1.1

Singlet fission

Singlet fission is a mechanism found in some organic materials, that a high energy singlet exciton could generate two lower energy triplet excitons. Figure 1a shows the schematic of singlet fission. Due to energy conservation, the triplet state energy E_T needs to be about half of the singlet state energy E_S for an efficient singlet fission to occur. The singlet exciton state first transitions into a triplet-triplet (TT) pair state¹. This TT pair state can then dissociate into two individual triplet excitons, effectively achieving energy down conversion. This down conversion process can be efficient because direct transition from singlet to triplet state is not allowed or inefficient due to selection rules. However, the TT pair state is a two particle system with a mixture of 9 possible states. Among the TT pair states, there are some pair states that have singlet state characteristics. Therefore, this transition from singlet states to TT pair states and then to two triplet excitons are allowed. In fact, there have been multiple studies showing efficient singlet fission rates in different organic materials².

Figure 1.

(a) Schematics of singlet fission. Singlet exciton Sj first transitions to a TT pair state and then splits into two triplet exciton states T₁. Direct transition from S₁ to T₁ is inefficient. (b) Efficiency of silicon solar cell with down conversion. This breakdown shows an additional 7.8% of extra energy collected with down conversion on an E_g=1.12eV solar cell.

1.2

Down conversion to overcome the Shockley-Queisser limit

In a perfect single junction solar cell, the theoretical maximum power conversion efficiency (PCE) is around 33.7%³. This is mainly due to the trade-off between thermalization loss for photons collected above bandgap and absorption loss below bandgap. With a down converter, that converts high energy excitons/photons 2E to two lower energy excitons/photons E, a solar cell can extract extra energy from thermalization loss. Figure 1b shows the breakdown of extra energy collected for solar cells with down conversion. In the blue area, the solar cell could utilize about twice more photocurrent where the spectrum E_hv > 2E_g. In this case, a Eg = 1.14eV solar cell collects about 33.4% energy from the spectrum, where down conversion can collect another additional 7.8%, giving the possibility of overcoming the Shockley-Queisser limit. In a silicon solar cell, the maximum intrinsic efficiency can be further limited to around 29% due to non-radiative Auger recombination⁴. Therefore, a silicon solar cell utilizing perfect down conversion has a theoretical maximum 35% PCE⁵.

1.3

Magnetic field effect in singlet fission rates

An external magnetic field can affect the singlet fission rates. This is particularly useful for identifying singlet fission as well as assisting the characterization of fission efficiencies. The magnetic field effect (MFE) of singlet fission rate comes from the modification of the amount of TT states that have singlet characteristics. As shown in figure 1a, TT states assists the transition from a singlet exciton to two triplet excitons. The fission rate first increases with magnetic field (0~0.03T) due to increasing TT pair states (3 to 6) with singlet characteristics. TT pair states then decrease to 2 states with singlet characteristics at high magnetic fields (0.03T→0.5T), thus slowing the fission rate.

The singlet fission MFE gives a distinctive dependency. In figure 2a, the triplet population MFE follows the fission rate because slower fission rates result in less triplet excitons. However, the singlet population MFE is oppo site where a slower fission rate results in more singlet excitons. These assists identification of singlet fission in organic materials. For example in figure 2b, the green and red shows the fluorescence change of the tetracene with magnetic fields, which follows the trend of singlet population. The blue curve shows the photocurrent change in a tetracene photovoltaic device. This shows the photocurrent are mainly collected from triplet excitons.

Figure 2.

(a) Simulated singlet and triplet population change under external magnetic fields. (b) MFE of fluorescence change in tetracene thin film (red) and crystals (green). MFE of photocurrent change in tetracene devices (blue)⁶.

2.1

Internal quantum efficiency of tetracene photovoltaics

Singlet exciton fission in photovoltaic devices is complicated by the presence of additional important loss pathways such as singlet exciton dissociation into charges. Practical characterization of singlet fission requires measurements of the triplet yield in devices. A lower limit for this yield can be defined by the internal quantum yield (IQE), which is the ratio of charges generated in the cell to photons absorbed for the specific layer. In a tetracene device, determination of the IQE is especially challenging, since its optical absorption overlaps with the usual acceptor material C₆₀.

The tetracene photovoltaic devices are fabricated with a PEDOT:PSS layer spin-coated on a cleaned ITO glass substrate. Then, m-MTDATA (8nm), tetracene (x nm), C60 (30 nm), BCP (15 nm) and silver (100 nm) are deposited onto the substrate subsequently with thermal evaporation. For thinner tetracene layer devices, we build photodetector structures with multiple pairs of tetracene/C₆₀ layers. To determine the IQE of tetracene in a solar cell device from external quantum efficiency (EQE), we need to calculate the absorption of each layer in the device to calculate the contributions. For each material, the optical n and k parameters are measured from wavelength dependent transmissions and reflections. With an optical transfer matrix¹⁰, we can estimate each layer’s absorption spectra in the device, fitting the overall wavelength dependent EQE by separately adjusting the respective IQEs of all layers, mainly tetracene and C₆₀.

To find the optimal, we measure the IQEs of different tetracene devices, and obtain a maximum IQE of 127±18% with tetracene layer thickness x = 25 nm. This optimal thickness is a balance between a thicker tetracene layer for more triplet exciton generation and a thinner layer for better collection efficiency. The IQE dependency on tetracene thickness is shown in figure 3d. Alongside is the comparison to the IQE of pentacene devices, which shows a better IQE of 160% at a thinner layer due to faster singlet fission rates.

Figure 3.

