depending on the value of the period:
- For small values (a ≤ 200 nm), one first note that the shape of the absorption spectrum is the same as the one of the reference but there is a small absorption enhancement due to a lower reflection. This can be explained by the fact that, the wavelength range [400 - 750 nm] is in the bandgap where there is no mode ; the PC behaves just as a uniform material whose refractive index is slightly lower.
- For larger periods (a > 200 nm), absorption peaks are observed at different wavelengths over the range [400 - 750 nm], those peaks are due to PC resonances. A peak of absorption can be observed when the life time of photons in PC modes is equal to that in the absorbing layer [24,25]. The lifetime of photons in those modes is directly proportional to the resonance quality factor QPC, and a coupled frequential/temporal analysis [14] permits to verify:
where τPC is the life time of photons in the PC mode, QPC the corresponding quality factor and ω the resonance pulsation.To complement Fig. 2(a), we have calculated the spectral density of absorbed photons per unit of area and time, as well as the integrated absorption enhancement G, weighted by the AM1.5 spectrum according to [15]:
where A(λ) and Aref(λ) are respectively the fraction of light absorbed by the active layer by respectively the patterned and reference structures. I(λ) is the intensity of light on the solar cell per unit of area and wavelength. In practice, we considered λ1 = 400 nm, λ2 = 700nm. One observes in Fig. 2(b) that the two gains G, weighted by the solar spectrum or not, are similar.As shown in Fig. 2, better absorption enhancement are achieved for higher periods a (note that we have obtained similar results when a is between 1 µm and 2.5 µm). Contrary to a common belief, we observe that the optimal value is not in the photonic crystal regime (a<λ). We want to point out that this can be interesting technologically, as structures with larger period may be easier to fabricate, whether with top-down or bottom-up [26] technologies.
To explain our observation in Fig. 2, 2D band diagram has been calculated for different periods a, keeping constant the air ratio (0.44%). Light at normal incidence excites unguided modes [27] at the Г point of the (ГMX) Brillouin Zone. The number of such modes, on the range λ1 = 400 nm ; λ2 = 700 nm, is plotted in Fig. 3.
Fig. 3 Number of modes calculated at k = Г (of ГXMГ Brillouin zone, see the inset) over the wavelength range [400-700] nm, as a function as the PC period a. The solid line shows the best fit to a function Y = α X2.
We notice that it is well described by a parabola, for values of the period larger than the wavelength (see the fit, represented with a solid line, Fig. 3). Two remarks can help to understand this point (i) the number of modes is counted in the interval [a/λ1 ; a/λ2], whose size increases with a, (ii) the density of mode in any band diagram increases with a/λ, as they tend to pack and form a continuum at high value of a/λ. Consequently, for large values of a the plane wave excites a quasi-continuum of modes and the resonances are less visible (see Fig. 2(a)).
Figure 4(a) compares the P3HT:PCBM absorption corresponding to the nanostructured cell with a period of 1000 nm (dashed line) to this of the reference cell (solid line) that does not contain any PC. Absorption enhancement due to the coupling of light with PC resonant modes is clearly seen all over the spectrum:
Fig. 4 (a) P3HT:PCBM absorption in the reference cell (solid line) compared to the P3HT:PCBM absorption in the patterned solar cell (dashed line) ; the period a is 1000 nm and air filling factor ffair is 0.44. (b) Overview of Fig. 4(a) showing the P3HT:PCBM absorption (solid line) in the patterned solar cell on the range λ = [400-600nm], for the ideal system. The total absorption of the patterned multilayer system (dashed line) is added for comparison (all imaginary parts of index are taken into account). (c) Calculation of absorption in each layers of the patterned cell. (d) Calculation of P3HT:PCBM absorption enhancement in patterned solar cell by taking into account all absorbing layers contributions: 20% enhancement is obtained compared to reference planar cell.
-In the [400-575 nm] range (strongly absorbing region), broad resonances can be found. Those resonances allow absorption to be greatly enhanced, especially at λ = 575 nm where it is doubled and reaches 100%.
-In the [575-700 nm] range (weakly absorbing region), there is a drop of P3HT: PCBM extinction coefficient, see [14]. Then, a longer optical path is needed in the absorbing layer to enhance absorption. This can happen only at very specific frequencies that corresponds to some modes of the PC slab with a larger quality factor. As seen in Figs. 2(a) and 4(a), this results in sharper peaks with very high absorption enhancement. For example, we can see in Fig. 4(a) that absorption can be multiplied by 10 at λ = 650 nm, albeit on a small λ-range. Finally, by integrating absorption over the whole spectrum we compute a total enhancement of 40%.
Figure 5 represents the 2D band diagram of a cubic array of air holes, whose period is a = 1000 nm, in a slab of index Neff575 = 1.85. We denote Neffλ the effective index of the multilayer at the wavelength λ (in nm). The PC mode responsible for the absorption enhancement at λ = 575 nm in Fig. 4(a) is found at the expected value a/λ = 1.74 in the diagram (Fig. 5). The associated band (black bold line) is represented in the XΓM contour of the Brillouin zone.
