Post-print of: Solar Energy Materials and Solar Cells Volume 104, September 2012, Pages 87–91

DOI: 10.1016/j.solmat.2012.04.047

Optical interference for the matching of the external and internal quantum efficiencies in organic photovoltaic cells

Rafael Betancur (a), Alberto Martínez-Otero (a), Xavier Elias (a), Pablo Romero-Gómez (a), Silvia Colodrero (b), Hernán Miguez (b), Jordi Martorell (a, c)

a ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain

b Instituto de Ciencia de Materiales de Sevilla, Consejo Superior de Investigaciones Científicas (CSIC), Américo Vespucio 49, 41092 Sevilla, Spain

c Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, 08222 Terrassa, Spain

Abstract

We demonstrate experimentally that an appropriate combination of the layer thicknesses in an inverted P3HT:PCBM cell leads to an optical interference such that the EQE amounts to 91% of IQE. We observe that reflectivity between layers is minimized in a wavelength range of more than 100 nm. In that range the EQE closely matches the IQE. The role played by the optical interference in improving the performance of the fabricated solar cells is confirmed by EQE calculated numerically using a model based on the transfer matrix method. Additionally, we observed that a similar cell with an active material 1.7 times thicker exhibited a lower PCE. The poor photon harvesting in the later cell configuration is attributed to an EQE that amounts only to 72% of the IQE.

Keywords

Optical interference; Organic solar cells; Photovoltaics

1. Introduction

To enhance photoconversion efficiency (PCE) of organic photovoltaic (OPV) cells it is rather important to optimize the photon harvesting provided the absorption band of the materials used is typically narrower when compared to other photovoltaic devices. In addition, OPV devices suffer from a short exciton diffusion length and a low mobility of charged carriers which prevents the use of thick materials for a more effective photon absorption [1]. Typically, a direct (or inverted) OPV cell is composed of a stack of five layers deposited on top of a

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transparent substrate, which are, sequentially, a transparent conducting layer (usually indium tin oxide, ITO), a charge blocking layer to block the electrons (or holes), an active polymer blend heterojunction, a second charge blocking layer to block the holes (or electrons), and a metal electrode. To reach an efficient photon absorption in such rather thin active polymer layers, one of the approaches is to disperse light more effectively within such active layer. Recently, special attention has been given to the inclusion of metal nano-particles to enhance absorption and scattering of light [2], [3] and [4]. Some encouraging results have been reached, showing an increase of the external quantum efficiency (EQE), defined as the ratio between current and incoming photons, for a broad range of wavelengths [2]. However, the EQEs that have been achieved in both cases are still well below the internal quantum efficiency (IQE), which is the quotient between current and absorbed photons. Here, we show experimentally that by combining the layer thicknesses in an inverted P3HT:PCBM cell, the optical interference is such that the EQE amounts to 91% of IQE. Additionally, we observe that reflectivity between layers is minimized in a wavelength range of more than 100 nm. In that range the EQE closely matches the IQE. Such experimental observation is confirmed by the EQE calculated numerically using a similar transfer matrix model as the one implemented by the authors of Refs. [5], [6] and [7]. At the same time we demonstrate that when the relative thicknesses of all layers are not combined properly, thicker cells may exhibit lower PCEs. As was shown in the past [6], [7], [8], [9] and [10], absorption within the active layer may be strongly affected by the relative thickness between the five layers that constitute the cell. Indeed, from an optical perspective, such organic solar cells can be seen as a stack of several layers with different refractive index which causes a significant reflection at each interface. An EQE approaching the internal one or, in other words, an effective photon harvesting is achieved when the overall reflectivity of such five layer structure is reduced to a minimum.

2. Optical absorption in an inverted cell architecture

We chose to study an inverted bulk hetero-junction cell where TiO2 nanoparticles (TiO2-np) are employed as hole blocking layer deposited on top of ITO. The active layer considered is a blend of P3HT:PCBM. In between such active region and the Ag top electrode we deposited an electron blocking layer of MoO3. As schematically shown in Fig. 1, in this cell architecture we allow to vary freely, within a limited range of thicknesses, the ITO, TiO2-np, active material and MoO3 layers.

