Drude-Smith Model Visualization

Explore the complex conductivity σ*(ω) = σ'(ω) + iσ''(ω)

Parameters

DC Conductivity (σ₀) 1000 S/m

Relaxation Time (τ₀) 20 fs

1st Order Parameter (c₁) -0.5

Controls first scattering event memory (-1: full backscattering, 0: Drude).

2nd Order Parameter (c₂) 0.1

Introduces higher-order scattering effects.

Models to Display:

Drude (c₁=0, c₂=0) Drude-Smith 1st (c₁) Drude-Smith 2nd (c₁, c₂)

Plot Type:

Frequency range: 1 GHz to 100 THz (log scale)

Model Explanation

The Drude model describes free electron conductivity. The Drude-Smith model extends this by incorporating carrier localization or preferential back-scattering, common in disordered materials or nanostructures.

Complex Conductivity: σ*(ω) = σ'(ω) + iσ''(ω)

Drude Model: σ*(ω) = σ₀ / (1 - iωτ₀)

Drude-Smith (1st Order): σ*(ω) = [σ₀ / (1 - iωτ₀)] * [1 + c₁ / (1 - iωτ₀)]

Drude-Smith (2nd Order): σ*(ω) = [σ₀ / (1 - iωτ₀)] * [1 + c₁ / (1 - iωτ₀) + c₂ / (1 - iωτ₀)²]

Where: σ₀ is DC conductivity, τ₀ is relaxation time, ω is angular frequency (2πf), c₁ (-1 ≤ c₁ ≤ 0) is the first scattering persistence parameter, and c₂ accounts for subsequent scattering memory.

Complex Permittivity: ε*(ω) = ε_∞ + i σ*(ω) / (ωε₀), where ε_∞ is the high-frequency permittivity constant and ε₀ is the vacuum permittivity (≈ 8.854 × 10⁻¹² F/m).