Matching Terahertz and Hall Mobilities as a Hallmark of Intrinsic Charge Transport in Metal-Halide Perovskites

Technical Summary: Matching Terahertz and Hall Mobilities in Metal-Halide Perovskites

Problem Statement
Charge carrier mobility in soft-lattice semiconductors, such as metal-halide perovskites, is frequently reported with significant discrepancies across different measurement techniques. These variations arise from the intrinsic heterogeneity of charge transport across length scales and the influence of extrinsic static disorder (defects, impurities, grain boundaries). While ultrafast optical techniques (like Optical Pump–Terahertz Probe, OPTP) measure local, transient mobility on nanometer scales before trapping occurs, steady-state electrical methods (like Hall effect or FETs) measure macroscopic transport over millimeter scales, often limited by defects. A critical open question remains: can a truly intrinsic charge transport regime, free from static disorder limitations, exist across macroscopic single crystals of these soft materials? Furthermore, there is a lack of experimental platforms that allow for the direct, quantitative comparison of local (optical) and macroscopic (electrical) mobilities on the exact same sample to benchmark intrinsic limits.

Methodology
To address these challenges, the authors developed an integrated device platform enabling concurrent Hall-effect and OPTP spectroscopic measurements on the same high-quality epitaxial CsPbBr₃ single-crystal device.

• Device Architecture: The platform consists of a macroscopic single-crystalline grain of epitaxial CsPbBr₃ grown on a mica substrate, featuring graphite contacts for current injection and Hall voltage detection, and a transparent parylene-N capping layer for encapsulation. This design allows for both dark electrical transport measurements and optical transmission spectroscopy.
• OPTP Measurements: Ultrafast optical pump pulses generate carriers, followed by a terahertz probe pulse to monitor free carrier dynamics. Mobility ($\mu_{OPTP}$) is extracted from the change in THz transmission ($\Delta T/T$) at specific time delays (2–4 ps) where carrier formation is complete but recombination has not yet begun. The study carefully determined safe excitation fluence limits to avoid artifacts such as amplified stimulated emission (ASE) and carrier-carrier scattering.
• Hall Effect Measurements: Steady-state magneto-transport measurements were performed in the dark on the same device. A magnetic field was swept to induce a Hall voltage, allowing the extraction of Hall mobility ($\mu_{Hall}$) and carrier type.
• Comparative Analysis: The study compared $\mu_{OPTP}$ and $\mu_{Hall}$ across a broad range of experimental conditions, including varying temperatures (125–315 K) and excitation fluences, to assess the consistency of transport mechanisms.

Key Results

1. Quantitative Agreement of Mobilities: On the same epitaxial CsPbBr₃ single-crystal device, the room-temperature Hall mobility was measured at $25.8 \pm 0.3$ cm²V⁻¹s⁻¹, while the OPTP mobility (at high fluence to ensure trap filling) was $19.8 \pm 0.4$ cm²V⁻¹s⁻¹. These values are among the highest reliably reported for CsPbBr₃. The close agreement (within ~20–30%) between a contactless, ultrafast local probe and a steady-state macroscopic electrical probe is unprecedented for soft-lattice materials.
2. Intrinsic Transport Regime: The convergence of local and macroscopic mobilities indicates that charge transport in these epitaxial single crystals is not limited by grain boundaries, interfaces, or extended defects over millimeter length scales. The material operates in a regime approaching its intrinsic limit.
3. Band-Like Temperature Dependence: Both techniques revealed a similar power-law temperature dependence for hole mobility ($\mu \propto T^{-b}$), with exponents $b \approx 1.10$ (OPTP) and $b \approx 1.29$ (Hall). This behavior, consistent with Drude-like delocalized carriers limited by phonon scattering, confirms that the same intrinsic transport mechanism governs both ultrafast and steady-state responses.
4. Fluence-Dependent Artifacts: The study identified critical fluence thresholds (40 $\mu$J/cm² at 300 K and 9 $\mu$J/cm² at 93 K) above which ASE and many-body interactions distort OPTP signals, leading to mobility underestimation. Below these thresholds, measurements remain reliable.
5. Material Quality and Stability: The epitaxial films demonstrated excellent spatial uniformity (<10% variation) and long-term stability in ambient air. In contrast, solution-cast (drop-cast) films exhibited significantly lower mobilities (~4 cm²V⁻¹s⁻¹), highlighting the impact of morphology and disorder.

Significance and Claims
The authors claim that this work demonstrates that defect-free, intrinsic charge transport is achievable in soft-lattice perovskites on macroscopic (millimeter) length scales. By establishing a direct, quantitative link between local ultrafast dynamics and macroscopic steady-state transport on a single sample, the study validates the epitaxial CsPbBr₃ system as a benchmark for intrinsic mobility.

The paper posits that the matching of OPTP and Hall mobilities serves as a "hallmark" of intrinsic transport. The developed co-localized characterization methodology provides a robust framework for distinguishing intrinsic material properties from extrinsic disorder effects. This approach offers a reliable strategy for benchmarking emerging soft semiconductors, ensuring that reported mobility values reflect the material's true potential rather than measurement artifacts or sample quality limitations. The work does not claim to have solved all mobility extraction challenges in all materials but establishes a rigorous protocol for identifying when a material operates in its intrinsic regime.