Tail states recombination limit of the open circuit voltage in bulk heterojunction organic solar cells Ling Li ⇑ , Jang Hyuk Kwon, Jin Jang Information Display Department, Kyung Hee University, Seoul, Republic of Korea article info Article history: Received 28 September 2011 Received in revised form 14 November 2011 Accepted 16 November 2011 Available online 3 December 2011 Keywords: Hopping transport Organic solar cell Open circuit voltage Bimolecular recombination abstract An analytical theory is presented for bimolecular recombination through tail states and open circuit voltage in bulk heterojunction organic solar cells. It is developed rigorously using the hopping transport and the drift diffusion theory. Based on the proposed model, a variety of temperature, energy disorders of the material and illumination intensity dependencies of the open circuit voltage can be well described. Good agreement between the calculation and recent experimental data is found. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Recombination processes in disordered hopping trans- port is of special current interest because it is one of the main factors limiting the conversion efficiency in organic solar cells. In the low mobility organic semiconductor, when the charge carrier hopping distance or the energy dissipation length of inelastic scattering is shorter than the Coulomb radius, the charge carrier bimolecular recom- bination is determined by the probability that the elec- trons and holes meet in space. This process is usually described by the Langevin theory [1], where the total rate of bimolecular recombination R rec is proportional to the charge carrier mobility and carrier concentration by R rec ¼ eðl e þ l h Þnp=ee 0 ¼ bnp, where l e and l h are the electron and hole motilities, respectively, ee 0 is the dielec- tric permittivity, n is the electron concentration, p is hole concentration, e is the elementary electronic charge, and b ¼ eðl e þ l h Þ=ee 0 is defined as the bimolecular recombi- nation coefficient [2]. Relative analytical and numerical models for bimolecular recombination rate or recombina- tion coefficient in the two dimensional lamellar structures of RRP3HT have been developed recently [2–4]. It was found that the recombination coefficient indeed depends on the total carrier concentration and the concentration dependence of the recombination rate should obey the power law as R rec / n c ¼ n 2:43 ; ð1Þ and thus b is weakly dependent on n as b / n 0:43 : ð2Þ These results were verified by Monte Carlo simulation [2]. In regular organic solar cell, the power law R rec / n c has also been reported [5–10]. However, experimental data show that the parameter c should be temperature depen- dent [11]. Moreover, charge transport in organic solar cells is typically described by multiple trapping or variable range hopping between the localized states [12–18], which should be taken into account as well in the recombination model. In this paper, we will present an analytical bimolecular recombination coefficient model to include the concentra- tion dependent mobility and the disorder of organic mate- rials. Based on this recombination theory, a temperature, light intensity and disorder dependent open circuit voltage of bulk heterojunction organic solar cell is formulated. 1566-1199/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2011.11.006 ⇑ Corresponding author. E-mail address: lingli@khu.ac.kr (L. Li). Organic Electronics 13 (2012) 230–234 Contents lists available at SciVerse ScienceDirect Organic Electronics journal homepage: www.elsevier.com/locate/orgel