Gunn Diode Simulator: GaAs Transferred-Electron Domains

Bias & Material

Applied field E_avg 4.0 kV/cm

Doping density N꜀ 1.0 ×10¹⁵ cm⁻³

Device length L 8 μm

Simulation speed 1.0×

Live Readouts

Terminal current density J

— kA/cm²

Domain transit frequency

— GHz

Peak domain field

— kV/cm

GaAs has a low-mass, high-mobility Γ valley and a heavy, low-mobility satellite L valley in its conduction band. Above the ~3.2 kV/cm threshold, hot electrons scatter Γ→L, drift velocity drops as field rises (negative differential mobility) and a thin high-field "domain" nucleates near the cathode and rides down the device.

How it works

This is the Ridley–Watkins–Hilsum / Gunn transferred-electron effect. The velocity–field curve (Copeland's analytic fit) has a peak and then falls toward a saturation velocity — the signature of negative differential mobility:

v(E) = (μ₀E + v_sat·(E/E꜀)⁴) / (1 + (E/E꜀)⁴)

Continuity:  ∂n/∂t = −∂(nv)/∂x + D·∂²n/∂x²
Poisson:     ∂E/∂x = (q/ε)·(n − N꜀)
Circuit:     (1/L)·∫E dx  =  E_avg  (fixed terminal bias)

μ₀ ≈ 8000 cm²/V·s — low-field Γ-valley mobility; v_sat ≈ 1×10⁷ cm/s — velocity once most electrons sit in the heavy L valley; E꜀ ≈ 3.2 kV/cm — the Ridley–Watkins–Hilsum threshold field for GaAs.
A short doping notch is built into the first few cells at the cathode. Because Poisson's equation ties field to local charge, the notch's slightly lower doping keeps re-triggering a domain there each time the previous one exits at the anode — the mechanism behind self-sustained Gunn oscillators.
The oscillation frequency of a real Gunn diode follows the transit-time rule f ≈ v_domain/L — the same rule this simulator measures live from the moving field peak, which is why shortening L (right slider) raises the readout toward the X-band frequencies (8–12 GHz) used in real GaAs Gunn oscillators and radar sources.
Diffusion coefficient D = μ₀·k_BT/q ≈ 207 cm²/s (Einstein relation at 300 K) smooths the domain edges; the 64-cell explicit solver is sub-stepped every frame at a diffusion-limited Δt for numerical stability.

— below threshold —

Local electric field E(x) Electron density n(x) Cathode (left) → Anode (right)

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