Space-Charge Limited Photocurrent

In 1971 Goodman and Rose predicted the occurrence of a fundamental electrostatic limit for the photocurrent in semiconductors at high light intensities. Blends of conjugated polymers and fullerenes are an ideal model system to observe this space-charge limit experimentally, since they combine an unbalanced charge transport, long lifetimes, high charge carrier generation efficiencies, and low mobility of the slowest charge carrier. The experimental photocurrents reveal all the characteristics of a space-charge limited photocurrent: a one-half power dependence on voltage, a three-quarter power dependence on light intensity, and a one-half power scaling of the voltage at which the photocurrent switches into full saturation with light intensity.

Figure 1

Experimental charge carrier mobility of the electrons (${\mu }_e$, ○) and holes (${\mu }_h$, △) as a function of temperature $T$. The ${\mu }_e$ and ${\mu }_h$ have been determined from space-charge limited measurements on $20:80$ blends of ${\mathrm{BEH}}_1{\mathrm{BMB}}_3$-PPV:PCBM. The inset schematically shows a photovoltaic device under illumination and the chemical structure of the ${\mathrm{BEH}}_1{\mathrm{BMB}}_3$-PPV, respectively.

Figure 2

Temperature dependence of the photocurrent (symbols) in a $20:80$ blend of ${\mathrm{BEH}}_1{\mathrm{BMB}}_3$-PPV:PCBM versus effective applied voltage ($V_0-V$) for a device of 275 nm thickness illuminated at an intensity of $80\mathrm{mW}/{\mathrm{cm}}^2$. The solid lines represent the square-root dependence of the photocurrent $J_{\mathrm{ph}}$ on effective voltage, used here as a guide for the eye.

Figure 3

Incident light power (ILP) dependence of the photocurrent ($J_{\mathrm{ph}}$) versus the effective voltage ($V_0-V$) measured at $T=210\mathrm{K}$. The solid (thick) lines represent the calculated $J_{\mathrm{ph}}$ from Eq. (4) using ${\mu }_h=1.2\times {10}^{-7}{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, ${\epsilon }_r=2.6$, and $G\propto \mathrm{ILP}$, where ILP was varied from 80 to $6\mathrm{mW}/{\mathrm{cm}}^2$. The arrow indicates the voltage ($V_{\mathrm{sat}}$) at which $J_{\mathrm{ph}}$ shows the transition to the saturation regime.

Figure 4

(a) Incident light power (ILP) dependence of the photocurrent $J_{\mathrm{ph}}$ taken from Fig. 3 at an effective voltage of $V_0-V=0.1\mathrm{V}$ and $V_0-V=10\mathrm{V}$ (symbols). (b) Saturation voltage ($V_{\mathrm{sat}}$) versus ILP as determined for Fig. 3. The slope ($S$) determined from the linear fit (solid lines) to the experimental data is written on the figure.