Chapter 1. Introduction
1.2 Charge Transport and Recombination of OSCs
1.2.1 Recombination Mechanisms
Charge recombination is generally divided into two type of recombination; radiative and non- radiative. Radiative recombination is also divided into two types; band-to-band radiative recombination and stimulated emission. The band-to-band recombination is occurred when electron excited to conduction band is came back to valence band with light emission. This effect is related to how light- emitting diodes can generate photons, and this recombination processes are usually occurred in direct bandgap materials. Stimulated emission is related to lasers. In OSCs, non-radiative recombination is general loss mechanisms of energy and extracted charge carriers. In this section, type of non-radiative recombination and their detailed properties are discussed.
When the light is absorbed to semiconductors, electron is excited to conduction band (or LUMO level in organic materials) and hole is generated in valence band (or HOMO level) at the same time.
Excited electron and hole pairs (i.e., excitons) are bound by electrostatic Coulomb force, and the excitons can be easily recombined if there is insufficient energy for separation into free charge carriers.
This is known as geminate (or monomolecular) recombination of excitons.
Excitons can be dissociated into weaker bound electron-hole pairs when appropriate combination of donor and acceptor materials are used with sufficient energy difference. These weaker bound state of electron-hole pairs are called as CT states. The CT states of electron-hole pairs are separated easily into free charge carriers by internal electric field in the devices or thermal energy.23-24 It can be quenched with geminate recombination, but it is not a major loss mechanism in typical high-performance OSCs.
At early stage in OSCs, organic semiconductors have low carrier mobilities and disordered structures in thin film state. With the low mobilities, charge carriers move slowly within donor and acceptor phases which results to make many chances to recombine electrons and holes each other. This situation is well matched with Langevin theory that the important factor related to recombination is the rate of how often holes and electrons meet each other rather than time in which recombination even takes place. The Langevin recombination rate is expressed by equation (1-6);
𝑅 𝑘 𝑛𝑝 𝑛 𝜇 𝜇 𝑛𝑝 𝑛 (1-6)
where kL is the Langevin recombination prefactor, ε0εr is the dielectric permittivity of the active layer, μn is electrons mobility, μp is holes mobility, n is the electron concentration, p is the hole concentration and ni is the intrinsic carrier concentration. In real experimental situation, non-geminate recombination
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is often reduced, and the time dependent recombination is also observed compared to Langevin model which is only applied in low-mobility system.25
Trap-assisted (or Shockley-Read-Hall, SRH) recombination is occurred when the charge carriers are trapped in the state of deep level in the bandgap or trap sites of interfacial defects or impurities in materials. In addition, bimolecular recombination is also important loss mechanism in OSCs.
Monomolecular and bimolecular recombination is the main loss mechanisms in OSCs, and the recombination have been investigated via various methods; transient photoconductivity, transient absorption spectroscopy, time-delayed dual pulse experiment, light intensity dependent measurements, etc. The light intensity dependent measurement is the simplest technique that can be conducted by just varying light intensity of incident light sources via neutral density filters, etc. It is obvious that charge transport and extraction properties are different by incident light intensities. If light intensity is lower than 1 sun intensity by an order of magnitude, generated photocurrents also reduced by an order of magnitude. In this low light intensity situation, photocurrents can be affected more by trap sites, diode currents (under dark) compared to intense light intensity (1 sun). From fitting JSC vs. light intensity (Ilight) and VOC vs. Ilight graphs, information of bimolecular and monomolecular recombination can be obtained, respectively. In general, JSC is proportional to Ilights. With a log-log scale plot of JSC vs. Ilight graphs, if the graphs showed nearly linear dependence (thus, s → 1), bimolecular recombination is relatively weak in this system. (Figure 1.7a) On the contrary, if the s is lower and far from than 1, it indicates that carrier losses exist which originated from bimolecular recombination. Information of monomolecular (trap assisted or SRH) recombination can be obtained from VOC vs. Ilight graphs. VOC is expressed by equation (1-7);
𝑉 ln (1-7)
where Egap is the energy difference between the HOMOdonor and LUMOacceptor, q is the elementary charge, T is temperature in Kelvin, PD is the dissociation probability of the electron (e)-hole (h) pairs, γ is the Langevin recombination constant, NC is the effective density of states, and G is the generation rate of bound electron-hole pairs. If VOC exhibited linear dependence on ln(Ilight) in semi log plots, only bimolecular recombination is loss mechanism in the given system. If slope of VOC vs. ln(Ilight) graphs is higher than kT/q, it indicates that additional trap-assisted recombination is involved. (Figure 1.7b) Detailed experimental examples are shown from Chapter 2 to Chapter 5.
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Figure. 1. 7. Schematic graphs of (a) JSC vs. Ilight and (b) VOC vs. Ilight characteristics for typical OSCs.
Charge recombination is also related to the energy loss in OSCs. Energy loss is determined by energy difference between optical bandgap (Eg) and eVOC. Energy of CT states (ECT) is determined by energy difference of quasi-Fermi level of HOMO and LUMO for donor and acceptor materials.
Therefore Eg – ECT can be tuned by modifying and designing molecular structures of donor and acceptor.
Energy loss originated by charge recombination is defined by difference between ECT and eVOC. ECT – eVOC is typically attributed by both radiative and non-radiative recombination. In the Shockley-Queisser limit, maximum VOC is achievable of Eg – 0.3 eV due to radiative recombination. Additional energy losses are occurred by non-radiative recombination, and this is expressed by equation (1-8);
∆𝑉 , ln 𝜙 (1-8)
where ф is the radiative efficiency of the system.26 To achieve high photocurrent and open-circuit voltages, it is important to avoid recombination losses by using appropriate donor and acceptor combination, morphology control, appropriate charge transport layers, and so on.
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