Photon absorption in the active layer was determined after integrating within the active layer volume the following expression:

Where is the electric field, the complex conjugate current density, ϵo the vacuum permittivity, n the refractive index, k the extinction coefficient, and λ the wavelength of the incident field in vacuum. The forward and backward fields within each layer between the

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substrate–ITO and the Ag–air interfaces, shown in Fig. 1, are added coherently, using the transfer matrix method [7], [8], [9], [10] and [11], to compute numerically the electric field intensity distribution |E(z)|2 inside the active layer. Reflection losses at the air–substrate first interface are accounted as an energy loss provided that the typical thickness of a substrate material is much larger than the sun coherence length. Parameters such as n and k were determined by ellipsometry in the 400–800 nm range for all layers except for the Ag layer, whose n and k dispersion curves were taken from the literature [12].

When all such parameters are known, the integration of Eq. (1) can be performed numerically as

where Δzi is the integration interval in the z-direction, zi the center value for z within that interval, A the surface on a plane perpendicular to the z-axis (cf. Fig. 1) for the volume of integration enclosing the active layer. The result of this summation is used to compute the absorption within the active layer. Note that the field distribution is modulated by the real and imaginary parts of the refractive index. Thus, explaining photon absorption solely in terms of the field distribution would be in certain cases hindered by the wavelength dependence of these two material parameters. Given the linearity of the field equations, the total number of sun photons absorbed can be computed by Fourier transforming the electric field and then adding the contribution at each wavelength weighted by the sun photon distribution. In an organic solar cell, photons when absorbed are converted to excitons which diffuse within the active layer. However, in a bulk hetero-junction, such created excitons would encounter a charge separation interface immediately after being created, which, among other things, has the positive effect of limiting recombination losses. The created charge carriers are separated by the electric field near the cathode [13]. In other words, the length excitons must diffuse is minimized in such bulk hetero-junction cells. Then, it is reasonable to take the photon to charge conversion efficiency as a dispersionless parameter. This constant should be multiplied by another dispersionless parameter proportional to the charge carrier separation and collection efficiencies [14]. The physical limit to such efficiencies is the charge recombination. Overall, we may assign a unique constant value, ϕ, to the absorbed photon to the final collected charge efficiency which may be considered independent of the wavelength associated to the photons [15]. This constant value, ranging between 0 and 1, is determined empirically after many experimental measurements of the EQE. Thus the EQE can be computed as the product of such ϕ and the result of the integration of Eq. (2). Combining the EQE and the sunlight photon flux F(λ) (under AM1.5G conditions) one may obtain the generated short-circuit current density (Jsc) using the equation

When the thicknesses of ITO, TiO2-np and MoO3 are fixed to 100, 80 and 3 nm, respectively, the Jsc dependence to the active layer thickness is shown in Fig. 2(a). Note that such combination of layer thicknesses leads to an optimal performance for cells whose active layer thickness is around 100 nm (corresponding to a configuration number in Fig. 2(a) close to

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2000). As can be seen from Fig. 2(c), optimization of cells whose active layer thickness were to be close to 151 nm (configuration number around 4000) would require to adjust the TiO2 thickness to 20 nm.

