Ballistic-like space-charge-limited currents in halide perovskites at room temperature

Abstract

The emergence of halide perovskites in photovoltaics has diversified the research on this material family and extended their application toward several fields in the optoelectronics, such as photo-and ionizing-radiation-detectors. One of the most basic characterization protocols consists of measuring the dark current-voltage (J À V) curve of symmetrically contacted samples for identifying the different regimes of the space-charge-limited current (SCLC). Customarily, J / V n indicates the Mott-Gurney law when n % 2 or the Child-Langmuir ballistic regime of SCLC when n ¼ 3=2. The latter has been found in perovskite samples. Herein, we start by discussing the interpretation of J / V 3=2 in relation to the masking effect of the dual electronic-ionic conductivity in halide perovskites. However, we do not discard the actual occurrence of SCLC transport with ballistic-like trends. Therefore, we introduce the models of quasi-ballistic velocity-dependent dissipation (QvD) and the ballistic-like voltage-dependent mobility (BVM) regimes of SCLC. The QvD model is shown to better describe electronic kinetics, whereas the BVM model results are suitable for describing both electronic and ionic kinetics in halide perovskites as a particular case of the Poole-Frenkel ionized-trap-assisted transport. The proposed formulations can be used as the characterization of effective mobilities, charge carrier concentrations and times-of-flight from J-V curves, and resistance from impedance spectroscopy spectra.

Surface versus Bulk Currents and Ionic Space-Charge Effects in CsPbBr3 Single Crystals

“…Notably, the experimental trend μ ∝ V –1/2 is in agreement with the BVM model, 21 if ξ = V / L (top axis in Figure 1 b) is considered. This may relate to mobile ions which modify the electronic transport properties upon biasing, even for the fast pulse perturbation in the ToF experiment.…”

“…Commonly, the ohmic region ( J ∝ V ) and a transition toward the classic mobility regime of space-charge-limited current (SCLC) are found, where the latter follows the Mott–Gourney law 17 , 18 Here L is the distance between electrodes, ϵ 0 is the vacuum permittivity, ϵ r is the dielectric constant (∼40 for CsPbBr 3 ), 19 L is the distance between electrodes, and μ is the mobility of the electronic charge carriers. Moreover, a trap-filled-limited region can occur when J ∝ V n , with n > 2, 18 , 20 and a ballistic-like voltage-dependent mobility (BVM) 21 regime can also take place when n = 3/2. The BVM regime resembles the Child–Langmuir law 22 , 23 in terms of the current trend above the threshold voltage V 0 with a law as …”

“… Time-of-flight measurements of a CsPbBr 3 single crystal: (a) photocurrent transients and (b) corresponding mobilities as a function of bias. The solid line in part b corresponds to an allometric fitting, following the trend of the BVM model, 21 as indicated. No GR connection was used for this experiment.…”

“…Furthermore, either with or without a GR, the trend R sc ∝ V –1/2 is observed, which agrees with the BVM regime of SCLC. Applying the differential resistance R = (dJ/dV) −1 definition to the current of eq 2 and neglecting ∂μ/∂V components in the derivative, one can find 21 …”

Coupling between Ion Drift and Kinetics of Electronic Current Transients in MAPbBr3 Single Crystals

“…As expected, dissimilar time scales are encountered for ion movement because of a change in transporting driving force. Experiments are analyzed either by means of the ionic dynamic doping model (IDD) , or the model of ballistic-like voltage-dependent mobility (BVM) regime of space-charge-limited currents (SCLCs) accounting for the separate regimes of ion diffusion and ion drift, respectively. Our findings suggest an ionic–electronic coupling in which purely electronic currents are measured that follow the slow kinetics of mobile ion redistribution.…”