Non-Langevin bimolecular recombination in low-mobility materials

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Abstract

We have investigated the bimolecular recombination coefficient (B) of charge carriers in low-mobility materials, in which the Langevin recombination is reduced: inorganic a-Si:H, μc-Si:H and the organic regioregular poly(3-hexylthiophene)/1-(3-methoxycarbonyl)propyl-1-phenyl-[6,6]-methanofullerene (RR-PHT/PCBM) blend. We have been using a multitude of experimental techniques, namely space-charge-limited current (SCLC), photogenerated charge carrier extraction by linearly increasing voltage (photo-CELIV) and double injection (DoI) current transient techniques for investigation of temperature and electric field dependencies of B. For RR-PHT/PCBM blends, we observed a weak dependence of B on electric field and the most significant reduction of Langevin recombination.

Introduction

In disordered low-mobility materials, when the charge carrier hopping distance (l) or energy dissipation length (lE) of inelastic scattering is shorter than the Coulomb radius (rC), the charge carrier bimolecular recombination is determined by the probability for the electrons and holes to meet in space. This is the so called Langevin-type recombination where the recombination coefficient is proportional to the charge carrier mobility by BL = e (μn + μp)/εε0 (here μn and μp are mobility of electrons and holes respectively; εε0 are dielectric permittivity) [1]. This is experimentally observed in amorphous inorganic (for example, a-Se [2]) and organic (for example, RRaPHT [3]) materials. The necessary condition that l or lE < rC also causes geminate recombination of Onsager-type, thus, lowering the efficiency of charge carrier photogeneration.

In order to achieve high current densities of photogenerated or injected charge carriers in electronic components, it is necessary to reduce the Langevin bimolecular recombination. Such a reduction in the bimolecular recombination coefficient has been observed in disordered materials (a-Si:H [4] and in organic polymer blends [5]). It was considered that the reduction of bimolecular recombination is caused by the separation of the electron and hole pathways due to the random potential in inorganic materials [6] or due to the nanomorphology of the bi-continuous interpenetrating network in the polymer blend [7]. There are possible other reasons of bimolecular recombination reduction, for example, due to formation of long radius excitons. In this paper, we present and discuss the results of our experimental investigation of the reduced bimolecular recombination compared to the Langevin-type (i.e. B/BL ratio) in different low-mobility materials.

Section snippets

Experimental methods

Generally the charge carrier recombination is measured from photocurrent transients after excitation by short pulse of light. However, in disordered structures the relaxation of photocurrent is caused by the time-dependence of both mobility and density of charge carriers. Therefore, for the investigation of the bimolecular recombination, we used different methods.

The following is the simplest experimental test for the existence of Langevin recombination, using space charge limited current

Results

In Fig. 3, typical hole density and mobility dependencies on time for RRaPHT are shown. By fitting the mobility relaxation as μ = at−0.42, we get the time-dependence of the Langevin recombination coefficient as B(t) = (t)/εε0. Thus, the charge carrier density follows the expressionp(t)=1p(0)+eεε0·at0.580.58-1,which is shown in Fig. 3 by the solid line. The good agreement of the experimental results and theory confirms that in low-mobility organic materials bimolecular recombination is of

Discussion

In a-Si:H, an absence of impact ionization at electric fields up to 1 MV/cm [11] points to the fact that energy dissipation length of charge carriers lE < 1.6 nm, i.e. much shorter than the Coulomb radius rC = 5 nm (at 300 K). In organic materials, the transport of charge carriers is caused by hopping, thus, the intermolecular hopping distance is much shorter than rC  16 nm. The latter shows that, after the charge carriers of opposite sign met in space, the probability for their dissociation is low. This

Conclusions

To eliminate the influence of mobility relaxation on the estimation of the bimolecular recombination coefficient, which is typical feature of disordered materials, we have been using different methods: SCLC transient techniques, photo-CELIV and DoI transient techniques. The most significant reduction of B/BL ratio (>103) has been obtained in RR-PHT/PCBM blends. This result correlates with quantum efficiency for charge generation close to unity. By decreasing the temperature or by increasing the

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