Langevin electron hole recombination

Van der Holst JJM, van Cost FWA, Coehoom R, Bobbert PA (2009) Electron-hole recombination in disordered organic semiconductors validity of the Langevin formula. Phys Rev B 80 235202... 

It is interesting to note that in the Langevin recombination mechanism with the yeh expressed by the sum of the individual carrier mobilities (4), the interrelation between z/e,h and po switches to the relations between electron and hole... 

The probability of bimolecular recombination is proportional to the product of the electron and hole concentrations and may become important for high-intensity exposures. In low-mobility materials, bimolecular recombination is usually described by a theoiy due to Langevin (1903). LangeviiTs expression for the recombination coefficient is... 

Non-geminate recombination can also limit the performance of an OPV [44,59, 60]. On the nanoscale, the degree of non-geminate recombination is perhaps most conveniently described by the non-geminate rate constant, f (such that finp is the total rate of non-geminate recombination, where n and p are the local electron and hole densities respectively). Expectations of the non-geminate recombination rate often stem from the Langevin equation ... 

Because Qcoii is a direct measure of the charge present in the layer at a delay time fd, the recombination dynamics can be determined via an iterative procedure [171]. For the data shown in Fig. 20, this analysis yields y = 3.5xl0 m s and y= 1.2 X 10 m s for the chloroform as-cast and the annealed P3HT PCBM layer, respectively. The value for the annealed sample agrees very well with the bimolecular recombination coefficient measured by TAS at carrier densities typical for steady-state AMI.5 illumination (see, e.g., [189, 195]). To compare these values to the Langevin limit, the mobilities of the electrons and the holes in the blend must be known. Information on these quantities can be gained from drift-diffusion simulations of the photocurrent transients with different collection biases (see Fig. 20b). This yields mobilities of 1.2 x 10" m and... 

---