Abstract
The steady-state charge-carrier mobility in semiconductors can be extracted from the space-charge-limited current in single-carrier devices. However, in many cases, a built-in voltage is present, which should be known accurately to obtain the correct mobility. Here, it is demonstrated that band bending at the injecting electrode has important consequences for the built-in voltage and the analytical description of the current-voltage characteristics. It is shown that the built-in voltage can be accurately determined from the slope of the current-voltage characteristics on a semilogarithmic scale. Knowing the effect of band bending on the injected current, a simple analytical equation for the drift-diffusion space-charge-limited current above the built-in voltage is derived, which allows for improved determination of the charge-carrier mobility from experimental data.
Highlights
A widely used method to determine the charge-carrier mobility in semiconductors and organic semiconductors, in particular, is the measurement of space-charge-limited currents [1,2]
Single-carrier devices are prepared, in which, depending on the work functions of the electrodes, either the electron or hole current through the semiconductor is measured as a function of the applied voltage
Builtin voltages can be estimated by fitting J -V characteristics with drift-diffusion simulations [5,9,10] or can be obtained by means of charge-extraction measurements [11]
Summary
Where q is the elementary charge, NC is the density of states, φb is the barrier at the extracting contact, k is the Boltzmann constant, T is the temperature, and b is the BI band-bending parameter given by [5]. This demonstrates that band bending at the injecting contact has important implications for the internal field in the device. For boundary conditions in the numerical simulations, the barrier at the injecting electrode is set to zero, while varying the barrier φb at the extracting electrode These parameters lead to a band-bending parameter of b = 0.19 V [Eq (3)]. Agreement between the analytical and numerical description is clearly superior to that obtained when neglecting band bending at the injecting contact (red lines) In this case, the built-in voltage is overestimated, leading to a disagreement between the Mott-Gurney law and the numerical simulations. This agreement holds when varying the input parameters, as shown in Current Density (A m–2) Current Density (A m–2) |Current Density| (A m–2)
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