Determination of Surface Recombination Velocities at Contacts in Organic Semiconductor Devices Using Injected Carrier Reservoirs

A method to determine surface recombination velocities at collecting contacts in interface-limited organic semiconductor devices, based on the extraction of injected carrier reservoirs in a single-carrier sandwich-type structure, is presented. The analytical framework is derived and verified with drift-diffusion simulations. The method is demonstrated on solution-processed organic semiconductor devices with hole-blocking ${\mathrm{TiO}}_2/\text{organic}$ and ${\mathrm{SiO}}_2/\text{organic}$ interfaces, relevant for solar cell and transistor applications, respectively.

Figure 1

(a) Schematic picture of surface recombination at a semiconductor-electrode contact for holes being collected at a metal electrode. In (b) and (c), a schematic picture of the CELIV technique is shown. A linear voltage pulse $u(t)$ is applied to extract charge carriers at the dc voltage $V$. From the corresponding extraction current transient $j(t)$ (corrected for the steady-state current), the extracted charge is obtained from $Q_{\text{extr}}={\int }_0^{t_{\text{extr}}}[j(t)-j_0]dt$, where $j_0=(ϵ{ϵ}_0/d)(du/dt)=(ϵ{ϵ}_0{u}_{\max }/d{t}_{\text{pulse}})$.

Figure 2

(a) Simulated energy level diagrams at $V=0$ (upper) and $V>V_{\mathrm{bi}}$ (lower) are shown for the case $S_R<v_D$ at the cathode ($x=d$). In (b), the simulated $\Delta Q$ as a function of applied voltage $V$ for varying $S_R$ is indicated by symbols. The analytical approximation Eq. (3) is depicted by the corresponding solid lines. The current density $J_D(V)$ is obtained from the simulated $JV$ curve (not shown). The dashed line corresponds to $\Delta Q=\frac{3}{2}CU$. In (c), the normalized $Q_{\text{norm}}/J_{\text{norm}}^{1/2}$ as a function of $S_R/(\mu kT/qd)$ is shown, where $Q_{\text{norm}}\equiv \Delta Q/CU$, $J_{\text{norm}}\equiv J_D/J_{\mathrm{SCLC}}$, and $\mu kT/qd\approx 0.13\mathrm{cm}/\mathrm{s}$. In the simulations we assume $V_{\mathrm{bi}}=0.5\mathrm{V}$, $d=200\mathrm{nm}$, $ϵ=3$, $T=300\mathrm{K}$, $\mu ={10}^{-4}{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, and an injection barrier of 0.20 eV at the anode.

Figure 3

In (a) and (b), the extracted charge $Q_{\text{extr}}$ and steady-state current density $J$, respectively, are shown for ${\mathrm{TiO}}_2/\mathrm{P}3\mathrm{HT}:\mathrm{PCBM}$ (circles) and ${\mathrm{SiO}}_2/\mathrm{P}3\mathrm{HT}$ (squares) interfaces at different $V$. In (c), the corresponding $S_R$ for holes is shown, as obtained by Eq. (5) (symbols). The open and solid squares indicate ${\mathrm{SiO}}_2/\mathrm{P}3\mathrm{HT}$ data that have been uncorrected ($R_{\mathrm{sh}}=\infty$) and corrected ($R_{\mathrm{sh}}\approx 1050\mathbf{\Omega }{\mathrm{m}}^2$) for the shunt resistance, respectively. The dashed lines in (a) and (c) correspond to $S_R=5.8\times {10}^{-6}\mathrm{cm}/\mathrm{s}$ and $S_R=4.5\times {10}^{-9}\mathrm{cm}/\mathrm{s}$ for ${\mathrm{TiO}}_2/\mathrm{P}3\mathrm{HT}:\mathrm{PCBM}$ and ${\mathrm{SiO}}_2/\mathrm{P}3\mathrm{HT}$, respectively. In (d), the extracted charge for ${\mathrm{SiO}}_2/\mathrm{P}3\mathrm{HT}$ [from (a)] is shown on the linear scale (symbols); the corresponding $dJ/dV$ [$\mathrm{mS}/{\mathrm{m}}^2$] as a function of $d{Q}_{\text{extr}}^2/dV$ [${(\mathrm{C}/{\mathrm{m}}^2)}^2/\mathrm{MV}$] are shown in the inset.