3. Materials and methods

3.1. Synthesis of TiO2 nanoparticles

Nanocrystalline TiO2 particles were synthesized using a procedure previously reported and based on a sol–gel technique followed by growth under hydrothermal conditions [16]. This recipe was slightly modified in order to obtain a really fine particle size suspension (6 nm in average), which allowed forming very uniform TiO2 films, and which have already been used to build highly reflectance structures in dye solar cells [17]. Concretely, titanium isopropoxide (20 ml, Aldrich 97%) was hydrolyzed after the addition to Milli-Q water (36 ml) and the stirring for 1 h. Once this stage was completed, the product was filtered using 1.2 μm RTTP Millipore membranes, washed several times with distilled water and placed in a teflon reactor with 3.9 ml of 0.6 M tetramethylammonium hydroxide (∼2.8 M, Fluka). After homogeneizing the suspension with a stir bar, the reactor was placed in an oven preheated at 120 °C, where it was kept for 3 h. Peptization process took place during the heating in the presence of tetramethylammonium hydroxide. After this, a bluish colloidal suspension of titanium oxide crystallites with anatase structure was obtained. Later centrifugation at 14,000 rpm for 10 min allowed eliminating some large aggregates from the dispersion.

3.2. Device fabrication and characterization

The entire fabrication of the devices except for the last two steps, which involve high vacuum deposition, was performed in ambient air conditions. A TiO2-np layer (6 nm nanoparticle size as describe above) was deposited by spin-coating on top of ITO covered fused silica substrate and thermally annealed on a hotplate in air (125 °C 10 min) resulting in a 77 nm layer with 4.1 eV work function. The active P3HT:PCBM (1:1 wt in oDCB) layer was deposited by spin-coating and treated by solvent annealing during 5 min. Finally a 3 nm MoO3 and 120 nm Ag layers were thermally evaporated to complete the devices. The obtained IV curves were measured using a solar simulator in AM1.5 conditions.

4. Results and discussion

We fabricated the inverted structure ITO/TiO2-np/P3HT:PCBM/MoO3/Ag to experimentally study the active layer thickness dependence shown in Fig. 2(a) while the ITO, TiO2 and MoO3 layers thicknesses were kept fixed at 100, 77 and 3 nm, respectively. All layer thicknesses were accurately measured using an atomic force microscope (AFM) in tapping mode after scratching the layers. The dependence of the Jsc on the blend thickness shown in Fig. 3(a) exhibits a very good agreement with the model prediction obtained using Eqs. (1) and (2). The relative maximum and minimum for the Jsc are a clear indication that optical interference is responsible for a field redistribution to enhance absorption within the active layer and subsequently improve the performance of the solar cell. Photovoltaic parameters for all the fabricated P3HT:PCBM cells are given in Table 1. As expected, while there is a correlation between the Jsc and active layer thickness, no such correlation can be found between such

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layer thickness and the Voc or FF. As seen in Fig. 2(b), the model predicts a weak dependence of the Jsc with the thickness of the hole blocking layer of TiO2-np. When the electron blocking layer is fixed to a thickness of 3 nm, the Jsc exhibits an oscillatory pattern, which is shown in Fig. 3(b) for three different active layer thicknesses. In the same Fig. 3(b), we observe that the position of maxima and minima for such oscillation move as the thickness of the active layer is changed. This is another indication that optical interference must be considered accounting all layers and not just an optical spacer. Experimental measurements of the Jsc for different thicknesses of the TiO2-np layer, shown in Fig. 3(b), indicate that to some extent, the experimental measurements follow the trend predicted by the theoretical model. More precise measurements are difficult to achieve in this case provided that the average size of the nano-particles is 6±3 nm. We also measured the Jsc dependence with the thickness of the electron blocking layer of MoO3. As seen in Fig. 3(c), we observe that, as predicted by the theoretical model, when the thickness of such layer increases, the Jsc diminishes. This is in agreement with earlier theoretical [8] and [9] results that have shown that the improvement brought by an optical spacer layer in between the active layer and the top metal contact may be justified only in cells where an optical optimization has not been reached [6], [18], [19] and [20]. In other words, an optical spacer alone may improve photon absorption in a non-optimized cell [9] but, at least for the architecture considered here, it cannot make an optimized device any better.

Representative IV curves for the region of the local minimum (active layer thickness around 150 nm), the region of the local maximum (active layer thickness around 100 nm) and the region of very thin active layers (active layer thickness less than 80 nm) are shown in Fig. 4. By measuring the IV curves during a 3 weeks period, we also determined the lifetime of non-encapsulated devices. After such 3 weeks of measuring we found a time constant of 4500 h confirming the very good stability of the devices.

