Determining the photoelectric parameters of an organic photoconductor by the photoelectromotive-force technique

We report on a theoretical model to describe the non-steady-state photoelectromotive-force (photo-EMF) effect in organic photoconductors. Unlike the conventional theory of the photo-EMF effect developed for crystalline materials, this model accounts for the field dependence of the charge generation quantum efficiency and charge carrier mobility. To verify our findings a detailed experimental study of the charge carrier generation and transport processes in a organic photorefractive composite was performed using the photo-EMF effect and ac photocurrent measurements. The investigated composite was based on a conjugated triphenyldiamine based polymer (TPD-PPV) sensitized with a highly soluble fullerene derivative (PCBM). Our results show that at zero and low dc field the dependence of the photo-EMF signal on frequency, grating period and external electric field is well described by the standard model originally developed for an inorganic monopolar photoconductor with finite charge carrier lifetime. In this regime the photo-EMF effect was used to determine zero- and low-field photoelectric material parameters including the low-field hole mobility $({\mu }_{0,h}=1.3\times {10}^{-4}{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s})$, the effective charge carrier lifetime $(\tau =45\mu \mathrm{s})$, the diffusion length $(L_D=114\mathrm{nm})$, and the primary charge carrier generation efficiency $(\Phi =5.3\times {10}^{-3}\%)$. In addition, the validity of the Einstein relation $(D∕\mu =25\mathrm{meV})$ was verified for the low-field regime. At high electric fields the signal behavior deviates significantly from the trend predicted by the standard model for inorganic photoconductors. This behavior which is mainly attributed to the strong field dependence of the charge generation rate is well described by our model.

Figure 1

Top: Molecular structure of the TPD-PPV polymer used in this work. Bottom: Schematic illustration of the three different experimental setups used for the photo-EMF measurements: (a) Conventional transmission configuration; the tilt between sample normal and bisector of the incident beams is required to obtain a component of the grating vector $\mathbf{K}$ in the direction of the collecting electrodes. (b) Transversal configuration; the need for a sample tilt is avoided as the grating vector is parallel to the collecting electrodes. (c) In reflection configuration large spatial frequencies can be achieved.

Figure 2

The amplitude of $j_{p\text{−}\mathrm{emf}}^{\Omega }$ as a function of the oscillation frequency of the interference grating for different light intensities: $0.8\mathrm{W}∕{\mathrm{cm}}^2$ (●), $0.4\mathrm{W}∕{\mathrm{cm}}^2$ (▴), $0.2\mathrm{W}∕{\mathrm{cm}}^2$ (◆). The solid lines represent weighted linear regression fits to the data. The amplitude of the alternating photocurrent signal at an external field of $E_0=37\mathrm{kV}∕\mathrm{cm}$ is also shown (엯).

Figure 3

The amplitude of the photo-EMF signal as a function of the spatial frequency. Modulation frequency $\Omega ∕2\pi =85\mathrm{Hz}$, modulation amplitude $\Delta =0.43\mathrm{rad}$, incident intensity $I=0.8\mathrm{W}∕{\mathrm{cm}}^2$. The linear increase of the signal indicates that the spatial frequency of the grating is small compared to the diffusion length of the charge carriers $(K{L}_D⪡1)$.

Figure 4

Alternating photocurrent $j_{\mathit{ph}}^{\Omega }$ signal normalized to the applied field versus applied field $E_{0,\mathit{ph}}$. The chopping frequency was $\Omega ∕2\pi =85\mathrm{Hz}$, the incident intensity $I=0.4\mathrm{W}∕{\mathrm{cm}}^2$. The line represents a power-law fit reflecting the expected proportionality of $j_{\mathit{ph}}^{\Omega }∕E_{0,\mathit{ph}}$ to the charge generation efficiency $\Phi \left(E_0\right)={\Phi }_0(1+a{E}_0^{\alpha })$.

Figure 5

(a) Field dependence of $j_{p\text{−}\mathrm{emf}}^{\Omega }$ in the small spatial frequency regime ($K{L}_D⪡1$, transmission configuration). At an effective external field of $E_0^{\prime }=2.2\mathrm{kV}∕\mathrm{cm}$ the amplitude of the signal reaches a minimum and the phase passes an inflection point. (b) At large spatial frequencies ($K{L}_D⪢1$, reflectance configuration) minimum and inflection point are reached at an external field $E_0^{″}=6.8\mathrm{kV}∕\mathrm{cm}$.

Figure 6

(a) The frequency dependent decay of the alternating photocurrent amplitude is analyzed for different electric fields to determine the field dependence of the charge carrier lifetime. Incident intensity $I=0.4\mathrm{W}∕{\mathrm{cm}}^2$. (b) The Arrhenius plot of $\ln ({\tau }_0∕\tau )$ versus $E^{1∕2}$ is used to determine the field dependent reduction of the activation energy $\beta$.

Figure 7

Comparison of the conventional photo-EMF model (dashed line), the model assuming $\alpha =1.6$ (dotted-dashed line), and the model assuming $\alpha =2.2$ (solid line) with the experimentally obtained field dependence of the photo-EMF signal.