Device model for the operation of polymer/fullerene bulk heterojunction solar cells

We have developed a numerical device model that consistently describes the current-voltage characteristics of polymer:fullerene bulk heterojunction solar cells. Bimolecular recombination and a temperature- and field-dependent generation mechanism of free charges are incorporated. It is demonstrated that in poly[2-methoxy-5-($3^{\prime },7^{\prime }$-dimethyloctyloxy)-$p$-phenylene vinylene]- ($\mathrm{O}{\mathrm{C}}_1{\mathrm{C}}_{10}\text{−}\mathrm{PPV}$-) and [6,6]-phenyl ${\mathrm{C}}_{61}$-butyric acid methyl ester- (PCBM-) $(1:4\mathrm{wt.}\%)$ based solar cells space-charge effects only play a minor role, leading to a relatively constant electric field in the device. Furthermore, at short-circuit conditions only 7% of all free carriers are lost due to bimolecular recombination. The model predicts that an increased hole mobility together with a reduction of the acceptor strength of $0.5\mathrm{eV}$ will lead to a maximum attainable efficiency of 5.5% in the PPV/PCBM-based solar cells.

Figure 1

(a) Schematic of the energy levels (energies given in eV) of the electron donating and electron accepting materials. After charge separation, the electron and hole are transported through the respective materials and collected by the electrodes. As the anode a layer of poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS) deposited on top of indium-tin-oxide (ITO) was used, while on top of the active layer lithium fluoride and aluminum were deposited by thermal evaporation under vacuum. (b) The resulting device model in the metal-insulator-metal representation with positive applied bias $V_a$, under operating conditions ($V_a$ smaller than open-circuit voltage).

Figure 2

Schematic of the charge carrier separation at the interface between donor $\left(D\right)$ and acceptor $\left(A\right)$. Upon excitation of the donor, an exciton is created which diffuses through the donor until it reaches the interface. At the interface, the electron is transfered to the acceptor, thus forming a bound electron-hole pair. This pair can either dissociate into free carriers or decay to the ground state.

Figure 3

Flow diagram of the simulation program. To solve the basic equations, Gummel iteration is used. First a guess is made for the potential and carrier densities. Subsequently, a correction $\delta \psi$ to the guess for the potential is calculated from the Poisson equation. This correction is added to the guessed potential and this is repeated until convergence is reached. Next, the carrier densities are calculated from the new potential by solving the continuity equations. This entire procedure is repeated until the change in the carrier densities becomes very small, i.e., until convergence is reached.

Figure 4

Photocurrent density $J_{\mathrm{ph}}$ as a function of effective applied voltage $(V_0-V_a)$. The symbols represent experimental data of $\mathrm{O}{\mathrm{C}}_1{\mathrm{C}}_{10}\text{−}\mathrm{PPV}∕\mathrm{PCBM}$ devices at room temperature. The solid line denotes the simulation, while the dashed line represents the result of Sokel and Hughes.

Figure 5

Experimental dark (squares) and light current (circles) of an $\mathrm{O}{\mathrm{C}}_1{\mathrm{C}}_{10}\text{−}\mathrm{PPV}∕\mathrm{PCBM}$ device at room temperature. The solid line denotes the simulation.

Figure 6

The device at short circuit, (a) shows the potential and current densities, (b) shows the carrier densities and the net generation rate.

Figure 7

The device at open circuit, (a) shows the potential and current densities, (b) shows the carrier densities and the net generation rate. Note that the scale on the right-hand side of (a) is enlarged as compared to Fig. 6a.