The experimentally measured and numerically calculated EQEs for three different layer thicknesses corresponding to the three regions of interest are shown in Fig. 5(a). We observe that when the active layer thickness equals 91 nm the EQE approaches the IQE predicted by the model, also shown in Fig. 5(a). Also note that the experimentally measured EQE agrees remarkably well with the numerically predicted one. In the wavelength range of 450–625 nm, where the majority of excitons are created, the EQE amounts to 91% of the IQE. This is in accordance to the better performance of the device expected from inspection of Fig. 3(a) or 4, which shows a maximum Jsc when the active layer thickness is close to 100 nm. When the active layer is 151 nm, corresponding to the relative minimum in Jsc seen in Fig. 3(a), the numerically predicted EQE in the same wavelength range considered above amounts to only 72% of the IQE. Such large differences in the EQE among the two cases considered can be attributed to significant differences in the reflectivities of both devices. As shown in Fig. 5(b), for the 91 nm active layer thickness case, the optical interference is such that reflectivity is minimized for the range where the majority of excitons are created. In fact, reflectivity is very close to just the reflectivity of the first substrate interface in the 450–550 nm range; the same range where the EQE almost perfectly matches the IQE. On the contrary, for the 151 nm case, the layer combination considered does not provide an adequate optical interference optimization and, as seen in Fig. 5(b), reflectivity does not approach zero at any wavelength of interest. However, as it can be inferred from Fig. 2(c), an optical based optimization, which

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would essentially require to change the TiO2 layer thickness, is possible for such later cell. In that event, the 151 nm active layer cell would exhibit a similar performance as the 91 nm active layer one. In other words, the appropriate optical interference may lead to cells whose active layer thickness is 60% of the thicker one but without any loss in efficiency. When the active layer thickness is 69 nm, as seen in Fig. 5(a), the behavior of the EQE relative to the IQE follows the increase in reflectivity relative to the 91 nm active layer case. Here, again, there is a very good agreement between the calculated and experimental EQEs. The trend is that when the active layer is thinner, deviations of the theoretical prediction from the experimentally measured EQEs are limited to the high energy range below 475 nm. As the active layer is made thicker such deviation extends to the long wavelength region.

5. Conclusions

In conclusion, we confirmed theoretically and experimentally that optical interference may play a very relevant role to enhance the overall performance of organic photovoltaic devices. As indicated by the authors of Ref. [6], an optical spacer alone may not be sufficient to significantly alter the field distribution inside the device to increase absorption within the active layer but the performance of the device can be modulated by changing the thickness of the active layer and the rest [6]. We showed, here, that a simultaneous adjustment of all the layers in the device may lead to an EQE that matches the IQE for a large wavelength range. Such matching is achieved for the wavelength range where the absorption of the active material is larger. Provided that in such range the IQE is very close to its maximum value, no further gain should be expected by the inclusion of elements, such as metal nano-particles, meant to enhance photon absorption and diffusion. On the other hand, when such elements are properly tailored, a larger gain should be possible for the long wavelength range where absorption is significantly lower. In addition, for the specific cell configuration considered here, we demonstrate that by adjusting the optical interference, a given device can perform equivalently to a device whose active layer thickness is 1.7 times larger. This may enable the fabrication of devices with active layers thinner than the absorption length. This may be particularly relevant when polymers such as PCDTBT [21], [22] and [23] or PTB7 [24] are used as active material. Such polymers, when compared to P3HT, exhibit a weak short-range molecular order [25].

Acknowledgments

JM acknowledges the Ministerio de Ciencia e Innovación which supported the work under Grants MAT2011-28665 and CONSOLIDER NANOLIGHTCSD2007-00046. HM acknowledges the Ministerio de Ciencia e Innovación for funding provided under Grants MAT2011-23593 and CONSOLIDER HOPECSD2007-00007. HM also acknowledges the Junta de Andalucía for Grants FQM3579 and FQM5247.

