Understanding the Thickness-Dependent Performance of Organic Bulk Heterojunction Solar Cells: The Influence of Mobility, Lifetime, and Space Charge

We investigate the reasons for the dependence of photovoltaic performance on the absorber thickness of organic solar cells using experiments and drift-diffusion simulations. The main trend in photocurrent and fill factor versus thickness is determined by mobility and lifetime of the charge carriers. In addition, space charge becomes more and more important the thicker the device is because it creates field free regions with low collection efficiency. The two main sources of space-charge effects are doping and asymmetric mobilities. We show that for our experimental results on Si-PCPDTBT:PC₇₁BM (poly­[(4,40-bis­(2-ethylhexyl)­dithieno­[3,2-<i>b</i>:20,30-<i>d</i>]­silole)-2,6-diyl-<i>alt</i>-(4,7-bis­(2-thienyl)-2,1,3-benzothiadiazole)-5,50-diyl]:[6,6]-phenyl C71-butyric acid methyl ester) solar cells, the influence of doping is most likely the dominant influence on the space charge and has an important effect on the thickness dependence of performance

Understanding the Effect of Donor Layer Thickness and a MoO₃ Hole Transport Layer on the Open-Circuit Voltage in Squaraine/C₆₀ Bilayer Solar Cells

Small molecule organic solar cells are becoming increasingly efficient through improved molecular design. However, there is still much to be understood regarding device operation. Here we study bilayer solar cells employing a 2,4-bis­[4-(<i>N,N</i>-diisobutylamino)-2,6-dihydroxyphenyl] squaraine (SQ) donor and fullerene acceptor to probe the effect of donor layer thickness and a MoO₃ electron transport layer on device performance. The thickness of SQ is seen to drastically affect the open-circuit voltage (<i>V</i>_OC) and fill factor (FF), while the short circuit current is not altered significantly. The fact that the <i>V</i>_OC of the bilayers with thin (6 nm) donor layers shows a strong dependence on the material and workfunction of the anode cannot be explained with a model for a perfect bilayer. Recombination of electrons from C₆₀ at the anode contact has to be possible to understand the strong effect of the anode workfunction. Using numerical simulations and a simple two-diode model we show that the most likely interpretation of the observed effects is that for thin SQ layers, the roughness of the interface is high enough to allow electrons in the C₆₀ to tunnel through the SQ to recombine directly at the anode. Thicker SQ layers will block most of these recombination pathways, which explains the drastic dependence of <i>V</i>_OC on thickness. Bulk-heterojunction devices were also fabricated to illustrate the effect of anode material on the <i>V</i>_OC

Understanding the Thickness-Dependent Performance of Organic Bulk Heterojunction Solar Cells: The Influence of Mobility, Lifetime, and Space Charge

We investigate the reasons for the dependence of photovoltaic performance on the absorber thickness of organic solar cells using experiments and drift-diffusion simulations. The main trend in photocurrent and fill factor versus thickness is determined by mobility and lifetime of the charge carriers. In addition, space charge becomes more and more important the thicker the device is because it creates field free regions with low collection efficiency. The two main sources of space-charge effects are doping and asymmetric mobilities. We show that for our experimental results on Si-PCPDTBT:PC₇₁BM (poly­[(4,40-bis­(2-ethylhexyl)­dithieno­[3,2-<i>b</i>:20,30-<i>d</i>]­silole)-2,6-diyl-<i>alt</i>-(4,7-bis­(2-thienyl)-2,1,3-benzothiadiazole)-5,50-diyl]:[6,6]-phenyl C71-butyric acid methyl ester) solar cells, the influence of doping is most likely the dominant influence on the space charge and has an important effect on the thickness dependence of performance

On the Differences between Dark and Light Ideality Factor in Polymer:Fullerene Solar Cells

Ideality factors are derived from either the slope of the dark current/voltage curve or the light intensity dependence of the open-circuit voltage in solar cells and are often a valuable method to characterize the type of recombination. In the case of polymer:fullerene solar cells, the ideality factors derived by the two methods usually differ substantially. Here we investigate the reasons for the discrepancies by determining both ideality factors differentially as a function of voltage and by comparing them with simulations. We find that both the dark and light ideality factors are sensitive to bulk recombination mechanisms at the internal donor:acceptor interface, as is often assumed in the literature. While the interpretation of the dark ideality factor is difficult due to resistive effects, determining the light ideality factor <i>differentially</i> indicates that the open-circuit voltage of many polymer:fullerene solar cells is limited by surface recombination, which leads to light ideality factors decreasing below one at high voltage

Understanding the Apparent Charge Density Dependence of Mobility and Lifetime in Organic Bulk Heterojunction Solar Cells

Energetic disorder in organic semiconductors leads to strong dependence of recombination kinetics and mobility on charge density. However, observed mobilities and reaction orders are normally interpreted assuming uniform charge carrier distributions. In this paper, we explore the effect of the spatial distribution of charge on the determination of mobility and recombination rate as a function of average charge density. Since the spatial gradient changes when the thickness of a device is varied, we study thickness series of two different polymer:fullerene systems and measure the charge density dependence of mobility and lifetime. Using simulations, we can show that the high apparent reaction orders frequently observed in the literature result from the spatial gradient of charge density at open circuit. However, the mobilities, measured at short circuit, are less affected by the gradients and therefore may show substantially different apparent charge density dependence than the recombination constants, especially for small device thicknesses

