Relation between charge carrier mobility and lifetime in organic photovoltaics
Chellappan Vijila, Samarendra P. Singh, Evan Williams, Prashant Sonar, Almantas Pivrikas, Bronson Philippa, Ronald White, Elumalai Naveen Kumar, S. Gomathy Sandhya, Sergey Gorelik, Jonathan Hobley, Akihiro Furube, Hiroyuki Matsuzaki, and Ryuzi Katoh. Journal of Applied Physics, doi:10.1063/1.4829456 (2013).
In a solar cell, a key energy loss mechanism is the recombination of electrons (negative charges) and holes (positive charges). Recombination occurs when these oppositely charged species meet and annihilate, converting their energy into heat or light. To make efficient solar cells, this recombination must be minimised, because every charge carrier that recombines is one that does not contribute fully to the power that is generated.
A useful concept for understanding recombination is the charge carrier lifetime. The lifetime gives an approximate time scale for how long a charge carrier can expect to survive recombination. It does not mean that a charge carrier will survive for exactly the lifetime, rather, it gives a typical (or average) time scale.
The lifetime depends upon the concentration of charge carriers inside the device. This is intuitively obvious: if the concentration is higher, then any given carrier will many opportunities to meet an oppositely charged partner and annihilate. Conversely, if the concentration is low, there are few potential partners around, and carriers will be forever alone. (But this is okay because lonely carriers survive for longer.)
There is a theoretical prediction for the strength of recombination due to Langevin in 1903. Langevin’s prediction from over a hundred years ago turns out to be an excellent description of many organic semiconductors. Langevin predicted that the strength of recombination should be proportional to the mobility of the carriers; in other words, if the carriers move twice as fast, they should also recombine twice as quickly.
If the strength of recombination is proportional to the mobility of carriers, then this presents a problem for organic solar cells. One wants to make the mobility as fast as possible to extract charges before they recombine. We want the transit time (the time taken to move through the film) to be less than the lifetime. Unfortunately, if Langevin’s prediction is true, then decreasing the transit time will also decrease the lifetime! You can’t change one without changing the other. This is a serious problem because it suggests that improving charge carrier mobility is less useful than it might otherwise appear.
This paper presents an experimental validation of this prediction. We vary the mobility of an organic solar cell by changing the temperature from room temperature down to 120 K. At the low temperatures, the mobility is reduced by more than ten times. (Lower temperatures equate to lower mobilities because organic materials use thermal energy to assist the hopping of charges from one place to another.) We measured the mobility and the carrier lifetime across this range of temperatures. As the transit time decreases, so does the lifetime. This is exactly the prediction of Langevin. Consequently, increasing the mobility is not enough to obtain higher performance organic solar cells. It is also necessary to find materials that disobey the Langevin theory. There are some materials like that, but unfortunately they’re rare. It’s not clear how to deliberately design new “non-Langevin” materials. Finding such design rules is an important open problem.