Ideal diode equation for organic heterojunctions. II. The role of polaron pair recombination

In paper I [N. C. Giebink, G. P. Wiederrecht, M. R. Wasielewski, and S. R. Forrest, Phys. Rev. B 82, 155305 (2010)], we proposed that current transport in a donor-acceptor heterojunction (HJ) depends on the balance of polaron pair (PP) dissociation and recombination. Here, we directly investigate these processes in archetype planar copper phthalocyanine $\left(\text{CuPc}\right)/{\text{C}}_{60}$ and boron subpthalocyanine chloride $\left(\text{SubPc}\right)/{\text{C}}_{60}$ HJs. Using intensity-modulated photocurrent spectroscopy (IMPS) along with emission from interfacial $\text{Pc}/{\text{C}}_{60}$ exciplex states, we monitor the geminate PP density at the HJ as a function of bias and illumination intensity. We find that the $\text{SubPc}/{\text{C}}_{60}$ PP density is limited by the dynamics of dissociation, where it increases from short circuit, and peaks at open circuit. In contrast, that of $\text{CuPc}/{\text{C}}_{60}$ is dominated by faster recombination kinetics and declines monotonically over the same voltage domain. We conclude that the PP recombination rate depends on electric field, and propose a simple expression that qualitatively explains the observed exciplex luminescence and IMPS behavior for these HJs. Our results provide insight into polaron pair recombination, which governs the current-voltage characteristics of organic heterojunctions in the dark and under illumination.

Figure 1

(Color online) (a) Emission spectra of the two solar cells. The red solid line shows $\text{SubPc}/{\text{C}}_{60}$ electroluminescence obtained at a constant drive current of $450\text{mA}/{\text{cm}}^2$. Black closed and blue open circles denote $\text{SubPc}/{\text{C}}_{60}$ and $\text{CuPc}/{\text{C}}_{60}$ photoluminescence, respectively, excited at ${\lambda }_{ex}=442\text{nm}$ with a modulated intensity of $2\text{mW}/{\text{cm}}^2$ rms. (b) Absolute $\text{SubPc}/{\text{C}}_{60}$ photoluminescence intensity measured for the following structure: BCP (10 nm)/${\text{C}}_{60}$ $\left(X\text{nm}\right)$/SubPc (11 nm) deposited on quartz, where $X=10$, 20, 30, and 40 nm. Inset: open squares and circles show the intensity for SubPc fluorescence and exciplex/fullerene emission integrated over the wavelength domains ${\lambda }_{em}=\left\{575,670\right\}\text{nm}$ and ${\lambda }_{em}=\left\{730,800\right\}\text{nm}$, respectively. Lines indicate the predictions of a combined optical interference and diffusion model, where the exciplex emission is taken to be proportional to the exciton diffusive flux reaching the $\text{SubPc}/{\text{C}}_{60}$ interface. The fluorescence intensity of SubPc decreases in spite of its constant thickness due to an interference minimum that develops at its location as the ${\text{C}}_{60}$ thickness increases.

Figure 2

(Color online) (a) Photoluminescence intensity as a function of electrical bias for $\text{CuPc}/{\text{C}}_{60}$ and $\text{SubPc}/{\text{C}}_{60}$ HJ devices obtained for a steady-state optical bias intensity of $10\text{mW}/{\text{cm}}^2$. The ${\lambda }_{em}=730\text{nm}$ trends follow the intensity of exciplex emission from the heterojunction of each cell whereas the ${\lambda }_{em}=615\text{nm}$ trend follows the SubPc fluorescence intensity. Solid lines are a guide for the eyes. (b) $\text{SubPc}/{\text{C}}_{60}$ exciplex emission for optical biases of 0.8 and $30\text{mW}/{\text{cm}}^2$, where emission from the $0.8\text{mW}/{\text{cm}}^2$ bias has lower intensity because the modulated signal excitation beam was decreased from 2 to $0.2\text{mW}/{\text{cm}}^2$ to prevent it from dominating the optical bias. The current-voltage characteristics for each device, obtained concurrently with the luminescence data, are shown by solid lines, with the scale on the right-hand ordinate. Red lines through the intensity data denote linear fits to estimate the emission peak positions, which scale with open-circuit voltage.

Figure 3

(Color) (a) Cole-Cole representation of IMPS for the $\text{SubPc}/{\text{C}}_{60}$ cell. Near short circuit, the complex quantum efficiency, $\tilde{\Phi }$ accumulates a small phase lag with increasing modulation frequency due to the charge-carrier transit time from the interface to the contacts. At open circuit, $\tilde{\Phi }$ exhibits a phase advance due to superposition of an oppositely directed bimolecular recombination current at the heterojunction. (b) Similar IMPS spectra obtained for $\text{CuPc}/{\text{C}}_{60}$. The contraction $\left|\tilde{\Phi }\right|\to 0$ and lack of phase advance at open circuit indicates that free carrier generation is suppressed due to geminate recombination.

Figure 4

(Color online) (a) Simulated IMPS spectra assuming constant $k_{PPr}={\left(100\text{ns}\right)}^{-1}$ (black solid lines) and ${\left(5\text{ns}\right)}^{-1}$ (blue dashed lines) using Eq. (5) in the text. (b) Simulated IMPS spectra assuming the field-dependent form for $k_{PPr}$ as given by Eq. (6) in text. In this case, the zero-field rates are $k_{PPr0}={\left(100\text{ns}\right)}^{-1}$ (black solid lines) and ${\left(5\text{ns}\right)}^{-1}$ (blue dashed lines). The inset shows the predicted polaron pair density in each case (solid lines), that agree with the $\text{SubPc}/{\text{C}}_{60}$ (black circles) and $\text{CuPc}/{\text{C}}_{60}$ (blue squares) exciplex data of Fig. 2a, up to the open-circuit voltage.

Figure 5

(Color online) Proposed field-dependent model of the recombination rate, $k_{PPr}$. The interfacial electric field modifies the polaron pair potential, and hence the activation energy required for polaron pair recombination. In reverse bias, $F_I<0$, reducing the PP potential to favor dissociation and increasing the barrier for recombination. As $F_I$ increases, the dissociation rate decreases and the recombination rate increases. The polaron pair Coulomb potential is asymmetric due to the offset between donor and acceptor lowest unoccupied molecular orbitals, whose energy scheme is shown at the top of the figure.