Fig. 5 The black lines show the 2D band diagram of a cubic array of air holes (period a = 1000 nm) in a dielectric slab whose index is the effective index of the multilayer at λ = 575 nm (Neff575). A PC mode is found, in Γ, when a/λ = 1.74. The corresponding band is represented in thick black line. Due to the difference between Neff 575 and Neff 650, the diagram for λ = 650 nm is shifted (see the arrow), and only one band has been represented for λ = 650 nm (thick blue line). On this band, a mode can be excited in Γ, when a/λ = 1.54.
At the wavelength 650 nm, another PC mode is excited (see Fig. 4(a)). The associated value of the excitation parameter (a/λ = 1.54) is almost the same than the one observed in the band diagram (a/λ = 1.53), see Fig. 5.
Note that, due to material dispersion, the effective index varies, and both band diagram at 575nm and 650nm are not identical. We choose to represent only the diagram for 575nm excitation in Fig. 5 (black lines), adding simply the band (blue bold line) that is excited at 650nm in the band diagram. To compute it, we used the method described above, with an effective index of 1.76 (Neff650).
One notices that changing the effective index merely shifts the bands (see the black arrow in Fig. 5). We precise that the resonance at λ = 419 nm (a/λ = 2.39) has been also found in the upper bands of the diagram where the density of modes is more important; but we have not represented it for more clarity.
3. Limit of light trapping and large periods effects
Whereas we considered the passive layers to be transparent – Im(n) = 0 – in section 2, we take into account their extinction coefficient in section 3. This permits to observe how the light trapping is affected (field distribution is different).
Figure 4(b) is an overview of Fig. 4(a) and shows the absorption of the P3HT:PCBM (solid line) in the ideal system described in section 2 – the range [400-600nm] is represented. The total absorption of the patterned multilayer absorbing system (dashed line) is also plotted for comparison (all imaginary parts of index are taken into account). The total absorption is obviously higher since supplementary loss in the system is provided. The spectral position of the peaks changes very slightly (see Fig. 4(b)) when one takes the losses into account. This is due to the fact Im(n) << Re(n) for all the dielectrics. In a very good approximation, the losses simply broaden the resonances (see for example at λ = 420 nm and 575nm) and the one with a very low quality factor become barely visible. At λ = 575nm, the amplitude of the peak (dashed line) is reduced, leading to a total absorption lower than absorption of P3HT:PCBM as single absorbing layer.
Figure 4(c) shows the distribution of absorbed energy between all the layers of the cell. Specific PC resonances are observed in ITO, PEDOT, and aluminum but not in the active layer which seems to have a “non resonant” behavior. As a consequence, the gain in the active layer is greatly reduced as shown in Fig. 4(d). Finally, this leads to total enhancement of 20%, which is half the absorption computed when only the active layer is absorbing (Fig. 4(a)).
Having noticed the negative effect of ineffective absorption (peak broadening, total absorption lowering, …), we now take it into account to find and optimized design of the PC slab. Here it appears interesting to find the best couple (period/ffair) in order to maximize absorption in this architecture. To achieve it, we have calculated the absorption enhancement as a function of two variables: period and ffair. As seen in contour map, Fig. 6, a maximum of absorption enhancement (23%) is reached for a 1.2 µm period with a 0.6 air filling factor. When we fix the air ratio to the value of 0.6 and calculate the absorption enhancement for periods larger than 1.2 µm (up to 2.5 µm), we observe a slow decrease of absorption enhancement (down to 20% at 2.5µm). The number of modes is constantly increasing with period, see Fig. 3. But the light trapping effect (which is an increase of the optical path due to the excitation of photonic crystal resonances) is destroyed for a>>λ. Indeed, for larger period, with a fixed filling factor, the hole diameter increases and the efficiency of the diffraction of the incoming plane wave by cylindrical apertures (at the interface between air and ITO) decreases. Then, a larger part of the injected energy would propagate through the slab without being coupled to PC modes. In fact it is exactly the opposite of what happens when a roughly textured layer is deposited at the top of the cell. In such case, diffraction is enhanced, and also the coupling to PC modes [28]. Thus it could be interesting to use a roughly textured layer in order to maximize the diffraction in the case the period is large.
Therefore, a tradeoff between the number of modes and their trapping efficiency creates an optimum absorption value. Among our calculations, the best value we have found, is for a period of 1.2 µm. This is an important result for such solar cells that could be fabricated without electron beam lithography, but using classical optical lithography.
4. Conclusion
We have presented a theoretical study of the optical absorption enhancement in organic solar cells, based on the use of resonant PC modes. For an ideal, non-absorbing, structure, we have observed resonances in the absorption spectrum, which are the signature of the Photonic Crystal modes that trap the light and enhance its absorption. The large improvement (40%) decreases if one takes the losses into account (20%). Still, it is possible to optimize the full structure, and obtain a gain of 23%. Finally, note that the light trapping (outside the bandgap) can be observed for periods larger than the wavelength, with a slightly better efficiency than what can be found in typical structures with subwavelength period. This is not a commonly known effect that is due to the higher density of state at larger period. We remark that future theoretical works will be needed in order to define the upper limit size of PC periods for light absorption enhancement in such solar cells, as well as to lower as much as possible the losses of the polymers used in the non-active layers.
Acknowledgments
This work has been financially supported by the French National Research Agency (Agence Nationale de la Recherche) in the frame of the project ANR-13-BS08-0003 “PhotoLighT”.
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