Bloch Oscillations & Esaki-Tsu Negative Resistance

Electrons in a periodic lattice under DC field — semiclassical transport theory

Band Structure E(k) & Electron Motion

Velocity v(k) & Current

Real-space position x(t)

Esaki-Tsu J(E) curve

Phase space (k,x)

Electric field E (kV/cm) 5.0 Scattering time τ (fs) 100 Bandwidth Δ (meV) 80 Lattice constant a (nm) 5.0

Physics: In a periodic lattice, electrons undergo Bloch oscillations with frequency ω_B = eEa/ℏ. The Esaki-Tsu formula gives current J ∝ E·τ/(1+(ω_B·τ)²) — peak at ω_B·τ = 1, then negative differential resistance (NDR) for stronger fields. NDR period: — | ω_B·τ = — | Regime: —