Electron diffusion in polymer:fullerene bulk heterojunctions

A method to study the bulk electron diffusion dynamics in poly(2-methoxy-5-($3^{\prime }$, $7^{\prime }$-dimethyloctyloxy)-1,4-phenylene-vinylene): 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6) ${\mathrm{C}}_{61}$ (PCBM) blend films with varying PCBM content is presented. The blends are spin coated on top of dense smooth $\mathrm{Ti}{\mathrm{O}}_2$ and excited with a visible laser pulse. The photogenerated electrons on PCBM diffuse through the blend film until they reach the interface with $\mathrm{Ti}{\mathrm{O}}_2$, which serves to collect the electrons. The resulting change in conductance of $\mathrm{Ti}{\mathrm{O}}_2$ is measured using the time-resolved microwave conductivity technique. Theoretical analysis of the time-dependent photoconductance gives the electron diffusion constant $\left(D_e\right)$ and the lower limit of the time for electrons to decay by trapping or recombination $\left({\tau }_e\right)$. $D_e$ increases from $7.0\times {10}^{-13}{\mathrm{m}}^2∕\mathrm{s}$ at a weight fraction PCBM $\left(W_{\mathit{PCBM}}\right)=0.11\text{to}3.5\times {10}^{-10}{\mathrm{m}}^2∕\mathrm{s}$ at $W_{\mathit{PCBM}}=0.50$, while, interestingly, at $W_{\mathit{PCBM}}=0.75$, a smaller value of $1.2\times {10}^{-10}{\mathrm{m}}^2∕\mathrm{s}$ is found. The electron diffusion length increases with PCBM content. The presence of PCBM clusters in blends with a high PCBM content extends the time for electrons to decay, so that the lower limit of the electron diffusion length exceeds the film thickness of $100\mathrm{nm}$, which is required for sufficient light absorption in a photovoltaic device.

Figure 1

(A) Schematic representation of the processes occurring in an $\mathrm{MDMO}\text{−}\mathrm{PPV}:\mathrm{PCBM}∕\mathrm{Ti}{\mathrm{O}}_2$ film upon excitation with visible light. Electrons generated upon photoinduced charge separation in the blend film (1) diffuse (2) until they reach the interface with $\mathrm{Ti}{\mathrm{O}}_2$ where they are injected into the $\mathrm{Ti}{\mathrm{O}}_2$ conduction band (3). Part of the electrons recombine or are trapped (4). (B) Energy-level diagram and the processes depicted in panel (A). (C) Schematic representation of the measurement cell with the sample in the configuration for front side photoexcitation. (D) Schematic representation of the sample in the configurations for front side (FS) or back side (BS) photoexcitations together with the different excitation profiles.

Figure 2

Absorption coefficients of MDMO-PPV on quartz (dotted; film thickness $L=359\mathrm{nm}$), of a $\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}∕\text{quartz}$ blend film (dot dash; $L=75\mathrm{nm}$), and of PCBM (dashed). The absorption spectrum of a bare $\mathrm{Ti}{\mathrm{O}}_2$ film on quartz (full line) is given on the right-hand axis for comparison. The molecular structures of MDMO-PPV and PCBM are also shown.

Figure 3

(A) Photoconductance transients on excitation at $510\mathrm{nm}$ of a pure MDMO-PPV film on $\mathrm{Ti}{\mathrm{O}}_2$ (squares) and of a $\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}∕\mathrm{Ti}{\mathrm{O}}_2$ film (circles). Excitation was from the back side with an intensity of $3.9\times {10}^{11}$ and $1.5\times {10}^{11}\text{photons}∕{\mathrm{cm}}^2$/pulse, respectively. In addition, the photoconductance of the $\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}∕\mathrm{Ti}{\mathrm{O}}_2$ film for excitation at $300\mathrm{nm}$ (triangles) is also shown. The full line gives the integrated intensity during the laser pulse convoluted with the $18\mathrm{ns}$ response time of detection. (B) IPCSE transients on excitation of the $\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}∕\mathrm{Ti}{\mathrm{O}}_2$ film under conditions as indicated in the figure. Note that the two transients on excitation at $600\mathrm{nm}$ coincide almost completely. (C) IPCSE transients on excitation of the $\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}∕\mathrm{Ti}{\mathrm{O}}_2$ blend film at different excitation intensities. The pulse-integrated intensities were (increasing in the direction of the arrow) $1.5\times {10}^{11}$, $5.3\times {10}^{11}$, $1.6\times {10}^{12}$, $5.0\times {10}^{12}$, $1.8\times {10}^{13}$, $5.8\times {10}^{13}$, $2.1\times {10}^{14}$, and $6.8\times {10}^{14}\text{photons}∕{\mathrm{cm}}^2$/pulse.

Figure 4

IPCSE transients on excitation at $510\mathrm{nm}$ of MDMO-PPV:PCBM blend films with (A) $W_{\mathit{PCBM}}=0.11$, (B) $W_{\mathit{PCBM}}=0.25$, (C) $W_{\mathit{PCBM}}=0.50$, and (D) $W_{\mathit{PCBM}}=0.75$, with an intensity of $(2\pm 1)\times {10}^{11}\text{photons}∕{\mathrm{cm}}^2$/pulse. Transients are shown for both FS and BS excitations, as indicated. The lines are fits to the data according to Eq. (6). In panel (A), the FS signal almost coincides with the horizontal axis.

Figure 5

Effect of parameter values on IPCSE transients calculated with Eq. (5). The full lines are obtained with parameter values from fits to experimental data [$\mathrm{MDMO}\text{−}\mathrm{PPV}:{\mathrm{PCBM}}_{0.50}$ $\left(\mathrm{Ti}{\mathrm{O}}_2\right)$] on BS excitation (upper curve) or FS excitation (lower curve). The effect of a two times higher $D_e$ $(D_e=7\times {10}^{-10}{\mathrm{m}}^2∕\mathrm{V}\mathrm{s})$ and a two times lower $D_e$ $(D_e=1.8\times {10}^{-10}{\mathrm{m}}^2∕\mathrm{V}\mathrm{s})$ is demonstrated by the dashed curves. In addition, the effect of a two times longer ${\tau }_e$ $({\tau }_e=2.2\times {10}^{-5}\mathrm{s})$ and a two times shorter ${\tau }_e$ $({\tau }_e=0.6\times {10}^{-5}\mathrm{s})$ is shown (dot dash).