Determination of charge-carrier transport in organic devices by admittance spectroscopy: Application to hole mobility in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-NPD (2007)

Hole mobility in $N,{N}^{\ensuremath{'}}$-diphenyl-$N,{N}^{\ensuremath{'}}$-bis(1-naphtylphenyl)-$1,{1}^{\ensuremath{'}}$-biphenyl-$4,{4}^{\ensuremath{'}}$-diamine ($\ensuremath{\alpha}$-NPD) is evaluated by electrical characterization in the ac regime. The frequency-dependent complex admittance and impedance of the structure consisting of the organic layer, grown by thermal evaporation, sandwiched by indium tin oxide and aluminum electrodes, are measured as functions of the applied dc voltage. The capacitance response shows negative values for frequencies below a characteristic value depending on the bias and ranging from $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ up to $20\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. It increases with the modulation frequency and reaches a peak, the magnitude and position of which are functions of the applied voltage. For higher frequencies, a minimum can be observed before the capacitance increases again up to a constant value. A final decreasing occurs at frequency of $4\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. The analysis of the experimental data is performed by a detailed theoretical study of the steady-state and small-signal electrical characteristics of the device. Numerical calculations are based on the solution of the basic semiconductor equations for the system consisting of two electrodes connected by the semiconducting channel formed by the organic layer. The description explicitly includes a continuous distribution of trap density of states and a field-dependent carrier mobility. The spatially dependent charge carrier and occupied trap concentrations, as well as the various components to the total current density, are obtained for the dc and ac regimes and are analyzed for given bias and frequency. Based on a formalism used in the study of inorganic semiconductors, the results of the simulation show that the inductive contribution to the capacitance response originates from the modulation of the hole concentration in the organic material, leading to the corresponding carrier transit time. Moreover, the low-frequency behavior of the capacitance curves could be explained by the presence of a band of defect states which modifies the charge distribution within the organic layer and the injection of electrons from the cathode. We show that the latter contribution is also responsible for the negative values of the capacitance measured below $10\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. Good agreement is observed between the experimental and theoretical electrical characteristics, in particular for the differential susceptance results and the subsequent hole mobility values. Our approach can be a useful contribution for the methodology of obtaining mobilities from admittance measurements as it allows one to clarify the physical origin of the measured frequency-dependent capacitance and to check for the experimental procedure. This work finally leads to the formulation of the conditions under which small-signal ac measurements can be used to determine carrier mobility in organic devices.