DrudeModell

The Drude-Modell is a classical theory of electrical conduction in metals, proposed by Paul Drude around 1900. It treats conduction electrons as a gas of free, non-interacting particles that move between random, instantaneous collisions with the ion lattice, characterized by a mean free time τ.

From the Boltzmann transport equation in the relaxation-time approximation, the model yields Ohm’s law in the dc limit: J = σE, with the conductivity σ = ne²τ/m, where n is the electron density, e the electron charge, and m the electron mass. For alternating electric fields, the model gives a frequency-dependent conductivity and a dielectric function ε(ω) = 1 − ω_p²/(ω² + iω/τ), where the plasma frequency ω_p is defined by ω_p² = ne²/(ε₀m).

The Drude model provides intuition for metallic conductivity, the existence of a finite dc conductivity, and a simple description of the optical response at low frequencies. It captures the basic plasmonic concept through the plasma frequency and explains high reflectivity of metals for certain frequencies.

Limitations are significant. The model neglects the crystal lattice potential and the detailed electronic band structure, quantum statistics, and electron–electron interactions. It assumes a constant relaxation time τ and does not account for interband transitions, which are important at higher frequencies. Consequently, while successful for qualitative and some quantitative descriptions of metals at room temperature, it is superseded in modern solid-state physics by quantum-mechanical band theory and the Drude–Sommerfeld extension.

Historically, the Drude model was later refined by Sommerfeld to incorporate Fermi-Dirac statistics, leading to the Drude–Sommerfeld model, and remains a foundational reference in plasmonics and introductory solid-state physics.