5.2 Terahertz conductivity and carrier dynamics

Terahertz conductivity and carrier dynamics are key to understanding how materials behave at super high frequencies. This topic dives into how electrons move around in materials when hit with terahertz waves, which is crucial for developing new tech.

We'll look at models that explain this behavior, like the Drude model, and explore how things like crystal structure and temperature affect conductivity. This knowledge helps us design better devices that work in the terahertz range.

Charge Carrier Transport at Terahertz Frequencies

Terahertz Frequency Range and Intraband Transitions

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  Frontiers | Charge Carrier Dynamics in Sn-Doped Two-Dimensional Lead Halide Perovskites Studied ... View original

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  Frontiers | The laws and effects of terahertz wave interactions with neurons View original

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  Frontiers | A Three-Dimensional Dual-Band Terahertz Perfect Absorber as a Highly Sensitive Sensor View original

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• Terahertz frequencies span 0.1 to 10 THz, corresponding to wavelengths of 3 mm to 30 μm
• Intraband transitions govern charge carrier transport at terahertz frequencies
  • Carriers move within the same energy band without crossing the bandgap
• Drude model describes frequency-dependent conductivity of free carriers
  • Particularly relevant for terahertz frequencies
• Various scattering mechanisms influence carrier dynamics
  • Phonon scattering (lattice vibrations)
  • Impurity scattering (dopants, defects)
  • Carrier-carrier scattering (electron-electron interactions)

Effective Mass and Complex Conductivity

• Effective mass concept determines carrier mobility and response to terahertz fields
  • Accounts for the influence of crystal structure on carrier behavior
  • Varies depending on material and band structure
• Terahertz conductivity exhibits complex-valued nature
  • Real component relates to resistive behavior
  • Imaginary component relates to reactive behavior
  • Both components contribute to overall material response
• Complex conductivity provides insights into carrier dynamics and material properties
  • Enables extraction of carrier density, mobility, and scattering rates

Carrier Mobility and Terahertz Conductivity

Drude-Lorentz Model and Conductivity Equation

• Carrier mobility (μ) defined as proportionality constant between drift velocity and applied electric field
  • Inversely related to scattering rate
• Drude-Lorentz model relates terahertz conductivity σ(ω) to carrier properties
  • Equation: $σ(ω) = \frac{ne²τ}{m*} / (1 - iωτ)$
  • n: carrier density
  • e: elementary charge
  • τ: scattering time
  • m*: effective mass
  • ω: angular frequency
• Scattering processes limit carrier mobility
  • Influence frequency dependence of terahertz conductivity
• Plasma frequency (ωp) determines transition between metallic and dielectric behavior
  • Equation: $ωp² = \frac{ne²}{ε₀m*}$
  • ε₀: vacuum permittivity

Advanced Conductivity Models and Analysis

• Carrier localization effects lead to deviations from simple Drude model
  • Observed in disordered systems (amorphous semiconductors)
  • Require more complex conductivity models (Drude-Smith model)
• Frequency-dependent scattering rate Γ(ω) extracted from terahertz conductivity measurements
  • Provides insights into various scattering mechanisms
• Terahertz conductivity spectra reveal information about carrier properties
  • Applicable to wide range of materials (semiconductors, metals, 2D materials)
• Analysis techniques for extracting meaningful parameters
  • Kramers-Kronig relations
  • Effective medium approximations

Material Properties and Terahertz Dynamics

Crystal Structure and Band Characteristics

• Crystal structure affects carrier scattering rates and terahertz conductivity
  • Lattice dynamics influence phonon-electron interactions
  • Symmetry impacts allowed scattering processes
• Band structure characteristics determine intrinsic mobility and terahertz response
  • Band degeneracy (multiple equivalent energy states)
  • Effective mass variations across different crystal directions
• Doping concentration and type modify terahertz conductivity
  • n-type doping (electron-rich)
  • p-type doping (hole-rich)
  • Affects carrier density and introduces additional scattering centers

Material Defects and Temperature Effects

• Defects, impurities, and grain boundaries act as scattering centers
  • Point defects (vacancies, interstitials)
  • Line defects (dislocations)
  • Planar defects (grain boundaries, stacking faults)
• Temperature dependence crucial for carrier dynamics
  • Affects phonon populations (increases with temperature)
  • Modifies scattering rates and carrier mobility
• Surface and interface effects important in nanostructured materials
  • Increased surface-to-volume ratio in nanoparticles
  • Quantum confinement in low-dimensional systems (quantum wells, nanowires)
  • Lead to unique terahertz carrier dynamics and conductivity spectra

Probing and Quantifying Terahertz Conductivity

Terahertz Spectroscopy Techniques

• Terahertz time-domain spectroscopy (THz-TDS) measures complex conductivity spectra
  • Non-contact technique
  • Provides both amplitude and phase information
• Optical pump-terahertz probe spectroscopy studies ultrafast carrier dynamics
  • Investigates non-equilibrium phenomena
  • Reveals carrier relaxation and recombination processes
• Terahertz emission spectroscopy examines carrier acceleration and transient currents
  • Useful for studying photocurrent generation in solar cells
  • Provides insights into carrier injection and transport

Complementary Measurement and Modeling Approaches

• Fourier transform infrared spectroscopy (FTIR) covers lower terahertz frequency range
  • Requires appropriate extensions (synchrotron radiation sources)
  • Enables conductivity measurements in far-infrared region
• High-frequency Hall effect measurements provide complementary information
  • Determines carrier density and mobility
  • Challenges in extending to terahertz frequencies
• Advanced numerical methods predict and interpret terahertz carrier dynamics
  • Density functional theory (DFT) calculates electronic structure
  • Monte Carlo simulations model carrier transport and scattering events
• Combine experimental techniques with theoretical modeling for comprehensive understanding
  • Validate theoretical predictions with experimental data
  • Refine models based on experimental observations