(a) and (b) are the fluorescence change δ_F and photocurrent change δ_I under a magnetic field (>0.4T) in both tetracene and pentacene. The fluorescence changes are measured in the same tetracene/C₆₀ structure to the photocurrent devices. (c) Tetracene and pentacene triplet exciton yields are modeled from fluorescence and photocurrent changes. (d) The IQEs of thin layers of pentacene and tetracene reflect the changes in triplet yield, and triplet diffusion losses in thick films.

2.2

Using magnetic field effect to characterize triplet yields

The MFE can also provide a quantitative model of the triplet exciton yield of tetracene. In figure 3ab, we plot the fluorescence and photocurrent change under large magnetic fields (>0.4T). The tetracene fluorescence change here is measured on a thin film which consists of the same tetracene/C₆₀ layers without the other layers. The photocurrent changes are calculated into consideration of its corresponding tetracene IQEs in figure 3d.

To calculate triplet yields, we model the exciton dynamics in the devices with a singlet fission rate at 0 and high field k_f0 k_fs, singlet exciton dissociation rate k_s (d) which depends on distance, and radiative rate k_R. For simplicity, we normalize all rates to k_f0, which gives us high field fission rate χ_fB, singlet dissociation rate χ_s(d) and radiative rate χ_R. With these rates, we can deduct the fluorescence and photocurrent change as,

Fitting the two equations (1) and (2) to δ_F and photocurrent change δ_I in figure 3ab, we can solve all the rates and singlet dissociation rate χ_s (d) at each tetracene thickness. This can then calculate the triplet yields with different tetracene devices which is shown in figure 3c. We can see that the tetracene triplet exciton yields are close to 200% for thick tetracene layers. However, as a comparison to pentacene, the tetracene triplet generation is much slower. For our optimal IQE device, the triplet yield is 153±5%.

3.1

Device structure

Figure 4a shows a simple schematics of the device structure. The silicon wafers are first clean with the RCA protocol. The silicon surface is then passivated with atomic layer deposition with HfO_xN_y. After passivation, 30 nm of tetracene is thermally deposited onto the silicon substrate.

3.2

Measurement setup

To measure the magnetic field effect of the silicon emission, we use an infrared spectrometer instead of an IR detector to make sure that the photoluminescence comes from silicon emission. Figure 4b is the setup to measure the MFE of the silicon emission spectrum. The samples are excited with a strong 532nm laser and placed between a strong electromagnet. This setup is also modified to measure the excitation spectrum, which is the silicon emission with different excitation wavelengths. The magnet is removed and the excitation light source is changed to a SuperK. Because silicon PL efficiency is also dependent on excitation wavelength, we also measure the silicon excitation spectrum without tetracene as normalization and comparison.

3.3

Photoluminescence result

The first indication of triplet exciton transfer is shown in figure 5a. The silicon emission first increases with small external magnetic fields and then decreases at large fields. This is the same trend as triplet MFE (figure 2a), which indicates that the silicon emissions are mediated by triplet excitons from tetracene.

Figure 5.

(a) Silicon spectrum changes with different magnetic fields. This spectral MFE is measured on a tetracene/HfO_xN_y(0.8 nm)/silicon device with 532 nm excitation. (b) The silicon emission excitation spectrum (blue) from the same device structure. The red and green curves are the fitted silicon and tettacene absorption contributions.

In figure 5b, the excitation spectra also shows the increase of silicon PL in the tettacene absorption region for wavelengths < 550nm. The red and green dashed curves are the fitted silicon and tettacene absorption to the excitation spectra, which shows the tettacene absorption contribution in the silicon PL.

3.4

Characterizing triplet exciton transfer

However, due to the electric-field-effect passivation possibility (figure 4a, orange), the above result does not directly indicate the triplet excitons transferred to the silicon. To determine triplet exciton transfer, we need to measure the passivation effects and exciton transfer separately. Silicon PL comes from the electron-hole pairs generated in silicon. When exciting with 532 nm, the triplet exciton generated in the tetracene can both affect the surface passivation and exciton transfer to increase the silicon PL. However, if we excite the sample with 785 nm at the same time with 532 nm, the electron-hole pairs generated by this red laser will be affected more by the passivation effects.

In figure 6a, we can see that the 532 nm + 785 nm, with red excitation intensity >> green, the magnetic field effect is less than 532 nm excitation. This indicates that other than magnetic field effect from passivation, there is also triplet exciton transfer to increase the silicon PL change.

Figure 6.

(a) The effect of the applied magnetic field on the photoluminescence of photoluminescent samples photoexcited at λ = 532 nm. To quantify the electric-field-effect passivation we employ a second beam at λ = 785 nm that is sensitive to passivation changes but does not drive energy transfer from the tetracene. The solid lines are fit to the singlet-fission characteristic in the tetracene, as determined from the fluorescence. (b) Silicon PL MFE with respect to HfO_xN_y thickness.

Using the data from the 532 nm and 532 nm + 785 nm excitation photoluminescence measurements that are shown in figure 6a, we employ a model to quantify the total exciton yields, which is the number of excitons transferred to silicon divided by the number of singlet excitons created in tettacene. By comparing the effects of the applied magnetic field on the photoluminescence of the samples, we obtain a peak total exciton yield of 133±13%.

3.5

Optimizing passivation layer thickness

We have also measured the MFE of the silicon PL with different HfO_xN_y passivation thicknesses. The optimal thickness is at 0.8 nm, shown in figure 6b. This is a tradeoff between the lack of surface passivation at the silicon surface, and blocking the triplet exciton for transferring into silicon. The fact that it is possible to turn this effect off by increasing the interlayer thickness suggests the presence of a tunneling process.