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Figure captions

Figure 1. Inverted cell architecture. The five layers of the cell are deposited on top of a transparent substrate. ITO corresponds to the cathode, TiO2-np the hole blocking layer, P3HT:PCBM the bulk hetero-junction active layer, MoO3 the electron blocking layer, and Ag the anode. When numerically determining the electric filed distribution it is assumed that the z-direction is perpendicular to all interfaces.

Figure 2. (a) Numerically calculated Jsc for 8000 different cell configurations (black solid line). The natural number on the x-axis is an arbitrary number assigned to a given configuration. The difference between one configuration and another is the thickness of the TiO2, P3HT:PCBM, and MoO3 layers. From left to right in the x-axis, the active layer thickness ranges from 60 to 220 nm. Numerically calculated Jsc when the thickness of the P3HT:PCBM layer changes from 60 to 220 nm and the thickness of the rest of the layers in the device are kept fixed to 80 nm for the TiO2-np, 100 nm for the ITO and 3 nm for MoO3 (red solid line). (b) The area marked in red in (a) is shown here in a 2D plot and corresponds to the Jsc dependence on TiO2 and MoO3 thicknesses when the ITO was fixed to 100 nm and P3HT:PCBM layer was chosen to be 91 nm. (c) Same as Fig. 2(b) but when the P3HT:PCBM was chosen to be 151 nm, corresponding to the area marked in blue in (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figure 3. (a) Calculated Jsc as a function of the active layer thickness (dashed black line) and experimentally determined Jsc for 8 different cells when the TiO2-np and MoO3 layer thicknesses are fixed to 77 nm and 3 nm, respectively. Inset: example of an AFM picture used to accurately determine all layer thicknesses. (b) Calculated Jsc as a function of the TiO2-np layer thickness (dashed black line) and experimentally determined Jsc for 5 different cells when the active and MoO3 layer thicknesses are fixed to 81 nm and 3 nm respectively. The dotted and dot-dashed lines show the changes in the Jsc pattern when the thickness of the active layer (AL) is modified. (c) Calculated Jsc as a function of the MoO3 layer thickness (dashed black line) and experimentally determined Jsc for 8 different cells when the active layer thickness ranges from 80 nm to 110 nm and the TiO2-np layer thickness is fixed to 95 nm. To account for a series resistance different than zero and a finite shunt resistance the theoretically computed curve was reduced by a 0.96 factor.

Figure 4. IV curves for different active layer thicknesses: 69 nm (blue), 102 nm (dark cyan) and 151 nm (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figure 5. (a) EQE numerically determined for a 69 nm active layer thick cell (blue solid line), experimentally measured for a 69 nm active layer thick cell (solid blue triangles), numerically determined for a 91 nm active layer thick cell (green solid line), experimentally measured for a 91 nm active layer thick cell (solid green circles), numerically determined for a 151 nm active layer thick cell (red solid line), and experimentally measured for a 151 nm active layer thick cell (solid red squares). Numerically determined IQE for a 69 nm active layer thick cell (blue dashed line), for a 91 nm active layer thick cell (green dashed line) and for a 151 nm active layer thick

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cell (red dashed line). The dotted lines connecting the experimental data points are only a guide for the eye. (b) Numerically determined reflectivities for a 69 nm active layer thick cell (blue solid line), for a 91 nm active layer thick cell (green solid line) and for a 151 nm active layer thick cell (red solid line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 1

Table 1. Device characteristic parameters.

Thickness (nm) Jsc (mA/cm2) Voc (mV) PCE (%) FF (%)69 −7.9 598 2.8 6184 −8.7 571 3.1 6391 −8.9 570 3.1 61102 −9.0 594 3.3 62110 −8.6 589 3.0 59128 −8.5 583 2.9 61142 −8.1 585 3.0 65151 −8.3 579 2.8 59

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Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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