Determination of Injection Barriers in Organic Semiconductor Devices from Capacitance Measurements

The low-frequency differential capacitance of single-carrier (metal/organic semiconductor/metal) devices with a sandwich structure is shown to display a distinct peak if the injection barrier of at least one of the electrodes is sufficiently small. The effect is shown to be caused by the diffusion contribution to the current density. Depending on the height of the injection barriers, the peak voltage can be a few tenths of a volt below the built-in voltage, $V_{\mathrm{bi}}$. We show how the peak voltage and the peak height can be used to accurately determine the injection barriers and $V_{\mathrm{bi}}$, and we demonstrate the method by applying it to polyfluorene-based devices.

Figure 1

Experimental $C(V)$ curves for hole-only ($A$) and electron-only ($B$ and $C$) devices with structures given in Table , at $T=295\mathrm{K}$ and $f=200\mathrm{Hz}$. The inset shows for hole-only devices the injection barriers, defined as the energy difference between the highest occupied molecular orbital (HOMO) and the Fermi level of each electrode.

Figure 2

Calculated $C(V)/C_{\mathrm{geom}}$ curves for devices with $L=100\mathrm{nm}$, $N_t=1\times {10}^{27}{\mathrm{m}}^{-3}$, and ${\epsilon }_r=3$, at $T=300\mathrm{K}$ and in the low-$f$ limit, for (a) symmetric devices (0.1 eV steps in $\varphi$), (b) devices with ${\varphi }_1=0\mathrm{eV}$ and a varying built-in voltage (0.25 V steps), and (c) devices with $V_{\mathrm{bi}}=0.5\mathrm{V}$, and a varying ${\varphi }_1$ (0.1 eV steps); (d) shows the effect of a temperature variation for $V_{\mathrm{bi}}=0.5\mathrm{V}$ (dotted lines: $f=1\mathrm{kHz}$).

Figure 3

(a) Lines in the $\{{\gamma }_1,{\gamma }_2\}$ space corresponding to the parameter variations taken in Figs. 2a, 2b, 2c, 2d; (b) dimensionless charge density at position $x$ across the device at $V_{\mathrm{peak}}$ for ${\gamma }_1=\infty$ and ${\gamma }_2=\infty$ (full curve), ${\gamma }_2={\gamma }_{2,\min }$ (dashed curve), and ${\gamma }_2\to 0$ (dotted curve); (c) contours in the $\{{\gamma }_1,{\gamma }_2\}$ space of equal $C_{\mathrm{peak}}/C_{\mathrm{geom}}$, and (d) of equal $e{V}_{\mathrm{peak}}/(k_{B}T)$. Dashed lines: contours of constant $e{V}_{\mathrm{bi}}/(k_{B}T)$.

Figure 4

Experimental (upper part) and calculated (lower part) $C(V)/C_{\mathrm{geom}}$ curves for device $A$, at $T_0=295\mathrm{K}$, with $V_{\mathrm{bi}}=1.62\mathrm{V}$ (arrow), $n_1=1\times {10}^{26}{\mathrm{m}}^{-3}$, $\mu =1\times {10}^{-10}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$, and ${\epsilon }_r=3.2$. The inset shows the shift of $V_{\mathrm{peak}}$ with temperature, with respect to $V_{\mathrm{peak}}(T_0)$.