Performance Evaluation of Semitransparent Perovskite Solar Cells for Application in Four-Terminal Tandem Cells

The efficiency of perovskite-based tandem solar cells and the respective efficiency gain over the single-junction operation of the bottom cell strongly depend on the performance of the component cells. Thus, a fair comparison of reported top cells is difficult. We therefore compute the tandem cell efficiency for the combination of several semitransparent perovskite top solar cells and crystalline silicon or chalcopyrite bottom cells from the literature. We focus on four-terminal configurations but also estimate and discuss the differences between four- and two-terminal configurations. For each top cell, we thereby determine the tandem cell performance as a function of the bottom cell efficiency, which results in a linear relationship. From these data, we extract two parameters to quantify the suitability of the top cell: (i) the slope of the tandem vs. bottom cell efficiency, which is the effective transparency of the top cell, and (ii) the tandem cell efficiency for a targeted bottom cell. These two figures of merit were calculated for a representative set of bottom cells and may serve for comparison of semitransparent perovskite top cells in the future

Analysis of the Relationship between Linearity of Corrected Photocurrent and the Order of Recombination in Organic Solar Cells

We address the claim that the dependence of the “corrected photocurrent” (defined as the difference between the light and dark currents) upon light intensity can be used to determine the charge recombination mechanism in an organic solar cell. We analyze a poly(3-hexylthiophene):[6,6]-phenyl C61-butyric acid methyl ester (P3HT:PCBM) device using corrected photocurrent and transient photovoltage experiments and show that whereas the corrected photocurrent is linear in light intensity the charge recombination rate scales superlinearly with charge carrier density. We explain this apparent discrepancy by measuring the charge carrier densities at different applied voltages and light intensities. We show that it is only safe to infer a linear recombination mechanism from a linear dependence of corrected photocurrent on light intensity under the following special conditions: (i) the photogenerated charge carrier density is much larger than the dark carrier density and (ii) the photogenerated carrier density is proportional to the photogeneration rate

Performance Evaluation of Semitransparent Perovskite Solar Cells for Application in Four-Terminal Tandem Cells

The efficiency of perovskite-based tandem solar cells and the respective efficiency gain over the single-junction operation of the bottom cell strongly depend on the performance of the component cells. Thus, a fair comparison of reported top cells is difficult. We therefore compute the tandem cell efficiency for the combination of several semitransparent perovskite top solar cells and crystalline silicon or chalcopyrite bottom cells from the literature. We focus on four-terminal configurations but also estimate and discuss the differences between four- and two-terminal configurations. For each top cell, we thereby determine the tandem cell performance as a function of the bottom cell efficiency, which results in a linear relationship. From these data, we extract two parameters to quantify the suitability of the top cell: (i) the slope of the tandem vs. bottom cell efficiency, which is the effective transparency of the top cell, and (ii) the tandem cell efficiency for a targeted bottom cell. These two figures of merit were calculated for a representative set of bottom cells and may serve for comparison of semitransparent perovskite top cells in the future

Sensitivity of the Mott–Schottky Analysis in Organic Solar Cells

The application of Mott–Schottky analysis to capacitance–voltage measurements of polymer:fullerene solar cells is a frequently used method to determine doping densities and built-in voltages, which have important implications for understanding the device physics of these cells. Here we compare drift-diffusion simulations with experiments to explore the influence and the detection limit of doping in situations where device thickness and doping density are too low for the depletion approximation to be valid. The results of our simulations suggest that the typically measured values on the order of 5 × 10¹⁶ cm^–3 for doping density in thin films of 100 nm or lower may not be reliably determined from capacitance measurements and could originate from a completely intrinsic active layer. In addition, we explain how the violation of the depletion approximation leads to a strong underestimation of the actual built-in voltage by the built-in voltage <i>V</i>_MS determined by Mott–Schottky analysis

Competition between the Charge Transfer State and the Singlet States of Donor or Acceptor Limiting the Efficiency in Polymer:Fullerene Solar Cells

We study the appearance and energy of the charge transfer (CT) state using measurements of electroluminescence (EL) and photoluminescence (PL) in blend films of high-performance polymers with fullerene acceptors. EL spectroscopy provides a direct probe of the energy of the interfacial states without the need to rely on the LUMO and HOMO energies as estimated in pristine materials. For each polymer, we use different fullerenes with varying LUMO levels as electron acceptors, in order to vary the energy of the CT state relative to the blend with [6,6]-phenyl C61-butyric acid methyl ester (PCBM). As the energy of the CT state emission approaches the absorption onset of the blend component with the smaller optical bandgap, <i>E</i>_opt,min ≡ min­{<i>E</i>_opt,donor; <i>E</i>_opt,acceptor}, we observe a transition in the EL spectrum from CT emission to singlet emission from the component with the smaller bandgap. The appearance of component singlet emission coincides with reduced photocurrent and fill factor. We conclude that the open circuit voltage <i>V</i>_OC is limited by the smaller bandgap of the two blend components. From the losses of the studied materials, we derive an empirical limit for the open circuit voltage: <i>V</i>_OC ≲ <i>E</i>_opt,min/<i>e</i> – (0.66 ± 0.08)­eV