Charge Transport in Spiro-OMeTAD Investigated through Space-Charge-Limited Current Measurements

Extracting charge-carrier mobilities for organic semiconductors from space-charge-limited conduction measurements is complicated in practice by nonideal factors such as trapping in defects and injection barriers. Here, we show that by allowing the bandlike charge-carrier mobility, trap characteristics, injection barrier heights, and the shunt resistance to vary in a multiple-trapping drift-diffusion model, a numerical fit can be obtained to the entire current density–voltage curve from experimental space-charge-limited current measurements on both symmetric and asymmetric $2,2^{\prime },7,7^{\prime }$-tetrakis($N,N$-di-4-methoxyphenylamine)-$9,9^{\prime }$-spirobifluorene (spiro-OMeTAD) single-carrier devices. This approach yields a bandlike mobility that is more than an order of magnitude higher than the effective mobility obtained using analytical approximations, such as the Mott-Gurney law and the moving-electrode equation. It is also shown that where these analytical approximations require a temperature-dependent effective mobility to achieve fits, the numerical model can yield a temperature-, electric-field-, and charge-carrier-density-independent mobility. Finally, we present an analytical model describing trap-limited current flow through a semiconductor in a symmetric single-carrier device. We compare the obtained charge-carrier mobility and trap characteristics from this analytical model to the results from the numerical model, showing excellent agreement. This work shows the importance of accounting for traps and injection barriers explicitly when analyzing current density–voltage curves from space-charge-limited current measurements.

Figure 1

Schematic of the energy-level diagrams of (a) symmetric electron-only device at thermodynamic equilibrium, where $q{\phi }_{\mathrm{inj}}$ and $q{\phi }_{\mathrm{ext}}$ represent the injection and extraction barrier heights, respectively, $E_C$ and $E_V$ are the conduction- and valence-band edge, respectively, $E_F$ is the Fermi level of the semiconductor at thermal equilibrium, and $F$ is the electric field. (b) Symmetric electron-only device with enough applied voltage to assume drift-dominant transport (Mott-Gurney regime). (c) Asymmetric electron-only device at equilibrium showing the energy barrier arising from a built-in voltage $q{V}_{\text{bi}}=q{\phi }_{\mathrm{ext}}-q{\phi }_{\mathrm{inj}}$. (d) Sketch of the total DOS including exponential tail states (the depth of the tails are given by their respective characteristic energies). Electron transport is shown for simplicity (hole transport is completely analogous). In (b) and (c), forward injection of electrons from the left-hand side is assumed.

Figure 2

(a) Electron density as a function of the spatial position of a trap-free device and a device with localized states in the form of exponential tail trap states in comparison with Eq. (8). (b) Average electron densities $n$ of the numerical calculation (red dashed line) and the analytical approximation Eq. (11) (green dashed line) and electron density in the middle of the device $n_0$ from the numerical calculation (solid red line) and from Eq. (9) (solid green line). (c) Schematic of the description of the localized states in the band gap. In this case, $T=0\mathrm{K}$ is assumed for the representation of the occupied density of states. (d) Electron density in the middle of the device calculated using Eq. (15) (solid lines) and from numerical calculations (dashed lines) when traps are included for three values of $E_{\mathrm{ch}}$ as indicated, 0.04, 0.06, and 0.08 eV.

Figure 3

(a) Molecular structure of spiro-OMeTAD. (b) Symmetric and asymmetric hole-only devices employing ${\mathrm{MoO}}_3/\mathrm{Al}$ and Al back contacts, respectively (energy levels are taken from the literature). The WFs of ${\mathrm{MoO}}_3$ and PEDOT-PSS will shift to match the HOMO of the organic compound through Fermi-level pinning, resulting in estimated built-in voltages of 0 and 0.9 V, respectively, for the two devices. The energy levels are all given relative to the vacuum level.

Figure 4

(a) Forward- and reverse-bias $J\text{−}V$ curves obtained from SCLC measurements of symmetric (gray circles) and asymmetric spiro-OMeTAD hole-only devices (orange and red circles) of 200 and 230 nm, respectively. Since the forward- and reverse-bias curves overlap for the symmetric device, only the forward-bias curve is shown. Mott-Gurney law forced “fits” and Ohm’s law fits are shown as solid and dashed lines, respectively. (b) Plots of $m=(d\log J)/(d\log V)$ of the asymmetric data in (a) against the voltage. (c) $J\text{−}V$ curves of symmetric spiro-OMeTAD devices at temperatures varying from 200 to 300 K in steps of 20 K, showing fitting with the Mott-Gurney law [Eq. (1), solid lines] and either the moving-electrode equation [Eq. (6), dashed lines] or Eq. (17). (d) $m\text{−}V$ curves of the $J\text{−}V$ curves shown in (c). The high-voltage slope values approach a value larger than 2 in both (a) and (c).

Figure 5

Numerical fits to SCLC data. (a) Forward- and reverse-bias current of an asymmetric device, (b) forward-bias current of a symmetric device (the forward- and reverse-bias currents overlap), and (c) forward-bias current of a symmetric device at varying temperatures. Results of the fits in (a) and (b) are shown in the graphs. An injection barrier of 0.11 eV and an exponential tail of trap states are required to consistently fit to the temperature series.

Figure 6

(a) Resulting mobility values using various techniques [red for numerical fitting, blue for the Mott-Gurney law fitting Eq. (1), and green for the moving-electrode equation fitting Eq. (6)]. The set of various symbols refers to values inferred from devices with different semiconducting layer thicknesses: 290 nm (squares), 190 nm (circles) and 115 nm (triangles), respectively. (b) Comparison of the bandlike mobility with the effective mobility from the MG law modified by the ratio of total to free charge carriers [Supplemental Material [25] Figs. S7(a) and S7(b)], and with the value estimated using Eq. (17). (c) Comparison of the bandlike mobility with the MG mobility modified for both traps and injection limitation at the metal-semiconductor interfaces. If the MG mobility is used to fit the entire voltage range for the 190-nm device, an apparent field dependence is observed, as shown in the Supplemental Material [25] Fig. S7(d).